From fe2558a57b942b4b2b59a522d46b6787e612890e Mon Sep 17 00:00:00 2001
From: "Jan H. Meinke" <j.meinke@fz-juelich.de>
Date: Wed, 31 Mar 2021 12:23:48 +0200
Subject: [PATCH] Material from High-Performance Computing with Python @ JSC
2020.
---
00_Bottlenecks.ipynb | 788 +
01_Introduction to IPython.ipynb | 959 +
02_NumPy_concepts.ipynb | 367 +
03_ThinkVector.ipynb | 845 +
04_Profiling a simple md code.ipynb | 648 +
05_Debugging.ipynb | 347 +
06_IDEs.ipynb | 276 +
07_LocalParallel.ipynb | 1822 ++
08_LocalTaskParallel.ipynb | 358 +
09_Numba vectorize.ipynb | 552 +
10_NumbaIntro.ipynb | 1206 +
11_Speeding up your code with Cython.ipynb | 1285 +
12_Writing your own Python bindings.ipynb | 1503 +
13_Introduction to Dask.ipynb | 605 +
14_Introduction to MPI.ipynb | 1589 +
15_Introduction to CuPy.ipynb | 386 +
16_CUDA for Python.ipynb | 1184 +
17_CUDA and MPI.ipynb | 519 +
build.sh | 19 +
code/point/.kdev4/point.kdev4 | 17 +
code/point/CMakeLists.txt | 4 +
code/point/point.kdev4 | 4 +
code/point/point3d.cpp | 45 +
code/point/point3d.h | 25 +
code/point/point3d_bind.cpp | 51 +
code/point/points.f90 | 52 +
code/text_stats/.kdev4/text_stats.kdev4 | 17 +
code/text_stats/CMakeLists.txt | 4 +
code/text_stats/text_stats.c | 6 +
code/text_stats/text_stats.h | 8 +
code/text_stats/text_stats.kdev4 | 4 +
code/text_stats/text_stats_bind.cpp | 27 +
code/text_stats/word_frequency.F90 | 8 +
data/iris.csv | 151 +
hpcpy20 | 20 +
images/.directory | 4 +
images/6nodes.png | Bin 0 -> 23306 bytes
images/6nodescoll1.png | Bin 0 -> 87200 bytes
images/6nodescoll2.png | Bin 0 -> 82043 bytes
images/6nodesptp.png | Bin 0 -> 98440 bytes
images/6nodeswcommranks.png | Bin 0 -> 70683 bytes
images/CPUGPUSchema.png | Bin 0 -> 21297 bytes
images/CPUGPUSchema.svg | 886 +
images/Debug_Floating_Bar.png | Bin 0 -> 3732 bytes
images/Debug_Floating_Bar_simple.png | Bin 0 -> 1528 bytes
images/Debug_selection.png | Bin 0 -> 6975 bytes
images/IPythoninTerminal.png | Bin 0 -> 62133 bytes
images/QtConsolewithDoc.png | Bin 0 -> 80179 bytes
images/QtConsolewithImageandDoc.png | Bin 0 -> 71119 bytes
images/Roofline_jureca_1.svg | 19848 ++++++++++++
images/Roofline_jureca_2.svg | 25290 +++++++++++++++
images/Roofline_juwels_1.svg | 20216 ++++++++++++
images/Roofline_juwels_2.svg | 25524 ++++++++++++++++
images/a_block_of_threads.svg | 4620 +++
images/a_single_thread.svg | 398 +
images/cupy.png | Bin 0 -> 7022 bytes
images/domain_decomposition_exploded.png | Bin 0 -> 16130 bytes
images/domain_decomposition_stencil.svg | 446 +
.../domain_decomposition_stencil_exploded.svg | 539 +
images/eric5.png | Bin 0 -> 103618 bytes
images/ipyparallel.svg | 401 +
images/motorcycleandbus.png | Bin 0 -> 274248 bytes
images/pycharm.png | Bin 0 -> 196450 bytes
images/splitsquaregrid.svg | 445 +
images/splitsquaregridwhalo02.svg | 446 +
images/splitsquaregridwhalo1.svg | 446 +
images/splitsquaregridwstencil.svg | 446 +
images/squaregrid.svg | 445 +
images/stencil.svg | 150 +
images/structure_CPU.pdf | Bin 0 -> 14852 bytes
images/structure_GPU.pdf | Bin 0 -> 15046 bytes
images/teams_with_threads.svg | 22988 ++++++++++++++
images/vim.png | Bin 0 -> 84142 bytes
images/vscode-oss.png | Bin 0 -> 194900 bytes
.../00_Bottlenecks-checkpoint.ipynb | 788 +
solutions/00_Bottlenecks.ipynb | 788 +
solutions/01_Introduction to IPython.ipynb | 959 +
solutions/02_NumPy_concepts.ipynb | 367 +
solutions/03_ThinkVector.ipynb | 1129 +
solutions/04_Profiling a simple md code.ipynb | 665 +
solutions/05_Debugging.ipynb | 347 +
solutions/06_IDEs.ipynb | 276 +
solutions/07_LocalParallel.ipynb | 1822 ++
solutions/08_LocalTaskParallel.ipynb | 358 +
solutions/09_Numba vectorize.ipynb | 603 +
solutions/10_NumbaIntro.ipynb | 1480 +
...11_Speeding up your code with Cython.ipynb | 1373 +
.../12_Writing your own Python bindings.ipynb | 1549 +
solutions/13_Introduction to Dask.ipynb | 797 +
solutions/14_Introduction to MPI.ipynb | 1787 ++
solutions/15_Introduction to CuPy.ipynb | 462 +
solutions/16_CUDA for Python.ipynb | 1482 +
solutions/17_CUDA and MPI.ipynb | 735 +
solutions/build.sh | 19 +
solutions/code | 1 +
solutions/data | 1 +
solutions/hpcpy20 | 20 +
solutions/images | 1 +
98 files changed, 157048 insertions(+)
create mode 100644 00_Bottlenecks.ipynb
create mode 100644 01_Introduction to IPython.ipynb
create mode 100644 02_NumPy_concepts.ipynb
create mode 100644 03_ThinkVector.ipynb
create mode 100644 04_Profiling a simple md code.ipynb
create mode 100644 05_Debugging.ipynb
create mode 100644 06_IDEs.ipynb
create mode 100644 07_LocalParallel.ipynb
create mode 100644 08_LocalTaskParallel.ipynb
create mode 100644 09_Numba vectorize.ipynb
create mode 100644 10_NumbaIntro.ipynb
create mode 100644 11_Speeding up your code with Cython.ipynb
create mode 100644 12_Writing your own Python bindings.ipynb
create mode 100644 13_Introduction to Dask.ipynb
create mode 100644 14_Introduction to MPI.ipynb
create mode 100644 15_Introduction to CuPy.ipynb
create mode 100644 16_CUDA for Python.ipynb
create mode 100644 17_CUDA and MPI.ipynb
create mode 100755 build.sh
create mode 100644 code/point/.kdev4/point.kdev4
create mode 100644 code/point/CMakeLists.txt
create mode 100644 code/point/point.kdev4
create mode 100644 code/point/point3d.cpp
create mode 100644 code/point/point3d.h
create mode 100644 code/point/point3d_bind.cpp
create mode 100644 code/point/points.f90
create mode 100644 code/text_stats/.kdev4/text_stats.kdev4
create mode 100644 code/text_stats/CMakeLists.txt
create mode 100644 code/text_stats/text_stats.c
create mode 100644 code/text_stats/text_stats.h
create mode 100644 code/text_stats/text_stats.kdev4
create mode 100644 code/text_stats/text_stats_bind.cpp
create mode 100644 code/text_stats/word_frequency.F90
create mode 100644 data/iris.csv
create mode 100644 hpcpy20
create mode 100644 images/.directory
create mode 100644 images/6nodes.png
create mode 100644 images/6nodescoll1.png
create mode 100644 images/6nodescoll2.png
create mode 100644 images/6nodesptp.png
create mode 100644 images/6nodeswcommranks.png
create mode 100644 images/CPUGPUSchema.png
create mode 100644 images/CPUGPUSchema.svg
create mode 100644 images/Debug_Floating_Bar.png
create mode 100644 images/Debug_Floating_Bar_simple.png
create mode 100644 images/Debug_selection.png
create mode 100644 images/IPythoninTerminal.png
create mode 100644 images/QtConsolewithDoc.png
create mode 100644 images/QtConsolewithImageandDoc.png
create mode 100644 images/Roofline_jureca_1.svg
create mode 100644 images/Roofline_jureca_2.svg
create mode 100644 images/Roofline_juwels_1.svg
create mode 100644 images/Roofline_juwels_2.svg
create mode 100644 images/a_block_of_threads.svg
create mode 100644 images/a_single_thread.svg
create mode 100644 images/cupy.png
create mode 100644 images/domain_decomposition_exploded.png
create mode 100644 images/domain_decomposition_stencil.svg
create mode 100644 images/domain_decomposition_stencil_exploded.svg
create mode 100644 images/eric5.png
create mode 100644 images/ipyparallel.svg
create mode 100644 images/motorcycleandbus.png
create mode 100644 images/pycharm.png
create mode 100644 images/splitsquaregrid.svg
create mode 100644 images/splitsquaregridwhalo02.svg
create mode 100644 images/splitsquaregridwhalo1.svg
create mode 100644 images/splitsquaregridwstencil.svg
create mode 100644 images/squaregrid.svg
create mode 100644 images/stencil.svg
create mode 100644 images/structure_CPU.pdf
create mode 100644 images/structure_GPU.pdf
create mode 100644 images/teams_with_threads.svg
create mode 100644 images/vim.png
create mode 100644 images/vscode-oss.png
create mode 100644 solutions/.ipynb_checkpoints/00_Bottlenecks-checkpoint.ipynb
create mode 100644 solutions/00_Bottlenecks.ipynb
create mode 100644 solutions/01_Introduction to IPython.ipynb
create mode 100644 solutions/02_NumPy_concepts.ipynb
create mode 100644 solutions/03_ThinkVector.ipynb
create mode 100644 solutions/04_Profiling a simple md code.ipynb
create mode 100644 solutions/05_Debugging.ipynb
create mode 100644 solutions/06_IDEs.ipynb
create mode 100644 solutions/07_LocalParallel.ipynb
create mode 100644 solutions/08_LocalTaskParallel.ipynb
create mode 100644 solutions/09_Numba vectorize.ipynb
create mode 100644 solutions/10_NumbaIntro.ipynb
create mode 100644 solutions/11_Speeding up your code with Cython.ipynb
create mode 100644 solutions/12_Writing your own Python bindings.ipynb
create mode 100644 solutions/13_Introduction to Dask.ipynb
create mode 100644 solutions/14_Introduction to MPI.ipynb
create mode 100644 solutions/15_Introduction to CuPy.ipynb
create mode 100644 solutions/16_CUDA for Python.ipynb
create mode 100644 solutions/17_CUDA and MPI.ipynb
create mode 100755 solutions/build.sh
create mode 120000 solutions/code
create mode 120000 solutions/data
create mode 100644 solutions/hpcpy20
create mode 120000 solutions/images
diff --git a/00_Bottlenecks.ipynb b/00_Bottlenecks.ipynb
new file mode 100644
index 0000000..c13468d
--- /dev/null
+++ b/00_Bottlenecks.ipynb
@@ -0,0 +1,788 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Bottlenecks\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "16 Nov 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## High-performance computing is computing at the limit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "CPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "I/O"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CPU\n",
+ "### On JUWELS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\n",
+ "Each core has the following features:\n",
+ "\n",
+ "- processor frequency of 2.7 GHz (up to 3.7 GHz in turbo mode)\n",
+ "- 512 bit wide vector unit (8 double precision numbers)\n",
+ "- 2 Fused multiply-add (FMA) units each performing an FMA operation in a single cycle (each FMA counts as 2 floating point operations)\n",
+ "- When running all cores each FMA unit runs at 2.5 GHz (max)\n",
+ "- Peak performance is 2.5 \\* 8 \\* 2 \\* 2 GFlop/s = 80 GFlop/s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "There are 24 cores per socket\n",
+ "- Peak performance of a socket is 24 * 80 GFlop/s = 1920 GFlop/s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is the limit most people think of first, but it's often not the crucial one. Each core on JUWELS can perform ca. 80 GFlop/s if the code is completely *vectorized* and performs a *multiply and an add operation* at *each step*. If your code doesn't fulfill those requirements its peak performance will be less.\n",
+ "\n",
+ "Actually the peak performance is a often less because the CPU temperature limit typically soon leads to throttling when using all cores. The guaranteed sustained frequency for the JUWELS FMA units is 1.9 GHz."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Memory hierarchy\n",
+ "### Caches"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* L1 (per core):\n",
+ " - 32 kiB data cache (+ 32 kiB instruction cache)\n",
+ " - Fastest memory (128 (load) + 64 (store)) B/cycle (latency: 4-5 cycles)\n",
+ "* L2 (per core): \n",
+ " - 1 MiB\n",
+ " - 64 B/cycle (latency: 14 cycles)\n",
+ "* L3 (shared): \n",
+ " - 33 MiB\n",
+ " - ?? B/cycle (latency: 50-70 cycles)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "\n",
+ "### Main memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The memory bandwidth of a JUWELS node is about "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "120 GB/s. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A simple operation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "c = c + a * b (multiply-add)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "3 DP read, 1 DP write -> 24 bytes read, 8 bytes write"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "120 GB/s / 24 bytes/op = 5 Gop/s (multiply-add -> 10 GFLOP/s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "I assume that we are dealing with double precision numbers (8 bytes). Then I have to read 3 * 8 bytes = 24 bytes and write 8 bytes. This is a multiply-add operation, so each core can do 40 billion of those per second, but it only receives 120 GB/s. 120GB/s / 24 B/op = 5Gop/s (10 GFLOP/s). This operation is clearly memory bound, if we have to get all the data from main memory."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is quite common. Let's look at a matrix multiplication $C=AB$. To calculate the element i, j of the result matrix C, we multiply row i of A with column j of B and sum the results. This is the scalar or dot product of row i of A and column j of B. In code this looks like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "\n",
+ "def dot(a, b):\n",
+ " \"\"\"Multiply the matrix a with the matrix b.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: ndarray\n",
+ " left matrix\n",
+ " b: ndarray\n",
+ " right matrix\n",
+ " \n",
+ " Return\n",
+ " ------\n",
+ " c: ndarray\n",
+ " result matrix\n",
+ " \"\"\"\n",
+ " c = numpy.zeros((a.shape[0], b.shape[1])) \n",
+ " for i in range(a.shape[0]): \n",
+ " for j in range(b.shape[1]): \n",
+ " for k in range(a.shape[1]): \n",
+ " c[i, j] += a[i, k] * b[k, j]\n",
+ " return c "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Let's take two small matrices A and B and see how long the above function takes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 256\n",
+ "a = numpy.random.random((n, n))\n",
+ "b = numpy.random.random((n, n))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot = %timeit -o dot(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "A matrix multiplication of two n by n matrices performs $2n^3$ operations. The dot function achieves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"%.3f GFLOP/s\" % (2e-9 * n**3 / t_dot.best)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Wow, that's bad. Let's see if we can make this faster."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Numba"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import jit\n",
+ "jdot = jit(dot)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_jit = %timeit -o jdot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"%.3f GFLOP/s\" % (2e-9 * n**3 / t_jit.best)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Access order and cache lines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "From our estimate above, we should be able to get at least twice this, but that's assuming we can achieve the maximum memory bandwidth. \n",
+ "\n",
+ "A numpy ndarray uses C-order (row-order) for storage. This means that the last index is continuous in memory and a change in any other index results in a jump from one memory location to another. The order of the loops therefore means that for both c and b, we don't get the maximum bandwidth, because we jump around and only use one element of the cache line. \n",
+ "\n",
+ "A datum is not loaded by itself. Instead everytime, a datum is needed that is not available in cache, a cache line containing the datum is loaded. On JUWELS the cache line is 64 bytes wide. \n",
+ "\n",
+ "We can improve the performance by exchanging the loops:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy; from numba import jit\n",
+ "\n",
+ "@jit\n",
+ "def dot2(a, b):\n",
+ " \"\"\"Multiply the matrix a with the matrix b.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: ndarray\n",
+ " left matrix\n",
+ " b: ndarray\n",
+ " right matrix\n",
+ " \n",
+ " Return\n",
+ " ------\n",
+ " c: ndarray\n",
+ " result matrix\n",
+ " \"\"\"\n",
+ " c = numpy.zeros((a.shape[0], b.shape[1])) \n",
+ " for i in range(a.shape[0]): \n",
+ " for k in range(a.shape[1]): \n",
+ " for j in range(b.shape[1]): \n",
+ " c[i, j] += a[i, k] * b[k, j]\n",
+ " return c "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, elements in c and b are accessed in the proper order and a[i, k] is constant for the loop. This changes our estimate, because, now we read 16 bytes/op. This gives us a maximum of 120 GB/s / 16 bytes/op = 7.5 GFLOP/s (15 GB/s). #Todo: shouldn't the last two not be gops and GFLOPs andtead of GFLOPs and GB/s??"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Effect on matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot2 = %timeit -o dot2(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_dot2.best, \"GFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is better than what we would expect from the bandwidth estimate, probably due to caching. One way to test this is to make the matrix larger, so that it doesn't fit in cache anymore."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 2048\n",
+ "a = numpy.random.random((n,n))\n",
+ "b = numpy.random.random((n,n))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot2_large = %timeit -o dot2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_dot2_large.best, \"GFLOP/s\") "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is quite close to my estimate and shows that I have to increase the number of operations per byte loaded from main memory. Improving vectorization or using multiple threads wouldn't help.\n",
+ "\n",
+ "To improve cache utilization, we have to change the algorithm. One way to improve the performance of the matrix multiplication is blocking (aka tiling). This is done, e.g., in OpenBLAS or Intel's Math Kernel Library (MKL)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how long numpy takes for this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy = %timeit -o numpy.dot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_numpy.best, \"GFLOP/s\") "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The numpy version we use here, uses a fast math library. That's what you want."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The roofline model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The roofline model shows the memory bandwidth bound and compute bound with respect to the computational intensity. The computational intensity is just given by the number of bytes used divided by the number of operations performed."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Depending on your algorithm, different limits may be relevant, for example, we only used a single thread, but used the peak performance of the entire processor with 24 cores. If the data fits completely in L2 cache the available bandwidth is higher once the data has been loaded. The following shows a plot with a few more limits."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## I/O"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### GPFS File System\n",
+ "$\\mathcal{O}(200)$ GB/s read/write speed for scratch"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Each node connected to file system with $\\mathcal{O}(100)$ GBit/s or about 12.5 GB/s."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The scratch file system achieves read/write bandwidths that are very similar to the main memory bandwidth, but not for a single node. Each node is connected to the GPFS file system with $\\mathcal{O}(100)$ GBit/s connection. In other words, we can read/write about 12.5 GB/s. If we had to load the data in the previous calculation from disk, we could only achieve 12.5 GB/s / 24 bytes/op = 520 Mop/s. The main memory bandwidth or the peak performance of the CPU doesn't matter in this case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/01_Introduction to IPython.ipynb b/01_Introduction to IPython.ipynb
new file mode 100644
index 0000000..a91423b
--- /dev/null
+++ b/01_Introduction to IPython.ipynb
@@ -0,0 +1,959 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to IPython and Jupyter Notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "<div class=\"dateauthor\">\n",
+ "2 July 2019 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Jupyter notebooks offer a flexible way to combine python (and other language), scripts, text (such as this one), plots, and other things into one document.\n",
+ "\n",
+ "There are two modi: command und edit. You enter edit mode by pressing ``Enter``. You can exit it by pressing ``Esc``. To see the shortcuts for each modus press ``Esc`` followed by ``h`` if you are using Jupyter Notebook. Look in the ``Commands`` tab on the left hand side if you are using JupyterLab.\n",
+ "\n",
+ "If you want a new input above your current cell, press ``a`` in command mode. If you would like a new cell below your current cell press ``b``.\n",
+ "\n",
+ "In the course, we'll use the *IPython kernel* within the Jupyter notebook. IPython is also available within a regular terminal (``ipython``) or in its own special terminal-like window called Jupyter QtConsole."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## IPython Shell & QtConsole"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "<img src=\"images/IPythoninTerminal.png\" alt=\"IPython in a terminal\" width=\"45%\" align=\"left\"/><img src=\"images/QtConsolewithImageandDoc.png\" alt=\"Jupyter Qt console with image and tooltip\" width=\"45%\" align=\"right\"/>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Magic and Help"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "IPyhon extends the normal Python shell with *magic commands*. You can get a list of available magic commands using the magic command ``%lsmagic``. Give it a try. Use ``Shift+Enter`` to execute the cell. Just pressing ``Enter`` only gives you a new line."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%lsmagic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Not all the magic commands may be obvious to you, so it's a good thing that IPython also includes a help system. If you want to know, for example, what ``%dhist`` does im comparison to ``%hist``, you call first ``%dhist?`` and then ``%hist?``. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You saw that ``%hist`` is just an alias for ``%history``.\n",
+ "\n",
+ "Some of the magic commands, e.g., ``%less``, ``%ls``, and ``%man`` are substitutes for their shell equivalents, others, e.g., ``%load``, ``%save``, ``%%writefile`` deal with reading and writing from (to) files. We'll encounter more magic commands as we go along. \n",
+ "\n",
+ "The question mark doesn't just work for magic functions but gives you access to the documentation included with most Python modules. If you want to know, for example, what the random module does, you use ``random?``. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If you didn't get the documentation but only ``Object `random` not found``. Try importing the module first. Start by typing ``im`` and hit the tab key. Then type ``r`` and hit tab again. You'll get a dropdown box with available modules. You can continue typing until your choice is unique or select an item from the list. Give it a try. \n",
+ "\n",
+ "Try ``random?`` after importing the module. If you use ``??`` instead of ``?`` you get the source code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import random"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Timing with %timeit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how fast random.uniform generates random numbers and compare it with numpy's random.uniform. We'll use the timeit magics for that (more about those later)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit \n",
+ "n = 1\n",
+ "[random.uniform(0, 1) for i in range(n)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 1\n",
+ "t = %timeit -o numpy.random.uniform(0, 1, size=n)\n",
+ "print(n * 1. / t.best)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Plotting"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We won't go into the details of using [matplotlib][] for plotting in this course, but a quick introduction can't hurt.\n",
+ "\n",
+ "We first need to initialize the interactive plotting routines. The easiest way to do this is to use some magic. \n",
+ "\n",
+ "The command ``%matplotlib inline`` sets up interactive plotting support without importing any modules. This allows us to import the modules that we want:\n",
+ "\n",
+ "```python\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "```\n",
+ "\n",
+ "Alternatively, the command ``%pylab inline`` sets up interactive plotting and pulls all functions and modules from ``numpy`` and ``matplotlib.pyplot`` into the namespace.\n",
+ "\n",
+ "\n",
+ "[matplotlib]: http://matplotlib.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Output format"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can set the output format of matplotlib, too. The following commands change the default format from png to pdf."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import set_matplotlib_formats\n",
+ "set_matplotlib_formats('pdf', 'svg')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Plots and labels"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x = numpy.linspace(0, 2 * numpy.pi, 120)\n",
+ "y = numpy.sin(x)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.plot(x, y, label=r\"$\\sin(x)$\")\n",
+ "plt.xlim([0, 2 * numpy.pi])\n",
+ "plt.grid(1)\n",
+ "plt.xticks(numpy.linspace(0, 2 * numpy.pi, 9), [0, r\"$\\frac{\\pi}{4}$\", \n",
+ " r\"$\\frac{\\pi}{4}$\", r\"$\\frac{3\\pi}{4}$\", r\"$\\pi$\", \n",
+ " r\"$\\frac{5\\pi}{4}$\", r\"$\\frac{3\\pi}{2}$\", r\"$\\frac{7\\pi}{4}$\"\n",
+ " , r\"$2\\pi$\"])\n",
+ "plt.xlabel('x')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Saving and Loading Files"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's say, we want to use the script that we wrote in the section [Plotting](#Plotting) later from outside the notebook. We can use the ``%save`` magic to do that. Each cell has a number ``In [60]`` for example. The ``%save`` command takes a file name and a space separated list of input cells. The content of the input cells is written to a file. You can give ranges and even reorder things, e.g.,\n",
+ "\n",
+ " %save plotsin.py 60 61 62\n",
+ " \n",
+ "saves the cells with index 60, 61, and 62 to plotsin.py. I could have also written 60-62 to give the range. Look at the cell indices in the previous section and write them to a file. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can load the file using ``%load``. Try loading the file you just wrote to disk. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The entire content of the file is written to a single cell. We can split (and join) cells (see the Edit menu) if we don't like this. For files that are contained in a single cell, we can use the ``%%writefile`` magic.\n",
+ "\n",
+ "Join the next three cells and write them to a file called gaussian.py by adding ``%%writefile filename`` to the top of the cell."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "1. Highlight the next three cells (use the Shift-key to highlight multiple cells)\n",
+ "2. See the Commands (Ctrl+Shift+C) tab on the left (or press `h` to check wich key is used for merging cells if you are using a classic Jupyter notebook).\n",
+ "3. Merge the cells\n",
+ "4. Write %%writefile gaussian.py at the top of cell"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "r = numpy.random.normal(size=1000000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"The average is %.3f and the standard deviation is %.3f\" % (r.mean(), r.std()))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n, b, p = plt.hist(r, bins=100, density=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If you try to run gaussian.py from the command line it won't work because it's missing the imports, but you can run it using ``ipython --pylab=auto gaussian.py``. You can also run the script from IPython using the ``%run`` magic, but you have to use `-i` to run the script within the current namespace. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%run -i gaussian.py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Load can also load scripts from a URL. Give it a try. Look at the script loaded and then execute it, too.\n",
+ "\n",
+ "**Note**, since our compute nodes don't have internet access, I executed the command for you."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# %load http://matplotlib.org/mpl_examples/mplot3d/surface3d_demo.py\n",
+ "'''\n",
+ "======================\n",
+ "3D surface (color map)\n",
+ "======================\n",
+ "\n",
+ "Demonstrates plotting a 3D surface colored with the coolwarm color map.\n",
+ "The surface is made opaque by using antialiased=False.\n",
+ "\n",
+ "Also demonstrates using the LinearLocator and custom formatting for the\n",
+ "z axis tick labels.\n",
+ "'''\n",
+ "\n",
+ "from mpl_toolkits.mplot3d import Axes3D\n",
+ "import matplotlib.pyplot as plt\n",
+ "from matplotlib import cm\n",
+ "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "fig = plt.figure()\n",
+ "ax = fig.gca(projection='3d')\n",
+ "\n",
+ "# Make data.\n",
+ "X = np.arange(-5, 5, 0.25)\n",
+ "Y = np.arange(-5, 5, 0.25)\n",
+ "X, Y = np.meshgrid(X, Y)\n",
+ "R = np.sqrt(X**2 + Y**2)\n",
+ "Z = np.sin(R)\n",
+ "\n",
+ "# Plot the surface.\n",
+ "surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,\n",
+ " linewidth=0, antialiased=False)\n",
+ "\n",
+ "# Customize the z axis.\n",
+ "ax.set_zlim(-1.01, 1.01)\n",
+ "ax.zaxis.set_major_locator(LinearLocator(10))\n",
+ "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
+ "\n",
+ "# Add a color bar which maps values to colors.\n",
+ "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Moving Around"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "IPython has two ways of moving around in the directory tree: ``%cd`` and ``%pushd/%popd``. Both retain their history. ``%cd``'s history is available through ``%dhist`` whereas ``%dirs`` shows the directory stack of ``%pushd/%popd``. The ``%cd `` command has some nifty options, for example, ``%cd -2`` gets you to the second to last visited directory and ``%cd --foo`` switches to the next directory in the history than contains ``foo``. You can also set ``%bookmark``s and use them with ``%cd``.\n",
+ "\n",
+ "Make a new sub directory called scripts/mandelbrot using ``%mkdir -p scripts/mandelbrot``. Change into the directory scripts/mandelbrot using ``%cd``. Go two levels up using ``%cd ..`` twice. Look at the history using ``%dhist``. Change into mandelbrot using ``%cd --brot``. Finally use ``%cd -0`` to get back to where you started from."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A Little Bit of History"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Every output is stored to the ``Out`` array and can be accessed through its index. It can even be assigned."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numpy.random.random([4,4])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = _ # Assigns the output of the previous cell"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = Out[13] # Assign Out[?] to a (replace with index from two cells above)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "IPython keeps your history. It's accessed through the ``%history`` magic. By default it prints the history from the current session. If you have edited a cell multiple times, ``%history`` gives you all the versions. You can add line numbers to the output with the ``-n`` option, give ranges of lines that you want to see, and even perform some pattern matching. Pattern matching is done for your complete IPython history, not just the current session. For details see ``%history?``.\n",
+ "\n",
+ "If you want to log your work to a file (possibly with time stamps.) you can use IPython's logging facilities. ``%logstart -t testlog rotate`` creates a rotating log with timestamps and starts logging. ``%logoff`` pauses your log and ``%logstop`` stops the logging and closes the file."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Some Introspection"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "After an extended IPython session you might have declared many variables and functions. IPython provides some commands to help you to keep track of those. The first two are ``%who`` and ``%whos``. ``%who`` lists the names of functions and variables in the default namespace. ``%whos`` provides more details and includes the type of the variable. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%who"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%whos"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from math import pi"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%who"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If the namespace gets too crowded you can search for a particular object using ``%psearch``. Remember, though, auto completion is your friend.\n",
+ "\n",
+ "Sometimes it may become necessary to reset the namespace, for example, if ``Out[]`` contains some large objects that are no longer needed. ``%reset`` has several options to reset variables including the history of directories, inputs, and output. Please, check ``%reset?`` for details."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "IPython has several other interesting features. To learn more check out [IPython's documentation].\n",
+ "\n",
+ "[IPython's documentation]: https://ipython.readthedocs.io/en/stable/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2019a",
+ "language": "python",
+ "name": "hpcpy19a"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/02_NumPy_concepts.ipynb b/02_NumPy_concepts.ipynb
new file mode 100644
index 0000000..1cc73ae
--- /dev/null
+++ b/02_NumPy_concepts.ipynb
@@ -0,0 +1,367 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# NumPy - an HPC perspective\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Olav Zimmermann\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Python is an interpreted language and as such it is extremely flexible, allowing to define everything, including code itself, \n",
+ "at runtime. This entails that the Python interpreter uses a lot of magic behind the scenes (e.g. type inferencing) to keep things\n",
+ "as simple and productive as possible for the programmer. This flexibility comes at the price of a markedly reduced runtime speed \n",
+ "compared to compiled languages such as C++.\n",
+ "Many problems encoded in Python do not require the full range of flexibility and could easily trade it for improved runtime \n",
+ "performance without giving up the development performance which is the key for Python's success."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Background"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "NumPy is a library, written in C, to enable fast numerical computing in Python. Since its inception in 1995, NumPy has become first choice for numeric data processing in python. The main sacrifice to enable its high speed is the restriction to \n",
+ "containers with uniform memory layout, i.e., arrays that contain items of uniform static datatype."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Despite this apparently severe restriction NumPy is quite versatile and a full introduction into NumPy would require a\n",
+ "course of its own. Hence we will focus on the concepts that allowed its wide adoption by developers and HPC vendors alike. For an overview of the available functionality the numpy website https://www.numpy.org is a good starting point."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Note:** NumPy is not a part of the vanilla Python distribution and needs to be installed separately. Then it can be used like any other Python library."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The numpy BLAS and LAPACK bindings\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "NumPy does not implement everything itself. Instead it uses the fact that with BLAS (low level routines), and LAPACK (high level routines, based on BLAS), two widely adopted interfaces for linear algebra routines exist and that for almost all distributions and operation systems at least one library suporting the BLAS/LAPACK interface exists."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "While not mandatory, NumPy can be linked against high performance linear algebra libraries such as Intel's MKL, AMD's BLIS or IBM's ESSL folowing the BLAS/LAPACK APIs. These libraries can give you speed-ups of up to two orders of magnitude compared to the standard LAPACK library. In fact a number of distributions provide numpy implementations that are statically linked to Intel's MKL and when building, NumPy gives a preference to the optimized libraries (MKL, BLIS) over the slower, more hardware independent libraries (OpenBLAS, ATLAS).\n",
+ "\n",
+ "**Notes:** \n",
+ "- Not all routines of MKL are necessarily faster than those in OpenBLAS, e.g. random number generation. \n",
+ "- By default NumPy prefers Intel MKL over AMD BLIS, even on AMD processors. MKL works with AMD processors, but by default does not use the fast AVX2 and AVX512 BLAS routines that it uses when it has detected Intel hardware but only the much slower SSE2 routines. While there are hacks to change that behaviour it may therefore be more reasonable to change the order of preference for the different BLAS libraries on AMD platforms."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "You can check which BLAS library has been linked during your build of NumPy by calling the `show_config()` function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "print(np.__version__)\n",
+ "print(np.show_config())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## ndarray"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "The main datatype in NumPy is an n-dimensional array object called `ndarray`. By default it has C-array memory layout \n",
+ "(last index fastest, 0 based indices) and a uniform fixed element type defined at instantiation of the ndarray. Element sizes range from 1 byte (bool, uint8) to 16 byte (complex256) with the default being `float64`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### introspection, shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Several meta data of an `ndarray` can be obtained among them `a.ndim,a.size,a.nbytes,a.flags,type(a)`.\n",
+ "The array interface enables in-depth introspection such as obtaining the address of an object, e.g. for debugging purposes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "myarr=np.array([[1,2,3],[4,5,6]])\n",
+ "print(f\" myarr is a {myarr.ndim}-dimensional {type(myarr)} of type {myarr.dtype} and shape {myarr.shape}. It starts at adress {hex(myarr.__array_interface__['data'][0])}.\")\n",
+ "print(f\"Each of its {myarr.size} {myarr.dtype}-elements has a size of {myarr.dtype.itemsize} byte therefore it has {myarr.nbytes} bytes in total and its strides (in bytes) are {myarr.strides}.\")\n",
+ "print(\"The flags stored for this array are:\")\n",
+ "print(myarr.flags)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## NumPy's ndarray as a foundation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "`ndarrays` support important concepts to enable vectorized processing of data, such as broadcasting, ufuncs, and reductions. Why just use this for numeric data? Almost anything can be cast into an `ndarray` and also labeled access is possible. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dt=np.dtype([('name','S10'),('income',np.int16),\\\n",
+ " ('revenue',([('q1',np.float32),('q2',np.float32),('q3',np.float32),('q4',np.float32)]))])\n",
+ "f=np.loadtxt('test.dat',dtype=dt, skiprows=2,delimiter=',')\n",
+ "print(f)\n",
+ "print(f\"this array has {f.ndim} dimension(s)\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "However, note that most functionality in NumPy is geared towards arrays of uniform numerical type. The above data type indicates that the entire row is treated as a single (albeit very complicated) type and the data in the table thereby become a one-dimensional array. If you need spreadsheet-like functionality, NumPy's 'structured arrays' or 'record type' arrays that are based on `ndarrays` are not adequate. Luckily `ndarrays` can be extended in functionality and even reimplemented in a compatible way."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Design features of the ndarray API"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Due to its dual interface in Python and C and its often (not always) regular memory layout ndarrays can relatively easy be mapped to data types described in other language contexts. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "A couple of clever design choices adds to the popularity of ndarrays as a standard API for high performance computing in Python:\n",
+ "- narrays support both C-style and Fortran-style memory layouts, as well as memory alignment and view interfaces.\n",
+ "- A Mixin class `NDArrayOperatorsMixin` provides all the necessary standard python interfaces like `__add__`, `__lt__` etc. making custom array containers more convenient to write.\n",
+ "- `ndarray.__array_ufunc__` and `__array_function__` are interfaces that split the function API from the excution engine. By overriding them, these functions allow to intercept calls to ufuncs and non-ufuncs and to dispatch these calls to alternative implementations. Several important packages already use this approach."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Packages that implement the ndarray interface:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "<table>\n",
+ " <tr><th>package/module</th><th>extension(s)</th><th>other HPC relevant characteristics</th></tr>\n",
+ " <tr><td><code><b>cuPy</b></code></td><td>cuPy array: subset of ndarray functionality</td><td>ndarrays on GPUs</td></tr>\n",
+ " <tr><td><code><b>pandas</b></code></td><td>pandas dataframe: labeled data, non-numerical data, multi-indexing, grouping</td><td>fast CSV-parser</td></tr>\n",
+ " <tr><td><code><b>cuDF</b></code></td><td>cuDF dataframe: subset of pandas dataframe functionality</td><td>pandas dataframes on GPUs</td></tr>\n",
+ " <tr><td><code><b>dask</b></code></td><td>dask array: only subset of ndarray functionality</td><td>tiled ndarrays larger than main memory, distributed processing on multiple nodes</td></tr>\n",
+ " <tr><td><code><b>dask</b></code></td><td>dask dataframe: only subset of pandas dataframe functionality</td><td>tiled dataframes larger than main memory, distributed processing on multiple nodes</td></tr>\n",
+ " <tr><td><code><b>dask-cuDF</b></code></td><td>cuDF dataframe: subset of pandas dataframe functionality</td><td>tiled dataframes on multiple GPUs and multiple nodes</td></tr>\n",
+ " <tr><td><code><b>sparse</b></code></td><td>ndarray functionality on sparse arrays (COO layout)</td><td></td></tr></table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Notable packages that do not implement the ndarray interface are `numpy.matrix, scipy.sparse, pytorch, JAX` while `tensorflow` has an experimental interface."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "End"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/03_ThinkVector.ipynb b/03_ThinkVector.ipynb
new file mode 100644
index 0000000..9d952ae
--- /dev/null
+++ b/03_ThinkVector.ipynb
@@ -0,0 +1,845 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Think Vector\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "16 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Dot product"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Many compute kernels include loops. Let's take the dot (or scalar) product, for example, for two vectors *v* and *w*:\n",
+ "\n",
+ "$$s = \\sum_{i=0}^n v_i w_i $$\n",
+ "\n",
+ "We can write this as"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create a random number generator that uses the Mersenne-Twister bit generator.\n",
+ "rng = numpy.random.Generator(numpy.random.MT19937())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v = rng.uniform(size=1000)\n",
+ "w = rng.uniform(size=1000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "s = 0\n",
+ "for i in range(len(v)):\n",
+ " s += v[i] * w[i]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can also think of this as a map operation followed by a reduction:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Map"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A map operation applies an operation (a function) to each element of an array separately."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Maps can be expressed using list comprehensions\n",
+ "vw = numpy.array([v[i] * w[i] for i in range(len(v))])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Reduce"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A reduction takes the elements of an array and *reduces* them to a single value. A typical example of a reduction is the summation over all elements."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Now let's do the reduction\n",
+ "s = 0\n",
+ "for i in range(len(v)):\n",
+ " s += vw[i]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We didn't have to use numpy.array for these operations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We are using numpy arrays, which define a number of operations on whole arrays, so we can think of them as vectors. The two operations above can be rewritten."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Map-Reduce with NumPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Map-reduce is a very common pattern. We first transform the elements of an array and then reduce the resulting array to a single element."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Map\n",
+ "vw = v * w\n",
+ "# Reduce\n",
+ "s = vw.sum()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The dot product is such a common operation that numpy has a special function for it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Everything in one call\n",
+ "s = v.dot(w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since Python 3.6 this can also be written as ``v@w``."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercise:**\n",
+ "\n",
+ "Let's go back through the cells and and add the ``%%timeit`` magic at the top of each cell. Start with cell 3 and work your way back down."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The last one is not just the simplest, it's also the fastest."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## ufunc"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Functions that act on one array (or several arrays of the same shape) and return a vector of the same shape are called ``ufuncs``. When we wrote vw = v * w, we executed the ufunc \\__mul\\__. Functions, like ``dot`` that have a different output shape than input shape are called generalized ufuncs."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Stencils"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Stencils use the value of the neighboring elements to update the current position, e.g., "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "$$a[i, j] = \\frac{1}{4} (a[i - 1, j] + a[i + 1, j] + a[i, j - 1] + a[i, j + 1])$$\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A system with fixed boundaries"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's look at an example. We start with a 2d array of random values and fix the left boundary to a value of 0 and the right boundary to a value of 1. We do not want to change these boundary values. The top and bottom boundaries are connected so that our system forms a cylinder (periodic boundary conditions along y)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A_orig = numpy.random.random((10, 10))\n",
+ "A_orig[:,0] = 0\n",
+ "A_orig[:,-1] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = A_orig.copy()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "B = A.copy()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Explicit nested for loop"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "for i in range(A.shape[0]):\n",
+ " for j in range(1, A.shape[1] - 1):\n",
+ " B[i, j] = 0.25 * (A[(i + 1) % A.shape[0] , j] + A[i - 1, j] \n",
+ " + A[i, (j + 1)] + A[i, j - 1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.subplot(1, 3, 1)\n",
+ "plt.imshow(A, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 2)\n",
+ "plt.imshow(B, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 3)\n",
+ "plt.imshow(A-B, interpolation=\"nearest\")\n",
+ "print(\"|A-B| = %.3f\" % numpy.linalg.norm(A-B))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, we assign B to A and repeat. Note that |A-B| becomes smaller with each iteration unless you happen to run into an oscillating minimum."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = B.copy()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "[Repeat](#Explicit-nested-for-loop)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The operation for each *i* and *j* is independent since *A* is only read. This is an ideal candidate for parallel calculations and we can write it in form of vector operations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Element-wise operation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = A_orig.copy()\n",
+ "B = numpy.empty_like(A)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "B = 0.25*(numpy.roll(A, 1,axis=0) + numpy.roll(A, -1, axis=0) + numpy.roll(A, 1,axis=1) + numpy.roll(A, -1,axis=1))\n",
+ "# Keep our boundaries at a fixed value\n",
+ "B[:, 0] = 0\n",
+ "B[:, -1] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.subplot(1, 3, 1)\n",
+ "plt.imshow(A, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 2)\n",
+ "plt.imshow(B, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 3)\n",
+ "plt.imshow(A-B, interpolation=\"nearest\")\n",
+ "print(\"|A-B| = %.3f\" % numpy.linalg.norm(A-B))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercises:**\n",
+ "\n",
+ "a) use `%%timeit` to compare the `for`-loop and the `numpy.roll()` versions of the stencil update\n",
+ " \n",
+ "b) Combine all the step of a single iteration in one cell, execute it multiple times, and watch how the system proceeds. Does the norm of the difference get smaller?\n",
+ "\n",
+ " Tip: If you use <Ctrl+Enter> to execute the cell, the cursor stays on the cell and you can execute again right away.\n",
+ "\n",
+ "c) Create a loop that terminates if the sum of the differences becomes smaller than some small value epsilon or the maximum number of allowed iterations has been reached. Plot the final state."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Programming exercise Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "The Mandelbrot set is the set of points *c* in the complex plane for which"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "$$z_{i+1} = z_i^2 + c$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "does not diverge.\n",
+ "\n",
+ "The series diverges if $|z_i|>2$ for any *i*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since it is impracticable to calculate an infinite number of iterations, one usually sets an upper limit for the number of iterations (the maximum of *i* ), for example, 20. To get pretty pictures, we can map the value of *i* for which $|z_i|>2$ is true for the first time to a color."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Here is a function that does this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Escape time algorithm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " p: complex\n",
+ " point in the complex plane\n",
+ " maxtime: int\n",
+ " maximum number of iterations to perform before p is considered in \n",
+ " the Mandelbrot set.\n",
+ " \"\"\"\n",
+ " z = 0j # This is a complex number in Python\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "M = [[escape_time(re + im, 40) for re in numpy.linspace(-2.2, 1, 640)] for im in numpy.linspace(-1.2j, 1.2j, 480)]\n",
+ "plt.imshow(M)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now, it's your turn. Rewrite the above algorithm using NumPy vector operations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Hints:** \n",
+ "\n",
+ "* You can use `numpy.meshgrid()` to generate your 2D array of points.\n",
+ "* You somehow need to mask the points that already diverged in future iterations.\n",
+ "* You don't have to put this in a function"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy \n",
+ "numpy.meshgrid?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/04_Profiling a simple md code.ipynb b/04_Profiling a simple md code.ipynb
new file mode 100644
index 0000000..070a3a5
--- /dev/null
+++ b/04_Profiling a simple md code.ipynb
@@ -0,0 +1,648 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Profiling\n",
+ "<div class=\"dateauthor\">\n",
+ "16 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Profiler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "cprofiler (standard module)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "line_profiler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Intel Advisor since 2017 beta"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Before you start to optimize a program, you should generate a profile. A profile shows how much time a program spends in which function, line of code, or even assembler instruction.\n",
+ "\n",
+ "There are several profiling tools,e.g., cprofile, which comes with Python and is always available. It measures performance on a function call level. We'll also look at line_profiler. Let's look at an example.\n",
+ "\n",
+ "The following functions implement a simple n-body simulation using a long range potential. This could be part of, e.g., an astrophysical simulation, a simulation of a many-electron system, or a molecular dynamics simulation.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Profiling a simple particle dynamics code"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "pair_force()\n",
+ "\n",
+ "force()\n",
+ "\n",
+ "calculate_all_forces()\n",
+ "\n",
+ "step()\n",
+ "\n",
+ "propagate_all_variables()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#%%writefile md.py\n",
+ "import numpy as np\n",
+ "from numba import jit\n",
+ "\n",
+ "#@jit\n",
+ "def pair_force(x0, y0, z0, m0, x1, y1, z1, m1):\n",
+ " \"\"\"Calculate the force on p0 due to p1.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x0: float\n",
+ " x-coordinate of the p0\n",
+ " y0: float\n",
+ " y-coordinate of the p0\n",
+ " z0: float\n",
+ " z-coordinate of the p0\n",
+ " m0: float\n",
+ " mass of the p0\n",
+ " x1: float\n",
+ " x-coordinate of the p1\n",
+ " y1: float\n",
+ " y-coordinate of the p1\n",
+ " z1: float\n",
+ " z-coordinate of the p1\n",
+ " m1: float\n",
+ " mass of the p1\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " f: ndarray\n",
+ " force on p0 due to p1\n",
+ " \n",
+ " \"\"\"\n",
+ " r2 = (x1 - x0) ** 2 + (y1 - y0) ** 2 + (z1 - z0) ** 2\n",
+ " f = m0 * m1 * np.array([(x1 - x0), (y1 - y0), (z1 - z0)]) * r2 ** (-1.5) if r2 else np.zeros(3)\n",
+ " return f\n",
+ "\n",
+ "#@jit\n",
+ "def force(x0, y0, z0, m0, x, y, z, m):\n",
+ " \"\"\"Calculates the force on the particle at (x0, y0, z0) due to all other particles.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x0: float\n",
+ " x-coordinate of the particle\n",
+ " y0: float\n",
+ " y-coordinate of the particle\n",
+ " z0: float\n",
+ " z-coordinate of the particle\n",
+ " m0: float\n",
+ " mass of the particle\n",
+ " x: ndarray\n",
+ " x-coordinates of all particles\n",
+ " y: ndarray\n",
+ " y-coordinates of all particles\n",
+ " z: ndarray\n",
+ " z-coordinates of all particles\n",
+ " m: ndarray\n",
+ " masses of all particles.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " f: ndarray\n",
+ " force on particle with mass m0 at (x0, y0, z0)\n",
+ " \"\"\"\n",
+ " f = np.zeros(3)\n",
+ " for x1, y1, z1, m1 in zip(x, y, z, m):\n",
+ " f += pair_force(x0, y0, z0, m0, x1, y1, z1, m1)\n",
+ " return f\n",
+ "\n",
+ "\n",
+ "def calculate_all_forces(x, y, z, m):\n",
+ " \"\"\"Calculates the force on each particle p due to all other particles.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x: ndarray\n",
+ " x-coordinates of all particles\n",
+ " y: ndarray\n",
+ " y-coordinates of all particles\n",
+ " z: ndarray\n",
+ " z-coordinates of all particles\n",
+ " m: ndarray\n",
+ " masses of all particles.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " f: ndarray\n",
+ " force on each particle due to all other particles.\n",
+ " \"\"\"\n",
+ " return np.array([force(x[i], y[i], z[i], m[i], x, y, z, m) for i in range(n)])\n",
+ "\n",
+ "def step(x, y, z, vx, vy, vz, m, f, dt):\n",
+ " \"\"\"Propagate the position and velocities.\n",
+ " \n",
+ " Starting from the current positions, velocities, and forces, propogate positions\n",
+ " and velocities by one time step of lenght dt.\n",
+ " \n",
+ " .. note:: This algorithm should not be used for real simulations!\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x: ndarray\n",
+ " x-coordinates of all particles\n",
+ " y: ndarray\n",
+ " y-coordinates of all particles\n",
+ " z: ndarray\n",
+ " z-coordinates of all particles\n",
+ " vx: ndarray\n",
+ " x-component of the velocity of all particles\n",
+ " vy: ndarray\n",
+ " y-component of the velocity of all particles\n",
+ " vz: ndarray\n",
+ " z-component of the velocity of all particles\n",
+ " m: ndarray\n",
+ " masses of all particles.\n",
+ " f: ndarray\n",
+ " forces on particles\n",
+ " dt: float\n",
+ " time step\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " x, y, z, vx, vy, vz at t + dt\n",
+ " \"\"\"\n",
+ " xn = x + vx * dt + 0.5 * f[0] / m * dt * dt\n",
+ " yn = y + vy * dt + 0.5 * f[1] / m * dt * dt\n",
+ " zn = y + vz * dt + 0.5 * f[2] / m * dt * dt\n",
+ " vxn = vx + f[0] / m * dt\n",
+ " vyn = vy + f[1] / m * dt\n",
+ " vzn = vz + f[2] / m * dt\n",
+ " return xn, yn, zn, vxn, vyn, vzn\n",
+ "\n",
+ "def propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt):\n",
+ " for i in range(n):\n",
+ " x[i], y[i], z[i], vx[i], vy[i], vz[i] = step(x[i], y[i], z[i], vx[i], vy[i], vz[i], m[i], f[i], dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The main program"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Initialization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# 1000 particles\n",
+ "n = 1000\n",
+ "# time step of 0.01\n",
+ "dt = 0.01\n",
+ "\n",
+ "# Initialize coordinates and velocities to random values.\n",
+ "x = np.random.random(n)\n",
+ "y = np.random.random(n)\n",
+ "z = np.random.random(n)\n",
+ "vx = np.zeros_like(x)\n",
+ "vy = np.zeros_like(x)\n",
+ "vz = np.zeros_like(x)\n",
+ "m = np.ones_like(x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### The algorithm\n",
+ "\n",
+ "There are basically two steps to this algorithm:\n",
+ "\n",
+ "1. Calculate the forces on all particles\n",
+ "2. Propagate all variables for a time step\n",
+ "3. Continue at 1. for nstep steps"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nsteps = 2\n",
+ "for i in range(nsteps):\n",
+ " f = calculate_all_forces(x, y, z, m)\n",
+ " propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This took quite some time. Let's measure how long it takes. Add a %%timeit statement just before nsteps (same line)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The base line"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit nsteps = 1\n",
+ "for i in range(nsteps):\n",
+ " f = calculate_all_forces(x, y, z, m)\n",
+ " propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "OK, that's our base line. Next, we want to know where all this time is spent. I mentioned the cprofile module at the beginning. IPython has a magic for that called %%prun. Use it in front of the loop this time."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Profiling with %%prun"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%prun -r nsteps=1\n",
+ "for i in range(nsteps):\n",
+ " f = calculate_all_forces(x, y, z, m)\n",
+ " propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ " 2003007 function calls in 8.561 seconds\n",
+ "\n",
+ " Ordered by: internal time\n",
+ "\n",
+ " ncalls tottime percall cumtime percall filename:lineno(function)\n",
+ " 1000000 5.209 0.000 7.073 0.000 <ipython-input-3-66a2b576efa3>:4(pair_force)\n",
+ " 999001 1.863 0.000 1.863 0.000 {built-in method numpy.core.multiarray.array}\n",
+ " 1000 1.480 0.001 8.555 0.009 <ipython-input-3-66a2b576efa3>:36(force)\n",
+ " 2000 0.003 0.000 0.003 0.000 {built-in method numpy.core.multiarray.zeros}\n",
+ " 1000 0.003 0.000 0.003 0.000 <ipython-input-3-66a2b576efa3>:89(step)\n",
+ " 1 0.001 0.001 0.004 0.004 <ipython-input-3-66a2b576efa3>:130(propagate_all_variables)\n",
+ " 1 0.001 0.001 8.557 8.557 <ipython-input-3-66a2b576efa3>:87(<listcomp>)\n",
+ " 1 0.000 0.000 8.561 8.561 {built-in method builtins.exec}\n",
+ " 1 0.000 0.000 8.557 8.557 <ipython-input-3-66a2b576efa3>:68(calculate_all_forces)\n",
+ " 1 0.000 0.000 8.561 8.561 <string>:1(<module>)\n",
+ " 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The overhead shouldn't be too bad. I got about 10%. Most of the time (about 80%) is spent in pair_force. And 20% of that time is spent on np.array>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Line by line profiling"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Unfortunately, this is a rather coarse grained profile. We don't know which part is the expensive part of this calculation and what we can do about it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext line_profiler"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%lprun -f pair_force force(x[0], y[0], z[0], m[0], x, y, z, m)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Total time: 9.86691 s \n",
+ "File: md.py \n",
+ "Function: pair_force at line 3 \n",
+ " \n",
+ " Line # Hits Time Per Hit % Time Line Contents\n",
+ " ============================================================== \n",
+ " 32 1000000 2269473 2.3 23.0 r2 = (x1 - x0) ** 2 + (y1 - y0) ** 2 + (z1 - z0) ** 2\n",
+ " 33 1000000 6864624 6.9 69.6 f = m0 * m1 * np.array([(x1 - x0), (y1 - y0), (z1 - z0)]) \n",
+ " * r2 **(-1.5) if r2 else np.zeros(3)\n",
+ " 34 1000000 732809 0.7 7.4 return f \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Timing individual operations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Calculating r2 takes 2.3 mus per call. Let's use %timeit to see how much time each operation takes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "(x1 - x0)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "(x1 - x0) ** 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "(x1 - x0) * (x1 - x0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "dx = (x1 - x0)\n",
+ "dx * dx"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can now change the code so it calculates dx, dy, and dz first and then uses them later in the calculation. We can also use numba to speed up the simulation."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Time the other operations and optimize the code"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/05_Debugging.ipynb b/05_Debugging.ipynb
new file mode 100644
index 0000000..23ef132
--- /dev/null
+++ b/05_Debugging.ipynb
@@ -0,0 +1,347 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Debugging Python\n",
+ "<div class=\"dateauthor\">\n",
+ "16 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "What do you do if a program doesn't produce the results you want? You can stare at the code and try to figure out the mistake. You can add lots of print statements to your code. Or you can use a debugger.\n",
+ "\n",
+ "You've probably done the first two things, but have you used a debugger before?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Debugging has its own terminology: You step in and out of functions. You move up and down the stack. You set break points, inspect variables, etc. This is the basic functionality that every debugger should (and every debugger I know does) support.\n",
+ "\n",
+ "In this notebook, we'll look at debugging a program with PDB in the notebook and pudb in a terminal window. You'll learn how to start a debugging session and do all the things, I talked about in the previous paragraph."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## PDB"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Python comes with its own debugger called \"The Python debugger\" (pdb). PDB is available from within a notebook, but it's not very convenient to use."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's take the following function, which contains a bug and throws an exception."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#%%writefile buggy.py\n",
+ "def imabuggyincrement(i,a):\n",
+ " \"\"\"Increment a[i] by 1.\"\"\"\n",
+ " if ii < len(a):\n",
+ " a[i] += 1;\n",
+ "\n",
+ "a = list(range(10))\n",
+ "ii = 4\n",
+ "imabuggyincrement(10, a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Debug magic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If a cell has just thrown an exception, you can inspect it with the %debug magic. Try `help` to see the available commands. Type `exit` to leave the debugger."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Use `p i` to print the value of `i`. You can also try to print out the value of `a[i]` using `p a[i]`. Inspect the other variables. Do you see what went wrong?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%debug"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Available debuggers"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "* pdb (builtin)\n",
+ "* pudb\n",
+ "* IDEs (All the IDEs we mentioned have debugging support)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Uncomment the ``%%writefile`` magic before the function defintion of ``imabuggyincrement`` and execute the cell again so that it gets written to file buggy.py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next start pudb in a terminal with the script name as an argument. If you haven't done this in this terminal shell before, you need to source hpcpy20:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```bash\n",
+ "source hpcpy20\n",
+ "pudb3 buggy.py\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We'll give you a short demonstration and then you can play with it for a little while."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Remote debugging"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "For example, PyDev, Wing Personal, Visual Studio, and PyCharm Professional (199 €/a with perpetual fallback license) support remote debugging. It can also be done with the ``ptvsd`` and Visual Studio Code."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Debugging Python extensions\n",
+ "We'll talk about this more tomorrow (maybe)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Note\n",
+ "\n",
+ "> It's better to ask for forgiveness than to ask for permission."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A better way to check for bounds as I did in `iambuggyincrement` is not to do it at all but use a try...except statement instead:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "```python\n",
+ "def imabuggyincrement(i, a):\n",
+ " \"\"\"Increment a[i] by 1.\"\"\"\n",
+ " try:\n",
+ " a[i] += 1;\n",
+ " except IndexError:\n",
+ " pass\n",
+ " \n",
+ "def main(arg=[]):\n",
+ " a = list(range(10)\n",
+ " ii = 4 # Now this is limited to the scope of main()\n",
+ " imabuggyincrement(10, a)\n",
+ " \n",
+ "if __name__ == \"__main__\":\n",
+ " main()\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The following video shows how to debug mixed Python and C++ code using Visual Studio.\n",
+ "\n",
+ "You can go back to to the beginning of the video to learn how write a Python extension in Visual Studio."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import YouTubeVideo\n",
+ "\n",
+ "YouTubeVideo(\"D9RlT06a1EI\", start=300)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2019a",
+ "language": "python",
+ "name": "hpcpy19a"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/06_IDEs.ipynb b/06_IDEs.ipynb
new file mode 100644
index 0000000..4ed11a5
--- /dev/null
+++ b/06_IDEs.ipynb
@@ -0,0 +1,276 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Integrated Development Environments (IDEs) for Python\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "3 July 2019 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Jupyter notebooks are great for interactive development and data analysis with IPython. IPython's auto completion is one of the best, but if you develop complex codes that span multiple files, you might want to use other IDE's."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Editors with Python Features"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Editors such as vi, emacs, kate, sublime, etc. do already more than just show your code. They offer syntax highlighting and at least simple auto completion and may be extended. They can give you an overview over the files in your projects. They can show the function and let you jump to the right file to look at them. They may even show doc string. It's often hard to tell if it's an editor or an IDE anymore."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Features of IDEs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Syntax highlighting, auto completion with tool tips"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Tree view of files, methods, and variables"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Running and debugging"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Integrated version control"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Kdevelop\n",
+ "\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Visual Studio Code (OSS)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## eric"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## PyCharm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## There's more"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Eclipse w/ PyDev"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Spyder"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Wing IDE (commercial), Wing Personal at no cost."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Visual Studio (Windows, commercial), Visual Studio Community Edition at no cost."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "For an overview see, e.g., [IntegratedDevelopmentEnvironments](https://wiki.python.org/moin/IntegratedDevelopmentEnvironments) on the Python Wiki."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2019a",
+ "language": "python",
+ "name": "hpcpy19a"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/07_LocalParallel.ipynb b/07_LocalParallel.ipynb
new file mode 100644
index 0000000..ff6caa3
--- /dev/null
+++ b/07_LocalParallel.ipynb
@@ -0,0 +1,1822 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Interactive Parallel Computing with IPython Parallel\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "17 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "*Computers have more than one core.* Wouldn't it be nice if we could use all the cores of our local machine or a compute node of a cluster from our [Jupyter][IP] notebook? \n",
+ "\n",
+ "Click on the ``+``-sign at the top of the Files tab on the left to start a new launcher. In the launcher click on Terminal. A terminal will open as a new tab. Grab the tab and pull it to the right to have the terminal next to your notebook.\n",
+ "\n",
+ "**Note**: The terminal does not have the same modules loaded as the notebook. To fix that type `source hpcpy20`.\n",
+ "\n",
+ "In the terminal type ``ipcluster``. You'll see the help message telling you that you need to give it subcommand. Take a look at the message and then enter \n",
+ "\n",
+ "``` bash\n",
+ "export OMP_NUM_THREADS=12\n",
+ "ipcluster start --n=4\n",
+ "```\n",
+ "\n",
+ "This will start a cluster with four engines and should limit the number of threads to 12 threads per engine to avoid oversubscription.\n",
+ "\n",
+ "> If you use the classical [Jupyter][IP] notebook, this is even easier if you have the cluster extension installed. (We don't have that one on our JupyterHub, yet). One of the tabs of your browser has the title \"Home\". If you switch to that tab, there are several tabs within the web page. One of them is called \"IPython Clusters\". Click on \"IPython Clusters\", increase the number of engines in the \"default\" profile to 4, and click on Start. The status changes from stopped to running. After you did that come back to this tab.\n",
+ "\n",
+ ">If the \"Clusters\" tab shows the message:\n",
+ "\n",
+ ">> Clusters tab is now provided by IPython parallel. See IPython parallel for installation details.\n",
+ " \n",
+ "> you need to quit your notebook server (make sure all your notebooks ar saved) and run the command \n",
+ "\n",
+ ">> ipcluster nbextension enable\n",
+ " \n",
+ ">Now, when you start `jupyter notebook` you should see a field that lets you set the number of engines in the \"IPython Clusters\" tab.\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "[IP]: http://www.jupyter.org"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Overview"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "IPyParallel has three parts: controller, engines, and client. The controller is the central hub. The client communicates only with the controller. The controller keeps track of the available engines and forwards requests from the client to the engines. It schedules the work and monitors its status. The results are communicated through the controller back to the client.\n",
+ "\n",
+ "All three components can run on different computers. A Jupyter notebook might run on your laptop and connect to an ipcontroller on a JUWELS login node, which in turn talks to engines running on a compute node."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The Client"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now let's see how we access the \"Cluster\". [IPython][IP] comes with a module [ipyparallel][IPp] that is used to access the engines, we just started. We first need to import Client.\n",
+ "\n",
+ "[IPp]: https://ipyparallel.readthedocs.io/en/latest/\n",
+ "[IP]: http://www.ipython.org"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rc = Client(profile=\"default\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can list the ids of the engines attached"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rc.ids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Views\n",
+ "\n",
+ "A *view* gives us access to a set of engines using a given scheduler. There are two types of views: a *direct view* and a *load-balanced* view."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As the name implies a *direct view* gives us direct control of the engines. We can push and pull data and apply functions using a couple of different methods. We are in control what runs where.\n",
+ "\n",
+ "A *load-balanced view* tries to balance the work between all the engines. We can submit tasks to it in the same way as before, but with a *load-balanced view*, the scheduler decides where a function is executed. It's also possible to define dependencies between tasks to build a dependency graph or even build this graph by hand. You'll learn a little more about dependencies in [Parallel, Task-Based Computing with Load Balancing on your Local Machine][LocalTaskParallel]\n",
+ "\n",
+ "Let's start with a *direct view* and learn about the methods used to execute code on the engines and move data around. \n",
+ "\n",
+ "We create a *direct view* of the engines by slicing the Client object:\n",
+ "\n",
+ "[LocalTaskParallel]: LocalTaskParallel.ipynb"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v01 = rc[0:2] # First two engines (0 and 1)\n",
+ "v23 = rc[2:4] # Engines 2 and 3\n",
+ "dview = rc[:] # All available engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Parallel Magic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Before we go into the details of the interface of a `DirectView`--that's the name of the class, let's look at IPython magic.\n",
+ "\n",
+ "IPython makes it very easy to use IPyParallel. It provides the magic commands ``%px`` and ``%%px`` to execute code in parallel. The target attribute is used to pick the engines, you want. By default, all the engines of the last Client object created are used. You can also specify if a command should be executed `blocking`--the default--or `non-blocking`.\n",
+ "\n",
+ "Note, the commands prefixed with ``%px`` are *not* executed locally. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px import numpy as np # import numpy on all engines as np\n",
+ "import numpy as np # do it locally, too."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since it's fairly common that you want to execute a cell remotely and locally, there's an option for that. Just add ``--local``.\n",
+ "\n",
+ "**Note**: This works only for ``%%px`` not ``%px``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --local \n",
+ "np.__version__ # print the numpy version of the engines. Note how the output is prefixed. It can be accessed that way, too. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ " The engines run ipython. Magic commands work, too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --local\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --local \n",
+ "import matplotlib.pyplot as plt\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The cell magic command ``%%px`` lets us execute more than one statement. The option ``--target`` lets us choose which engines we want to use. Here we are using engines 0 to 3."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --target 0:4\n",
+ "a = np.random.random([10,10])\n",
+ "plt.imshow(a, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Yes, the output can be graphical.\n",
+ "\n",
+ "Remember that the imports, we performed with ``%px`` are not available in our notebook. We can fix that by using"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "with rc[:].sync_imports():\n",
+ " import matplotlib.pyplot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Unfortunately mapping of namespaces does not work that way."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Using the Direct View"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As mentioned above a *direct view* lets you control each engine directly. You can also decide if a command should be blocking or not.\n",
+ "\n",
+ "We can, for example, create two random 100 by 100 element matrices on each engine, multiply them, and then display them. On each engine the code would look like this"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = np.random.random([100, 100])\n",
+ "b = np.random.random([100, 100])\n",
+ "c = a.dot(b)\n",
+ "plt.imshow(c, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As we learned before, we can use the ``%%px`` cell magic to execute this on all engines. Here we use the ``--target`` option to specify every second engine starting at 0. ``%px`` and ``%%px`` use the currently active view. By default that's the first view created. You can make a view active by calling ``view.activate(suffix)``. Use ``view.activate?`` to learn more about suffix."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --target 0::2\n",
+ "a = np.random.random([100, 100])\n",
+ "b = np.random.random([100, 100])\n",
+ "c = a.dot(b)\n",
+ "plt.imshow(c, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Magic commands are blocking by default, i.e., the next cell can only be executed after all the engines have finished their work. We can pass the option ``--noblock`` to change that behavior."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --noblock\n",
+ "a = np.random.random([2000, 2000])\n",
+ "b = np.random.random([2000, 2000])\n",
+ "c = a.dot(b)\n",
+ "c.sum() / 4.0e9"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We get an AsyncResult back. We can continue working in our notebook and pick up the result, when we are ready to do so."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%result"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Execute and Apply"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The foundation of executing code with a ``DirectView`` is ``apply``. It calls a function (the first argument) with args and kwargs. The values of the arguments are taken from the notebook and pushed to the engines."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c = dview.apply(np.dot, a, b) # This uses a and b from the notebook"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c.done()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c = c.result()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c[0].shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function can be a lambda function:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c = dview.apply(lambda a,b : a + b, a, b)\n",
+ "c.done()\n",
+ "c = c.result()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c[0].shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "It can also be ``exec``:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.apply(exec, 'c = a + b') # Note, this uses the variables defined on the engines."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview['c'][0].shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.execute('c=a+b')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview['c']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Remote functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "There are two decorators ``@parallel`` and ``@remote`` that can create functions that are executed on the engines.\n",
+ "\n",
+ "A function decorated with ``@parallel`` takes a sequence or an array as argument and distributes the work over the engines. Each engine still gets a sequence or array and should return one, too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import parallel, remote"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@dview.parallel(block=True)\n",
+ "def even(x):\n",
+ " \"\"\"Return only even elements of x\n",
+ " \n",
+ " Paramters\n",
+ " ---------\n",
+ " x : sequence or array\n",
+ " A list of values\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " res : like x\n",
+ " even elements of x\n",
+ " \"\"\"\n",
+ " return [e for e in x if not e % 2]\n",
+ "# return None if x % 2 else x\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "even(list(range(0,16)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "A `remote` function, on the other hand just runs on each engine with the full set of data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@dview.remote(block=True)\n",
+ "def scale(a):\n",
+ " for i in range(len(a)):\n",
+ " a[i] *= 2\n",
+ " \n",
+ " return a"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "scale(list(range(0, 16)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Moving data around"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "So far the runtime has taken care of moving data to and from the engines, but we can do this explicitely. There are 4 commands to do that:\n",
+ "\n",
+ "* push\n",
+ "* pull\n",
+ "* scatter\n",
+ "* gather"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Push takes a dictionary with the remote variable name as key:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "localA = list(range(10))\n",
+ "dview.push(dict(remoteA=localA))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can get a variable back with pull. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.pull('remoteA')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "There's also a shorthand notation, where we treat the view as a dictionary."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview['remoteA']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The methods ``push`` and ``pull`` push/pull the same data to/from all engines. They don't take a list and distribute it. That's what ``scatter`` and ``gather`` do. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.scatter('a',list(range(24)))\n",
+ "dview['a']"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.gather('a')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## List comprehension"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "With those methods at hand, we can build a parallel list comprehension."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.scatter('x',list(range(64)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px y = [i**10 for i in x]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "y = dview.gather('y')\n",
+ "y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exploring Latency and Bandwidth"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Latency (the time until something happens) and bandwith (the amount of data we get through the network) are two important properties of your parallel system that define what is practical and what is not. We will use the ``%timeit`` magic to measure these properties. ``%timit`` and its sibbling ``%%timeit`` measure the run time of a statement (cell in the case of ``%%timeit``) by executing the statement multiple times (by default at least 3 times). For short running routines many loops of 3 executions are performed and the minimum time measured is then displayed. The number of loops and the number of executions can be adjusted. Take a look at the documentation. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Lets first see how long it takes to send off a new task using ``execute`` and ``apply``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block = False"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --noblock --local\n",
+ "a = np.random.random([2000, 2000])\n",
+ "b = np.random.random([2000, 2000])\n",
+ "c = a.dot(b)\n",
+ "c.sum() / 4.0e9"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's first execute nothing."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.execute('')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next we'll use a very minimal function. It just returns its argument. In this case the argument is empty."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.apply(lambda x : x, '')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Here, we'll tell every engine to perform a matrix-matrix multiplication (see [Matrix-Matrix Multiplication Using a DirectView](Matrix-Matrix-Multiplication-Using-a-DirectView) below for more about matrix multiplications)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 4 dview.execute('c = a.dot(b)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now, we'll make the execution blocking. This means, we are measuring the time the function needs to return a result instead of just the time needed to launch the task."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.execute('')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.apply(lambda x : x, '')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 4 rc[0].execute('c = a.dot(b)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit a.dot(b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=False"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can start about 500 parallel tasks per second and finish about a quarter as many. This gives an estimate of the granularity we need to use this model for efficient parallelization. Any task that takes less time than this will be dominated by the overhead."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "To get an idea about the bandwidth available let's push some arrays to the engines. We make this blocking."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = np.random.random(256*1024)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.push(dict(a=a))\n",
+ "%timeit dview.push(dict(a=a[:128*1024]))\n",
+ "%timeit dview.push(dict(a=a[:64*1024]))\n",
+ "%timeit dview.push(dict(a=a[:32*1024]))\n",
+ "%timeit dview.push(dict(a=a[:16*1024]))\n",
+ "%timeit dview.push(dict(a=a[:8*1024]))\n",
+ "%timeit dview.push(dict(a=a[:4*1024]))\n",
+ "%timeit dview.push(dict(a=a[:2*1024]))\n",
+ "%timeit dview.push(dict(a=a[:1024]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Calculate the bandwidth for the largest array and the smallest array."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "bwmax = len(rc) * 256 * 8 / 12.1e-3\n",
+ "bwmin = len(rc) * 8 / 9.05e-3\n",
+ "print(\"The bandwidth is between %.2f kB/s and %.2f kB/s.\" %( bwmin, bwmax))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Matrix-Matrix Multiplication Using a DirectView"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Matrix multiplication is one of the favorites in High Performance Computing (HPC). It's computationally intensive---if done right---, easily parallelized with little communication, and the basis of many real world applications.\n",
+ "\n",
+ "Let's say, we have two matrices A and B, where\n",
+ "\n",
+ "$$ A = \\left ( \\begin{array}{cccc}\n",
+ " 4 & 3 & 1 & 6 \\\\\n",
+ " 1 & 2 & 0 & 3 \\\\\n",
+ " 7 & 9 & 2 & 0 \\\\\n",
+ " 2 & 2 & -1 & 4 \\\\\n",
+ " \\end{array}\n",
+ " \\right ) $$\n",
+ "\n",
+ "and \n",
+ "\n",
+ "$$ B = \\left ( \\begin{array}{cc}\n",
+ " \\frac{1}{12} & \\frac{1}{2} \\\\\n",
+ " \\frac{1}{9} & \\frac{1}{4} \\\\\n",
+ " \\frac{1}{3} & 1 \\\\\n",
+ " \\frac{1}{7} & -\\frac{1}{3}\n",
+ " \\end{array}\n",
+ " \\right ). $$\n",
+ "\n",
+ "To calculate the element of $C = A B$ at row *i* and column *j*, we perform a dot (scalar) product of the ith row of A and the jth column of B:\n",
+ "\n",
+ "$$ C_{ij} = \\sum_k A_{i,k} B_{k, j} $$.\n",
+ "\n",
+ "For this to work, the number of columns in $A$ has to be equal to the number of rows in $B$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can generate two matrices of size n by n filled with random numbers using ``np.random.random``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 16\n",
+ "A = np.random.random([n, n])\n",
+ "B = np.random.random([n, n])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "NumPy includes the dot product. For 2-dimensional arrays ``np.dot`` performs a matrix-matrix multiplication."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "C = np.dot(A, B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit np.dot(A, B)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "There are different ways to parallelize a matrix-matrix multiplication. Each element of the matrix can be calculated independently."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit \n",
+ "p = len(rc)\n",
+ "# Distribute the elements of the result viewmatrix round robin.\n",
+ "C1h = [[rc[(i * n + j) % p].apply(np.dot, A[i,:], B[:,j]) for j in range(n)] for i in range(n)]\n",
+ "# Wait until the calculation is done\n",
+ "dview.wait()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This, however, produces $n^2$ short tasks and the overhead (latency) is just overwhelming.\n",
+ "\n",
+ "We want to calculate\n",
+ "\n",
+ "$$ C = \\left ( \\begin{array}{cccc}\n",
+ " 4 & 3 & 1 & 6 \\\\\n",
+ " 1 & 2 & 0 & 3 \\\\\n",
+ " 7 & 9 & 2 & 0 \\\\\n",
+ " 2 & 2 & -1 & 4 \\\\\n",
+ " \\end{array}\n",
+ " \\right ) \n",
+ " \\left ( \\begin{array}{cc}\n",
+ " \\frac{1}{12} & \\frac{1}{2} \\\\\n",
+ " \\frac{1}{9} & \\frac{1}{4} \\\\\n",
+ " \\frac{1}{3} & 1 \\\\\n",
+ " \\frac{1}{7} & -\\frac{1}{3}\n",
+ " \\end{array}\n",
+ " \\right ). \n",
+ "$$\n",
+ "\n",
+ "We can split the matrices into tiles. In the above example, we might use a 2 by 2 tile.\n",
+ "\n",
+ "$$ C = \\left ( \\begin{array} {cc}\n",
+ " a_{00} & a_{01} \\\\\n",
+ " a_{10} & a_{11}\n",
+ " \\end{array} \\right )\n",
+ " \\left ( \\begin{array} {c}\n",
+ " b_{00} \\\\\n",
+ " b_{10}\n",
+ " \\end{array} \\right )\n",
+ " = \\left ( \\begin{array} {c}\n",
+ " a_{00} b_{00} + a_{01} b_{10} \\\\\n",
+ " a_{10} b_{00} + a_{11} b_{10}\n",
+ " \\end{array} \\right )\n",
+ " ,\n",
+ "$$\n",
+ "\n",
+ "where, for example, $a_{00}= \\left ( \\begin{array}{cc} 4 & 3 \\\\ 1 & 2 \\end{array} \\right )$. $a_{00}b_{00}$ is a matrix-matrix product and the addition of two matrices of the same shape is defined element by element."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In our example, we have two $n$ by $n$ matrices and we are going to split them in quadrants."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 4096\n",
+ "A = np.random.random([n, n])\n",
+ "B = np.random.random([n, n])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "tdot = %timeit -o np.dot(A,B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "type(n // 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nhalf = n // 2\n",
+ "a00 = A[:nhalf, :nhalf]\n",
+ "a01 = A[:nhalf, nhalf:]\n",
+ "a10 = A[nhalf:, :nhalf]\n",
+ "a11 = A[nhalf:, nhalf:]\n",
+ "b00 = B[:nhalf, :nhalf]\n",
+ "b01 = B[:nhalf, nhalf:]\n",
+ "b10 = B[nhalf:, :nhalf]\n",
+ "b11 = B[nhalf:, nhalf:]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The calculation of the partial results in Python looks very similar to the mathematical description above:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00 = np.dot(a00, b00) + np.dot(a01, b10)\n",
+ "c01 = np.dot(a00, b01) + np.dot(a01, b11)\n",
+ "c10 = np.dot(a10, b00) + np.dot(a11, b10)\n",
+ "c11 = np.dot(a10, b01) + np.dot(a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit -o\n",
+ "c00 = np.dot(a00, b00) + np.dot(a01, b10)\n",
+ "c01 = np.dot(a00, b01) + np.dot(a01, b11)\n",
+ "c10 = np.dot(a10, b00) + np.dot(a11, b10)\n",
+ "c11 = np.dot(a10, b01) + np.dot(a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "_.best / tdot.best"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Hm, this is slower than doing it directly...\n",
+ "\n",
+ "Next we create one view per engine."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "d0 = rc[0]\n",
+ "d1 = rc[1]\n",
+ "d2 = rc[2]\n",
+ "d3 = rc[3]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit d0.apply(lambda A, B : np.dot(A, B), A, B).wait()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00h = d0.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = d1.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = d2.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = d3.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00 = c00h.get()\n",
+ "c01 = c01h.get()\n",
+ "c10 = c10h.get()\n",
+ "c11 = c11h.get()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "c00h = d0.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = d1.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = d2.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = d3.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)\n",
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Nothing says, we have to stop at 4 tiles nor do we have to use square tiles. We could also recursively subdivide our tiles.\n",
+ "\n",
+ "The code is not any faster, because our implementation of numpy already blocks the matrices and uses all cores, but it shows the principle."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Slideshow",
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/08_LocalTaskParallel.ipynb b/08_LocalTaskParallel.ipynb
new file mode 100644
index 0000000..c98ba02
--- /dev/null
+++ b/08_LocalTaskParallel.ipynb
@@ -0,0 +1,358 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Parallel, Task-Based Computing with Load Balancing on your Local Machine"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our first session [Interactive Parallel Computing on the Local Machine][LocalParallel], we used a direct view to access our engines. This is great as long as we want to do the same task on all engines and don't have many more tasks than engines. If we have many tasks, however, and don't care where each task is executed, the DirectView is not the most convenient view available.\n",
+ "\n",
+ "[LocalParallel]: LocalParallel.ipynb"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rc = Client()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A *direct view* is created by slicing the client. A *load-balanced view* is created by calling rc's method `load_balanced_view()`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "lview = rc.load_balanced_view()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%px import numpy as np\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 4096\n",
+ "A = np.random.random([n, n])\n",
+ "B = np.random.random([n, n])\n",
+ "C = np.dot(A, B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "tnp = %timeit -o A@B"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "a00 = A[:n // 2, :n // 2]\n",
+ "a01 = A[:n // 2, n // 2:]\n",
+ "a10 = A[n // 2:, :n // 2]\n",
+ "a11 = A[n // 2:, n // 2:]\n",
+ "b00 = B[:n // 2, :n // 2]\n",
+ "b01 = B[:n // 2, n // 2:]\n",
+ "b10 = B[n // 2:, :n // 2]\n",
+ "b11 = B[n // 2:, n // 2:]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "c00h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "c00 = c00h.get()\n",
+ "c01 = c01h.get()\n",
+ "c10 = c10h.get()\n",
+ "c11 = c11h.get()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "c00h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)\n",
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compare this time with the one from the [Interactive Parallel Computing on the Local Machine][LocalParallel] where we used a *direct view*. Is it better? Worse? About the same?\n",
+ "\n",
+ "[LocalParallel]: LocalParallel.ipynb#Matrix-Matrix-Multiplication-Using-a-DirectView"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It's probably about the same, so why would we use the *load-balanced view*? For starters, we can throw more tasks at our engines than there are workers. In the previous example, we split our matrices in four blocks. Let's write a function that takes a square matrix with n rows and columns, where n is multiple of threshold, that uses tiles of size threshold."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def BlockMatrixMultiply(A, B, threshold = 256):\n",
+ " \"\"\"Calculates the matrix product of two square matrices of size :math:`n^2` by dividing\n",
+ " matrices into smaller blocks.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " A : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2 \n",
+ " B : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2\n",
+ " threshold: int\n",
+ " Size of blocks\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " output : ndarray\n",
+ " Returns the matrix product of A and B.\n",
+ " \"\"\"\n",
+ " \n",
+ " if threshold > A.shape[0]:\n",
+ " threshold = A.shape[0]\n",
+ " numberOfTiles = A.shape[0] // threshold\n",
+ " C = np.array([[np.sum([np.dot(A[i*threshold:(i+1)*threshold, k*threshold:(k+1)*threshold], \n",
+ " B[k*threshold:(k+1)*threshold, j*threshold:(j+1)*threshold]) \n",
+ " for k in range(numberOfTiles)], axis=0) # Add up all submatrices that belong to tile i,j\n",
+ " for j in range(numberOfTiles)] # Loop over columns of result matrix\n",
+ " for i in range(numberOfTiles)]) # Loop over rows of result matrix\n",
+ "\n",
+ " return C.swapaxes(1,2).reshape(A.shape)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "C1 = BlockMatrixMultiply(A, B, n // 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.allclose(C, C1) # Tests is the difference of all array elements is less than some threshold. Use np.allclose? to get details."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit C=np.dot(A,B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit BlockMatrixMultiply(A, B, n // 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def BlockMatrixMultiplyLB(A, B, lview, threshold = 256):\n",
+ " \"\"\"Calculates the matrix product of two square matrices of size :math:`n^2` by dividing\n",
+ " matrices into smaller blocks.\n",
+ " \n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " A : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2\n",
+ " B : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2\n",
+ " threshold: int\n",
+ " Size of blocks\n",
+ " view:\n",
+ " An IPython parallel view\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " output : ndarray\n",
+ " Returns the matrix product of A and B.\n",
+ " \"\"\"\n",
+ " if threshold > A.shape[0]:\n",
+ " threshold = A.shape[0]\n",
+ " n = A.shape[0] // threshold\n",
+ " Ch = [ [lview.apply(lambda a, b, threshold, n, i, j : \n",
+ " np.sum([np.dot(a[:, k*threshold:(k+1)*threshold], \n",
+ " b[k*threshold:(k+1)*threshold,:]) \n",
+ " for k in range(n)], axis=0), # Add up all the matrices that belong to tile i,j\n",
+ " A[i*threshold:(i+1)*threshold,:], B[:,j*threshold:(j+1)*threshold], threshold, n, i, j) # Arguments to lambda\n",
+ " for j in range(n)] # Loop over columns of result matrix\n",
+ " for i in range(n)] # Loop over rows of result matrix\n",
+ "\n",
+ " #lview.wait() # Let's finish all the work that has been started in this view\n",
+ " \n",
+ " # Instead of waiting for the view, we can wait for all our asyncs to finish:\n",
+ " for r in Ch:\n",
+ " for c in r:\n",
+ " c.wait()\n",
+ " \n",
+ " return np.array([[c.get() for c in r] for r in Ch]).swapaxes(1,2).reshape(A.shape)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "C2 = BlockMatrixMultiplyLB(A, B, lview, n // 4) # Creates 16 tasks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.allclose(C, C2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n)\n",
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n // 2) # 4 tasks\n",
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n // 4) # 16 tasks\n",
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n // 8) # 64 tasks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "BlockMatrixMultiply?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/09_Numba vectorize.ipynb b/09_Numba vectorize.ipynb
new file mode 100644
index 0000000..bd1e1cd
--- /dev/null
+++ b/09_Numba vectorize.ipynb
@@ -0,0 +1,552 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Numba vectorize\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "17 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba offers a decorator `@vectorize` that allows us to generate **fast** [ufuncs](https://numpy.org/doc/stable/reference/ufuncs.html). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numba\n",
+ "import numpy\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A simple trig function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's implement a simple trig function:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import math"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def sinacosb(a, b):\n",
+ " \"\"\"Calculate the product of sin(a) and cos(b)\"\"\"\n",
+ " return math.sin(a) * math.cos(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Passing numpy arrays as arguments"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 1000000\n",
+ "a = np.ones(n, dtype='int8')\n",
+ "b = 2 * a"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function sinasinb is only defined for scalars, so we have to do something if we want to pass an array."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## numpy.vectorize"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "NumPy provides the function `vectorize`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "npsinacosb = np.vectorize(sinacosb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit npsinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## numba.vectorize"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Dynamic ufuncs"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "usinacosb = numba.vectorize(sinacosb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit usinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function usinacosb is a *dynamic ufunc*. The arguments are determined when the function is called and only then is the function compiled."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Eager compilation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Assume, we know with what kind of arguments a function is called, then numba can generate code as soon as we call numba vectorize. The decorator can take a list of [type specification](https://numba.readthedocs.io/en/stable/reference/types.html#signatures) strings of the form \"f8(f8, f8)\", where the type before the parentheses is the return type and the types within the parentheses are the argument types."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@numba.vectorize(['f8(i8,i8)', 'f4(f4,f4)', 'f8(f8,f8)'], nopython=True)\n",
+ "def usinacosb(a,b):\n",
+ " return math.sin(a) * math.cos(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### target"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If I use eager compilation I can give an addition keyword argument: *target*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "target=\"cpu\": default, run in a single thread on the CPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "target=\"parallel\": run in multiple threads"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "target=\"cuda\": run on a CUDA-capable GPU"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "pusinacosb = numba.vectorize(['f8(i8,i8)', 'f4(f4,f4)', 'f8(f8,f8)', ], nopython=True, target=\"parallel\")(sinacosb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit pusinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 100_000_000\n",
+ "a = np.ones(n, dtype='int8')\n",
+ "b = 2 * a"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit usinacosb(a, b)\n",
+ "%timeit pusinacosb(a, b) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Exercise: The Mandelbrot set"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The Mandelbrot set is the set of points *c* in the complex plane for which"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$z_{i+1} = z_i^2 + c$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "does not diverge.\n",
+ "\n",
+ "The series diverges if $|z_i|>2$ for any *i*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since it is impracticable to calculate an infinite number of iterations, one usually sets an upper limit for the number of iterations, for example, 20."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Escape time algorithm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A simple implementation of this algorithm is the following:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " p: complex\n",
+ " point in the complex plane\n",
+ " maxtime: int\n",
+ " maximum number of iterations to perform before p is considered in \n",
+ " the Mandelbrot set.\n",
+ " \"\"\"\n",
+ " z = 0j\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Todo:\n",
+ "\n",
+ "1. Generate a grid of size n times m of complex numbers with the real part taken from the interval [-2.2, 1.5] and the imaginary part taken from the interval [-1.5, 1.5]. Hint, numpy.meshgrid can help.\n",
+ "\n",
+ "2. Vectorize escape_time using numba.vectorize and apply it to the array above. Note, the output is an integer.\n",
+ "\n",
+ "3. Visualize the generated array using matplotlib.pyplot.imshow. \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit M = escape_time_vec(P, 50)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/10_NumbaIntro.ipynb b/10_NumbaIntro.ipynb
new file mode 100644
index 0000000..616ce58
--- /dev/null
+++ b/10_NumbaIntro.ipynb
@@ -0,0 +1,1206 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to Numba's jit compiler\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "17 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba provides a just-in-time (jit) compiler, a decorator `vectorize` that we can use to define `ufunc`s that are fast and flexible, and an interface to CUDA- and ROCm-capable GPUs that allows us to write CUDA kernels in Python! In this notebook, we'll focus on the jit compiler."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Python is an interpreted language"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The Python interpreter parses and executes code when it encounters it. This makes it very flexible but it also precludes many optimizations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "from numba import jit\n",
+ "from matplotlib import pyplot as plt "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## A simple example\n",
+ "Let's start with a simple sum. In Python we may define the sum like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def python_sum(a, start=0):\n",
+ " res = start\n",
+ " for x in a:\n",
+ " res += x\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "When we call `python_sum`, the interpreter goes through it line by line. For each item it has to interpret `res += x` and execute it, i.e., call apropriate C routines that have been compiled for the processor. The only requirements for `a` in this function ar that it is iterable and its elements support the `+` operator. For the following little benchmark, we'll use an `ndarray` of random numbers."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rng = numpy.random.Generator(numpy.random.MT19937())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = rng.uniform(size=10000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_python_sum = %timeit -o python_sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Please calculate the floating point operations per second for `python_sum`. Btw., remember the peak performance of a single core on JUWELS is about 40 GFLOP/s."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Compiled languages"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "In compiled languages such as C, C++, Fortran, and Rust a compiler would translate the code once \n",
+ "and store the results in machine code for a particular processor, but it doesn't translate it \n",
+ "literally, but can look for optimization and map the work optimally to the capabilities of the \n",
+ "processor. That's what makes this much faster but also less flexible. In C++ the sum may be written \n",
+ "like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```cpp\n",
+ "#include <vector>\n",
+ "template <class T>\n",
+ "auto cpp_sum(std::vector<T>& a, T start){\n",
+ " auto res = start;\n",
+ " for (auto x : a){\n",
+ " res += x;\n",
+ " }\n",
+ " return res;\n",
+ "}\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "With C++20 you could get even closer to the functionality of `python_sum`, but this will do for now.\n",
+ "\n",
+ "A part of the assembler code generated for the loop might look something like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```nasm\n",
+ "..B1.14: # Preds ..B1.14 ..B1.13\n",
+ " vaddpd ymm3, ymm3, YMMWORD PTR [rdi+rcx*8] #7.9\n",
+ " vaddpd ymm2, ymm2, YMMWORD PTR [32+rdi+rcx*8] #7.9\n",
+ " vaddpd ymm1, ymm1, YMMWORD PTR [64+rdi+rcx*8] #7.9\n",
+ " vaddpd ymm0, ymm0, YMMWORD PTR [96+rdi+rcx*8] #7.9\n",
+ " add rcx, 16 #6.19\n",
+ " cmp rcx, rax #6.19\n",
+ " jb ..B1.14 # Prob 82% #6.19\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Yes, there are good reasons to love Python (and other higher programming languages).\n",
+ "\n",
+ "Let's run the code:\n",
+ "```\n",
+ "$ ./simple_sum\n",
+ "Sum: 5033.24 in 0.717281 µs. 13941.5 MFLOP. \n",
+ "```\n",
+ "\n",
+ "The function takes about 0.7 µs. This is about 2000 times faster than the interpreted Python loop. \n",
+ "Wouldn't it be great if we could take the Python code in `python_sum` and compile it to machine \n",
+ "code to get some of this speedup?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Compiling a program to machine code involves at least to phases. In the first phase the human readable \n",
+ "program is translated into something that is more palable to a computer such as an \n",
+ "[abstract syntax tree][AST] or [AST][]. Many compilers then perform a first analysis and pattern \n",
+ "matching on the [AST][] before machine specific optimization are applied.\n",
+ "\n",
+ "A popular open source framework for these steps is [LLVM][]. LLVM provides both the language parser, e.g., \n",
+ "clang for C and clang++ for C++ and a toolchain for the language independent optimization steps. The \n",
+ "language parser generates a well defined intermediate representation that can than be optimized. \n",
+ "\n",
+ "[Numba][] uses this infrastructure to optimize a subset of Python to machine code during program \n",
+ "execution. These kind of live compiler are called just-in-time (JIT) compiler. \n",
+ "\n",
+ "[AST]: https://en.wikipedia.org/wiki/Abstract_syntax_tree\n",
+ "[LLVM]: http://llvm.org/\n",
+ "[Numba]: https://numba.pydata.org/"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Python_sum compiled"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how well [Numba][] does with the sum. We imported `numba.jit` at the top of the notebook.\n",
+ "The function `jit` returns a `callable`---which makes it usable as a `decorator` as well---that we can \n",
+ "assign to a variable. The variable can then be used just like a regular function:\n",
+ "\n",
+ "[AST]: https://en.wikipedia.org/wiki/Abstract_syntax_tree\n",
+ "[LLVM]: http://llvm.org/\n",
+ "[Numba]: https://numba.pydata.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "numba_sum = jit(python_sum)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 1 numba_sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The first time a \"jitted\" function is called with a specific argument type, numba compiles the code, which takes fairly long. Future calls are much faster:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_jit_sum = %timeit -o numba_sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This is quite an impressive speed up although not quite as fast as the compiled C++ code. Please, \n",
+ "calculate the performance again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's compare the performance with numpy's `sum`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy_sum = %timeit -o numpy.sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "It's a little faster."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"Numpy's sum achieves {1e-6 * a.shape[0] / t_numpy_sum.best:.3f} MFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A more complex example and nopython\n",
+ "Numba likes simple expressions with simple loops:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def mm(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = rng.uniform(size=(100, 100))\n",
+ "b = rng.uniform(size=(100, 100))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_python_mm = %timeit -o mm(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy_mm = %timeit -o a.dot(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "OK, the Python loop is about 30000 times slower than numpy's `dot` method. Let's see if we can't make this faster using numba. This time, we'll use `jit` as a decorator."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit\n",
+ "def numba_mm(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 1 numba_mm(a,b) # Warmup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm = %timeit -o numba_mm(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = rng.uniform(size=(1000, 1000))\n",
+ "b = rng.uniform(size=(1000, 1000))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm_1000 = %timeit -o numba_mm(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy_mm_1000 = %timeit -o a.dot(b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"The version of numpy, we used has been compiled against Intel's math kernel library (MKL) and is therefore about %.0f times faster.\" \n",
+ " \"If we used a version that has not been compiled against a fast BLAS library, it would take about the same time as the numba routine.\" \n",
+ " % (t_numba_mm_1000.best / t_numpy_mm_1000.best))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise: prange\n",
+ "Numba can parallelize loops with ``prange``. Import ``prange`` from numba and change the range in row into a prange. You also need to add the arguments ``nopython=True`` and ``parallel=True`` to the jit decorator.\n",
+ "\n",
+ "Rerun and compare.\n",
+ "\n",
+ "**Extra credit:** Look at the changes we did to the matrix-matrix multiplication in the Bottlenecks notebook. Can you include them, too. Does it help? You might want to compare the results of your own calculation with that of numpy. The function ``numpy.allclose`` is useful for that."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Some other variations\n",
+ "\n",
+ "Let's try some other variations and how they do."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit\n",
+ "def numba_mm2(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " res[row, col] = a[row].dot(b[:,col])\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -r 1 -n 1 numba_mm2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm2_1000 = %timeit -o numba_mm2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Most of the computation should now be done with numpy, but it's much harder to optimize a dot product than the matrix multiplication. Think back to our discussion about bottlenecks. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit(nopython=True)\n",
+ "def numba_mm3(a, b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " res[row, col] = a[row]@b[:,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -r 1 -n 1 numba_mm3(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit(nopython = True)\n",
+ "def numba_mm4(a, b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_mm4(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm4_1000 = %timeit -o numba_mm4(a, b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "20min"
+ ]
+ },
+ "source": [
+ "## Exercise: Mandelbrot with Numba\n",
+ "Now, it's your turn again. Use Numba's jit operator to write a program to calculate the Mandelbrot set."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Type inference"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As mentioned above, [Numba][]'s jit operator doesn't directly return a compiled function, because \n",
+ "it needs to figure out the type of every variable once a function has been called with specific \n",
+ "arguments. It only compiles a function once for each type of arguments used to call it. The function\n",
+ "signature is then stored in its `signatures` property.\n",
+ "\n",
+ "[Numba]: https://numba.pydata.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.signatures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise: Call numba_sum with an ndarray of type float32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now there is a second function signature:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.signatures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Numba allows us to look at its type inferrence using "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.inspect_types(signature=numba_sum.signatures[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, this is interesting. If you look at Line 3 of the version called with float32, it still defines\n",
+ "`res` as a double precision number! This will prevent it from vectorizing the loop using single \n",
+ "precision arguments, which potentially cuts performance in half!\n",
+ "\n",
+ "Now, let's see if we can do better."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum(a_s, numpy.float32(0.0))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.signatures"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.inspect_types(signature=numba_sum.signatures[2]) # Try adding pretty=True "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now, res is of type `float32`. Let's see if this speeds up things."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit numba_sum(a_s, numpy.float32(0.0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Doesn't look like it. \n",
+ "\n",
+ "Let's dig a little deeper. A speedup would come from the fact that the Skylake-X processor used for \n",
+ "JUWELS Cluster can operate on 16 single precision numbers at once compared to 8 double precision \n",
+ "numbers, but that assumes it's using the right instructions. For that we have to look at the assembler.\n",
+ "\n",
+ "We define a helper function to find instructions in the assembler code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# This function has been borrowed from https://github.com/numba/numba-examples/blob/master/notebooks/simd.ipynb\n",
+ "def find_instr(func, keyword, sig=0, limit=5):\n",
+ " count = 0\n",
+ " for l in func.inspect_asm(func.signatures[sig]).split('\\n'):\n",
+ " if keyword in l:\n",
+ " count += 1\n",
+ " print(l)\n",
+ " if count >= limit:\n",
+ " break\n",
+ " if count == 0:\n",
+ " print('No instructions found')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "find_instr(numba_sum, \"add\", 2, limit=10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The instruction `vaddss` performs an addition of two single precision numbers. It's not vectorized \n",
+ "and uses the smallest register available. For some reason the compilation wasn't done using the best\n",
+ "available instruction set.\n",
+ "\n",
+ "The reason in this case is that we are doing a *reduction*. We are adding up all the values in `a`.\n",
+ "When the compiler vectorizes this, the order of the addition may change. While this is not a problem\n",
+ "if we work with real number, it is a problem for the finite precision math that computers do. The \n",
+ "order of the addition may change the result.\n",
+ "\n",
+ "To allow reordering of operations, we add the option `fastmath=True`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "fast_numba_sum = jit(python_sum, fastmath=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit fast_numba_sum(a_s, numpy.float32(0.0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now let's look at the assembler again:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "find_instr(fast_numba_sum, \"vaddp\", sig=0, limit=10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This is much better. The `ps` at the end of `vaddps` stands for *packed single precision* indicating \n",
+ "a SIMD instruction. The `ymm` registers used are 256 bits wide, which corresponds to 8 single precision\n",
+ "numbers at a time.\n",
+ "\n",
+ "Skylake-X also has `zmm` registers with a width of 512 bit or 16 single precision numbers, but when\n",
+ "they are used the maximum frequency of the processor is reduced. It can happen that the performance \n",
+ "using `ymm` registers at higher frequency is actually better."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise: Call fast_numba_sum with double precision\n",
+ "\n",
+ "Call `fast_numba_sum` with arguments of type float64 and measure the run time. Compare the result\n",
+ "with the one obtained from `numba_sum`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"The difference is {fast_numba_sum(a, numpy.float64(0.0)) - numba_sum(a, numpy.float64(0.0))}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/11_Speeding up your code with Cython.ipynb b/11_Speeding up your code with Cython.ipynb
new file mode 100644
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--- /dev/null
+++ b/11_Speeding up your code with Cython.ipynb
@@ -0,0 +1,1285 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Speeding up your code with Cython"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "<div class=\"dateauthor\">\n",
+ "18 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Cython"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "> “Cython is a language that makes writing C extensions for the Python language as easy as Python itself”"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Cython allows you to write C extensions to Python in a very pythonic manner. In this notebook we'll explore the syntax of Cython and see what kind of speed up we can achieve.\n",
+ "\n",
+ "Cython provides an extension for Jupyter notebooks that makes working with Cython very convenient. If you enter `%load_ext Cython` the `%%cython` magic becomes available."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let us start with something simple. The following function calculates the dot product between two vectors:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def pydot(v, w):\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v = numpy.arange(0, 10000, dtype=int)\n",
+ "w = numpy.arange(0, 10000, dtype=int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit a = range(10000); b = range(10000)\n",
+ "pydot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "pydot_timing = %timeit -o pydot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Elementwise access to NumPy arrays can in the meantime be just as fast as access for lists.\n",
+ "\n",
+ "Now let us invoke Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "def dot(v, w):\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit a = range(10000); b = range(10000)\n",
+ "dot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot1_timing = %timeit -o dot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can check what Cython does by invoking the cell magic with the option `-a`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "def dot(v, w):\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This produces an annotated listing. The darker the yellow, the more Python code is in that line. You can click on each line to see the C code that was generated for it. Go ahead and explore.\n",
+ "\n",
+ "There are many references to Python objects and functions. Basically, you only save the overhead of interpreting. Let's see if we can do a little better."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Declaring types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The arguments `v` and `w` are very general. If we know, however, that we are only going to pass ndarrays of integers, we can be more specific:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy\n",
+ "cimport numpy\n",
+ "\n",
+ "def dot(numpy.ndarray[numpy.int_t, ndim = 1] v, numpy.ndarray[numpy.int_t, ndim = 1] w):\n",
+ " cdef long res = 0\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "I also added ``cdef long res = 0``. This declares a C variable. C variables are not visible to a Python program. Here this doesn't matter since res is only used within the function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot2_timing = %timeit -o dot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note that ``cdef long res = 0`` is white. It's translated directly into C. `len(v)` is a Python call. It can be pulled out and assigned to an integer variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "\n",
+ "def dot(np.ndarray[np.int_t, ndim = 1] v, np.ndarray[np.int_t, ndim = 1] w):\n",
+ " cdef long res = 0\n",
+ " cdef int n = 0\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " for i in range(0, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot3_timing = %timeit -o dot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you look at line 10, you'll notice that there are some bounds checks, but they are unnecessary since we check the bounds beforehand already. Let's do away with them."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Skipping checks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot4_timing = %timeit -o dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can dispense of wraparound a[-1]->a[len(a)-1], too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False)\n",
+ "@cython.wraparound(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot5_timing = %timeit -o dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Adding compiler option\n",
+ "### Cython magic"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython --compile-args=-O2 --compile-args=-march=native --force\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False)\n",
+ "@cython.wraparound(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = 0\n",
+ " for i in range(0, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Sometimes we need (or want) to pass some options to the compiler. The cython magic can take compile-args and link-args that are passed to the underlying compiler. Later, we'll show you how to integrate all of this in a setup.py script to compile your extension outside of a notebook.\n",
+ "\n",
+ "The [documentation shows you, which options can be passed to the magic command](https://cython.readthedocs.io/en/latest/src/userguide/source_files_and_compilation.html#compiling-with-a-jupyter-notebook)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot5a_timing = %timeit -o -r 13 dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Adding OpenMP"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since Cython generates compiled Python extensions, we can release the GIL and run things in parallel if we don't make calls to the Python API.\n",
+ "\n",
+ "As we've seen our inner loop is free of any Python calls (the annotated code is white). Since OpenMP supports reductions, we can parallelize the loop using Cython's ``prange``. Within ``prange`` we have to explicitely release the GIL by setting ``nogil=True``. We also need to pass the compiler and linker flags for OpenMP."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython --compile-args=-fopenmp --compile-args=-O2 --compile-args=-march=native --link-args=-fopenmp --force\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "from cython.parallel import parallel, prange\n",
+ "\n",
+ "@cython.boundscheck(False)\n",
+ "@cython.wraparound(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = v[0] * w[0]\n",
+ " for i in prange(1, n, nogil=True):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot6_timing = %timeit -o dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Our data set is too small to benefit from parallelization. The overhead due to starting multiple threads is too large for this problem size."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Function declaration with def, cdef, and cpdef"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In short, functions defined using **def** are visible from Python and treated like Python functions even within Cython. Functions defined with **cdef** are C functions and are not visible from Python at all. Functions declared with **cpdef** are C functions that can be called efficiently from within Cython but also have a Python wrapper so they can be accessed from Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "#### Exercise\n",
+ "* Define a function `add` in Cython using `cdef` that takes two float values as arguments and returns the sum. \n",
+ "* Try calling it from outside Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Write your function here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "\n",
+ "Now use cpdef instead."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Copy the function from above and use cpdef instead of cdef"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Building a Cython extension outside of a notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "So far we have used IPython and the Cython magic to build and test our extension within a notebook. Once we are satisfied and want to put our extension in production, we want to be able to build the extension without IPython. The recommended way to do that is to use `distutils` and a `setup.py` file."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### A simple setup.py file"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```python\n",
+ "from distutils.core import setup\n",
+ "from Cython.Build import cythonize\n",
+ "setup(name=\"Sum of integers\",\n",
+ " ext_modules=cythonize(\"sum.pyx\"),\n",
+ " zip_safe=False\n",
+ " )\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Adding compiler options "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "To add compiler options, for example, to compile with OpenMP, we need to set up an Extension first. Then, we use the Extension instead of the file name in the setup function. Our new setup.py file now looks like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```python\n",
+ "from distutils.core import setup\n",
+ "from distutils.extension import Extension\n",
+ "from Cython.Build import cythonize\n",
+ "\n",
+ "ext_modules = [\n",
+ " Extension(\"sum\",\n",
+ " [\"sum.pyx\"],\n",
+ " extra_compile_args = [\"-fopenmp\"],\n",
+ " extra_link_args = [\"-fopenmp\"]\n",
+ " )\n",
+ "]\n",
+ "setup(name=\"Sum of integers\",\n",
+ " ext_modules=cythonize(ext_modules),\n",
+ " zip_safe=False\n",
+ " )\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercise:** Take the Cython code that defines dot using `prange` in [Adding OpenMP](#Adding-OpenMP) and write it to `dot.pyx` using the `%%writefile` magic. Make sure to comment out the `cython magic`. Take the above code for setup.py and copy it into a file called `setup.py`. Change the setup.py code to build a module named dot and use `dot.pyx`. Then build the extension in a terminal window with the command. **Note:** Make sure our environment is loaded `source hpcpy20`.\n",
+ "\n",
+ "```bash\n",
+ "python setup.py build_ext --inplace\n",
+ "```\n",
+ "\n",
+ "If the build fails with `#include \"numpy/arrayobject.h\" not found`, you need to add the include path for numpy. Luckily, numpy has a function for that: `numpy.get_include()`. Add the include path to the extra_compile_args. Include paths are added using `-I/path/to/be/included`. Since `setup.py` is a Python script you can call `numpy.get_include()` in the script and don't have to hardcode the path.\n",
+ "\n",
+ "Write a test program that loads and tests the extension. Add a doc string to the dot function and include an example section like this:\n",
+ "\n",
+ "```python\n",
+ "def dot(...):\n",
+ "\"\"\" Add description and parameters ...\n",
+ "\n",
+ "Examples\n",
+ "--------\n",
+ ">>> import numpy\n",
+ ">>> from dot import dot\n",
+ ">>> v = numpy.arange(0, 10, dtype=int)\n",
+ ">>> w = numpy.arange(0, 10, dtype=int)\n",
+ ">>> print(dot(v, w))\n",
+ "285\n",
+ "\n",
+ "\"\"\"\n",
+ "```\n",
+ "\n",
+ "Rebuild the extension and run [doctest](https://docs.python.org/3.6/library/doctest.html) (`python -m doctest -v dot.pyx`). Without `-v` only failed tests are reported."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Comparison with Numba"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Numba, can generate fast functions, too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import int64, jit\n",
+ "@jit(nopython=True)\n",
+ "def udot(v, w):\n",
+ " res = 0\n",
+ " for i in range(0, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import int64, jit\n",
+ "@jit(nopython=False)\n",
+ "def udotg(v, w):\n",
+ " res = 0\n",
+ " for i in range(0, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numbadot_timing = %timeit -o udot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numbadotg_timing = %timeit -o udotg(v,w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit a = range(10000); b = range(10000)\n",
+ "udotg(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "npdot_timing = %timeit -o np.dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "tunits = {'ns':10**-9, 'us':10**-6, 'ms':10**-3, 's':1.0}\n",
+ "timers = [pydot_timing, dot1_timing, dot2_timing, dot3_timing, dot4_timing, dot5_timing, \n",
+ " dot6_timing, numbadot_timing, numbadotg_timing, npdot_timing]\n",
+ "times = np.array([t.best for t in timers])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(12,6))\n",
+ "plt.subplot(1,2,1)\n",
+ "plt.bar(np.arange(len(times)) + 1, times * 1e6)\n",
+ "plt.ylabel(u\"µs\")\n",
+ "plt.xticks([1, 2, 3, 4, 5, 6, 7, 8, 9, 10],[\"Python\", \"Cython\", \"types1\", \"types2\", \"bounds\", \"wraparound\", \"parallel\", \n",
+ " \"Numba\", \"NumbaG\", \"np.dot\"], rotation=45)\n",
+ "plt.subplot(1,2,2)\n",
+ "plt.bar(np.arange(2, len(times[2:]) + 2) + 1, times[2:] * 1e6)\n",
+ "plt.ylabel(u\"µs\")\n",
+ "plt.xticks([3, 4, 5, 6, 7, 8, 9, 10],[\"types1\", \"types2\", \"bounds\", \"wraparound\", \"parallel\", \n",
+ " \"Numba\", \"NumbaG\", \"np.dot\"], rotation=45)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Finally, let's compare the performance for a larger data set. Remember the last version of our dot function uses OpenMP."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v = np.arange(10000000, dtype=int)\n",
+ "w = np.arange(10000000, dtype=int)\n",
+ "%timeit -n 1 pydot(v,w)\n",
+ "%timeit dot(v,w)\n",
+ "%timeit udot(v,w)\n",
+ "%timeit np.dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Cython and classes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Sometimes, we want to do more than just wrap a function. We might want an efficient data type that implements some operators, for example. For this Cython allows us to declare classes just like in Python:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "class Point:\n",
+ " \"\"\"A simple class representing a point in the x-y plane.\"\"\"\n",
+ " def __init__(self, x, y):\n",
+ " self.x = x\n",
+ " self.y = y\n",
+ " def __repr__(self):\n",
+ " return \"(%.1f, %.1f)\" % (self.x, self.y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "p = Point(0,1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Extension types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "There is a second type of classes called *[extension types](http://cython.readthedocs.io/en/latest/src/userguide/extension_types.html)*. An extension type stores its members and methods in a C struct instead of a Python dictionary. This makes them more efficient but also more restrictive. Let's look at an example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "from math import sqrt,asin,pi\n",
+ "\n",
+ "cpdef double rad2deg(double alpha):\n",
+ " return 180 * alpha / pi\n",
+ "\n",
+ "cdef class Point:\n",
+ " \"\"\"A point in 2d.\"\"\"\n",
+ " cdef double x, y\n",
+ "\n",
+ " cdef double distance2origin(Point self):\n",
+ " return sqrt(self.x * self.x + self.y * self.y)\n",
+ " \n",
+ " cdef alpha(Point self):\n",
+ " return asin(self.y / self.distance2origin())\n",
+ " \n",
+ " def __cinit__(self, t_x, t_y):\n",
+ " self.x = t_x\n",
+ " self.y = t_y\n",
+ " \n",
+ " def __repr__(self):\n",
+ " return \"(r=%.2f, alpha=%.2f°)\" % (self.distance2origin(), rad2deg(self.alpha()))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The first thing to note is the definition using `cdef class`. It's the reason extension types are also referred to as cdef classes. We can define functions that are only visible to C using `cdef` and Python functions using `def` (or both at once with `cpdef`). For functions defined with `cdef`, we need to give the type of self as well as a return type.\n",
+ "\n",
+ "We can use the new class as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "p = Point(0.5, 1)\n",
+ "print(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Try which methods of Point you can call."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Cython Tutorial at SciPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The following video is from a half-day tutorial on Cython."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import YouTubeVideo\n",
+ "YouTubeVideo(\"gMvkiQ-gOW8\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/12_Writing your own Python bindings.ipynb b/12_Writing your own Python bindings.ipynb
new file mode 100644
index 0000000..239be1a
--- /dev/null
+++ b/12_Writing your own Python bindings.ipynb
@@ -0,0 +1,1503 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Writing language bindings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"dateauthor\">\n",
+ "18 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Why bindings?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* Use existing optimized code as a library\n",
+ "* Avoid overhead of calling a binary via `popen` and communication via pipes\n",
+ "* Cleaner code"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Python is often used as a \"glue language\" that combines calls to compiled programs and libraries to get the job done. Many libraries provide Python bindings that allows you to call them from Python. Numpy, for example, can call vendor-optimized routines to perform linear algebra operation near peak machine performance, but others don't.\n",
+ "\n",
+ "Python also allows you to call other programs from within Python and pipe the in- and output. This often requires conversion of data, for example, into text and back, which can result in a lot of overhead.\n",
+ "\n",
+ "These are just two cases, when you might want to write your own Python bindings."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "There are wrapper programs such as [swig](http://www.swig.org/), [sip](https://www.riverbankcomputing.com/software/sip/intro), or [binder](http://cppbinder.readthedocs.io/en/latest/) that can help you generate bindings, but you will frequently need to tune the generated wrappers.\n",
+ "\n",
+ "In this notebook we'll use [cffi](https://cffi.readthedocs.io/en/latest/) to wrap a single function with simple data types. We use [Cython][] to wrap more complex C/C++ functions and even C++ classes and compare this with [PyBind11](https://pybind11.readthedocs.io/en/latest/). Finally we use [f2py](https://docs.scipy.org/doc/numpy/f2py/) to generate bindings for a Fortran code and compare it to wrapping the same Fortran code with [Cython][].\n",
+ "\n",
+ "[Cython]: http://cython.org"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Preparations\n",
+ "\n",
+ "Before we can look at the bindings, we need to build our libraries. Open a terminal, switch to the tutorial directory and run\n",
+ "\n",
+ "```bash\n",
+ "./build.sh\n",
+ "```\n",
+ "\n",
+ "Wait until the build has finished and then continue with this notebook.\n",
+ "\n",
+ "**Tip:** You can open a terminal from within JupyterLab by going to File->New->Terminal. To get the right environment in a terminal `source hpcpy20` in the tutorial directory."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Ctypes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "While ``ctypes`` is a Python standard module it is not very convenient and I'm not going to talk about it. You can look at the [documentation](https://docs.python.org/3/library/ctypes.html) instead if you want to learn more."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Foreign function interface"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's start with a simple function signature. This function is in declared in a header file ``text_stats.h`` and it's part of the library ``libtext_stats.so``."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```c\n",
+ "/** Counts the occurences of a string in a file.\n",
+ " * \n",
+ " * @param filename name of file to open\n",
+ " * @param word string to look for in file\n",
+ " *\n",
+ " * @return number of occurences of word in file with filename\n",
+ " */\n",
+ "int word_frequency(char* filename, char* word);\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A quick way to access this function is to use the module ``cffi``."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Foreign function interface\n",
+ "### Calling word_frequency from Python"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import cffi"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ffi = cffi.FFI()\n",
+ "ffi.cdef(\"\"\"\n",
+ " int word_frequency(char* filename, char* word);\n",
+ "\"\"\") # The definition is the same as in the header file.\n",
+ "\n",
+ "TS = ffi.dlopen(\"./code/text_stats/build/libtext_stats.so\")\n",
+ "wc = TS.word_frequency(b\"test.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "What if word_frequency had been written Fortran?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ "function word_frequency(filename, word)\n",
+ " implicit none\n",
+ " character(len=*), intent(in) :: filename\n",
+ " character(len=*), intent(in) :: word\n",
+ " integer :: word_frequency\n",
+ " ...\n",
+ "end function word_frequency\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can access Fortran functions almost like C functions. The exact function name may differ, though. The default symbol \n",
+ "when compiled with ifort or gfortran is ``word_frequency_``. This can be changed with the option `-fno-underscoring` (gcc) or `-assume nounderscore` (Intel).\n",
+ "\n",
+ "On JUWELS, we are using the Intel Fortran compiler ifort. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "Use the terminal that you used earlier to run `build.sh` or open a new one. Make sure you are in the \n",
+ "tutorial directory. Source `hpcpy20` using `source hpcpy20`. Change into code/textstats/ and compile \n",
+ "the file word_frequency.F90 with the following command:\n",
+ "\n",
+ "```bash\n",
+ "ifort word_frequency.F90 -shared -O2 -o build/libwf.so -fPIC\n",
+ "```\n",
+ "\n",
+ "```bash\n",
+ "nm build/libwf.so | grep word_frequency\n",
+ "```\n",
+ "\n",
+ "to check the symbol.\n",
+ "\n",
+ "Change the cell below to use libwf.so instead of libtext_stats.so. Don't forget to adjust the function declaration.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ffi = cffi.FFI()\n",
+ "ffi.cdef(\"\"\"\n",
+ " int word_frequency(char* filename, char* word);\n",
+ "\"\"\") # The definition is the same as in the header file.\n",
+ "\n",
+ "TS = ffi.dlopen(\"./code/text_stats/build/libtext_stats.so\")\n",
+ "wc = TS.word_frequency(b\"test.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you compiled the library with the option `-assume nounderscore`, you could use the original declaration without underscore with libwf.so.\n",
+ "\n",
+ "**Note**: There is no way to *reload* a library using cffi."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## ISO_C_BINDING"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Fortran 2003 improved the interoperability between Fortran and C with the `iso_c_binding`. It provides data kinds that are C compatible and the `bind` attribute. The function definition can be changed to"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ "function word_frequency(filename, word) bind(C)\n",
+ " use iso_c_binding\n",
+ " implicit none\n",
+ " character(kind=c_char, len=1), intent(in) :: filename\n",
+ " character(kind=c_char, len=1), intent(in) :: word\n",
+ " integer :: word_frequency\n",
+ " ...\n",
+ "end function word_frequency\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, the name of the function will always be `word_frequency`. `bind` takes as optional argument the name under which the function should be known to C: bind(c, name=\"wf\") would let us call the function as `wf(filename, word)` from C (and Python).\n",
+ "\n",
+ "To learn more about [CFFI](https://bitbucket.org/cffi/cffi) look at it's [documentation](https://cffi.readthedocs.io/en/latest/)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext cython"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Cython generates C code that is compiled to an extension. It can trivially call C (and even C++) \n",
+ "functions, which we can use to write Python bindings. But first an annotated example of a \"normal\"\n",
+ "cython module. The following code will make the function `cysum` available to Cython and Python:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy\n",
+ "cimport numpy # Make C-style calls available\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False) # Turn off boundary checks for array access.\n",
+ "# Functions defined with `def` are visible from Python and Cython\n",
+ "def cysum(numpy.ndarray[numpy.float_t, ndim=1] a): # Define the input type as 1d ndarray of floats\n",
+ " \"\"\"Sum up the elements of a.\n",
+ " \n",
+ " Paramters\n",
+ " ---------\n",
+ " a : ndarray\n",
+ " array to sum over\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " res: float\n",
+ " sum of the elements of a\n",
+ " \"\"\"\n",
+ " cdef float res = 0.0; # Define a C-only variable using `cdef`\n",
+ " cdef int n = len(a)\n",
+ " for i in range(n):\n",
+ " res += a[i]\n",
+ " return res\n",
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's wrap `word_frequency` using cython. We need to pass compile and link arguments to the call as described in [Adding compiler options][CompilerOptions].\n",
+ "\n",
+ "[CompilerOptions]: ./Speeding%20up%20your%20code%20with%20Cython.ipynb#Adding-compiler-options\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -I code/text_stats -L code/text_stats/build -l text_stats\n",
+ "cdef extern from \"text_stats.h\":\n",
+ " cpdef int word_frequency(char* filename, char* word)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "word_frequency(b\"text.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note** Unfortunately, this doesn't work the way it's supposed to. Although `-L` should add the path to the library to the search path of the linker, the linker still doesn't find the library. To make it work, I added the path to libtext_stats.so to the `LD_LIBRARY_PATH` when the kernel is loaded."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Adapting types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function `word_frequency` takes bytes instead of strings because the C function uses char\\*, which is mapped to bytes in Python 3. We would want a Python function that takes strings, though. We can do this by calling our C function from a Python function within Cython and take care of the argument conversion ourselves."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Cython\n",
+ "cdef extern from \"text_stats.h\":\n",
+ " cdef int word_frequency(char* filename, char* word)\n",
+ " \n",
+ "def wordfrequency(filename, word):\n",
+ " \"\"\"Counts the occurences of a string in a file.\"\"\"\n",
+ " # We first need to decode the strings\n",
+ " filenameb = filename.encode('UTF-8')\n",
+ " wordb = word.encode('UTF-8')\n",
+ " # Now we can convert them to C strings\n",
+ " cdef char* filenamec = filenameb\n",
+ " cdef char* wordc = wordb\n",
+ " # And finally pass them to our C function\n",
+ " return word_frequency(filenamec, wordc)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The function wordfrequency takes two Python strings and encodes them to get the proper byte representation that is then passed to the original C function. A complete implementation with doc string and compiler arguments can look like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -I code/text_stats -L code/text_stats/build -ltext_stats\n",
+ "cdef extern from \"text_stats.h\":\n",
+ " cdef int word_frequency(char* filename, char* word)\n",
+ " \n",
+ "def wordfrequency(filename, word):\n",
+ " \"\"\"Counts the occurences of a string in a file.\n",
+ "\n",
+ " Paramters\n",
+ " ---------\n",
+ " filename: string\n",
+ " name of file to open\n",
+ " word: string\n",
+ " string to look for in file\n",
+ "\n",
+ " Returns\n",
+ " -------\n",
+ " ct: int \n",
+ " number of occurences of word in file with filename\n",
+ " \"\"\"\n",
+ " # We first need to decode the strings\n",
+ " filenameb = filename.encode('UTF-8')\n",
+ " wordb = word.encode('UTF-8')\n",
+ " # Now we can convert them to C strings\n",
+ " cdef char* filenamec = filenameb\n",
+ " cdef char* wordc = wordb\n",
+ " # And finally pass them to our C function\n",
+ " return word_frequency(filenamec, wordc)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "wordfrequency(\"text.txt\", \"you\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Wrapping Fortran"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can do almost the same thing as above, to wrap the Fortran function `word_frequency`. We don't have a header file, so we skip that part:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -Lcode/text_stats/build -lwf\n",
+ "cdef extern:\n",
+ " cdef int word_frequency_(char* filename, char* word)\n",
+ " \n",
+ "def wordfrequency2(filename, word):\n",
+ " \"\"\"Counts the occurences of a string in a file.\"\"\"\n",
+ " # We first need to decode the strings\n",
+ " filenameb = filename.encode('UTF-8')\n",
+ " wordb = word.encode('UTF-8')\n",
+ " # Now we can convert them to C strings\n",
+ " cdef char* filenamec = filenameb\n",
+ " cdef char* wordc = wordb\n",
+ " # And finally pass them to our C function\n",
+ " return word_frequency_(filenamec, wordc)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "wordfrequency2(\"text.txt\", \"you\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If we cannot/don't want to change our original source code by adding `bind` for example or using the kinds from iso_c_binding or we don't have access to the source code in the first place, we can write a wrapper in Fortran that includes the binding. Look [here](http://www.fortran90.org/src/best-practices.html#interfacing-with-c) for an example."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Wrapping C++"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can use Cython to wrap C++ as well. Let's start with a simple 3d point class."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```c++\n",
+ "#pragma once\n",
+ "\n",
+ "#include <vector>\n",
+ "\n",
+ "class Point3D{\n",
+ "public:\n",
+ " Point3D(const double x, const double y, const double z);\n",
+ " Point3D(const std::vector<double> r);\n",
+ " void translate(const double dx, const double dy, const double dz);\n",
+ " void translate(const std::vector<double> dr);\n",
+ " const std::vector<double> coordinates();\n",
+ "private:\n",
+ " double _x, _y, _z;\n",
+ "};\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "For starters, I'm only going to wrap `Point3D(x, y, z)`, `translate(dx, dy, dz)`, and `coordinates()`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Cython needs to know that we are dealing with C++ now. Usually, this is added to the setup.py or .pxd file, but it can be done in a notebook cell, too. That's what the second line in the following cell is doing.\n",
+ "\n",
+ "First, you need to import the header and then define the functions that should be made available to Cython. Since these are methods of a class, you define that too using the **cppclass** keyword.\n",
+ "\n",
+ "An important part of C++ is the standard library. Cython comes with a number of prepared wrappers, for example, for std::vector. These are imported from libcpp."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -Icode/point -Lcode/point/build -lpoint\n",
+ "# distutils: language = c++\n",
+ "from libcpp.vector cimport vector\n",
+ "\n",
+ "cdef import from \"point3d.h\":\n",
+ " cdef cppclass Point3D:\n",
+ " Point3D(double x, double y, double z)\n",
+ " void translate(double dx, double dy, double dz)\n",
+ " vector[double] coordinates()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As before, so far these functions are only available to Cython. To make them available to Python, you have to write a wrapper. There are two new functions that are used to deal with classes: initialization is done in \\_\\_cinit\\_\\_ and there's a corresponding destructor function called \\_\\_dealloc\\_\\_."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "By convention a pointer to the object called `thisptr` is kept as part of the wrapper object."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -Icode/point -Lcode/point/build -lpoint\n",
+ "# distutils: language = c++\n",
+ "from libcpp.vector cimport vector\n",
+ "\n",
+ "cdef import from \"point3d.h\":\n",
+ " cdef cppclass Point3D:\n",
+ " Point3D(double x, double y, double z)\n",
+ " void translate(double dx, double dy, double dz)\n",
+ " vector[double] coordinates()\n",
+ " \n",
+ "cdef class PyPoint3D: # This is an extension type (aka cdef class)\n",
+ " cdef Point3D *thisptr\n",
+ " \n",
+ " def __cinit__(self, double x, double y, double z):\n",
+ " self.thisptr = new Point3D(x, y, z)\n",
+ " \n",
+ " def __dealloc__(self):\n",
+ " del self.thisptr"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "You can now construct an object of type PyPoint3D, which keeps a reference to it's copy of Point3D."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "origin = PyPoint3D(0,0,0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, let's wrap the two functions as well."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython --compile-args=-Icode/point --link-args=-Lcode/point/build --link-args=-lpoint\n",
+ "# distutils: language = c++\n",
+ "from libcpp.vector cimport vector\n",
+ "\n",
+ "cdef import from \"point3d.h\":\n",
+ " cdef cppclass Point3D:\n",
+ " Point3D(double x, double y, double zwf)\n",
+ " void translate(double dx, double dy, double dz)\n",
+ " vector[double] coordinates()\n",
+ " \n",
+ "cdef class PyPoint3D:\n",
+ " cdef Point3D *thisptr\n",
+ " \n",
+ " def __cinit__(self, x, y, z):\n",
+ " self.thisptr = new Point3D(x, y, z)\n",
+ " \n",
+ " def __dealloc__(self):\n",
+ " del self.thisptr\n",
+ " \n",
+ " def translate(self, dx, dy, dz):\n",
+ " \"\"\"Move this point by (dx, dy, dz).\n",
+ " \n",
+ " Paramters\n",
+ " ---------\n",
+ " dx : float\n",
+ " shift along x-axis\n",
+ " dy : float\n",
+ " shift along y-axis\n",
+ " dz : float\n",
+ " shift along z-axis\n",
+ " \"\"\"\n",
+ " self.thisptr.translate(dx, dy, dz)\n",
+ " \n",
+ " def coordinates(self):\n",
+ " \"\"\"Get the coordinates of this point.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " r : list\n",
+ " coordinates of this point.\n",
+ " \"\"\"\n",
+ " return self.thisptr.coordinates()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, let's construct a point, shift it and return its coordinates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_point_cython = %timeit -o p = PyPoint3D(1,1,1); p.translate(-0.5, -0.5, -0.5);p.coordinates()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## PyBind11"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A powerful alternative to Cython for writing bindings for C++ code is PyBind11. In contrast to Cython, which adds some additional keywords to Python, PyBind11 is a header-only library that make Python types available in C++ and allows you to write Python bindings in C++. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's start with the `word_frequency` example again. This is the PyBind11 code that wraps this function:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```c++\n",
+ "#include <pybind11/pybind11.h>\n",
+ "\n",
+ "extern \"C\" {\n",
+ " #include <text_stats.h>\n",
+ "}\n",
+ "\n",
+ "namespace py = pybind11; // This is purely for convenience\n",
+ "\n",
+ "PYBIND11_MODULE(text_stats, m){\n",
+ " m.doc() = \"Some functions that provide statistical information about a text.\";\n",
+ " m.def(\"word_frequency\", &word_frequency, R\"doc(Counts the occurences of a string in a file.\n",
+ "\n",
+ "Paramters\n",
+ "---------\n",
+ "filename: string\n",
+ " name of file to open\n",
+ "word: string\n",
+ " string to look for in file\n",
+ "\n",
+ "Returns\n",
+ "-------\n",
+ "ct: int \n",
+ " number of occurences of word in file with filename \n",
+ ")doc\");\n",
+ "\n",
+ "}\n",
+ "\n",
+ "```\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Compiling the extension"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This code can be compiled like this:\n",
+ "\n",
+ "```bash\n",
+ "icpc -O3 -shared -fpic -std=c++14 `python3-config --includes` -I/p/project/training2020/packages/lib/python3.8/site-packages/pybind11/include -I code/text_stats `python3-config --cflags --ldflags` code/text_stats/text_stats_bind.cpp -o text_stats.so -L code/text_stats/build -ltext_stats\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "!icpc -O3 -shared -fpic -std=c++14 `python3-config --includes` -I/p/project/training2020/packages/lib/python3.8/site-packages/pybind11/include -I code/text_stats code/text_stats/text_stats_bind.cpp -o text_stats.so `python3-config --cflags --ldflags` -L code/text_stats/build -ltext_stats "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Using the extension"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import text_stats"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "text_stats.word_frequency(\"text.txt\", \"you\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note that we didn't have to convert our string at all. It's done automatically by PyBind11."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Wrapping a class with Pybind11"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "PyBind11 can deal with classes, too. The following code wraps the Point3D class:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "```c++\n",
+ "#include <vector>\n",
+ "#include <pybind11/pybind11.h>\n",
+ "#include <pybind11/stl.h>\n",
+ "#include <point3d.h>\n",
+ "\n",
+ "namespace py = pybind11; // This is purely for convenience\n",
+ "\n",
+ "PYBIND11_MODULE(points, m){\n",
+ " m.doc() = \"A collection of functions and objects to deal with 3D points.\";\n",
+ "\n",
+ " py::class_<Point3D>(m, \"Point3D\")\n",
+ " .def(py::init<double, double, double>())\n",
+ " .def(py::init<std::vector<double>>())\n",
+ " .def(\"translate\", (void (Point3D::*)(double, double, double)) &Point3D::translate,\n",
+ " R\"doc(Move this point by (dx, dy, dz).\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " dx : float\n",
+ " shift along x-axis\n",
+ " dy : float\n",
+ " shift along y-axis\n",
+ " dz : float\n",
+ " shift along z-axis\n",
+ " )doc\")\n",
+ " .def(\"coordinates\", &Point3D::coordinates,\n",
+ " R\"doc(Get the coordinates of this point.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " r : list\n",
+ " coordinates of this point.\n",
+ " )doc\")\n",
+ " .def(\"rotate\", &Point3D::rotate, R\"doc(Rotates this point about x, y, and z\n",
+ " \n",
+ " The rotation is performed as if this point was first rotated by alpha around the x-axis, \n",
+ " then rotated by beta around the y-axis, and finally rotated by gamma around the z-axis.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " alpha: float\n",
+ " rotation around x-axis in rad\n",
+ " beta: float \n",
+ " rotation arounx y-axis in rad\n",
+ " gamma: float \n",
+ " rotation around z-axis in rad\n",
+ " )doc\");\n",
+ "}\n",
+ "\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## F2Py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The methods to wrap Fortran that we looked at so far relied on Fortran's C interface/compatibility. For Fortran 77/90/95 code you can also use `f2py` to generate bindings in a very convenient way. F2Py is distributed together with NumPy."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In Fortran, you can use a module to store the points."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ "! points.f90\n",
+ "module points\n",
+ "implicit none\n",
+ "\n",
+ "real, allocatable, dimension(:) :: x\n",
+ "real, allocatable, dimension(:) :: y\n",
+ "real, allocatable, dimension(:) :: z\n",
+ "\n",
+ "contains\n",
+ " subroutine init(N)\n",
+ " integer, intent(in) :: N\n",
+ " \n",
+ " allocate(x(N))\n",
+ " allocate(y(N))\n",
+ " allocate(z(N))\n",
+ " \n",
+ " end subroutine init\n",
+ "\n",
+ " subroutine coordinates(idx, tx, ty, tz)\n",
+ " integer, intent(inout) :: idx\n",
+ " real, intent(out) :: tx\n",
+ " real, intent(out) :: ty\n",
+ " real, intent(out) :: tz\n",
+ " tx = x(idx)\n",
+ " ty = y(idx)\n",
+ " tz = z(idx)\n",
+ " end subroutine coordinates\n",
+ "\n",
+ " ...\n",
+ " \n",
+ " subroutine finalize\n",
+ " deallocate (x, y, z)\n",
+ " end subroutine finalize\n",
+ " \n",
+ "end module points\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note**: Remember that you can use '!' to call programs as if you were doing it from the terminal."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "numpy.__file__"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "!f2py -c code/point/points.f90 -m points_f"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from points_f import points"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "points.init(1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "points.set(1, 1.0, 1.0, 1.0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "points.translate(1, -0.5, -0.5, -0.5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x, y, z = points.coordinates(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Note that f2py honors the intent defined in the Fortran module. The subroutine coordinates takes one input value idx and has three \"return arguments\" tx, ty, tz that contain the coordinates of the particle idx. F2py converts this into a Python function that takes one argument and returns a tuple with three values."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Wrapping F77"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Fortran 77 doesn't know anything about intents nor modules, so how can we use f2py to generate nice Python bindings to older Fortran code?\n",
+ "\n",
+ "In Fortran 77, the translate function might be written like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```Fortran\n",
+ " subroutine translate(idx, dx, dy, dz, x, y, z, N)\n",
+ " implicit none\n",
+ " integer idx, N\n",
+ " real*8 dx, dy, dz\n",
+ " real*8 x(N), y(N), z(N)\n",
+ " x(idx) = x(idx) + dx\n",
+ " y(idx) = y(idx) + dy\n",
+ " z(idx) = z(idx) + dz\n",
+ " end subroutine translate\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### cf2py comments for better bindings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can use f2py comments to add the intents like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ " subroutine translate(idx, dx, dy, dz, x, y, z, N)\n",
+ " implicit none\n",
+ " integer idx, N\n",
+ " real*8 dx, dy, dz\n",
+ " real*8 x(N), y(N), z(N)\n",
+ "cf2py intent(in) idx, N\n",
+ "cf2py intent(in) dx, dy, dz\n",
+ "cf2py intent(in,out) x, y, z\n",
+ "cf2py depend(N) x, y, z\n",
+ " x(idx) = x(idx) + dx\n",
+ " y(idx) = y(idx) + dy\n",
+ " z(idx) = z(idx) + dz\n",
+ " end subroutine translate\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The Fortran compiler will ignore the comments, but f2py will use them to generate the proper wrapper."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Although f2py is part of NumPy, little work has been done on it to improve support for modern Fortran. This will hopefully [change](https://www.youtube.com/watch?v=56M40Y2jl9Y)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/13_Introduction to Dask.ipynb b/13_Introduction to Dask.ipynb
new file mode 100644
index 0000000..35f2975
--- /dev/null
+++ b/13_Introduction to Dask.ipynb
@@ -0,0 +1,605 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to Dask\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Olav Zimmermann\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Dask implements flexible **intra- and inter-node parallel execution based on a task model**. It features data structures that 'feel' like ordinary numpy ndarrys or pandas dataframes but under the hood have been enabled to work on **distributed data**.\n",
+ "While the task based scheduling enables parallel execution of even highly irregular computation pipelines, the distributed data structures make dask also an interesting choice for processing of data volumes that are larger than main memory.\n",
+ "\n",
+ "Among the distinctive features of dask is peer-to-peer data sharing between workers, and high resilience provided by nanny processes that can restart failing workers.\n",
+ "\n",
+ "Dask has been developed by Continuum Analytics, the company that also developed Numba etc."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.delayed "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`dask.delayed` can be used to formulate arbitrary task graphs. \n",
+ "\n",
+ "It can either be employed as a decorator `@delayed` (not show in this tutorial) or as a wrapper function `dask.delayed(func)`. \n",
+ "This function marks a function to be scheduled by Dask. Delayed functions will be evaluated lazily, e.g. not before their result is needed. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This is similar in spirit to other lazy evaluation schemes in python (e.g. `eval()`, `lambda` or `concurrent.futures`) and also similar to other task frameworks such as tensorflow. \n",
+ "\n",
+ "As dask.delayed works on the level of individual functions, the user remains in control which functions will be evaluated eagerly and which ones lazily. Although Dask has a sophisticated scheduler for lazy task evaluation, eager evaluation can be preferable in some situations, e.g. for functions that control routing in the task graph, such as functions calculating data used in `if-`statements."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We first do some settings:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import warnings\n",
+ "warnings.filterwarnings('ignore')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The next cell implements some dummy functions and builds a simple pipeline with some data dependencies."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import random\n",
+ "from time import sleep\n",
+ "from dask import delayed\n",
+ "\n",
+ "def input_task(myinput):\n",
+ " #sleep(random.random() / 2)\n",
+ " sleep(0.5)\n",
+ "input_task=delayed(input_task)\n",
+ "\n",
+ "def common_task():\n",
+ " #sleep(random.random() / 2 + 2.5)\n",
+ " sleep(3)\n",
+ "common_task=delayed(common_task)\n",
+ "\n",
+ "def mapitem_task(item, common):\n",
+ " #sleep(random.random() * 4)\n",
+ " sleep(2)\n",
+ "mapitem_task=delayed(mapitem_task)\n",
+ "\n",
+ "def summarize_task(intermediates):\n",
+ " #sleep(random.random() *2)\n",
+ " sleep(1)\n",
+ "summarize_task=delayed(summarize_task)\n",
+ "\n",
+ "## taskgraph\n",
+ "\n",
+ "prepared = [input_task(i) for i in range(8)]\n",
+ "common_data=common_task()\n",
+ "intermediates=[mapitem_task(item,common_data) for item in prepared]\n",
+ "dlresult=summarize_task(intermediates)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Try to think about it ahead of running the next cells:\n",
+ "- What is the minimal wall time possible?\n",
+ "- How many tasks does the task graph have for range(8) in prepared?\n",
+ "- How many inputs could you process maximally in the same time it takes for 8 inputs?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The task graph generated by `dask` can be visualized (don't try this for large graphs!)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import graphviz\n",
+ "dlresult.visualize(format='svg')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The computation of any of the tasks is delayed until the execution is triggered by an explicit command to compute dlresult upon which the individual tasks are scheduled according to the dependency structure."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%time dlresult.compute()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "- How close to optimal is the observed scheduling?\n",
+ "- What is the largest number of inputs you can process under 8 seconds? Why?\n",
+ "- Change the program in a way that enables you to estimate how much overhead per task is incurred by Dask."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Poll"
+ ]
+ },
+ "source": [
+ "Poll: \n",
+ "- largest number of inputs you can process under 8 seconds: A) 12 B) 24 C) 48 D) 96\n",
+ "- task overhead per task: A) 100µs B) 200µs C) 1ms D) 2ms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## (Semi)structured data processing tasks with dask (bag, dataframe, array)\n",
+ "\n",
+ "Dask supports three datatypes that allow for structured and semi-structured computation patterns:\n",
+ "\n",
+ "- The slowest, most general data structure is **`dask.bag`** which implements parallel list processing. \n",
+ "- **`dask.dataframe`** is a faster structure that can be used like a tiled Pandas dataframe. \n",
+ "- Similarly **`dask.array`** works like a tiled `numpy.ndarray`. \n",
+ "\n",
+ "While some restrictions apply, an important subset of Panda's/NumPy's functions are available for [**`dask.dataframe`**](http://dask.pydata.org/en/latest/dataframe-api.html) and [**`dask.array`**](http://dask.pydata.org/en/latest/array-api.html), respectively and typically have the identical interfaces."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.bag\n",
+ "\n",
+ "A **dask.bag** can contain arbitrary data items (including complex types). Dask bags are processed in chunks called partitions. Setting the number of partitions allows to adapt processing to the number of CPUs and the amount of RAM available. \n",
+ "\n",
+ "Typical ways to generate a bag are:\n",
+ "\n",
+ "- `from_sequence(seq)` (where *seq* is an iterable, such as a list)\n",
+ "- `read_text(fn_or_glob)` (where *fn_or_glob* is either a filename or a glob string, creates one partition per file)\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from operator import add\n",
+ "import dask.bag as db"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "l=[x for x in range(1000000)]\n",
+ "s= db.from_sequence(l,npartitions=4) # you can manually set the number of partitions\n",
+ "mysum=s.fold(add) # fold performs a parallel reduction "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "mysum.visualize()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%time result=mysum.compute()\n",
+ "result=mysum.compute\n",
+ "result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%time r=list(s.filter(lambda x: x % 2 == 0).map(lambda x: x * 1.2))\n",
+ "r[:5] #note: apparently no type coercion!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "(The syntax is kind of unfortunate since Python is moving away from filter and map to list comprehensions and generator expressions.)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercise:**\n",
+ "\n",
+ "Code the same operations without dask, i.e. using a) just python and b) using numpy and measure the runtime of the calculations. \n",
+ "\n",
+ "Conclusions? "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.dataframe\n",
+ "\n",
+ "**`dask.dataframe`** behaves like a distributed [Pandas](https://pandas.pydata.org/pandas-docs/stable/) DataFrame. It also uses Pandas functionality under the hood, such as Pandas' fast `read_csv`-method. However, only a small part of the large Pandas functionality is [available](http://dask.pydata.org/en/latest/dataframe-api.html)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import dask.dataframe as dd\n",
+ "df = dd.read_csv(\"data/iris.csv\") # not a reasonably sized task (too small!)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "h=df.groupby(df.Name).SepalLength.mean()\n",
+ "h.compute()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.array\n",
+ "\n",
+ "**`dask.dataframe`** is the distributed equivalent of numpy ndarray."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import dask.array as da\n",
+ "x = da.ones((5, 15), chunks=(5, 5))\n",
+ "x.dask"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x.visualize()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "## numpy or dask.array?\n",
+ "\n",
+ "Despite the sophisticated parallelization, the general rule applies,\n",
+ "that numpy arrays are faster and should be therefore preferred over dask arrays for normal computation if the arrays fit into main memory.\n",
+ "However, Dask allows for many optimizations. Apart from a sophisticated user-tweakable optimizer the chunking can be changed for different workloads.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "x_np = np.random.normal(10, 0.1, size=(10000,3000))\n",
+ "y_np = x_np.transpose()\n",
+ "result=x_np.dot(y_np)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from dask.diagnostics import ProgressBar\n",
+ "import dask.array as da"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x_dask = da.random.normal(10, 0.1, size=(10000,3000), chunks=(5000,3000)) # using as many chunks as CPU cores is good for random number calculation\n",
+ "x_rechunked=x_dask.rechunk((1000,3000)) # larger chunks are no longer better for dot product calculation\n",
+ "y_dask = x_rechunked.transpose()\n",
+ "result=x_dask.dot(y_dask)\n",
+ "#with ProgressBar():\n",
+ "%timeit result.compute(scheduler=\"threads\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.distributed\n",
+ "\n",
+ "`dask.distributed` extends `dask` to distributed computing on several nodes."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "`dask.distributed` features a sophisticated **web-based monitoring** based on the package `bokeh`. See **Dashboard** when you started the client above that shows the address and port of the web server."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "### dask.distributed working with schedulers\n",
+ "There are external packages like `dask.jobqueue` that allow dask to work on top of scheduling systems such as Sun Grid Engine, Slurm, Torque etc. (For details read the docs [(link)](https://jobqueue.dask.org/en/latest/index.html).)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "## dask and other packages\n",
+ "\n",
+ "### dask on sparse data\n",
+ "Dask does currently not support sparse matrix formats directly but dask's chunks can work with any in-memory array representation that follows the `numpy.ndarray` API. One such library is `sparse` [(link)](https://sparse.pydata.org/en/stable/), written by the main dask developer, Matthew Rocklin, but it only supports coordinate list layout (COO) for sparse matrices. Note that the `scipy.sparse` format, which additionally supports compressed sparse row (CSR) and compressed sparse column (CSC) layouts, does not follow the `numpy.ndarray` API but the `numpy.matrix` API and hence is not compatible with dask. Therefore even the popular dask-ML package for machine learning suggests to convert scipy sparse matrices (e.g. from sklearn outputs) to dense matrices. There are some other projects such as `Sparsity` [(link)](https://sparsity.readthedocs.io/en/latest/) that have goals similar to `sparse` but are much younger."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "### x-array project \n",
+ "The [x-array](http://xarray.pydata.org/en/stable/) project provides an n-dimensional equivalent of a Pandas DataFrame and can employ dask for distributed processing. This project was originally developed for applications in the Earth sciences. It provides, e.g. a convenient in-memory representation of netCDF files."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "### Multi-GPU processing with Rapids and dask\n",
+ "\n",
+ "Rapids [(link)](https://rapids.ai/) is an open source project supported by nVidia that provides several libraries GPU data science and data analytics project.\n",
+ "cuDF, one of the Rapids libraries, is a single-GPU library that implements a subset of the pandas dataframe functionality on GPUs.\n",
+ "Using dask-cuDF [(link)](https://github.com/rapidsai/cudf/tree/main/python/dask_cudf) allows for scaling cuDF to multiple (nVidia) GPUs, both single and multi-node."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/14_Introduction to MPI.ipynb b/14_Introduction to MPI.ipynb
new file mode 100644
index 0000000..60062bb
--- /dev/null
+++ b/14_Introduction to MPI.ipynb
@@ -0,0 +1,1589 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to MPI\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "MPI (Message Passing Interface) is the most used protocol for communicating between processes. It doesn't matter if the processes that want to talk to each other are on the same or different nodes (i.e., computers). In this tutorial, we'll use `mpi4py` to learn about MPI and its API.\n",
+ "\n",
+ "An MPI program can run on a single computer/node with one or more processes that share memory or on multiple computers that are connected to each other via some network (not shown)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Communicators"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "MPI processes talk to each other via communicators. The global communicator `MPI.COMM_WORLD` connects all MPI processes. Each process has a unique *rank* within `MPI.COMM_WORLD`. The process with `rank=0` is usually called the root process. MPI processes can participate in different communicators and may have a different rank in these communicators."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Point to point communication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Sending messages from one MPI task to another is the foundation of MPI. Messages consist of some meta information such as the *source* and the *destination*, a *tag* that identifies the message, the *data type*, and the *count* of data items and the actual data.\n",
+ "\n",
+ "For each `Send` there has to be a matching `Recv`. This means that the meta information has to fit (including the tag). There are some wildcards and some additional commands that make this more flexible.\n",
+ "\n",
+ "Sending and receiving can be blocking or non-blocking. In the latter case, the flow of the program continuous after the call. In the former the program waits until the message has been transmitted. There is a very real danger for deadlocks here!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Collective communication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Collective calls are performed by all ranks of a communicator and thus *must* be called by all ranks. Examples for collective calls are `Bcast`, `Scatter`, `Gather`, and `Allreduce`. We'll look at some collective calls later in the notebook."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "You could implement collective calls yourself using `Send` and `Recv`, but using the provided collective calls makes your code easier to read and allows vendors to optimize MPI for their platform. For example, in the picture above all the calls share the bandwidth of rank 0. One could use a tree-like pattern to balance the network load instead."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You can find more information about MPI at http://materials.jeremybejarano.com/MPIwithPython/index.html, the documentation of mpi4py at https://mpi4py.readthedocs.io/en/stable/ (take a look at the tutorials), and the API reference at https://mpi4py.bitbucket.io/apiref/index.html."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "from matplotlib import pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Starting the engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Note, this is only needed to run MPI programs from a Jupyter notebook.**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can use ipyparallel to run MPI from a notebook. To do that, we need to start some IPython engines. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Click on the ``+``-sign at the top of the Files tab on the left to start a new launcher. In the launcher click on Terminal. A terminal will open as a new tab. Grab the tab and pull it to the right to have the terminal next to your notebook.\n",
+ "\n",
+ "**Note**: The terminal does not have the same modules loaded as the notebook. To fix that type `source hpcpy20`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Next start the ipcontroller: `ipcontroller &`. After that we can launch 4 MPI tasks with 12 threads each like this\n",
+ "\n",
+ "```bash\n",
+ "export OMP_NUM_THREADS=12\n",
+ "srun -n 4 -c 12 --ntasks-per-node 4 ipengine start\n",
+ "```\n",
+ "\n",
+ "**Note**, you can can start the controller and the engines in separate terminals. That will keep the output separate."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Connecting to the engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next, we want to connect to the engines:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client\n",
+ "rc = Client()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rc.ids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Next, we need to create a view and activate it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "view = rc[:]\n",
+ "view.activate()\n",
+ "view.block = True"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Setting up for MPI"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We are now ready to use MPI with our IPython notebook.\n",
+ "\n",
+ "We will use the cell magic ``%%px`` and the line magic ``%px`` to execute commands on all the engines. So, whenenver you see ``%%px`` the cell is executed on *all* the engines, but not in the process that controls your notebook!\n",
+ "\n",
+ "**Note**: Everything that appears *after* ``%%px`` and ``%px`` would be part of a regular mpi4py program."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px from mpi4py import MPI # Import and initialize MPI on the engines\n",
+ "#from mpi4py import MPI # Import and initialize MPI in the notebook "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px import numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Importing MPI initializes the MPI and sets up the default communicator `COMM_WORLD`, which includes all processes involved in this MPI program.\n",
+ "\n",
+ "Using `COMM_WORLD`, each process can determine its *rank* and the total number of ranks available:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm = MPI.COMM_WORLD\n",
+ "rank = comm.Get_rank()\n",
+ "size = comm.Get_size()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "print(\"I'm %d of %d. Resistance is futile.\" % (rank + 1, size))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Point to point"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can send messages from one rank to another. \n",
+ "\n",
+ "The sender will use `Send` and the receiver a corresponding `Recv`. To get the doc string, you can run"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%px --target 0 \n",
+ "help(MPI.Comm.Send)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The `buf` argument needs to implement the [buffer protocol](https://docs.python.org/3/c-api/buffer.html). This is true, for example, for numpy arrays, but not for primitive types such as float. That's the reason we use `numpy.ones` and `numpy.zeros` of size 1 below.\n",
+ "\n",
+ "The following exercises will only work if more than one process is available."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "import sys\n",
+ "import numpy\n",
+ "comm = MPI.COMM_WORLD\n",
+ "a = numpy.ones(1)\n",
+ "b = numpy.zeros(1)\n",
+ "if (size < 2):\n",
+ " print (\"Warning! Not enough ranks available!\" )\n",
+ "else:\n",
+ " if rank == 0:\n",
+ " print (\"I'm rank zero and I'm sending a datum.\")\n",
+ " comm.Send(a[0], dest = 1) # Default destination is 0!\n",
+ " elif rank == 1:\n",
+ " print (\"I'm rank one and I'm receiving a datum.\")\n",
+ " comm.Recv(b, source = 0) # Default source is 0!\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Note**, how we used `rank` to perform different work on the task with rank 0 and the task with rank 1 using if statements. This is a common pattern in MPI programs. The task with rank 0 is often referred to as *root*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Sendrecv"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you need to send data to another rank and receive data from the same rank, combining `Send` and `Recv` command is dangerous and easily leads to deadlocks. Use `Sendrecv` instead."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "a = numpy.ones(1) * rank\n",
+ "b = numpy.ones(1) * rank\n",
+ "if rank == 0:\n",
+ " comm.Sendrecv(a, 1, recvbuf=b, source=1)\n",
+ " print(f\"[{rank}] {b[0]}\")\n",
+ "elif rank == 1:\n",
+ " comm.Sendrecv(a, 0, recvbuf=b, source=0)\n",
+ " print(f\"[{rank}] {b[0]}\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Parallel reduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We'll generate an array of random number on rank 0 and distribute (scatter) it to all ranks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "N = 1000\n",
+ "a_partial = numpy.empty(N)\n",
+ "if rank == 0:\n",
+ " rng = numpy.random.Generator(numpy.random.MT19937())\n",
+ " a = rng.uniform(size=N * size)\n",
+ "else:\n",
+ " a = numpy.empty(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since we are dealing with NumPy arrays, we can use the efficient uppercase versions of the MPI calls. Scatter distributes an array evenly among all nodes. Note, the sendbuf only needs to be allocated on node zero, but the variable must exist everywhere."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm.Scatter(a, a_partial, root = 0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "sum_partial = numpy.sum(a_partial)\n",
+ "total = comm.reduce(sum_partial)\n",
+ "if rank == 0:\n",
+ " print(\"The sum of the random numbers is %f. The average is %f.\" % (total, total / len(a)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Upper vs. lowercase in mpi4py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "`mpi4py` offers two version of many calls. The first one is written in uppercase. It uses memory buffers, e.g., `np.array`, and maps the call directly to the appropriate C call. The second version is written in lower case and takes arbitrary Python object. The result is given as the return value. Note, that for the uppercase versions all a_partial must have the same size!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "a_all = None\n",
+ "if rank == 0:\n",
+ " a_all = numpy.empty([size, len(a_partial)], dtype='f8')\n",
+ "comm.Gather(a_partial, a_all, root=0)\n",
+ "if rank == 0:\n",
+ " print(type(a_all))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "%timeit comm.Gather(a_partial, a_all, root=0) # Don't use %timeit outside IPython."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The following works independent of the size of a_partial:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "a_all = comm.gather(a_partial)\n",
+ "if rank == 0:\n",
+ " print(type(a_all))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, `a_all` contains a `list` of `np.array`s.\n",
+ "\n",
+ "This second version is convenient, but it is **much** slower:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "%timeit a_all = comm.gather(a_partial)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "It gets worse as arrays get bigger.\n",
+ "\n",
+ "To retrieve the result, we use the `view` again."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "## Remarks\n",
+ "While Jupyter notebooks are a nice way to teach MPI and well tested MPI routines can be quite useful within a notebook, developing MPI code within notebooks can quickly become awkward because mistakes lead to blocking engines. I find it easier to write and test my MPI routines outside Jupyter notebooks and start the program with `mpiexec`/`srun` from the command line.\n",
+ "\n",
+ "For example, you could write the following program and save it to a file:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile helloparallelworld.py\n",
+ "from mpi4py import MPI\n",
+ "import numpy as np\n",
+ "\n",
+ "rank = MPI.COMM_WORLD.Get_rank()\n",
+ "numberOfRanks = MPI.COMM_WORLD.Get_size()\n",
+ "\n",
+ "a = np.zeros(1)\n",
+ "if rank == 0:\n",
+ " print(\"There are %d MPI ranks.\" % numberOfRanks)\n",
+ " a = np.random.random(1)\n",
+ "\n",
+ "print(\"I'm rank %d.\" % rank)\n",
+ "if numberOfRanks < 2:\n",
+ " print(\"Not enough MPI tasks!\")\n",
+ " exit(1)\n",
+ "if rank == 0:\n",
+ " MPI.COMM_WORLD.Send(a, dest=1)\n",
+ "elif rank == 1:\n",
+ " MPI.COMM_WORLD.Recv(a, source=0)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You can then switch to a terminal and execute it as `srun -n 2 --ntasks-per-node 2 python helloparallelworld.py`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercises"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Peak to Peak\n",
+ "Write a program that generates random numbers from a Gaussian distribution and then finds the minimum and maximum number generated.\n",
+ "\n",
+ "a) Generate the random numbers on rank 0 and scatter them. Calculate the maximum and minimum for the partial data for \n",
+ " each rank and send the results back to rank 0. Find the maximum and minimum on rank 0 and compare it with numpy's\n",
+ " `ptp` function.\n",
+ " \n",
+ "b) Generate random numbers at each rank. Calculate the minimum and maximum and use `Reduce` to find the extrema and send \n",
+ " them to rank 0."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Domain decomposition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If at least some of the interactions we are dealing with are short ranged, we can often split a system into multiple domains that can be treated independently. These domains don't have to be regular. Sometimes it's better to use [space filling curves](https://en.wikipedia.org/wiki/Space-filling_curve) to split up a problem. In this section, however, we'll look at a regular grid."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In [Think Vector][TV] we looked at [stencils][TV_Stencils]. In this section, we'll distribute a 2d stencil calculation using a domain decomposition with MPI. \n",
+ "\n",
+ "Remember our system looked something like this (I made it a little wider this time.):\n",
+ "\n",
+ "[TV]: ThinkVector.ipynb\n",
+ "[TV_Stencils]: ThinkVector.ipynb#Stencils"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = numpy.random.random((10, 30))\n",
+ "A[:,0] = 0\n",
+ "A[:,-1] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(15, 5))\n",
+ "plt.imshow(A)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The system is basically a square grid. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's assume we want to split our system in three parts along the horizontal axis. Each processor get's an equal share of the grid. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "To calculate the value for each point, we need all its neighbors. When we work on the field at the boundary, this includes data from the neighboring domain. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The data from the neighnboring domains is stored as a *halo* to the main domain that the rank is working on. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The data in the halos needs to be transferred from the neighbor(s) and updated after each iterations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "I would recommend using an editor for this exercise. Jupyter Lab comes with an editor that supports syntax highlighting but no auto completion. You can find it under File->New->Text File. The new file will be called `Untitled.txt`. You can change the file name by righ-clicking on the editor tab or right-clicking on the file in the file browser view on the left."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "1. Take the program from the [Stencil][TV_Stencils] and use a 1d domain decomposition as described \n",
+ " above to parallelize the program using MPI over 3 domains using 3 MPI ranks. Construct the grid \n",
+ " in such a way that you can easily divide it into 3 domains. Use [point to point communication](#Point-to-point). The program should run to convergence determined by epsilon just as before.\n",
+ "\n",
+ " Tip: It may be easier to turn the problem by 90° or use Fortran order for the NumPy arrays.\n",
+ " \n",
+ "2. Extend the program from the first part of the exercise to use more than 3 ranks with 1 domain \n",
+ " per rank.\n",
+ "\n",
+ "3. Time the execution of the program from the second part of the exercise.\n",
+ "\n",
+ " a) Keep the size of the system constant and increase the number of ranks/domain, e.g., using 2, \n",
+ " 4, 8, and 16 ranks. How \n",
+ " \n",
+ " b) Keep the size of the domains constant, i.e., the total size is a multiple of the number of \n",
+ " ranks. Again increase the number of ranks\n",
+ "\n",
+ "[TV_Stencils]: ThinkVector.ipynb#Stencils"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Amdahl's law"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We already talked about a number of ways to parallelize our code, but we haven't discussed how much speedup we might expect from our parallelized code compared to the serial version.\n",
+ "\n",
+ "If we get a profile for our code, we have an idea of how much time the function we parallelized takes, when we run this on a single core. With that information and some assumption, we can estimate the possbile speedup using Amdahl's law."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Assume that the total runtime of a program can be split into a serial and a perfectly parallelizable part."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$t_1 = t_s + t_p$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The runtime for $n$ processors is then"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$t_n = t_s + t_p / n$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "From this, we can calculate the speedup compared to a single core"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{t_1}{t_n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "or"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{t_s + t_p}{t_s + t_p / n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let $f$ be the fraction of the parallelizable part then we can rewrite $s_n$ as"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{t_1}{(1-f)t_1 + ft_1/n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Elimintating $t_1$, we get"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{1}{(1-f) + f/n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Speedup using Amdahl's law"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's plot this vs the number of processors."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def amdahl_speedup(f, n):\n",
+ " return 1.0 / ((1-f) + f / n)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = numpy.arange(1, 1000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(5, 2.5), dpi=150)\n",
+ "for f in [0.5, 0.75, 0.8, 0.9, 0.95]:\n",
+ " plt.plot(amdahl_speedup(f, n), label=f\"{f * 100}%\")\n",
+ " plt.legend(); plt.ylim([0, 20]);plt.xlabel('n'); plt.ylabel('s')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Speedup using Amdahl's law"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(5, 2.5), dpi=150)\n",
+ "for f in [0.5, 0.75, 0.8, 0.9, 0.95, 0.99]:\n",
+ " plt.plot(amdahl_speedup(f, n), label=f\"{f * 100}%\")\n",
+ " plt.legend(); plt.ylim([0, 100]);plt.xlabel('n'); plt.ylabel('s')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## IPyParallel and MPI"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can use ipyparallel to push data to and pull data from the engines. All the operations that we used in [Interactive Parallel Computing with IPython Parallel][IPCIP] are still available and can be combined with mpi4py.\n",
+ "\n",
+ "[IPCIP]: Interactive%20;Parallel%20;Computing%20;with%20;IPython%20;Parallel.ipynb"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's start by creating an array of random numbers and scattering it to all the ranks, i.e., each rank gets some part of the array."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Variables that are defined on the engines can be retrieved through the `view`. To get the variable rank, e.g., you can write"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ranks = view['rank']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Until recently, the ranks were not in any particular order, which can be annoying, but we can get the right order by casting ranks to an ndarray and calling argsort. The result gives us the engines in MPI rank order. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ranksort = numpy.array(ranks).argsort()\n",
+ "rank0 = int(ranksort[0])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# This cell is executed within the notebook. The engines don't know anything about it\n",
+ "rng = numpy.random.Generator(numpy.random.MT19937())\n",
+ "a = np.random.normal(size=100000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# First push the array to the engine with MPI rank 0\n",
+ "%px a = None\n",
+ "view.push({'a':a}, targets=rank0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next, we scatter the data from rank 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "view.scatter('a_partial', a)\n",
+ "view[\"a_partial\"][0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can now calculate the partial sum on each rank and then sum up the partial results using mpi4py's `reduce` function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "sum_partial = np.sum(a_partial)\n",
+ "total = comm.reduce(sum_partial)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Use the view to get the result back into the notebook."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "total = view.pull('total', targets=rank0)\n",
+ "sum_partial = view['sum_partial']\n",
+ "print(\"The sum of the random numbers is %f. The average is %f.\" % (total, total / len(a)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sum_partial"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sum(sum_partial)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/15_Introduction to CuPy.ipynb b/15_Introduction to CuPy.ipynb
new file mode 100644
index 0000000..38287e1
--- /dev/null
+++ b/15_Introduction to CuPy.ipynb
@@ -0,0 +1,386 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to CuPy\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Jan H. Meinke\n",
+ "</div>\n",
+ "<img src=\"images/cupy.png\" style=\"float:right\">"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CuPY\n",
+ "### A NumPy-like interface to GPU programming"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "> The best way to program a GPU is to let other people do the work!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "[CuPy][] provides a [NumPy][]-like interface to use and program GPUs.\n",
+ "\n",
+ "[CuPy]: https://cupy.dev/\n",
+ "[NumPy]: https://numpy.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import cupy\n",
+ "N = 2048\n",
+ "A = cupy.random.random((N, N))\n",
+ "B = cupy.random.random((N, N))\n",
+ "C = A@B"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This cell creates two random arrays of size N by N on the GPU and performs a matrix multiplication using Nvidia's optimized linar algebra library cuBLAS."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "In [Think Vector][TV], you [calculated the Mandelbrot set][TV_Mandelbrot] using [NumPy][] and vectorization. Take either your solution or ours and convert it to [CuPy][]. Visualize the result.\n",
+ "\n",
+ "Tip: If you get an error message when visualizing the results, take a look [below](#CuPy-Arrays).\n",
+ "\n",
+ "[CuPy]: https://cupy.dev/\n",
+ "[NumPy]: https://numpy.org/\n",
+ "[TV]: ThinkVector.ipynb\n",
+ "[TV_Mandelbrot]: ThinkVector.ipynb#Programming-exercise-Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## GPU Libraries"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* cuBLAS\n",
+ "* cuDNN\n",
+ "* cuRand \n",
+ "* cuSolver\n",
+ "* cuSPARSE\n",
+ "* cuFFT\n",
+ "* NCCL "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CuPy is the fastest and easiest way to use Nvidia's GPU libraries."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "a) Time the execution of C=A@B for different matrix sizes, e.g., 256, 512, 1024, 2048, 4096. Calculate the performance in GFLOP/s using gflops = 2e-9 * N ** 3 / t and store the sizes and the times in an ndarray.\n",
+ "\n",
+ "b) Do the same using numpy. How do the numbers compare."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CuPy Arrays"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CuPy arrays live on the GPU. To retrieve them you can use"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "A = cupy.random.random((N, N))\n",
+ "A1_np = A.get()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A2_np = cupy.asnumpy(A)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The first command only works for GPU arrays, but the second can also be used for a NumPy array. If A is a GPU array, the data will be copied from the CPU to the GPU. If A is a NumPy array, no copy will be made and A2_np becomes a reference to A."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "x = numpy.linspace(0, 1, 10)\n",
+ "x_gpu = cupy.asarray(x) # Copy x to the GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "To transfer data to the GPU use `cupy.asarray`. This doesn't just work with NumPy arrays, but also, for example, with lists."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "Create a 2D array of random number on the GPU. Transfer it to the CPU. Subtract 0.5 from all elements. Copy the result back to the GPU. Clculate the average value of all elements on the GPU and write the result to the screen."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Picking a Device"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CuPy always works on the *current device*. On multi-GPU nodes this can be changed using"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "cupy.cuda.Device(1).use()\n",
+ "A_on_gpu1 = cupy.random.random((N, N))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you need to switch devices regularly, you can use a `with` statement:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "with cupy.cuda.Device(2):\n",
+ " A_on_gpu2 = cupy.random.random((N, N))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note, that you can only access `A_on_gpu2` while device 1 is active. Otherwise, you'll get an error message."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/16_CUDA for Python.ipynb b/16_CUDA for Python.ipynb
new file mode 100644
index 0000000..e11ca82
--- /dev/null
+++ b/16_CUDA for Python.ipynb
@@ -0,0 +1,1184 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Numba and GPUs\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "20 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba supports Nvidia and AMD GPUs. In this course, however, we are going to focus on CUDA capable GPUs from Nvidia. \n",
+ "\n",
+ "Hint: If you are working with an older version of Numba and want to use an already installed CUDA SDK, there are two environment variables that might have to be set to let numba know where it can find the libraries it needs. On JUWELS this it *not* necessary.\n",
+ "\n",
+ "```bash\n",
+ "export NUMBA_NVVM=$CUDA_HOME/nvvm/lib64/libnvvm.so\n",
+ "export NUMBA_LIBDEVICE=$CUDA_HOME/nvvm/libdevice/\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Let's ignore some deprecation warnings\n",
+ "from numba.core.errors import NumbaDeprecationWarning, NumbaPendingDeprecationWarning\n",
+ "import warnings\n",
+ "\n",
+ "warnings.simplefilter('ignore', category=NumbaDeprecationWarning)\n",
+ "warnings.simplefilter('ignore', category=NumbaPendingDeprecationWarning)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Ufunc"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We already learned how to vectorize a function. Remember the Mandelbrot set. We defined a function that returns the number of iterations needed to decide if the algorithm diverges."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import vectorize\n",
+ "\n",
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \"\"\"\n",
+ " z = 0j\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "x = numpy.linspace(-2, 2, 500)\n",
+ "y = numpy.linspace(-1.5, 1.5, 375)\n",
+ "zr, zc = numpy.meshgrid(x, 1j * y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "escape_time_v = vectorize(\"int64(complex128, int64)\", \n",
+ " target=\"parallel\")(escape_time)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_cpu = %timeit -o escape_time_v(zr + zc, 500)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you replace `target=\"parallel\"` with `target=\"cuda\"` the function runs on the GPU instead. Give it a try and compare the performance for different sizes of the grid:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Your code goes here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CUDA for Python"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba allows you to write CUDA programs in Python. \n",
+ "\n",
+ "While a complete introduction to CUDA is beyond the scope of this course---there are other courses for this, for example, GPU Programming with CUDA @ JSC and also many online resources available---here you'll get the nutshell version and some of the differences between CUDA C++ and CUDA Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CPU vs. GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## CPU vs. GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "CPUs are optimized for latency."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A CPU tries to execute a given instruction as quickly as possible, i.e., it tries to keep the latency (the time between issuing and executing an instruction) as short as possible. CPUs use caches and a lot of control logic to achieve this goal."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs are optimized for throughput."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## CPU vs. GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "GPUs were (and are) made to display graphics on your screen. It doesn't matter how quickly a GPU can update a single pixel. It's important how quickly it can update all of the pixels on the screen (more than 2 million on an HD display). In addition it often must perform the same operation on a lot of vertices or pixels. \n",
+ "\n",
+ "These two conditions let to a different execution model."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "\n",
+ "## GPU execution model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs use *many* lightweight threads."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs hide latency instead of avoiding it"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs work best if the problem can me mapped on a grid, but other models are possible."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Kernels"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can calculate the Mandelbrot set using `escape_time` like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "maxiter = 20\n",
+ "rlim = (-2.2, 1.5)\n",
+ "ilim = (-1.5, 1.5)\n",
+ "nx = 100\n",
+ "ny = 75\n",
+ "\n",
+ "dx = (rlim[1] - rlim[0]) / nx\n",
+ "dy = (ilim[1] - ilim[0]) / ny\n",
+ "\n",
+ "M = numpy.zeros((ny, nx), dtype=int)\n",
+ "\n",
+ "for i in range(ny):\n",
+ " for j in range(nx):\n",
+ " p = rlim[0] + j * dx + (ilim[0] + i * dy) * 1j\n",
+ " M[i, j] = escape_time(p, maxiter)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "plt.imshow(M, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Notice that for every pair (i, j), we calculate the escape time. This makes\n",
+ "\n",
+ "```python\n",
+ " p = rlim[0] + j * dx + (ilim[0] + i * dy) * 1j\n",
+ " M[i, j] = escape_time(p, maxiter)\n",
+ "```\n",
+ "\n",
+ "our kernel that we execute on the grid spanned by the two for loops. It's quite apparent on the image above, where the coordinates for each value are shown in index space."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Threads and blocks and grids, oh my!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The basic unit of execution is a thread. All the threads of a kernel call execute the same code."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Thread blocks"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Threads are organized in blocks. All threads in a block are executed on the same *streaming multiprocessor* (SM, comparable to a core on a CPU). They can share fast *shared memory* and synchronize easily. A thread block is pinned to the SM, i.e., once it was launched on a particular SM it stays there.\n",
+ "\n",
+ "A thread block can have one, two, or three dimensions to make mapping the problem to the thread model easier. The choice is up to the programmer.The maximum dimension of a thread block is 1024x1024x64, where the volume of the thread block (the number of threads in the block) must be 1024 or less."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Grid of thread blocks"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Thread blocks are organized in a grid to cover all the threads needed to solve you problem. A grid can have one, two, or three dimensions. The dimensionality of the grid is in principle independent of the dimensionality of the blocks it contains. The maximum grid dimensions are 2147483647྾65535྾65535 blocks!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Thread ID"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Each thread has an x, y, and z index that can be queried in a kernel."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "``` python\n",
+ "from numba import cuda\n",
+ "\n",
+ "@cuda.jit\n",
+ "def my_kernel:\n",
+ " x,y,z = cuda.grid(3) # use 2 if you only need x, y and 1 for x\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Writing a kernel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "For writing a CUDA kernel, we use `cuda.jit` instead of `jit` as decorator (see above). The kernel can also call other functions that have been decorated with `cuda.jit(device=True)`. A Mandelbrot kernel could look like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import cuda\n",
+ "\n",
+ "escape_time_gpu = cuda.jit(device=True)(escape_time)\n",
+ "\n",
+ "@cuda.jit\n",
+ "def mandelbrot_gpu(M, real_min, real_max, imag_min, imag_max):\n",
+ " \"\"\"Calculate the Mandelbrot set on the GPU.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " M : numpy.ndarray\n",
+ " a two-dimensional integer array that will contain the \n",
+ " escape times for each point.\n",
+ " real_min, real_max: float\n",
+ " minimum and maximums value on the real axis\n",
+ " imag_min, imag_max: float\n",
+ " minimum and maximum value on the imaginary axis\n",
+ " \"\"\"\n",
+ " ny, nx = M.shape\n",
+ " i, j = cuda.grid(2)\n",
+ " \n",
+ " if i < nx and j < ny:\n",
+ " dx = (real_max - real_min) / nx\n",
+ " dy = (imag_max - imag_min) / ny\n",
+ " p = real_min + dx * i + (imag_min + dy * j) * 1j\n",
+ " M[j, i] = escape_time_gpu(p, 20)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note, that there is no return value. CUDA kernels have to return their result through an argument. In the above kernel, the result will be in M"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Calling a kernel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CUDA needs to know how many blocks and how many threads per block you want to launch. This is called the *launch configuration*. To calculate the Mandelbrot set with of two 1024 by 1024 points with a block size of 32 by 32, we need 1024/32=32 by 1024/32=32 blocks.\n",
+ "\n",
+ "If we want to calculate the set for 1032 by 1032 points, we have to add an extra block. The following lines take care of that:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "M = numpy.zeros((1024, 1024), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0], M.shape[1] // block[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "The launch configuration is passed in square brackets before the function arguments."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit mandelbrot_gpu[grid, block](M, -2.2, 1.2, -1.6, 1.6)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(M, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If the dimension of your system is not a *multiple of your block size*, you need to add an extra block. The following code snippet takes care of this. (There are other ways to do this, too.)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "M = numpy.zeros((1000, 1000), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0] if M.shape[0] % block[0] == 0 \n",
+ " else M.shape[0] // block[0] + 1,\n",
+ " M.shape[1] // block[1] if M.shape[1] % block[1] == 0 \n",
+ " else M.shape[1] // block[1] + 1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit mandelbrot_gpu[grid, block](M, -2.2, 1.2, -1.6, 1.6)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(M, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Profile the Mandelbrot calculation on the GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "a) Use %timeit to measure the speed of the GPU implementation and compare it to the vectorized version."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "b) The kernel calculates dx and dy for every pixel although it is the same for all of them. Change the kernel so that it takes dx and dy as arguments and calculate dx and dy before you call the kernel. Does this improve the performance?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "c) Add an additional argument escape_time to the kernel, so that you can time the kernel for different escape time values. Don't forget to add the new argument to the documentation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Explicit memory management"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Discrete GPUs have their own memory. Data needs to be transferred from the host and results have to transferred back to the host as necessary. Numba takes care of the memory transfers but it does so in a very conservative way: all data is transferred back to the host after a kernel finished. This behavior can be avoided by [managing memory explicitely](http://numba.pydata.org/numba-doc/latest/cuda/memory.html#data-transfer)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Often, we want to copy an existing array to the GPU. For this we can use `numba.cuda.to_device`. This will allocate memory on the GPU and copy data from the CPU to the GPU, for example,"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "```Python\n",
+ "l = numpy.linspace(0, 10, 100)\n",
+ "d_l = cuda.to_device(l)\n",
+ "# Run kernel\n",
+ "...\n",
+ "# Copy data back\n",
+ "l = d_l.copy_to_host()\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You can allocate an empty array on the GPU using `numba.cuda.device_array`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Python\n",
+ "n = 1000\n",
+ "d_random = cuda.device_array(n)\n",
+ "# Run kernel\n",
+ "...\n",
+ "# Copy data back\n",
+ "myRandom = d_random.copy_to_host()\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Use explicitly managed memory for Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The M array is transferred to the GPU before the kernel runs. This is not necessary. Use a device array instead. Compare the runtime to the previous version."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Write a kernel, where each thread calculates one element of the result matrix $C=AB$, where A and B are matrices.\n",
+ "\n",
+ "For the algorithm, you can take a look at Bottlenecks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Using shared memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As you learned in Bottlenecks, the matrix matrix multiplication tends to be memory bandwidth bound. This is true on the GPU, too.\n",
+ "\n",
+ "The way to make it faster is to use faster memory. On a CPU this usually means, dividing the matrix into blocks that fit in cache and hope for the best. On a GPU at lease part of the fast memory is usually programmable. In CUDA this memory is called *shared memory*.\n",
+ "\n",
+ "Shared memory is available to all *threads in a thread block*. Usually, each thread loads data from device memory into shared memory. This is followed by barrier, so that all threads are finished reading. Then the shared memory is reused as often as possible. Another barrier makes sure that all threads are done."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's look at an example:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Matrix multiplication with shared memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The following function performs a matrix multiplication on the GPU using shared memory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import cuda, float32\n",
+ "# Controls threads per block and shared memory usage.\n",
+ "# The computation will be done on blocks of TPBxTPB elements.\n",
+ "TPB = 16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@cuda.jit\n",
+ "def fast_matmul(A, B, C):\n",
+ " # Define an array in the shared memory\n",
+ " # The size and type of the arrays must be known at compile time\n",
+ " sA = cuda.shared.array(shape=(TPB, TPB), dtype=float32)\n",
+ " sB = cuda.shared.array(shape=(TPB, TPB), dtype=float32)\n",
+ "\n",
+ " x, y = cuda.grid(2)\n",
+ " tx = cuda.threadIdx.x\n",
+ " ty = cuda.threadIdx.y\n",
+ " bpg = cuda.gridDim.x # blocks per grid\n",
+ "\n",
+ " if x >= C.shape[0] and y >= C.shape[1]:\n",
+ " # Quit if (x, y) is outside of valid C boundary\n",
+ " return\n",
+ "\n",
+ " # Each thread computes one element in the result matrix.\n",
+ " # The dot product is chunked into dot products of TPB-long vectors.\n",
+ " tmp = 0.\n",
+ " for i in range(bpg):\n",
+ " # Preload data into shared memory\n",
+ " sA[tx, ty] = A[x, ty + i * TPB]\n",
+ " sB[tx, ty] = B[tx + i * TPB, y]\n",
+ "\n",
+ " # Wait until all threads finish preloading\n",
+ " cuda.syncthreads()\n",
+ "\n",
+ " # Computes partial product on the shared memory\n",
+ " for j in range(TPB):\n",
+ " tmp += sA[tx, j] * sB[j, ty]\n",
+ "\n",
+ " # Wait until all threads finish computing\n",
+ " cuda.syncthreads()\n",
+ "\n",
+ " C[x, y] = tmp"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The above example shows most special functions used in CUDA kernels:\n",
+ "\n",
+ "All the cuda specific API is found in numbas cuda module (line 1) \n",
+ "\n",
+ "CUDA kernels are defined like regular Python functions with the added decorator `@cuda.jit` (line 7). The decorator makes sure that the function is compiled for the GPU.\n",
+ "\n",
+ "As mentioned above, CUDA kernels are executed as a grid of blocks of threads. cuda.grid (line 14) returns the global indices of the current thread, e.g., `x, y = cuda.grid(2)` for a two dimensional grid. The argument gives the number of dimensions (1, 2, 3). This function does not exist in CUDA C++.\n",
+ "\n",
+ "In CUDA C++, the programmer usually calculates the global index from the thread index `threadIdx`, the block index `blockIdx`, and the size (dimension) of the block stored in `blockDim`\n",
+ "\n",
+ "```C++\n",
+ "int x = blockIdx.x * blockDim.x + threadIdx.x;\n",
+ "```\n",
+ "\n",
+ "In numba these are available through the cuda module, so that you can rewrite the C++ code above as \n",
+ "\n",
+ "```Python\n",
+ "x = cuda.blockIdx.x * cuda.blockDim.x + cuda.threadIdx.x\n",
+ "```\n",
+ "\n",
+ "In `fast_matmul` these functions are used to get the local index of the thread, which is important to use the shared memory (lines 16--18).\n",
+ "\n",
+ "Shared memory is a programmable cache accessible to all threads within a block. In C++ it is allocated within a kernel as\n",
+ "\n",
+ "```C++\n",
+ "__shared__ float sA[TPB, TPB]; // Allocate a 2D array of floats of size TPB\n",
+ "```\n",
+ "\n",
+ "The cuda module provides shared.array (line 11 & 12) to do the same thing.\n",
+ "\n",
+ "The last function from the cuda module used in `fast_matmul` is cuda.syncthreads(), which implements a barrier for the threads within a block. It corresponds to `__syncthreads()` in CUDA C++.\n",
+ "\n",
+ "These functions cover most kernels."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Not all CUDA features are implemented in Numba. Some missing features are listed at http://numba.pydata.org/numba-doc/dev/cuda/overview.html#missing-cuda-features. Currently they include dynamic parallelism and texture memory."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/17_CUDA and MPI.ipynb b/17_CUDA and MPI.ipynb
new file mode 100644
index 0000000..a67e71f
--- /dev/null
+++ b/17_CUDA and MPI.ipynb
@@ -0,0 +1,519 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# CUDA for Python and MPI4Py\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "20 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "To use MPI in a notebook, we have to use the ipengines again:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Starting the engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can combine ipyparalle and MPI. To do that, we need to start some IPython engines. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Click on the ``+``-sign at the top of the Files tab on the left to start a new launcher. In the launcher click on Terminal. A terminal will open as a new tab. Grab the tab and pull it to the right to have the terminal next to your notebook.\n",
+ "\n",
+ "**Note**: The terminal does not have the same modules loaded as the notebook. To fix that type `source hpcpy20`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next start the ipcontroller: `ipcontroller &`. After that we can launch 4 MPI tasks with 6 threads each like this\n",
+ "\n",
+ "```bash\n",
+ "export OMP_NUM_THREADS=10\n",
+ "srun -n 4 -c 12 ipengine start\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client\n",
+ "rc = Client()\n",
+ "view = rc[:]\n",
+ "view.activate()\n",
+ "view.block = True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "# Let's ignore some deprecation warnings\n",
+ "from numba.errors import NumbaDeprecationWarning, NumbaPendingDeprecationWarning\n",
+ "import warnings\n",
+ "\n",
+ "warnings.simplefilter('ignore', category=NumbaDeprecationWarning)\n",
+ "warnings.simplefilter('ignore', category=NumbaPendingDeprecationWarning)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The Kernel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "CUDA kernels cannot make any MPI calls. If you need to pass information from one GPU to another it's done by the main program. Here's a simple example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client\n",
+ "rc = Client()\n",
+ "view = rc[:]\n",
+ "view.activate()\n",
+ "view.block = True"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CUDA kernels cannot make any MPI calls. If you need to pass information from one GPU to another it's done by the main program. Here's a simple example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "import numpy\n",
+ "import mpi4py.MPI as MPI\n",
+ "from numba import cuda"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Here's a simple kernel that shifts all values in v by a:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "@cuda.jit\n",
+ "def shift(a, v):\n",
+ " \"\"\"Shift all values in v by a.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: float\n",
+ " shift\n",
+ " v: numpy.ndarray\n",
+ " one-dimensional array with values that are to be shifted.\n",
+ " \"\"\"\n",
+ " i = cuda.grid(1)\n",
+ " if i < v.shape[0]:\n",
+ " v[i] += a"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Setting things up"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, we set up MPI, and generate random number on rank 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm = MPI.COMM_WORLD\n",
+ "my_rank = comm.Get_rank()\n",
+ "number_of_ranks = comm.Get_size()\n",
+ "N = 1000\n",
+ "a_partial = numpy.empty(N)\n",
+ "if my_rank == 0:\n",
+ " a = numpy.random.random(N * number_of_ranks)\n",
+ "else:\n",
+ " a = numpy.empty(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since we are dealing with NumPy arrays, we can use the efficient uppercase versions of the MPI calls. Scatter distributes an array evenly among all nodes. Note, the sendbuf only needs to be allocated on node zero, but the variable must exist everywhere."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm.Scatter(a, a_partial, root = 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Setup and call the kernel."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Calling the kernel"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "block = 256\n",
+ "grid = N // block if N % block == 0 else N // block + 1 \n",
+ "\n",
+ "shift[grid, block](-0.5, a_partial)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Gather works the oposite way to Scatter. Again *a* only needs to have capacity on rank 0."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Collecting the data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm.Gather(a_partial, a, root = 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We generated a uniform distribution between 0 and 1 and then shifted it by -0.5. The mean value should now be close to zero."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "if my_rank == 0:\n",
+ " print(\"The average of a is %.2f\" % numpy.mean(a)) # Result should be near zero."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Picking a device"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As you see from the example above, there's nothing special when using MPI with GPUs. The one thing that might bite you is using *multiple* MPI ranks for *multiple* GPUs on a *single* node. In this case, you might have to tell your MPI rank which GPU to use.\n",
+ "\n",
+ "If you have, for example, 4 GPUs and you know that your scheduler chooses a compact configuration, i.e., rank 0, 1, 2, 3 are on the first node, rank 4, 5, 6, 7 are on the second node, etc., you can use you rank to assign a GPU to your process:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "```python\n",
+ "\n",
+ "cuda.select_device(my_rank % number_of_gpus_per_node)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Shift"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "a) Write the above program to a file. Remember that you can move cells with the arrow buttons above and then merge them. There's a cell magic to write a cell to a file.\n",
+ "\n",
+ "b) Run the program on one node with 4 MPI processes.\n",
+ "\n",
+ "c) Add the cuda.select_device call to the program and run it again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Multi-GPU Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Calculate the Mandelbrot set on multiple GPUs."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/build.sh b/build.sh
new file mode 100755
index 0000000..9509e2f
--- /dev/null
+++ b/build.sh
@@ -0,0 +1,19 @@
+#!/bin/bash
+#source hpcpy19
+# Build points
+pushd code/point
+rm -rf build
+mkdir -p build
+cd build
+CC=icc CXX=icpc cmake .. > /dev/null
+make
+popd
+
+# Build text_stats
+pushd code/text_stats
+rm -rf build
+mkdir -p build
+cd build
+CC=icc CXX=icpc cmake .. > /dev/null
+make
+popd
diff --git a/code/point/.kdev4/point.kdev4 b/code/point/.kdev4/point.kdev4
new file mode 100644
index 0000000..1d66f7d
--- /dev/null
+++ b/code/point/.kdev4/point.kdev4
@@ -0,0 +1,17 @@
+[Buildset]
+BuildItems=@Variant(\x00\x00\x00\t\x00\x00\x00\x00\x01\x00\x00\x00\x0b\x00\x00\x00\x00\x01\x00\x00\x00\n\x00p\x00o\x00i\x00n\x00t)
+
+[CMake]
+Build Directory Count=1
+Current Build Directory Index=0
+
+[CMake][CMake Build Directory 0]
+Build Directory Path=/home/meinke/Teaching/HPCPY/code/point/build
+Build Type=Release
+CMake Binary=/usr/bin/cmake
+Environment Profile=
+Extra Arguments=
+Install Directory=
+
+[Project]
+VersionControlSupport=kdevgit
diff --git a/code/point/CMakeLists.txt b/code/point/CMakeLists.txt
new file mode 100644
index 0000000..4e19f73
--- /dev/null
+++ b/code/point/CMakeLists.txt
@@ -0,0 +1,4 @@
+cmake_minimum_required(VERSION 3.5)
+project(point)
+add_library(point SHARED point3d.cpp)
+set_property(TARGET point PROPERTY CXX_STANDARD 14)
diff --git a/code/point/point.kdev4 b/code/point/point.kdev4
new file mode 100644
index 0000000..1d3b001
--- /dev/null
+++ b/code/point/point.kdev4
@@ -0,0 +1,4 @@
+[Project]
+CreatedFrom=CMakeLists.txt
+Manager=KDevCMakeManager
+Name=point
diff --git a/code/point/point3d.cpp b/code/point/point3d.cpp
new file mode 100644
index 0000000..39401a3
--- /dev/null
+++ b/code/point/point3d.cpp
@@ -0,0 +1,45 @@
+#include <cmath>
+#include "point3d.h"
+
+Point3D::Point3D(const double x, const double y, const double z) : _x{x}, _y{y}, _z{z}
+{}
+
+Point3D::Point3D(const std::vector<double> r) : _x{r[0]}, _y{r[1]}, _z{r[2]}
+{}
+
+void Point3D::translate(const double dx, const double dy, const double dz)
+{
+ _x += dx;
+ _y += dy;
+ _z += dz;
+}
+
+void Point3D::translate(const std::vector<double> dr)
+{
+ _x += dr[0];
+ _y += dr[1];
+ _z += dr[2];
+}
+
+void Point3D::rotate(const double alpha, const double beta, const double gamma)
+{
+ auto tx = _x * cos(beta) * cos(gamma) - _y * sin(gamma) * cos(beta) + _z * sin(beta);
+ auto ty = _x * (sin(alpha) * sin(beta) * cos(gamma) + sin(gamma)*cos(alpha)) +
+ _y * (-sin(alpha) * sin(beta) * sin(gamma) + cos(alpha) * cos(gamma)) -
+ _z * sin(alpha) * cos(beta);
+ auto tz = _x * (sin(alpha) * sin(gamma) - sin(beta) * cos(alpha) * cos(gamma)) +
+ _y * (sin(alpha) * cos(gamma) + sin(beta) * cos(alpha) * sin(gamma)) +
+ _z * cos(alpha) * cos(beta);
+ _x = tx;
+ _y = ty;
+ _z = tz;
+}
+
+
+const std::vector<double> Point3D::coordinates()
+{
+ std::vector<double> result {_x, _y, _z};
+ return result;
+}
+
+
diff --git a/code/point/point3d.h b/code/point/point3d.h
new file mode 100644
index 0000000..484e776
--- /dev/null
+++ b/code/point/point3d.h
@@ -0,0 +1,25 @@
+#pragma once
+
+#include <vector>
+
+class Point3D{
+public:
+ Point3D(const double x, const double y, const double z);
+ Point3D(const std::vector<double> r);
+ void translate(const double dx, const double dy, const double dz);
+ void translate(const std::vector<double> dr);
+ /** Rotates this point about x, y, and z.
+ *
+ * The rotation is performed as if this point was first rotated by alpha around the x-axis,
+ * then rotated by beta around the y-axis, and finally rotated by gamma around the z-axis.
+ *
+ * @param alpha rotation around x-axis
+ * @param beta rotation arounx y-axis
+ * @param gamma rotation around z-axis
+ *
+ */
+ void rotate(const double alpha, const double beta, const double gamma);
+ const std::vector<double> coordinates();
+private:
+ double _x, _y, _z;
+};
diff --git a/code/point/point3d_bind.cpp b/code/point/point3d_bind.cpp
new file mode 100644
index 0000000..9fa5d00
--- /dev/null
+++ b/code/point/point3d_bind.cpp
@@ -0,0 +1,51 @@
+#include <vector>
+#include <pybind11/pybind11.h>
+#include <pybind11/stl.h>
+#include <point3d.h>
+
+namespace py = pybind11; // This is purely for convenience
+
+PYBIND11_PLUGIN(points){
+ py::module m("points", "A collection of functions and objects to deal with 3D points.");
+
+ py::class_<Point3D>(m, "Point3D")
+ .def(py::init<double, double, double>())
+ .def(py::init<std::vector<double>>())
+ .def("translate", (void (Point3D::*)(double, double, double)) &Point3D::translate,
+ R"doc(Move this point by (dx, dy, dz).
+
+ Parameters
+ ----------
+ dx : float
+ shift along x-axis
+ dy : float
+ shift along y-axis
+ dz : float
+ shift along z-axis
+ )doc")
+ .def("coordinates", &Point3D::coordinates,
+ R"doc(Get the coordinates of this point.
+
+ Returns
+ -------
+ r : list
+ coordinates of this point.
+ )doc")
+ .def("rotate", &Point3D::rotate, R"doc(Rotates this point about x, y, and z
+
+ The rotation is performed as if this point was first rotated by alpha around the x-axis,
+ then rotated by beta around the y-axis, and finally rotated by gamma around the z-axis.
+
+ Parameters
+ ----------
+ alpha: float
+ rotation around x-axis in rad
+ beta: float
+ rotation arounx y-axis in rad
+ gamma: float
+ rotation around z-axis in rad
+ )doc")
+ ;
+
+ return m.ptr();
+}
diff --git a/code/point/points.f90 b/code/point/points.f90
new file mode 100644
index 0000000..02291ee
--- /dev/null
+++ b/code/point/points.f90
@@ -0,0 +1,52 @@
+module points
+
+real, allocatable, dimension(:) :: x
+real, allocatable, dimension(:) :: y
+real, allocatable, dimension(:) :: z
+
+contains
+ subroutine init(N)
+ integer, intent(in) :: N
+
+ allocate(x(N))
+ allocate(y(N))
+ allocate(z(N))
+
+ end subroutine init
+
+ subroutine translate(idx, dx, dy, dz)
+ integer, intent(in) :: idx
+ real, intent(in) :: dx
+ real, intent(in) :: dy
+ real, intent(in) :: dz
+ x(idx) = x(idx) + dx
+ y(idx) = y(idx) + dy
+ z(idx) = z(idx) + dz
+ end subroutine translate
+
+ subroutine coordinates(idx, tx, ty, tz)
+ integer, intent(inout) :: idx
+ real, intent(out) :: tx
+ real, intent(out) :: ty
+ real, intent(out) :: tz
+ tx = x(idx)
+ ty = y(idx)
+ tz = z(idx)
+ end subroutine coordinates
+
+ subroutine set(idx, tx, ty, tz)
+ integer, intent(in) :: idx
+ real, intent(in) :: tx
+ real, intent(in) :: ty
+ real, intent(in) :: tz
+ x(idx) = tx
+ y(idx) = ty
+ z(idx) = tz
+ end subroutine set
+
+ subroutine finalize
+ deallocate (x, y, z)
+ end subroutine finalize
+
+end module points
+
diff --git a/code/text_stats/.kdev4/text_stats.kdev4 b/code/text_stats/.kdev4/text_stats.kdev4
new file mode 100644
index 0000000..eb1a43e
--- /dev/null
+++ b/code/text_stats/.kdev4/text_stats.kdev4
@@ -0,0 +1,17 @@
+[Buildset]
+BuildItems=@Variant(\x00\x00\x00\t\x00\x00\x00\x00\x01\x00\x00\x00\x0b\x00\x00\x00\x00\x01\x00\x00\x00\x14\x00t\x00e\x00x\x00t\x00_\x00s\x00t\x00a\x00t\x00s)
+
+[CMake]
+Build Directory Count=1
+Current Build Directory Index=0
+
+[CMake][CMake Build Directory 0]
+Build Directory Path=/home/meinke/Teaching/HPCPY/code/text_stats/build
+Build Type=
+CMake Binary=/usr/bin/cmake
+Environment Profile=
+Extra Arguments=
+Install Directory=/usr/local
+
+[Project]
+VersionControlSupport=kdevgit
diff --git a/code/text_stats/CMakeLists.txt b/code/text_stats/CMakeLists.txt
new file mode 100644
index 0000000..9a4e342
--- /dev/null
+++ b/code/text_stats/CMakeLists.txt
@@ -0,0 +1,4 @@
+cmake_minimum_required(VERSION 3.5)
+project(test_stats)
+add_library(text_stats SHARED text_stats.c)
+set_property(TARGET text_stats PROPERTY CXX_STANDARD 14)
diff --git a/code/text_stats/text_stats.c b/code/text_stats/text_stats.c
new file mode 100644
index 0000000..946001c
--- /dev/null
+++ b/code/text_stats/text_stats.c
@@ -0,0 +1,6 @@
+#include "text_stats.h"
+
+int word_frequency(char* filename, char* word)
+{
+ return 42;
+}
diff --git a/code/text_stats/text_stats.h b/code/text_stats/text_stats.h
new file mode 100644
index 0000000..c93ab2a
--- /dev/null
+++ b/code/text_stats/text_stats.h
@@ -0,0 +1,8 @@
+/** Counts the occurences of a string in a file.
+ *
+ * @param filename name of file to open
+ * @param word string to look for in file
+ *
+ * @return number of occurences of word in file with filename
+ */
+int word_frequency(char* filename, char* word);
diff --git a/code/text_stats/text_stats.kdev4 b/code/text_stats/text_stats.kdev4
new file mode 100644
index 0000000..0b93f5c
--- /dev/null
+++ b/code/text_stats/text_stats.kdev4
@@ -0,0 +1,4 @@
+[Project]
+CreatedFrom=CMakeLists.txt
+Manager=KDevCMakeManager
+Name=text_stats
diff --git a/code/text_stats/text_stats_bind.cpp b/code/text_stats/text_stats_bind.cpp
new file mode 100644
index 0000000..277ec9e
--- /dev/null
+++ b/code/text_stats/text_stats_bind.cpp
@@ -0,0 +1,27 @@
+#include <pybind11/pybind11.h>
+
+extern "C" {
+ #include <text_stats.h>
+}
+
+namespace py = pybind11; // This is purely for convenience
+
+PYBIND11_PLUGIN(text_stats){
+ py::module m("text_stats", "Some functions that provide statistical information about a text.");
+ m.def("word_frequency", &word_frequency, R"doc(Counts the occurences of a string in a file.
+
+Paramters
+---------
+filename: string
+ name of file to open
+word: string
+ string to look for in file
+
+Returns
+-------
+ct: int
+ number of occurences of word in file with filename
+)doc");
+
+ return m.ptr();
+}
diff --git a/code/text_stats/word_frequency.F90 b/code/text_stats/word_frequency.F90
new file mode 100644
index 0000000..205d9f4
--- /dev/null
+++ b/code/text_stats/word_frequency.F90
@@ -0,0 +1,8 @@
+function word_frequency(filename, word)
+ implicit none
+ character(len=*), intent(in) :: filename
+ character(len=*), intent(in) :: word
+ integer :: word_frequency
+ word_frequency = 42
+end function word_frequency
+
diff --git a/data/iris.csv b/data/iris.csv
new file mode 100644
index 0000000..c19b9c3
--- /dev/null
+++ b/data/iris.csv
@@ -0,0 +1,151 @@
+SepalLength,SepalWidth,PetalLength,PetalWidth,Name
+5.1,3.5,1.4,0.2,Iris-setosa
+4.9,3.0,1.4,0.2,Iris-setosa
+4.7,3.2,1.3,0.2,Iris-setosa
+4.6,3.1,1.5,0.2,Iris-setosa
+5.0,3.6,1.4,0.2,Iris-setosa
+5.4,3.9,1.7,0.4,Iris-setosa
+4.6,3.4,1.4,0.3,Iris-setosa
+5.0,3.4,1.5,0.2,Iris-setosa
+4.4,2.9,1.4,0.2,Iris-setosa
+4.9,3.1,1.5,0.1,Iris-setosa
+5.4,3.7,1.5,0.2,Iris-setosa
+4.8,3.4,1.6,0.2,Iris-setosa
+4.8,3.0,1.4,0.1,Iris-setosa
+4.3,3.0,1.1,0.1,Iris-setosa
+5.8,4.0,1.2,0.2,Iris-setosa
+5.7,4.4,1.5,0.4,Iris-setosa
+5.4,3.9,1.3,0.4,Iris-setosa
+5.1,3.5,1.4,0.3,Iris-setosa
+5.7,3.8,1.7,0.3,Iris-setosa
+5.1,3.8,1.5,0.3,Iris-setosa
+5.4,3.4,1.7,0.2,Iris-setosa
+5.1,3.7,1.5,0.4,Iris-setosa
+4.6,3.6,1.0,0.2,Iris-setosa
+5.1,3.3,1.7,0.5,Iris-setosa
+4.8,3.4,1.9,0.2,Iris-setosa
+5.0,3.0,1.6,0.2,Iris-setosa
+5.0,3.4,1.6,0.4,Iris-setosa
+5.2,3.5,1.5,0.2,Iris-setosa
+5.2,3.4,1.4,0.2,Iris-setosa
+4.7,3.2,1.6,0.2,Iris-setosa
+4.8,3.1,1.6,0.2,Iris-setosa
+5.4,3.4,1.5,0.4,Iris-setosa
+5.2,4.1,1.5,0.1,Iris-setosa
+5.5,4.2,1.4,0.2,Iris-setosa
+4.9,3.1,1.5,0.1,Iris-setosa
+5.0,3.2,1.2,0.2,Iris-setosa
+5.5,3.5,1.3,0.2,Iris-setosa
+4.9,3.1,1.5,0.1,Iris-setosa
+4.4,3.0,1.3,0.2,Iris-setosa
+5.1,3.4,1.5,0.2,Iris-setosa
+5.0,3.5,1.3,0.3,Iris-setosa
+4.5,2.3,1.3,0.3,Iris-setosa
+4.4,3.2,1.3,0.2,Iris-setosa
+5.0,3.5,1.6,0.6,Iris-setosa
+5.1,3.8,1.9,0.4,Iris-setosa
+4.8,3.0,1.4,0.3,Iris-setosa
+5.1,3.8,1.6,0.2,Iris-setosa
+4.6,3.2,1.4,0.2,Iris-setosa
+5.3,3.7,1.5,0.2,Iris-setosa
+5.0,3.3,1.4,0.2,Iris-setosa
+7.0,3.2,4.7,1.4,Iris-versicolor
+6.4,3.2,4.5,1.5,Iris-versicolor
+6.9,3.1,4.9,1.5,Iris-versicolor
+5.5,2.3,4.0,1.3,Iris-versicolor
+6.5,2.8,4.6,1.5,Iris-versicolor
+5.7,2.8,4.5,1.3,Iris-versicolor
+6.3,3.3,4.7,1.6,Iris-versicolor
+4.9,2.4,3.3,1.0,Iris-versicolor
+6.6,2.9,4.6,1.3,Iris-versicolor
+5.2,2.7,3.9,1.4,Iris-versicolor
+5.0,2.0,3.5,1.0,Iris-versicolor
+5.9,3.0,4.2,1.5,Iris-versicolor
+6.0,2.2,4.0,1.0,Iris-versicolor
+6.1,2.9,4.7,1.4,Iris-versicolor
+5.6,2.9,3.6,1.3,Iris-versicolor
+6.7,3.1,4.4,1.4,Iris-versicolor
+5.6,3.0,4.5,1.5,Iris-versicolor
+5.8,2.7,4.1,1.0,Iris-versicolor
+6.2,2.2,4.5,1.5,Iris-versicolor
+5.6,2.5,3.9,1.1,Iris-versicolor
+5.9,3.2,4.8,1.8,Iris-versicolor
+6.1,2.8,4.0,1.3,Iris-versicolor
+6.3,2.5,4.9,1.5,Iris-versicolor
+6.1,2.8,4.7,1.2,Iris-versicolor
+6.4,2.9,4.3,1.3,Iris-versicolor
+6.6,3.0,4.4,1.4,Iris-versicolor
+6.8,2.8,4.8,1.4,Iris-versicolor
+6.7,3.0,5.0,1.7,Iris-versicolor
+6.0,2.9,4.5,1.5,Iris-versicolor
+5.7,2.6,3.5,1.0,Iris-versicolor
+5.5,2.4,3.8,1.1,Iris-versicolor
+5.5,2.4,3.7,1.0,Iris-versicolor
+5.8,2.7,3.9,1.2,Iris-versicolor
+6.0,2.7,5.1,1.6,Iris-versicolor
+5.4,3.0,4.5,1.5,Iris-versicolor
+6.0,3.4,4.5,1.6,Iris-versicolor
+6.7,3.1,4.7,1.5,Iris-versicolor
+6.3,2.3,4.4,1.3,Iris-versicolor
+5.6,3.0,4.1,1.3,Iris-versicolor
+5.5,2.5,4.0,1.3,Iris-versicolor
+5.5,2.6,4.4,1.2,Iris-versicolor
+6.1,3.0,4.6,1.4,Iris-versicolor
+5.8,2.6,4.0,1.2,Iris-versicolor
+5.0,2.3,3.3,1.0,Iris-versicolor
+5.6,2.7,4.2,1.3,Iris-versicolor
+5.7,3.0,4.2,1.2,Iris-versicolor
+5.7,2.9,4.2,1.3,Iris-versicolor
+6.2,2.9,4.3,1.3,Iris-versicolor
+5.1,2.5,3.0,1.1,Iris-versicolor
+5.7,2.8,4.1,1.3,Iris-versicolor
+6.3,3.3,6.0,2.5,Iris-virginica
+5.8,2.7,5.1,1.9,Iris-virginica
+7.1,3.0,5.9,2.1,Iris-virginica
+6.3,2.9,5.6,1.8,Iris-virginica
+6.5,3.0,5.8,2.2,Iris-virginica
+7.6,3.0,6.6,2.1,Iris-virginica
+4.9,2.5,4.5,1.7,Iris-virginica
+7.3,2.9,6.3,1.8,Iris-virginica
+6.7,2.5,5.8,1.8,Iris-virginica
+7.2,3.6,6.1,2.5,Iris-virginica
+6.5,3.2,5.1,2.0,Iris-virginica
+6.4,2.7,5.3,1.9,Iris-virginica
+6.8,3.0,5.5,2.1,Iris-virginica
+5.7,2.5,5.0,2.0,Iris-virginica
+5.8,2.8,5.1,2.4,Iris-virginica
+6.4,3.2,5.3,2.3,Iris-virginica
+6.5,3.0,5.5,1.8,Iris-virginica
+7.7,3.8,6.7,2.2,Iris-virginica
+7.7,2.6,6.9,2.3,Iris-virginica
+6.0,2.2,5.0,1.5,Iris-virginica
+6.9,3.2,5.7,2.3,Iris-virginica
+5.6,2.8,4.9,2.0,Iris-virginica
+7.7,2.8,6.7,2.0,Iris-virginica
+6.3,2.7,4.9,1.8,Iris-virginica
+6.7,3.3,5.7,2.1,Iris-virginica
+7.2,3.2,6.0,1.8,Iris-virginica
+6.2,2.8,4.8,1.8,Iris-virginica
+6.1,3.0,4.9,1.8,Iris-virginica
+6.4,2.8,5.6,2.1,Iris-virginica
+7.2,3.0,5.8,1.6,Iris-virginica
+7.4,2.8,6.1,1.9,Iris-virginica
+7.9,3.8,6.4,2.0,Iris-virginica
+6.4,2.8,5.6,2.2,Iris-virginica
+6.3,2.8,5.1,1.5,Iris-virginica
+6.1,2.6,5.6,1.4,Iris-virginica
+7.7,3.0,6.1,2.3,Iris-virginica
+6.3,3.4,5.6,2.4,Iris-virginica
+6.4,3.1,5.5,1.8,Iris-virginica
+6.0,3.0,4.8,1.8,Iris-virginica
+6.9,3.1,5.4,2.1,Iris-virginica
+6.7,3.1,5.6,2.4,Iris-virginica
+6.9,3.1,5.1,2.3,Iris-virginica
+5.8,2.7,5.1,1.9,Iris-virginica
+6.8,3.2,5.9,2.3,Iris-virginica
+6.7,3.3,5.7,2.5,Iris-virginica
+6.7,3.0,5.2,2.3,Iris-virginica
+6.3,2.5,5.0,1.9,Iris-virginica
+6.5,3.0,5.2,2.0,Iris-virginica
+6.2,3.4,5.4,2.3,Iris-virginica
+5.9,3.0,5.1,1.8,Iris-virginica
\ No newline at end of file
diff --git a/hpcpy20 b/hpcpy20
new file mode 100644
index 0000000..d159b3d
--- /dev/null
+++ b/hpcpy20
@@ -0,0 +1,20 @@
+#!/bin/bash
+module purge --force
+module load Stages/2020
+module load Intel
+module load ParaStationMPI
+module load Graphviz
+module load SciPy-Stack
+module load numba
+module load dask
+module load mpi4py
+module load CUDA
+module load CMake
+#export NUMBAPRO_NVVM=$CUDA_HOME/nvvm/lib64/libnvvm.so
+#export NUMBAPRO_LIBDEVICE=$CUDA_HOME/nvvm/libdevice
+export LD_LIBRARY_PATH=/p/project/training2020/resources/code/text_stats/build:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=/p/project/training2020/resources/code/point/build:$LD_LIBRARY_PATH
+export PYTHONPATH=/p/project/training2020/packages/lib/python3.8/site-packages:$PYTHONPATH
+export PATH=$PATH:/p/project/training2020/packages/bin
+export PS1='π20[\u@\h \W]\$ '
+
diff --git a/images/.directory b/images/.directory
new file mode 100644
index 0000000..e2a415b
--- /dev/null
+++ b/images/.directory
@@ -0,0 +1,4 @@
+[Dolphin]
+PreviewsShown=true
+Timestamp=2017,5,9,9,11,25
+Version=4
diff --git a/images/6nodes.png b/images/6nodes.png
new file mode 100644
index 0000000000000000000000000000000000000000..b916504acf7da67d0812281fac47d72fb107ee0a
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new file mode 100644
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new file mode 100644
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diff --git a/solutions/.ipynb_checkpoints/00_Bottlenecks-checkpoint.ipynb b/solutions/.ipynb_checkpoints/00_Bottlenecks-checkpoint.ipynb
new file mode 100644
index 0000000..c13468d
--- /dev/null
+++ b/solutions/.ipynb_checkpoints/00_Bottlenecks-checkpoint.ipynb
@@ -0,0 +1,788 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Bottlenecks\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "16 Nov 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## High-performance computing is computing at the limit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "CPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "I/O"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CPU\n",
+ "### On JUWELS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\n",
+ "Each core has the following features:\n",
+ "\n",
+ "- processor frequency of 2.7 GHz (up to 3.7 GHz in turbo mode)\n",
+ "- 512 bit wide vector unit (8 double precision numbers)\n",
+ "- 2 Fused multiply-add (FMA) units each performing an FMA operation in a single cycle (each FMA counts as 2 floating point operations)\n",
+ "- When running all cores each FMA unit runs at 2.5 GHz (max)\n",
+ "- Peak performance is 2.5 \\* 8 \\* 2 \\* 2 GFlop/s = 80 GFlop/s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "There are 24 cores per socket\n",
+ "- Peak performance of a socket is 24 * 80 GFlop/s = 1920 GFlop/s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is the limit most people think of first, but it's often not the crucial one. Each core on JUWELS can perform ca. 80 GFlop/s if the code is completely *vectorized* and performs a *multiply and an add operation* at *each step*. If your code doesn't fulfill those requirements its peak performance will be less.\n",
+ "\n",
+ "Actually the peak performance is a often less because the CPU temperature limit typically soon leads to throttling when using all cores. The guaranteed sustained frequency for the JUWELS FMA units is 1.9 GHz."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Memory hierarchy\n",
+ "### Caches"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* L1 (per core):\n",
+ " - 32 kiB data cache (+ 32 kiB instruction cache)\n",
+ " - Fastest memory (128 (load) + 64 (store)) B/cycle (latency: 4-5 cycles)\n",
+ "* L2 (per core): \n",
+ " - 1 MiB\n",
+ " - 64 B/cycle (latency: 14 cycles)\n",
+ "* L3 (shared): \n",
+ " - 33 MiB\n",
+ " - ?? B/cycle (latency: 50-70 cycles)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "\n",
+ "### Main memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The memory bandwidth of a JUWELS node is about "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "120 GB/s. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A simple operation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "c = c + a * b (multiply-add)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "3 DP read, 1 DP write -> 24 bytes read, 8 bytes write"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "120 GB/s / 24 bytes/op = 5 Gop/s (multiply-add -> 10 GFLOP/s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "I assume that we are dealing with double precision numbers (8 bytes). Then I have to read 3 * 8 bytes = 24 bytes and write 8 bytes. This is a multiply-add operation, so each core can do 40 billion of those per second, but it only receives 120 GB/s. 120GB/s / 24 B/op = 5Gop/s (10 GFLOP/s). This operation is clearly memory bound, if we have to get all the data from main memory."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is quite common. Let's look at a matrix multiplication $C=AB$. To calculate the element i, j of the result matrix C, we multiply row i of A with column j of B and sum the results. This is the scalar or dot product of row i of A and column j of B. In code this looks like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "\n",
+ "def dot(a, b):\n",
+ " \"\"\"Multiply the matrix a with the matrix b.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: ndarray\n",
+ " left matrix\n",
+ " b: ndarray\n",
+ " right matrix\n",
+ " \n",
+ " Return\n",
+ " ------\n",
+ " c: ndarray\n",
+ " result matrix\n",
+ " \"\"\"\n",
+ " c = numpy.zeros((a.shape[0], b.shape[1])) \n",
+ " for i in range(a.shape[0]): \n",
+ " for j in range(b.shape[1]): \n",
+ " for k in range(a.shape[1]): \n",
+ " c[i, j] += a[i, k] * b[k, j]\n",
+ " return c "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Let's take two small matrices A and B and see how long the above function takes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 256\n",
+ "a = numpy.random.random((n, n))\n",
+ "b = numpy.random.random((n, n))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot = %timeit -o dot(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "A matrix multiplication of two n by n matrices performs $2n^3$ operations. The dot function achieves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"%.3f GFLOP/s\" % (2e-9 * n**3 / t_dot.best)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Wow, that's bad. Let's see if we can make this faster."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Numba"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import jit\n",
+ "jdot = jit(dot)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_jit = %timeit -o jdot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"%.3f GFLOP/s\" % (2e-9 * n**3 / t_jit.best)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Access order and cache lines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "From our estimate above, we should be able to get at least twice this, but that's assuming we can achieve the maximum memory bandwidth. \n",
+ "\n",
+ "A numpy ndarray uses C-order (row-order) for storage. This means that the last index is continuous in memory and a change in any other index results in a jump from one memory location to another. The order of the loops therefore means that for both c and b, we don't get the maximum bandwidth, because we jump around and only use one element of the cache line. \n",
+ "\n",
+ "A datum is not loaded by itself. Instead everytime, a datum is needed that is not available in cache, a cache line containing the datum is loaded. On JUWELS the cache line is 64 bytes wide. \n",
+ "\n",
+ "We can improve the performance by exchanging the loops:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy; from numba import jit\n",
+ "\n",
+ "@jit\n",
+ "def dot2(a, b):\n",
+ " \"\"\"Multiply the matrix a with the matrix b.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: ndarray\n",
+ " left matrix\n",
+ " b: ndarray\n",
+ " right matrix\n",
+ " \n",
+ " Return\n",
+ " ------\n",
+ " c: ndarray\n",
+ " result matrix\n",
+ " \"\"\"\n",
+ " c = numpy.zeros((a.shape[0], b.shape[1])) \n",
+ " for i in range(a.shape[0]): \n",
+ " for k in range(a.shape[1]): \n",
+ " for j in range(b.shape[1]): \n",
+ " c[i, j] += a[i, k] * b[k, j]\n",
+ " return c "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, elements in c and b are accessed in the proper order and a[i, k] is constant for the loop. This changes our estimate, because, now we read 16 bytes/op. This gives us a maximum of 120 GB/s / 16 bytes/op = 7.5 GFLOP/s (15 GB/s). #Todo: shouldn't the last two not be gops and GFLOPs andtead of GFLOPs and GB/s??"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Effect on matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot2 = %timeit -o dot2(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_dot2.best, \"GFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is better than what we would expect from the bandwidth estimate, probably due to caching. One way to test this is to make the matrix larger, so that it doesn't fit in cache anymore."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 2048\n",
+ "a = numpy.random.random((n,n))\n",
+ "b = numpy.random.random((n,n))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot2_large = %timeit -o dot2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_dot2_large.best, \"GFLOP/s\") "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is quite close to my estimate and shows that I have to increase the number of operations per byte loaded from main memory. Improving vectorization or using multiple threads wouldn't help.\n",
+ "\n",
+ "To improve cache utilization, we have to change the algorithm. One way to improve the performance of the matrix multiplication is blocking (aka tiling). This is done, e.g., in OpenBLAS or Intel's Math Kernel Library (MKL)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how long numpy takes for this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy = %timeit -o numpy.dot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_numpy.best, \"GFLOP/s\") "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The numpy version we use here, uses a fast math library. That's what you want."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The roofline model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The roofline model shows the memory bandwidth bound and compute bound with respect to the computational intensity. The computational intensity is just given by the number of bytes used divided by the number of operations performed."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Depending on your algorithm, different limits may be relevant, for example, we only used a single thread, but used the peak performance of the entire processor with 24 cores. If the data fits completely in L2 cache the available bandwidth is higher once the data has been loaded. The following shows a plot with a few more limits."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## I/O"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### GPFS File System\n",
+ "$\\mathcal{O}(200)$ GB/s read/write speed for scratch"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Each node connected to file system with $\\mathcal{O}(100)$ GBit/s or about 12.5 GB/s."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The scratch file system achieves read/write bandwidths that are very similar to the main memory bandwidth, but not for a single node. Each node is connected to the GPFS file system with $\\mathcal{O}(100)$ GBit/s connection. In other words, we can read/write about 12.5 GB/s. If we had to load the data in the previous calculation from disk, we could only achieve 12.5 GB/s / 24 bytes/op = 520 Mop/s. The main memory bandwidth or the peak performance of the CPU doesn't matter in this case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/00_Bottlenecks.ipynb b/solutions/00_Bottlenecks.ipynb
new file mode 100644
index 0000000..c13468d
--- /dev/null
+++ b/solutions/00_Bottlenecks.ipynb
@@ -0,0 +1,788 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Bottlenecks\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "16 Nov 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## High-performance computing is computing at the limit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "CPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "I/O"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CPU\n",
+ "### On JUWELS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\n",
+ "Each core has the following features:\n",
+ "\n",
+ "- processor frequency of 2.7 GHz (up to 3.7 GHz in turbo mode)\n",
+ "- 512 bit wide vector unit (8 double precision numbers)\n",
+ "- 2 Fused multiply-add (FMA) units each performing an FMA operation in a single cycle (each FMA counts as 2 floating point operations)\n",
+ "- When running all cores each FMA unit runs at 2.5 GHz (max)\n",
+ "- Peak performance is 2.5 \\* 8 \\* 2 \\* 2 GFlop/s = 80 GFlop/s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "There are 24 cores per socket\n",
+ "- Peak performance of a socket is 24 * 80 GFlop/s = 1920 GFlop/s"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is the limit most people think of first, but it's often not the crucial one. Each core on JUWELS can perform ca. 80 GFlop/s if the code is completely *vectorized* and performs a *multiply and an add operation* at *each step*. If your code doesn't fulfill those requirements its peak performance will be less.\n",
+ "\n",
+ "Actually the peak performance is a often less because the CPU temperature limit typically soon leads to throttling when using all cores. The guaranteed sustained frequency for the JUWELS FMA units is 1.9 GHz."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Memory hierarchy\n",
+ "### Caches"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* L1 (per core):\n",
+ " - 32 kiB data cache (+ 32 kiB instruction cache)\n",
+ " - Fastest memory (128 (load) + 64 (store)) B/cycle (latency: 4-5 cycles)\n",
+ "* L2 (per core): \n",
+ " - 1 MiB\n",
+ " - 64 B/cycle (latency: 14 cycles)\n",
+ "* L3 (shared): \n",
+ " - 33 MiB\n",
+ " - ?? B/cycle (latency: 50-70 cycles)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "\n",
+ "### Main memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The memory bandwidth of a JUWELS node is about "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "120 GB/s. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A simple operation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "c = c + a * b (multiply-add)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "3 DP read, 1 DP write -> 24 bytes read, 8 bytes write"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "120 GB/s / 24 bytes/op = 5 Gop/s (multiply-add -> 10 GFLOP/s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "I assume that we are dealing with double precision numbers (8 bytes). Then I have to read 3 * 8 bytes = 24 bytes and write 8 bytes. This is a multiply-add operation, so each core can do 40 billion of those per second, but it only receives 120 GB/s. 120GB/s / 24 B/op = 5Gop/s (10 GFLOP/s). This operation is clearly memory bound, if we have to get all the data from main memory."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is quite common. Let's look at a matrix multiplication $C=AB$. To calculate the element i, j of the result matrix C, we multiply row i of A with column j of B and sum the results. This is the scalar or dot product of row i of A and column j of B. In code this looks like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "\n",
+ "def dot(a, b):\n",
+ " \"\"\"Multiply the matrix a with the matrix b.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: ndarray\n",
+ " left matrix\n",
+ " b: ndarray\n",
+ " right matrix\n",
+ " \n",
+ " Return\n",
+ " ------\n",
+ " c: ndarray\n",
+ " result matrix\n",
+ " \"\"\"\n",
+ " c = numpy.zeros((a.shape[0], b.shape[1])) \n",
+ " for i in range(a.shape[0]): \n",
+ " for j in range(b.shape[1]): \n",
+ " for k in range(a.shape[1]): \n",
+ " c[i, j] += a[i, k] * b[k, j]\n",
+ " return c "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Let's take two small matrices A and B and see how long the above function takes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 256\n",
+ "a = numpy.random.random((n, n))\n",
+ "b = numpy.random.random((n, n))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot = %timeit -o dot(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "A matrix multiplication of two n by n matrices performs $2n^3$ operations. The dot function achieves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"%.3f GFLOP/s\" % (2e-9 * n**3 / t_dot.best)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Wow, that's bad. Let's see if we can make this faster."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Numba"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import jit\n",
+ "jdot = jit(dot)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_jit = %timeit -o jdot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"%.3f GFLOP/s\" % (2e-9 * n**3 / t_jit.best)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Access order and cache lines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "From our estimate above, we should be able to get at least twice this, but that's assuming we can achieve the maximum memory bandwidth. \n",
+ "\n",
+ "A numpy ndarray uses C-order (row-order) for storage. This means that the last index is continuous in memory and a change in any other index results in a jump from one memory location to another. The order of the loops therefore means that for both c and b, we don't get the maximum bandwidth, because we jump around and only use one element of the cache line. \n",
+ "\n",
+ "A datum is not loaded by itself. Instead everytime, a datum is needed that is not available in cache, a cache line containing the datum is loaded. On JUWELS the cache line is 64 bytes wide. \n",
+ "\n",
+ "We can improve the performance by exchanging the loops:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy; from numba import jit\n",
+ "\n",
+ "@jit\n",
+ "def dot2(a, b):\n",
+ " \"\"\"Multiply the matrix a with the matrix b.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: ndarray\n",
+ " left matrix\n",
+ " b: ndarray\n",
+ " right matrix\n",
+ " \n",
+ " Return\n",
+ " ------\n",
+ " c: ndarray\n",
+ " result matrix\n",
+ " \"\"\"\n",
+ " c = numpy.zeros((a.shape[0], b.shape[1])) \n",
+ " for i in range(a.shape[0]): \n",
+ " for k in range(a.shape[1]): \n",
+ " for j in range(b.shape[1]): \n",
+ " c[i, j] += a[i, k] * b[k, j]\n",
+ " return c "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, elements in c and b are accessed in the proper order and a[i, k] is constant for the loop. This changes our estimate, because, now we read 16 bytes/op. This gives us a maximum of 120 GB/s / 16 bytes/op = 7.5 GFLOP/s (15 GB/s). #Todo: shouldn't the last two not be gops and GFLOPs andtead of GFLOPs and GB/s??"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Effect on matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot2 = %timeit -o dot2(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_dot2.best, \"GFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is better than what we would expect from the bandwidth estimate, probably due to caching. One way to test this is to make the matrix larger, so that it doesn't fit in cache anymore."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 2048\n",
+ "a = numpy.random.random((n,n))\n",
+ "b = numpy.random.random((n,n))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_dot2_large = %timeit -o dot2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_dot2_large.best, \"GFLOP/s\") "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This is quite close to my estimate and shows that I have to increase the number of operations per byte loaded from main memory. Improving vectorization or using multiple threads wouldn't help.\n",
+ "\n",
+ "To improve cache utilization, we have to change the algorithm. One way to improve the performance of the matrix multiplication is blocking (aka tiling). This is done, e.g., in OpenBLAS or Intel's Math Kernel Library (MKL)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how long numpy takes for this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy = %timeit -o numpy.dot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(2e-9 * n**3 / t_numpy.best, \"GFLOP/s\") "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The numpy version we use here, uses a fast math library. That's what you want."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The roofline model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The roofline model shows the memory bandwidth bound and compute bound with respect to the computational intensity. The computational intensity is just given by the number of bytes used divided by the number of operations performed."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Depending on your algorithm, different limits may be relevant, for example, we only used a single thread, but used the peak performance of the entire processor with 24 cores. If the data fits completely in L2 cache the available bandwidth is higher once the data has been loaded. The following shows a plot with a few more limits."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## I/O"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### GPFS File System\n",
+ "$\\mathcal{O}(200)$ GB/s read/write speed for scratch"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Each node connected to file system with $\\mathcal{O}(100)$ GBit/s or about 12.5 GB/s."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The scratch file system achieves read/write bandwidths that are very similar to the main memory bandwidth, but not for a single node. Each node is connected to the GPFS file system with $\\mathcal{O}(100)$ GBit/s connection. In other words, we can read/write about 12.5 GB/s. If we had to load the data in the previous calculation from disk, we could only achieve 12.5 GB/s / 24 bytes/op = 520 Mop/s. The main memory bandwidth or the peak performance of the CPU doesn't matter in this case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/01_Introduction to IPython.ipynb b/solutions/01_Introduction to IPython.ipynb
new file mode 100644
index 0000000..a91423b
--- /dev/null
+++ b/solutions/01_Introduction to IPython.ipynb
@@ -0,0 +1,959 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to IPython and Jupyter Notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "<div class=\"dateauthor\">\n",
+ "2 July 2019 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Jupyter notebooks offer a flexible way to combine python (and other language), scripts, text (such as this one), plots, and other things into one document.\n",
+ "\n",
+ "There are two modi: command und edit. You enter edit mode by pressing ``Enter``. You can exit it by pressing ``Esc``. To see the shortcuts for each modus press ``Esc`` followed by ``h`` if you are using Jupyter Notebook. Look in the ``Commands`` tab on the left hand side if you are using JupyterLab.\n",
+ "\n",
+ "If you want a new input above your current cell, press ``a`` in command mode. If you would like a new cell below your current cell press ``b``.\n",
+ "\n",
+ "In the course, we'll use the *IPython kernel* within the Jupyter notebook. IPython is also available within a regular terminal (``ipython``) or in its own special terminal-like window called Jupyter QtConsole."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## IPython Shell & QtConsole"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "<img src=\"images/IPythoninTerminal.png\" alt=\"IPython in a terminal\" width=\"45%\" align=\"left\"/><img src=\"images/QtConsolewithImageandDoc.png\" alt=\"Jupyter Qt console with image and tooltip\" width=\"45%\" align=\"right\"/>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Magic and Help"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "IPyhon extends the normal Python shell with *magic commands*. You can get a list of available magic commands using the magic command ``%lsmagic``. Give it a try. Use ``Shift+Enter`` to execute the cell. Just pressing ``Enter`` only gives you a new line."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%lsmagic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Not all the magic commands may be obvious to you, so it's a good thing that IPython also includes a help system. If you want to know, for example, what ``%dhist`` does im comparison to ``%hist``, you call first ``%dhist?`` and then ``%hist?``. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You saw that ``%hist`` is just an alias for ``%history``.\n",
+ "\n",
+ "Some of the magic commands, e.g., ``%less``, ``%ls``, and ``%man`` are substitutes for their shell equivalents, others, e.g., ``%load``, ``%save``, ``%%writefile`` deal with reading and writing from (to) files. We'll encounter more magic commands as we go along. \n",
+ "\n",
+ "The question mark doesn't just work for magic functions but gives you access to the documentation included with most Python modules. If you want to know, for example, what the random module does, you use ``random?``. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If you didn't get the documentation but only ``Object `random` not found``. Try importing the module first. Start by typing ``im`` and hit the tab key. Then type ``r`` and hit tab again. You'll get a dropdown box with available modules. You can continue typing until your choice is unique or select an item from the list. Give it a try. \n",
+ "\n",
+ "Try ``random?`` after importing the module. If you use ``??`` instead of ``?`` you get the source code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import random"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Timing with %timeit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how fast random.uniform generates random numbers and compare it with numpy's random.uniform. We'll use the timeit magics for that (more about those later)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit \n",
+ "n = 1\n",
+ "[random.uniform(0, 1) for i in range(n)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 1\n",
+ "t = %timeit -o numpy.random.uniform(0, 1, size=n)\n",
+ "print(n * 1. / t.best)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Plotting"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We won't go into the details of using [matplotlib][] for plotting in this course, but a quick introduction can't hurt.\n",
+ "\n",
+ "We first need to initialize the interactive plotting routines. The easiest way to do this is to use some magic. \n",
+ "\n",
+ "The command ``%matplotlib inline`` sets up interactive plotting support without importing any modules. This allows us to import the modules that we want:\n",
+ "\n",
+ "```python\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "```\n",
+ "\n",
+ "Alternatively, the command ``%pylab inline`` sets up interactive plotting and pulls all functions and modules from ``numpy`` and ``matplotlib.pyplot`` into the namespace.\n",
+ "\n",
+ "\n",
+ "[matplotlib]: http://matplotlib.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Output format"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can set the output format of matplotlib, too. The following commands change the default format from png to pdf."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import set_matplotlib_formats\n",
+ "set_matplotlib_formats('pdf', 'svg')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Plots and labels"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x = numpy.linspace(0, 2 * numpy.pi, 120)\n",
+ "y = numpy.sin(x)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.plot(x, y, label=r\"$\\sin(x)$\")\n",
+ "plt.xlim([0, 2 * numpy.pi])\n",
+ "plt.grid(1)\n",
+ "plt.xticks(numpy.linspace(0, 2 * numpy.pi, 9), [0, r\"$\\frac{\\pi}{4}$\", \n",
+ " r\"$\\frac{\\pi}{4}$\", r\"$\\frac{3\\pi}{4}$\", r\"$\\pi$\", \n",
+ " r\"$\\frac{5\\pi}{4}$\", r\"$\\frac{3\\pi}{2}$\", r\"$\\frac{7\\pi}{4}$\"\n",
+ " , r\"$2\\pi$\"])\n",
+ "plt.xlabel('x')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Saving and Loading Files"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's say, we want to use the script that we wrote in the section [Plotting](#Plotting) later from outside the notebook. We can use the ``%save`` magic to do that. Each cell has a number ``In [60]`` for example. The ``%save`` command takes a file name and a space separated list of input cells. The content of the input cells is written to a file. You can give ranges and even reorder things, e.g.,\n",
+ "\n",
+ " %save plotsin.py 60 61 62\n",
+ " \n",
+ "saves the cells with index 60, 61, and 62 to plotsin.py. I could have also written 60-62 to give the range. Look at the cell indices in the previous section and write them to a file. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can load the file using ``%load``. Try loading the file you just wrote to disk. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The entire content of the file is written to a single cell. We can split (and join) cells (see the Edit menu) if we don't like this. For files that are contained in a single cell, we can use the ``%%writefile`` magic.\n",
+ "\n",
+ "Join the next three cells and write them to a file called gaussian.py by adding ``%%writefile filename`` to the top of the cell."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "1. Highlight the next three cells (use the Shift-key to highlight multiple cells)\n",
+ "2. See the Commands (Ctrl+Shift+C) tab on the left (or press `h` to check wich key is used for merging cells if you are using a classic Jupyter notebook).\n",
+ "3. Merge the cells\n",
+ "4. Write %%writefile gaussian.py at the top of cell"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "r = numpy.random.normal(size=1000000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"The average is %.3f and the standard deviation is %.3f\" % (r.mean(), r.std()))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n, b, p = plt.hist(r, bins=100, density=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If you try to run gaussian.py from the command line it won't work because it's missing the imports, but you can run it using ``ipython --pylab=auto gaussian.py``. You can also run the script from IPython using the ``%run`` magic, but you have to use `-i` to run the script within the current namespace. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%run -i gaussian.py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Load can also load scripts from a URL. Give it a try. Look at the script loaded and then execute it, too.\n",
+ "\n",
+ "**Note**, since our compute nodes don't have internet access, I executed the command for you."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# %load http://matplotlib.org/mpl_examples/mplot3d/surface3d_demo.py\n",
+ "'''\n",
+ "======================\n",
+ "3D surface (color map)\n",
+ "======================\n",
+ "\n",
+ "Demonstrates plotting a 3D surface colored with the coolwarm color map.\n",
+ "The surface is made opaque by using antialiased=False.\n",
+ "\n",
+ "Also demonstrates using the LinearLocator and custom formatting for the\n",
+ "z axis tick labels.\n",
+ "'''\n",
+ "\n",
+ "from mpl_toolkits.mplot3d import Axes3D\n",
+ "import matplotlib.pyplot as plt\n",
+ "from matplotlib import cm\n",
+ "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "fig = plt.figure()\n",
+ "ax = fig.gca(projection='3d')\n",
+ "\n",
+ "# Make data.\n",
+ "X = np.arange(-5, 5, 0.25)\n",
+ "Y = np.arange(-5, 5, 0.25)\n",
+ "X, Y = np.meshgrid(X, Y)\n",
+ "R = np.sqrt(X**2 + Y**2)\n",
+ "Z = np.sin(R)\n",
+ "\n",
+ "# Plot the surface.\n",
+ "surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,\n",
+ " linewidth=0, antialiased=False)\n",
+ "\n",
+ "# Customize the z axis.\n",
+ "ax.set_zlim(-1.01, 1.01)\n",
+ "ax.zaxis.set_major_locator(LinearLocator(10))\n",
+ "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
+ "\n",
+ "# Add a color bar which maps values to colors.\n",
+ "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Moving Around"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "IPython has two ways of moving around in the directory tree: ``%cd`` and ``%pushd/%popd``. Both retain their history. ``%cd``'s history is available through ``%dhist`` whereas ``%dirs`` shows the directory stack of ``%pushd/%popd``. The ``%cd `` command has some nifty options, for example, ``%cd -2`` gets you to the second to last visited directory and ``%cd --foo`` switches to the next directory in the history than contains ``foo``. You can also set ``%bookmark``s and use them with ``%cd``.\n",
+ "\n",
+ "Make a new sub directory called scripts/mandelbrot using ``%mkdir -p scripts/mandelbrot``. Change into the directory scripts/mandelbrot using ``%cd``. Go two levels up using ``%cd ..`` twice. Look at the history using ``%dhist``. Change into mandelbrot using ``%cd --brot``. Finally use ``%cd -0`` to get back to where you started from."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A Little Bit of History"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Every output is stored to the ``Out`` array and can be accessed through its index. It can even be assigned."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numpy.random.random([4,4])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = _ # Assigns the output of the previous cell"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = Out[13] # Assign Out[?] to a (replace with index from two cells above)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "IPython keeps your history. It's accessed through the ``%history`` magic. By default it prints the history from the current session. If you have edited a cell multiple times, ``%history`` gives you all the versions. You can add line numbers to the output with the ``-n`` option, give ranges of lines that you want to see, and even perform some pattern matching. Pattern matching is done for your complete IPython history, not just the current session. For details see ``%history?``.\n",
+ "\n",
+ "If you want to log your work to a file (possibly with time stamps.) you can use IPython's logging facilities. ``%logstart -t testlog rotate`` creates a rotating log with timestamps and starts logging. ``%logoff`` pauses your log and ``%logstop`` stops the logging and closes the file."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Some Introspection"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "After an extended IPython session you might have declared many variables and functions. IPython provides some commands to help you to keep track of those. The first two are ``%who`` and ``%whos``. ``%who`` lists the names of functions and variables in the default namespace. ``%whos`` provides more details and includes the type of the variable. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%who"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%whos"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from math import pi"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%who"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If the namespace gets too crowded you can search for a particular object using ``%psearch``. Remember, though, auto completion is your friend.\n",
+ "\n",
+ "Sometimes it may become necessary to reset the namespace, for example, if ``Out[]`` contains some large objects that are no longer needed. ``%reset`` has several options to reset variables including the history of directories, inputs, and output. Please, check ``%reset?`` for details."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "IPython has several other interesting features. To learn more check out [IPython's documentation].\n",
+ "\n",
+ "[IPython's documentation]: https://ipython.readthedocs.io/en/stable/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2019a",
+ "language": "python",
+ "name": "hpcpy19a"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/02_NumPy_concepts.ipynb b/solutions/02_NumPy_concepts.ipynb
new file mode 100644
index 0000000..1cc73ae
--- /dev/null
+++ b/solutions/02_NumPy_concepts.ipynb
@@ -0,0 +1,367 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# NumPy - an HPC perspective\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Olav Zimmermann\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Python is an interpreted language and as such it is extremely flexible, allowing to define everything, including code itself, \n",
+ "at runtime. This entails that the Python interpreter uses a lot of magic behind the scenes (e.g. type inferencing) to keep things\n",
+ "as simple and productive as possible for the programmer. This flexibility comes at the price of a markedly reduced runtime speed \n",
+ "compared to compiled languages such as C++.\n",
+ "Many problems encoded in Python do not require the full range of flexibility and could easily trade it for improved runtime \n",
+ "performance without giving up the development performance which is the key for Python's success."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Background"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "NumPy is a library, written in C, to enable fast numerical computing in Python. Since its inception in 1995, NumPy has become first choice for numeric data processing in python. The main sacrifice to enable its high speed is the restriction to \n",
+ "containers with uniform memory layout, i.e., arrays that contain items of uniform static datatype."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Despite this apparently severe restriction NumPy is quite versatile and a full introduction into NumPy would require a\n",
+ "course of its own. Hence we will focus on the concepts that allowed its wide adoption by developers and HPC vendors alike. For an overview of the available functionality the numpy website https://www.numpy.org is a good starting point."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Note:** NumPy is not a part of the vanilla Python distribution and needs to be installed separately. Then it can be used like any other Python library."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The numpy BLAS and LAPACK bindings\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "NumPy does not implement everything itself. Instead it uses the fact that with BLAS (low level routines), and LAPACK (high level routines, based on BLAS), two widely adopted interfaces for linear algebra routines exist and that for almost all distributions and operation systems at least one library suporting the BLAS/LAPACK interface exists."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "While not mandatory, NumPy can be linked against high performance linear algebra libraries such as Intel's MKL, AMD's BLIS or IBM's ESSL folowing the BLAS/LAPACK APIs. These libraries can give you speed-ups of up to two orders of magnitude compared to the standard LAPACK library. In fact a number of distributions provide numpy implementations that are statically linked to Intel's MKL and when building, NumPy gives a preference to the optimized libraries (MKL, BLIS) over the slower, more hardware independent libraries (OpenBLAS, ATLAS).\n",
+ "\n",
+ "**Notes:** \n",
+ "- Not all routines of MKL are necessarily faster than those in OpenBLAS, e.g. random number generation. \n",
+ "- By default NumPy prefers Intel MKL over AMD BLIS, even on AMD processors. MKL works with AMD processors, but by default does not use the fast AVX2 and AVX512 BLAS routines that it uses when it has detected Intel hardware but only the much slower SSE2 routines. While there are hacks to change that behaviour it may therefore be more reasonable to change the order of preference for the different BLAS libraries on AMD platforms."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "You can check which BLAS library has been linked during your build of NumPy by calling the `show_config()` function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "print(np.__version__)\n",
+ "print(np.show_config())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## ndarray"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "The main datatype in NumPy is an n-dimensional array object called `ndarray`. By default it has C-array memory layout \n",
+ "(last index fastest, 0 based indices) and a uniform fixed element type defined at instantiation of the ndarray. Element sizes range from 1 byte (bool, uint8) to 16 byte (complex256) with the default being `float64`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### introspection, shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Several meta data of an `ndarray` can be obtained among them `a.ndim,a.size,a.nbytes,a.flags,type(a)`.\n",
+ "The array interface enables in-depth introspection such as obtaining the address of an object, e.g. for debugging purposes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "myarr=np.array([[1,2,3],[4,5,6]])\n",
+ "print(f\" myarr is a {myarr.ndim}-dimensional {type(myarr)} of type {myarr.dtype} and shape {myarr.shape}. It starts at adress {hex(myarr.__array_interface__['data'][0])}.\")\n",
+ "print(f\"Each of its {myarr.size} {myarr.dtype}-elements has a size of {myarr.dtype.itemsize} byte therefore it has {myarr.nbytes} bytes in total and its strides (in bytes) are {myarr.strides}.\")\n",
+ "print(\"The flags stored for this array are:\")\n",
+ "print(myarr.flags)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## NumPy's ndarray as a foundation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "`ndarrays` support important concepts to enable vectorized processing of data, such as broadcasting, ufuncs, and reductions. Why just use this for numeric data? Almost anything can be cast into an `ndarray` and also labeled access is possible. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dt=np.dtype([('name','S10'),('income',np.int16),\\\n",
+ " ('revenue',([('q1',np.float32),('q2',np.float32),('q3',np.float32),('q4',np.float32)]))])\n",
+ "f=np.loadtxt('test.dat',dtype=dt, skiprows=2,delimiter=',')\n",
+ "print(f)\n",
+ "print(f\"this array has {f.ndim} dimension(s)\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "However, note that most functionality in NumPy is geared towards arrays of uniform numerical type. The above data type indicates that the entire row is treated as a single (albeit very complicated) type and the data in the table thereby become a one-dimensional array. If you need spreadsheet-like functionality, NumPy's 'structured arrays' or 'record type' arrays that are based on `ndarrays` are not adequate. Luckily `ndarrays` can be extended in functionality and even reimplemented in a compatible way."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Design features of the ndarray API"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Due to its dual interface in Python and C and its often (not always) regular memory layout ndarrays can relatively easy be mapped to data types described in other language contexts. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "A couple of clever design choices adds to the popularity of ndarrays as a standard API for high performance computing in Python:\n",
+ "- narrays support both C-style and Fortran-style memory layouts, as well as memory alignment and view interfaces.\n",
+ "- A Mixin class `NDArrayOperatorsMixin` provides all the necessary standard python interfaces like `__add__`, `__lt__` etc. making custom array containers more convenient to write.\n",
+ "- `ndarray.__array_ufunc__` and `__array_function__` are interfaces that split the function API from the excution engine. By overriding them, these functions allow to intercept calls to ufuncs and non-ufuncs and to dispatch these calls to alternative implementations. Several important packages already use this approach."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Packages that implement the ndarray interface:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "<table>\n",
+ " <tr><th>package/module</th><th>extension(s)</th><th>other HPC relevant characteristics</th></tr>\n",
+ " <tr><td><code><b>cuPy</b></code></td><td>cuPy array: subset of ndarray functionality</td><td>ndarrays on GPUs</td></tr>\n",
+ " <tr><td><code><b>pandas</b></code></td><td>pandas dataframe: labeled data, non-numerical data, multi-indexing, grouping</td><td>fast CSV-parser</td></tr>\n",
+ " <tr><td><code><b>cuDF</b></code></td><td>cuDF dataframe: subset of pandas dataframe functionality</td><td>pandas dataframes on GPUs</td></tr>\n",
+ " <tr><td><code><b>dask</b></code></td><td>dask array: only subset of ndarray functionality</td><td>tiled ndarrays larger than main memory, distributed processing on multiple nodes</td></tr>\n",
+ " <tr><td><code><b>dask</b></code></td><td>dask dataframe: only subset of pandas dataframe functionality</td><td>tiled dataframes larger than main memory, distributed processing on multiple nodes</td></tr>\n",
+ " <tr><td><code><b>dask-cuDF</b></code></td><td>cuDF dataframe: subset of pandas dataframe functionality</td><td>tiled dataframes on multiple GPUs and multiple nodes</td></tr>\n",
+ " <tr><td><code><b>sparse</b></code></td><td>ndarray functionality on sparse arrays (COO layout)</td><td></td></tr></table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Notable packages that do not implement the ndarray interface are `numpy.matrix, scipy.sparse, pytorch, JAX` while `tensorflow` has an experimental interface."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "End"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/03_ThinkVector.ipynb b/solutions/03_ThinkVector.ipynb
new file mode 100644
index 0000000..f557f7f
--- /dev/null
+++ b/solutions/03_ThinkVector.ipynb
@@ -0,0 +1,1129 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Think Vector\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "16 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Dot product"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Many compute kernels include loops. Let's take the dot (or scalar) product, for example, for two vectors *v* and *w*:\n",
+ "\n",
+ "$$s = \\sum_{i=0}^n v_i w_i $$\n",
+ "\n",
+ "We can write this as"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create a random number generator that uses the Mersenne-Twister bit generator.\n",
+ "rng = numpy.random.Generator(numpy.random.MT19937())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v = rng.uniform(size=1000)\n",
+ "w = rng.uniform(size=1000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "s = 0\n",
+ "for i in range(len(v)):\n",
+ " s += v[i] * w[i]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can also think of this as a map operation followed by a reduction:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Map"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A map operation applies an operation (a function) to each element of an array separately."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Maps can be expressed using list comprehensions\n",
+ "vw = numpy.array([v[i] * w[i] for i in range(len(v))])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Reduce"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A reduction takes the elements of an array and *reduces* them to a single value. A typical example of a reduction is the summation over all elements."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Now let's do the reduction\n",
+ "s = 0\n",
+ "for i in range(len(v)):\n",
+ " s += vw[i]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We didn't have to use numpy.array for these operations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We are using numpy arrays, which define a number of operations on whole arrays, so we can think of them as vectors. The two operations above can be rewritten."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Map-Reduce with NumPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Map-reduce is a very common pattern. We first transform the elements of an array and then reduce the resulting array to a single element."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Map\n",
+ "vw = v * w\n",
+ "# Reduce\n",
+ "s = vw.sum()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The dot product is such a common operation that numpy has a special function for it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Everything in one call\n",
+ "s = v.dot(w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"v·w = %.3f\" % s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since Python 3.6 this can also be written as ``v@w``."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercise:**\n",
+ "\n",
+ "Let's go back through the cells and and add the ``%%timeit`` magic at the top of each cell. Start with cell 3 and work your way back down."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The last one is not just the simplest, it's also the fastest."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "# As an example, we'll do the last timing operation\n",
+ "# Note, since this is a one-liner, we could have used %timeit instead."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "s = v.dot(w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## ufunc"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Functions that act on one array (or several arrays of the same shape) and return a vector of the same shape are called ``ufuncs``. When we wrote vw = v * w, we executed the ufunc \\__mul\\__. Functions, like ``dot`` that have a different output shape than input shape are called generalized ufuncs."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Stencils"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Stencils use the value of the neighboring elements to update the current position, e.g., "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "$$a[i, j] = \\frac{1}{4} (a[i - 1, j] + a[i + 1, j] + a[i, j - 1] + a[i, j + 1])$$\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A system with fixed boundaries"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's look at an example. We start with a 2d array of random values and fix the left boundary to a value of 0 and the right boundary to a value of 1. We do not want to change these boundary values. The top and bottom boundaries are connected so that our system forms a cylinder (periodic boundary conditions along y)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A_orig = numpy.random.random((10, 10))\n",
+ "A_orig[:,0] = 0\n",
+ "A_orig[:,-1] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = A_orig.copy()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "B = A.copy()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Explicit nested for loop"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "for i in range(A.shape[0]):\n",
+ " for j in range(1, A.shape[1] - 1):\n",
+ " B[i, j] = 0.25 * (A[(i + 1) % A.shape[0] , j] + A[i - 1, j] \n",
+ " + A[i, (j + 1)] + A[i, j - 1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.subplot(1, 3, 1)\n",
+ "plt.imshow(A, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 2)\n",
+ "plt.imshow(B, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 3)\n",
+ "plt.imshow(A-B, interpolation=\"nearest\")\n",
+ "print(\"|A-B| = %.3f\" % numpy.linalg.norm(A-B))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, we assign B to A and repeat. Note that |A-B| becomes smaller with each iteration unless you happen to run into an oscillating minimum."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = B.copy()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "[Repeat](#Explicit-nested-for-loop)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The operation for each *i* and *j* is independent since *A* is only read. This is an ideal candidate for parallel calculations and we can write it in form of vector operations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Element-wise operation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = A_orig.copy()\n",
+ "B = numpy.empty_like(A)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "B = 0.25*(numpy.roll(A, 1,axis=0) + numpy.roll(A, -1, axis=0) + numpy.roll(A, 1,axis=1) + numpy.roll(A, -1,axis=1))\n",
+ "# Keep our boundaries at a fixed value\n",
+ "B[:, 0] = 0\n",
+ "B[:, -1] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.subplot(1, 3, 1)\n",
+ "plt.imshow(A, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 2)\n",
+ "plt.imshow(B, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 3)\n",
+ "plt.imshow(A-B, interpolation=\"nearest\")\n",
+ "print(\"|A-B| = %.3f\" % numpy.linalg.norm(A-B))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercises:**\n",
+ "\n",
+ "a) use `%%timeit` to compare the `for`-loop and the `numpy.roll()` versions of the stencil update\n",
+ " \n",
+ "b) Combine all the step of a single iteration in one cell, execute it multiple times, and watch how the system proceeds. Does the norm of the difference get smaller?\n",
+ "\n",
+ " Tip: If you use <Ctrl+Enter> to execute the cell, the cursor stays on the cell and you can execute again right away.\n",
+ "\n",
+ "c) Create a loop that terminates if the sum of the differences becomes smaller than some small value epsilon or the maximum number of allowed iterations has been reached. Plot the final state."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution to b)\n",
+ "# A = A_orig.copy()\n",
+ "# B = numpy.empty_like(A)\n",
+ "B = 0.25*(numpy.roll(A, 1,axis=0) + numpy.roll(A, -1, axis=0) + numpy.roll(A, 1,axis=1) + numpy.roll(A, -1,axis=1))\n",
+ "# Keep our boundaries at a fixed value\n",
+ "B[:, 0] = 0\n",
+ "B[:, -1] = 1\n",
+ "plt.subplot(1, 3, 1)\n",
+ "plt.imshow(A, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 2)\n",
+ "plt.imshow(B, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 3)\n",
+ "plt.imshow(A-B, interpolation=\"nearest\")\n",
+ "print(\"|A-B| = %.3f\" % numpy.linalg.norm(A-B))\n",
+ "A = B.copy()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution to c)\n",
+ "A = A_orig.copy()\n",
+ "B = numpy.empty_like(A)\n",
+ "epsilon = 1e-2\n",
+ "max_iteration = 1000\n",
+ "i = 0\n",
+ "diffAB = 10 * epsilon\n",
+ "while diffAB > epsilon and i < max_iteration: \n",
+ " i += 1\n",
+ " B = 0.25*(numpy.roll(A, 1,axis=0) + numpy.roll(A, -1, axis=0) + numpy.roll(A, 1,axis=1) + numpy.roll(A, -1,axis=1))\n",
+ " # Keep our boundaries at a fixed value\n",
+ " B[:, 0] = 0\n",
+ " B[:, -1] = 1\n",
+ " diffAB = numpy.linalg.norm(A-B)\n",
+ " print(f\"{i: 5d}: |A-B| = {diffAB:.3f}\")\n",
+ " A = B.copy()\n",
+ "\n",
+ "plt.subplot(1, 3, 1)\n",
+ "plt.imshow(A, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 2)\n",
+ "plt.imshow(B, interpolation=\"nearest\")\n",
+ "plt.subplot(1, 3, 3)\n",
+ "plt.imshow(A-B, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Programming exercise Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "The Mandelbrot set is the set of points *c* in the complex plane for which"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "$$z_{i+1} = z_i^2 + c$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "does not diverge.\n",
+ "\n",
+ "The series diverges if $|z_i|>2$ for any *i*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since it is impracticable to calculate an infinite number of iterations, one usually sets an upper limit for the number of iterations (the maximum of *i* ), for example, 20. To get pretty pictures, we can map the value of *i* for which $|z_i|>2$ is true for the first time to a color."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Here is a function that does this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Escape time algorithm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " p: complex\n",
+ " point in the complex plane\n",
+ " maxtime: int\n",
+ " maximum number of iterations to perform before p is considered in \n",
+ " the Mandelbrot set.\n",
+ " \"\"\"\n",
+ " z = 0j # This is a complex number in Python\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "M = [[escape_time(re + im, 40) for re in numpy.linspace(-2.2, 1, 640)] for im in numpy.linspace(-1.2j, 1.2j, 480)]\n",
+ "plt.imshow(M)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now, it's your turn. Rewrite the above algorithm using NumPy vector operations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Hints:** \n",
+ "\n",
+ "* You can use `numpy.meshgrid()` to generate your 2D array of points.\n",
+ "* You somehow need to mask the points that already diverged in future iterations.\n",
+ "* You don't have to put this in a function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "#### Setting up the grid"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "You can use NumPy's meshgrid function to construct a two-dimensional grid:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy \n",
+ "numpy.meshgrid?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Let's take the same ranges for real and imaginary numbers as above\n",
+ "re = numpy.linspace(-2.2, 1, 640)\n",
+ "im = numpy.linspace(-1.2j, 1.2j, 480)\n",
+ "# X and Y will have a shape of (640, 480) with the values taken from re and im.\n",
+ "X, Y = numpy.meshgrid(re, im)\n",
+ "# Finally, add X and Y to get our grid\n",
+ "P = X + Y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "#### Prepare the loop"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "maxtime = 50\n",
+ "M = numpy.ones_like(P, dtype=int) * maxtime\n",
+ "Z = numpy.zeros_like(P)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "#### How to select the points to continue"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "In the above code, each point was done by itself, but now all points are evaluated at once. How do we assign the right level to each point?\n",
+ "\n",
+ "One way is to use a mask. All points for which the absolute value of `Z` becomes greater than 2 in the current iteration should be assigned that value. The following statement returns `True` for all points where this is true and `False` otherwise:\n",
+ "\n",
+ "```Python\n",
+ " mask = numpy.abs(Z) > 2\n",
+ "```\n",
+ "\n",
+ "We can use such a mask for assignment:\n",
+ "\n",
+ "```Python\n",
+ " M[mask] = iter\n",
+ "```\n",
+ "\n",
+ "This is not enough, though. Once `abs(Z) > 2` is true for a point, it remains true for all future iterations, but we don't want the program to keep increasing the value of `M` for that point. \n",
+ "\n",
+ "The easiest way to avoid this, is to set `P` and `Z` to zeros for those points:\n",
+ "\n",
+ "```Python\n",
+ " Z[mask] = 0\n",
+ " P[mask] = 0\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "The loop can then be written like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "for iter in range(maxtime):\n",
+ " Z = Z * Z + P\n",
+ " mask = numpy.abs(Z) > 2\n",
+ " M[mask] = iter\n",
+ " P[mask] = 0\n",
+ " Z[mask] = 0"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "Note that this modifies our input array `P`, which might be undesirable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(M)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/04_Profiling a simple md code.ipynb b/solutions/04_Profiling a simple md code.ipynb
new file mode 100644
index 0000000..06ba32f
--- /dev/null
+++ b/solutions/04_Profiling a simple md code.ipynb
@@ -0,0 +1,665 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Profiling\n",
+ "<div class=\"dateauthor\">\n",
+ "16 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Profiler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "cprofiler (standard module)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "line_profiler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Intel Advisor since 2017 beta"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Before you start to optimize a program, you should generate a profile. A profile shows how much time a program spends in which function, line of code, or even assembler instruction.\n",
+ "\n",
+ "There are several profiling tools,e.g., cprofile, which comes with Python and is always available. It measures performance on a function call level. We'll also look at line_profiler. Let's look at an example.\n",
+ "\n",
+ "The following functions implement a simple n-body simulation using a long range potential. This could be part of, e.g., an astrophysical simulation, a simulation of a many-electron system, or a molecular dynamics simulation.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Profiling a simple particle dynamics code"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "pair_force()\n",
+ "\n",
+ "force()\n",
+ "\n",
+ "calculate_all_forces()\n",
+ "\n",
+ "step()\n",
+ "\n",
+ "propagate_all_variables()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#%%writefile md.py\n",
+ "import numpy as np\n",
+ "from numba import jit\n",
+ "\n",
+ "#@jit\n",
+ "def pair_force(x0, y0, z0, m0, x1, y1, z1, m1):\n",
+ " \"\"\"Calculate the force on p0 due to p1.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x0: float\n",
+ " x-coordinate of the p0\n",
+ " y0: float\n",
+ " y-coordinate of the p0\n",
+ " z0: float\n",
+ " z-coordinate of the p0\n",
+ " m0: float\n",
+ " mass of the p0\n",
+ " x1: float\n",
+ " x-coordinate of the p1\n",
+ " y1: float\n",
+ " y-coordinate of the p1\n",
+ " z1: float\n",
+ " z-coordinate of the p1\n",
+ " m1: float\n",
+ " mass of the p1\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " f: ndarray\n",
+ " force on p0 due to p1\n",
+ " \n",
+ " \"\"\"\n",
+ " r2 = (x1 - x0) ** 2 + (y1 - y0) ** 2 + (z1 - z0) ** 2\n",
+ " f = m0 * m1 * np.array([(x1 - x0), (y1 - y0), (z1 - z0)]) * r2 ** (-1.5) if r2 else np.zeros(3)\n",
+ " return f\n",
+ "\n",
+ "#@jit\n",
+ "def force(x0, y0, z0, m0, x, y, z, m):\n",
+ " \"\"\"Calculates the force on the particle at (x0, y0, z0) due to all other particles.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x0: float\n",
+ " x-coordinate of the particle\n",
+ " y0: float\n",
+ " y-coordinate of the particle\n",
+ " z0: float\n",
+ " z-coordinate of the particle\n",
+ " m0: float\n",
+ " mass of the particle\n",
+ " x: ndarray\n",
+ " x-coordinates of all particles\n",
+ " y: ndarray\n",
+ " y-coordinates of all particles\n",
+ " z: ndarray\n",
+ " z-coordinates of all particles\n",
+ " m: ndarray\n",
+ " masses of all particles.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " f: ndarray\n",
+ " force on particle with mass m0 at (x0, y0, z0)\n",
+ " \"\"\"\n",
+ " f = np.zeros(3)\n",
+ " for x1, y1, z1, m1 in zip(x, y, z, m):\n",
+ " f += pair_force(x0, y0, z0, m0, x1, y1, z1, m1)\n",
+ " return f\n",
+ "\n",
+ "\n",
+ "def calculate_all_forces(x, y, z, m):\n",
+ " \"\"\"Calculates the force on each particle p due to all other particles.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x: ndarray\n",
+ " x-coordinates of all particles\n",
+ " y: ndarray\n",
+ " y-coordinates of all particles\n",
+ " z: ndarray\n",
+ " z-coordinates of all particles\n",
+ " m: ndarray\n",
+ " masses of all particles.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " f: ndarray\n",
+ " force on each particle due to all other particles.\n",
+ " \"\"\"\n",
+ " return np.array([force(x[i], y[i], z[i], m[i], x, y, z, m) for i in range(n)])\n",
+ "\n",
+ "def step(x, y, z, vx, vy, vz, m, f, dt):\n",
+ " \"\"\"Propagate the position and velocities.\n",
+ " \n",
+ " Starting from the current positions, velocities, and forces, propogate positions\n",
+ " and velocities by one time step of lenght dt.\n",
+ " \n",
+ " .. note:: This algorithm should not be used for real simulations!\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " x: ndarray\n",
+ " x-coordinates of all particles\n",
+ " y: ndarray\n",
+ " y-coordinates of all particles\n",
+ " z: ndarray\n",
+ " z-coordinates of all particles\n",
+ " vx: ndarray\n",
+ " x-component of the velocity of all particles\n",
+ " vy: ndarray\n",
+ " y-component of the velocity of all particles\n",
+ " vz: ndarray\n",
+ " z-component of the velocity of all particles\n",
+ " m: ndarray\n",
+ " masses of all particles.\n",
+ " f: ndarray\n",
+ " forces on particles\n",
+ " dt: float\n",
+ " time step\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " x, y, z, vx, vy, vz at t + dt\n",
+ " \"\"\"\n",
+ " xn = x + vx * dt + 0.5 * f[0] / m * dt * dt\n",
+ " yn = y + vy * dt + 0.5 * f[1] / m * dt * dt\n",
+ " zn = y + vz * dt + 0.5 * f[2] / m * dt * dt\n",
+ " vxn = vx + f[0] / m * dt\n",
+ " vyn = vy + f[1] / m * dt\n",
+ " vzn = vz + f[2] / m * dt\n",
+ " return xn, yn, zn, vxn, vyn, vzn\n",
+ "\n",
+ "def propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt):\n",
+ " for i in range(n):\n",
+ " x[i], y[i], z[i], vx[i], vy[i], vz[i] = step(x[i], y[i], z[i], vx[i], vy[i], vz[i], m[i], f[i], dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The main program"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Initialization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# 1000 particles\n",
+ "n = 1000\n",
+ "# time step of 0.01\n",
+ "dt = 0.01\n",
+ "\n",
+ "# Initialize coordinates and velocities to random values.\n",
+ "x = np.random.random(n)\n",
+ "y = np.random.random(n)\n",
+ "z = np.random.random(n)\n",
+ "vx = np.zeros_like(x)\n",
+ "vy = np.zeros_like(x)\n",
+ "vz = np.zeros_like(x)\n",
+ "m = np.ones_like(x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### The algorithm\n",
+ "\n",
+ "There are basically two steps to this algorithm:\n",
+ "\n",
+ "1. Calculate the forces on all particles\n",
+ "2. Propagate all variables for a time step\n",
+ "3. Continue at 1. for nstep steps"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nsteps = 2\n",
+ "for i in range(nsteps):\n",
+ " f = calculate_all_forces(x, y, z, m)\n",
+ " propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This took quite some time. Let's measure how long it takes. Add a %%timeit statement just before nsteps (same line)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The base line"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit nsteps = 1\n",
+ "for i in range(nsteps):\n",
+ " f = calculate_all_forces(x, y, z, m)\n",
+ " propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "OK, that's our base line. Next, we want to know where all this time is spent. I mentioned the cprofile module at the beginning. IPython has a magic for that called %%prun. Use it in front of the loop this time."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Profiling with %%prun"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%prun -r nsteps=1\n",
+ "for i in range(nsteps):\n",
+ " f = calculate_all_forces(x, y, z, m)\n",
+ " propagate_all_variables(x, y, z, vx, vy, vz, m, f, dt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ " 2003007 function calls in 8.561 seconds\n",
+ "\n",
+ " Ordered by: internal time\n",
+ "\n",
+ " ncalls tottime percall cumtime percall filename:lineno(function)\n",
+ " 1000000 5.209 0.000 7.073 0.000 <ipython-input-3-66a2b576efa3>:4(pair_force)\n",
+ " 999001 1.863 0.000 1.863 0.000 {built-in method numpy.core.multiarray.array}\n",
+ " 1000 1.480 0.001 8.555 0.009 <ipython-input-3-66a2b576efa3>:36(force)\n",
+ " 2000 0.003 0.000 0.003 0.000 {built-in method numpy.core.multiarray.zeros}\n",
+ " 1000 0.003 0.000 0.003 0.000 <ipython-input-3-66a2b576efa3>:89(step)\n",
+ " 1 0.001 0.001 0.004 0.004 <ipython-input-3-66a2b576efa3>:130(propagate_all_variables)\n",
+ " 1 0.001 0.001 8.557 8.557 <ipython-input-3-66a2b576efa3>:87(<listcomp>)\n",
+ " 1 0.000 0.000 8.561 8.561 {built-in method builtins.exec}\n",
+ " 1 0.000 0.000 8.557 8.557 <ipython-input-3-66a2b576efa3>:68(calculate_all_forces)\n",
+ " 1 0.000 0.000 8.561 8.561 <string>:1(<module>)\n",
+ " 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The overhead shouldn't be too bad. I got about 10%. Most of the time (about 80%) is spent in pair_force. And 20% of that time is spent on np.array>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Line by line profiling"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Unfortunately, this is a rather coarse grained profile. We don't know which part is the expensive part of this calculation and what we can do about it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext line_profiler"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%lprun -f pair_force force(x[0], y[0], z[0], m[0], x, y, z, m)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Total time: 9.86691 s \n",
+ "File: md.py \n",
+ "Function: pair_force at line 3 \n",
+ " \n",
+ " Line # Hits Time Per Hit % Time Line Contents\n",
+ " ============================================================== \n",
+ " 32 1000000 2269473 2.3 23.0 r2 = (x1 - x0) ** 2 + (y1 - y0) ** 2 + (z1 - z0) ** 2\n",
+ " 33 1000000 6864624 6.9 69.6 f = m0 * m1 * np.array([(x1 - x0), (y1 - y0), (z1 - z0)]) \n",
+ " * r2 **(-1.5) if r2 else np.zeros(3)\n",
+ " 34 1000000 732809 0.7 7.4 return f \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Timing individual operations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Calculating r2 takes 2.3 mus per call. Let's use %timeit to see how much time each operation takes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "(x1 - x0)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "(x1 - x0) ** 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "(x1 - x0) * (x1 - x0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit x0 = x[0]; y0=y[0]; z0 = z[0]; x1 = x[1]; y1=y[1]; z1 = z[1];\n",
+ "dx = (x1 - x0)\n",
+ "dx * dx"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can now change the code so it calculates dx, dy, and dz first and then uses them later in the calculation. We can also use numba to speed up the simulation."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Time the other operations and optimize the code"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "### Solution\n",
+ "There is no unique solution to this exercise. It's about playing around with `%timeit` and getting an impression for the different costs of operations. Any change in speed is good.\n",
+ "\n",
+ "Btw., timings can differ between different versions of Python especially for more complex operations. Your goal should always be to choose the best algorithm and express your intent as clearly as possible. We'll learn more about accelerating key functions later."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/05_Debugging.ipynb b/solutions/05_Debugging.ipynb
new file mode 100644
index 0000000..23ef132
--- /dev/null
+++ b/solutions/05_Debugging.ipynb
@@ -0,0 +1,347 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Debugging Python\n",
+ "<div class=\"dateauthor\">\n",
+ "16 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "What do you do if a program doesn't produce the results you want? You can stare at the code and try to figure out the mistake. You can add lots of print statements to your code. Or you can use a debugger.\n",
+ "\n",
+ "You've probably done the first two things, but have you used a debugger before?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Debugging has its own terminology: You step in and out of functions. You move up and down the stack. You set break points, inspect variables, etc. This is the basic functionality that every debugger should (and every debugger I know does) support.\n",
+ "\n",
+ "In this notebook, we'll look at debugging a program with PDB in the notebook and pudb in a terminal window. You'll learn how to start a debugging session and do all the things, I talked about in the previous paragraph."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## PDB"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Python comes with its own debugger called \"The Python debugger\" (pdb). PDB is available from within a notebook, but it's not very convenient to use."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's take the following function, which contains a bug and throws an exception."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#%%writefile buggy.py\n",
+ "def imabuggyincrement(i,a):\n",
+ " \"\"\"Increment a[i] by 1.\"\"\"\n",
+ " if ii < len(a):\n",
+ " a[i] += 1;\n",
+ "\n",
+ "a = list(range(10))\n",
+ "ii = 4\n",
+ "imabuggyincrement(10, a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Debug magic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If a cell has just thrown an exception, you can inspect it with the %debug magic. Try `help` to see the available commands. Type `exit` to leave the debugger."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Use `p i` to print the value of `i`. You can also try to print out the value of `a[i]` using `p a[i]`. Inspect the other variables. Do you see what went wrong?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%debug"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Available debuggers"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "* pdb (builtin)\n",
+ "* pudb\n",
+ "* IDEs (All the IDEs we mentioned have debugging support)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Uncomment the ``%%writefile`` magic before the function defintion of ``imabuggyincrement`` and execute the cell again so that it gets written to file buggy.py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next start pudb in a terminal with the script name as an argument. If you haven't done this in this terminal shell before, you need to source hpcpy20:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```bash\n",
+ "source hpcpy20\n",
+ "pudb3 buggy.py\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We'll give you a short demonstration and then you can play with it for a little while."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Remote debugging"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "For example, PyDev, Wing Personal, Visual Studio, and PyCharm Professional (199 €/a with perpetual fallback license) support remote debugging. It can also be done with the ``ptvsd`` and Visual Studio Code."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Debugging Python extensions\n",
+ "We'll talk about this more tomorrow (maybe)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Note\n",
+ "\n",
+ "> It's better to ask for forgiveness than to ask for permission."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A better way to check for bounds as I did in `iambuggyincrement` is not to do it at all but use a try...except statement instead:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "```python\n",
+ "def imabuggyincrement(i, a):\n",
+ " \"\"\"Increment a[i] by 1.\"\"\"\n",
+ " try:\n",
+ " a[i] += 1;\n",
+ " except IndexError:\n",
+ " pass\n",
+ " \n",
+ "def main(arg=[]):\n",
+ " a = list(range(10)\n",
+ " ii = 4 # Now this is limited to the scope of main()\n",
+ " imabuggyincrement(10, a)\n",
+ " \n",
+ "if __name__ == \"__main__\":\n",
+ " main()\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The following video shows how to debug mixed Python and C++ code using Visual Studio.\n",
+ "\n",
+ "You can go back to to the beginning of the video to learn how write a Python extension in Visual Studio."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import YouTubeVideo\n",
+ "\n",
+ "YouTubeVideo(\"D9RlT06a1EI\", start=300)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2019a",
+ "language": "python",
+ "name": "hpcpy19a"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/06_IDEs.ipynb b/solutions/06_IDEs.ipynb
new file mode 100644
index 0000000..4ed11a5
--- /dev/null
+++ b/solutions/06_IDEs.ipynb
@@ -0,0 +1,276 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Integrated Development Environments (IDEs) for Python\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "3 July 2019 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Jupyter notebooks are great for interactive development and data analysis with IPython. IPython's auto completion is one of the best, but if you develop complex codes that span multiple files, you might want to use other IDE's."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Editors with Python Features"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Editors such as vi, emacs, kate, sublime, etc. do already more than just show your code. They offer syntax highlighting and at least simple auto completion and may be extended. They can give you an overview over the files in your projects. They can show the function and let you jump to the right file to look at them. They may even show doc string. It's often hard to tell if it's an editor or an IDE anymore."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Features of IDEs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Syntax highlighting, auto completion with tool tips"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Tree view of files, methods, and variables"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Running and debugging"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Integrated version control"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Kdevelop\n",
+ "\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Visual Studio Code (OSS)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## eric"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## PyCharm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## There's more"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Eclipse w/ PyDev"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Spyder"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Wing IDE (commercial), Wing Personal at no cost."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "Visual Studio (Windows, commercial), Visual Studio Community Edition at no cost."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "For an overview see, e.g., [IntegratedDevelopmentEnvironments](https://wiki.python.org/moin/IntegratedDevelopmentEnvironments) on the Python Wiki."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2019a",
+ "language": "python",
+ "name": "hpcpy19a"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/07_LocalParallel.ipynb b/solutions/07_LocalParallel.ipynb
new file mode 100644
index 0000000..ff6caa3
--- /dev/null
+++ b/solutions/07_LocalParallel.ipynb
@@ -0,0 +1,1822 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Interactive Parallel Computing with IPython Parallel\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "17 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "*Computers have more than one core.* Wouldn't it be nice if we could use all the cores of our local machine or a compute node of a cluster from our [Jupyter][IP] notebook? \n",
+ "\n",
+ "Click on the ``+``-sign at the top of the Files tab on the left to start a new launcher. In the launcher click on Terminal. A terminal will open as a new tab. Grab the tab and pull it to the right to have the terminal next to your notebook.\n",
+ "\n",
+ "**Note**: The terminal does not have the same modules loaded as the notebook. To fix that type `source hpcpy20`.\n",
+ "\n",
+ "In the terminal type ``ipcluster``. You'll see the help message telling you that you need to give it subcommand. Take a look at the message and then enter \n",
+ "\n",
+ "``` bash\n",
+ "export OMP_NUM_THREADS=12\n",
+ "ipcluster start --n=4\n",
+ "```\n",
+ "\n",
+ "This will start a cluster with four engines and should limit the number of threads to 12 threads per engine to avoid oversubscription.\n",
+ "\n",
+ "> If you use the classical [Jupyter][IP] notebook, this is even easier if you have the cluster extension installed. (We don't have that one on our JupyterHub, yet). One of the tabs of your browser has the title \"Home\". If you switch to that tab, there are several tabs within the web page. One of them is called \"IPython Clusters\". Click on \"IPython Clusters\", increase the number of engines in the \"default\" profile to 4, and click on Start. The status changes from stopped to running. After you did that come back to this tab.\n",
+ "\n",
+ ">If the \"Clusters\" tab shows the message:\n",
+ "\n",
+ ">> Clusters tab is now provided by IPython parallel. See IPython parallel for installation details.\n",
+ " \n",
+ "> you need to quit your notebook server (make sure all your notebooks ar saved) and run the command \n",
+ "\n",
+ ">> ipcluster nbextension enable\n",
+ " \n",
+ ">Now, when you start `jupyter notebook` you should see a field that lets you set the number of engines in the \"IPython Clusters\" tab.\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "[IP]: http://www.jupyter.org"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Overview"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "IPyParallel has three parts: controller, engines, and client. The controller is the central hub. The client communicates only with the controller. The controller keeps track of the available engines and forwards requests from the client to the engines. It schedules the work and monitors its status. The results are communicated through the controller back to the client.\n",
+ "\n",
+ "All three components can run on different computers. A Jupyter notebook might run on your laptop and connect to an ipcontroller on a JUWELS login node, which in turn talks to engines running on a compute node."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The Client"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now let's see how we access the \"Cluster\". [IPython][IP] comes with a module [ipyparallel][IPp] that is used to access the engines, we just started. We first need to import Client.\n",
+ "\n",
+ "[IPp]: https://ipyparallel.readthedocs.io/en/latest/\n",
+ "[IP]: http://www.ipython.org"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rc = Client(profile=\"default\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can list the ids of the engines attached"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rc.ids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Views\n",
+ "\n",
+ "A *view* gives us access to a set of engines using a given scheduler. There are two types of views: a *direct view* and a *load-balanced* view."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As the name implies a *direct view* gives us direct control of the engines. We can push and pull data and apply functions using a couple of different methods. We are in control what runs where.\n",
+ "\n",
+ "A *load-balanced view* tries to balance the work between all the engines. We can submit tasks to it in the same way as before, but with a *load-balanced view*, the scheduler decides where a function is executed. It's also possible to define dependencies between tasks to build a dependency graph or even build this graph by hand. You'll learn a little more about dependencies in [Parallel, Task-Based Computing with Load Balancing on your Local Machine][LocalTaskParallel]\n",
+ "\n",
+ "Let's start with a *direct view* and learn about the methods used to execute code on the engines and move data around. \n",
+ "\n",
+ "We create a *direct view* of the engines by slicing the Client object:\n",
+ "\n",
+ "[LocalTaskParallel]: LocalTaskParallel.ipynb"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v01 = rc[0:2] # First two engines (0 and 1)\n",
+ "v23 = rc[2:4] # Engines 2 and 3\n",
+ "dview = rc[:] # All available engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Parallel Magic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Before we go into the details of the interface of a `DirectView`--that's the name of the class, let's look at IPython magic.\n",
+ "\n",
+ "IPython makes it very easy to use IPyParallel. It provides the magic commands ``%px`` and ``%%px`` to execute code in parallel. The target attribute is used to pick the engines, you want. By default, all the engines of the last Client object created are used. You can also specify if a command should be executed `blocking`--the default--or `non-blocking`.\n",
+ "\n",
+ "Note, the commands prefixed with ``%px`` are *not* executed locally. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px import numpy as np # import numpy on all engines as np\n",
+ "import numpy as np # do it locally, too."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since it's fairly common that you want to execute a cell remotely and locally, there's an option for that. Just add ``--local``.\n",
+ "\n",
+ "**Note**: This works only for ``%%px`` not ``%px``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --local \n",
+ "np.__version__ # print the numpy version of the engines. Note how the output is prefixed. It can be accessed that way, too. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ " The engines run ipython. Magic commands work, too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --local\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --local \n",
+ "import matplotlib.pyplot as plt\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The cell magic command ``%%px`` lets us execute more than one statement. The option ``--target`` lets us choose which engines we want to use. Here we are using engines 0 to 3."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --target 0:4\n",
+ "a = np.random.random([10,10])\n",
+ "plt.imshow(a, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Yes, the output can be graphical.\n",
+ "\n",
+ "Remember that the imports, we performed with ``%px`` are not available in our notebook. We can fix that by using"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "with rc[:].sync_imports():\n",
+ " import matplotlib.pyplot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Unfortunately mapping of namespaces does not work that way."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Using the Direct View"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As mentioned above a *direct view* lets you control each engine directly. You can also decide if a command should be blocking or not.\n",
+ "\n",
+ "We can, for example, create two random 100 by 100 element matrices on each engine, multiply them, and then display them. On each engine the code would look like this"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = np.random.random([100, 100])\n",
+ "b = np.random.random([100, 100])\n",
+ "c = a.dot(b)\n",
+ "plt.imshow(c, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As we learned before, we can use the ``%%px`` cell magic to execute this on all engines. Here we use the ``--target`` option to specify every second engine starting at 0. ``%px`` and ``%%px`` use the currently active view. By default that's the first view created. You can make a view active by calling ``view.activate(suffix)``. Use ``view.activate?`` to learn more about suffix."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --target 0::2\n",
+ "a = np.random.random([100, 100])\n",
+ "b = np.random.random([100, 100])\n",
+ "c = a.dot(b)\n",
+ "plt.imshow(c, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Magic commands are blocking by default, i.e., the next cell can only be executed after all the engines have finished their work. We can pass the option ``--noblock`` to change that behavior."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --noblock\n",
+ "a = np.random.random([2000, 2000])\n",
+ "b = np.random.random([2000, 2000])\n",
+ "c = a.dot(b)\n",
+ "c.sum() / 4.0e9"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We get an AsyncResult back. We can continue working in our notebook and pick up the result, when we are ready to do so."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%result"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Execute and Apply"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The foundation of executing code with a ``DirectView`` is ``apply``. It calls a function (the first argument) with args and kwargs. The values of the arguments are taken from the notebook and pushed to the engines."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c = dview.apply(np.dot, a, b) # This uses a and b from the notebook"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c.done()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c = c.result()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c[0].shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function can be a lambda function:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c = dview.apply(lambda a,b : a + b, a, b)\n",
+ "c.done()\n",
+ "c = c.result()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c[0].shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "It can also be ``exec``:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.apply(exec, 'c = a + b') # Note, this uses the variables defined on the engines."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview['c'][0].shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.execute('c=a+b')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview['c']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Remote functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "There are two decorators ``@parallel`` and ``@remote`` that can create functions that are executed on the engines.\n",
+ "\n",
+ "A function decorated with ``@parallel`` takes a sequence or an array as argument and distributes the work over the engines. Each engine still gets a sequence or array and should return one, too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import parallel, remote"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@dview.parallel(block=True)\n",
+ "def even(x):\n",
+ " \"\"\"Return only even elements of x\n",
+ " \n",
+ " Paramters\n",
+ " ---------\n",
+ " x : sequence or array\n",
+ " A list of values\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " res : like x\n",
+ " even elements of x\n",
+ " \"\"\"\n",
+ " return [e for e in x if not e % 2]\n",
+ "# return None if x % 2 else x\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "even(list(range(0,16)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "A `remote` function, on the other hand just runs on each engine with the full set of data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@dview.remote(block=True)\n",
+ "def scale(a):\n",
+ " for i in range(len(a)):\n",
+ " a[i] *= 2\n",
+ " \n",
+ " return a"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "scale(list(range(0, 16)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Moving data around"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "So far the runtime has taken care of moving data to and from the engines, but we can do this explicitely. There are 4 commands to do that:\n",
+ "\n",
+ "* push\n",
+ "* pull\n",
+ "* scatter\n",
+ "* gather"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Push takes a dictionary with the remote variable name as key:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "localA = list(range(10))\n",
+ "dview.push(dict(remoteA=localA))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can get a variable back with pull. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.pull('remoteA')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "There's also a shorthand notation, where we treat the view as a dictionary."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview['remoteA']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The methods ``push`` and ``pull`` push/pull the same data to/from all engines. They don't take a list and distribute it. That's what ``scatter`` and ``gather`` do. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.scatter('a',list(range(24)))\n",
+ "dview['a']"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.gather('a')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## List comprehension"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "With those methods at hand, we can build a parallel list comprehension."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.scatter('x',list(range(64)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px y = [i**10 for i in x]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "y = dview.gather('y')\n",
+ "y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exploring Latency and Bandwidth"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Latency (the time until something happens) and bandwith (the amount of data we get through the network) are two important properties of your parallel system that define what is practical and what is not. We will use the ``%timeit`` magic to measure these properties. ``%timit`` and its sibbling ``%%timeit`` measure the run time of a statement (cell in the case of ``%%timeit``) by executing the statement multiple times (by default at least 3 times). For short running routines many loops of 3 executions are performed and the minimum time measured is then displayed. The number of loops and the number of executions can be adjusted. Take a look at the documentation. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Lets first see how long it takes to send off a new task using ``execute`` and ``apply``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block = False"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px --noblock --local\n",
+ "a = np.random.random([2000, 2000])\n",
+ "b = np.random.random([2000, 2000])\n",
+ "c = a.dot(b)\n",
+ "c.sum() / 4.0e9"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's first execute nothing."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.execute('')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next we'll use a very minimal function. It just returns its argument. In this case the argument is empty."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.apply(lambda x : x, '')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Here, we'll tell every engine to perform a matrix-matrix multiplication (see [Matrix-Matrix Multiplication Using a DirectView](Matrix-Matrix-Multiplication-Using-a-DirectView) below for more about matrix multiplications)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 4 dview.execute('c = a.dot(b)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now, we'll make the execution blocking. This means, we are measuring the time the function needs to return a result instead of just the time needed to launch the task."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.execute('')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.apply(lambda x : x, '')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 4 rc[0].execute('c = a.dot(b)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit a.dot(b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=False"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can start about 500 parallel tasks per second and finish about a quarter as many. This gives an estimate of the granularity we need to use this model for efficient parallelization. Any task that takes less time than this will be dominated by the overhead."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "To get an idea about the bandwidth available let's push some arrays to the engines. We make this blocking."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dview.block=True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = np.random.random(256*1024)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit dview.push(dict(a=a))\n",
+ "%timeit dview.push(dict(a=a[:128*1024]))\n",
+ "%timeit dview.push(dict(a=a[:64*1024]))\n",
+ "%timeit dview.push(dict(a=a[:32*1024]))\n",
+ "%timeit dview.push(dict(a=a[:16*1024]))\n",
+ "%timeit dview.push(dict(a=a[:8*1024]))\n",
+ "%timeit dview.push(dict(a=a[:4*1024]))\n",
+ "%timeit dview.push(dict(a=a[:2*1024]))\n",
+ "%timeit dview.push(dict(a=a[:1024]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Calculate the bandwidth for the largest array and the smallest array."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "bwmax = len(rc) * 256 * 8 / 12.1e-3\n",
+ "bwmin = len(rc) * 8 / 9.05e-3\n",
+ "print(\"The bandwidth is between %.2f kB/s and %.2f kB/s.\" %( bwmin, bwmax))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Matrix-Matrix Multiplication Using a DirectView"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Matrix multiplication is one of the favorites in High Performance Computing (HPC). It's computationally intensive---if done right---, easily parallelized with little communication, and the basis of many real world applications.\n",
+ "\n",
+ "Let's say, we have two matrices A and B, where\n",
+ "\n",
+ "$$ A = \\left ( \\begin{array}{cccc}\n",
+ " 4 & 3 & 1 & 6 \\\\\n",
+ " 1 & 2 & 0 & 3 \\\\\n",
+ " 7 & 9 & 2 & 0 \\\\\n",
+ " 2 & 2 & -1 & 4 \\\\\n",
+ " \\end{array}\n",
+ " \\right ) $$\n",
+ "\n",
+ "and \n",
+ "\n",
+ "$$ B = \\left ( \\begin{array}{cc}\n",
+ " \\frac{1}{12} & \\frac{1}{2} \\\\\n",
+ " \\frac{1}{9} & \\frac{1}{4} \\\\\n",
+ " \\frac{1}{3} & 1 \\\\\n",
+ " \\frac{1}{7} & -\\frac{1}{3}\n",
+ " \\end{array}\n",
+ " \\right ). $$\n",
+ "\n",
+ "To calculate the element of $C = A B$ at row *i* and column *j*, we perform a dot (scalar) product of the ith row of A and the jth column of B:\n",
+ "\n",
+ "$$ C_{ij} = \\sum_k A_{i,k} B_{k, j} $$.\n",
+ "\n",
+ "For this to work, the number of columns in $A$ has to be equal to the number of rows in $B$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can generate two matrices of size n by n filled with random numbers using ``np.random.random``."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 16\n",
+ "A = np.random.random([n, n])\n",
+ "B = np.random.random([n, n])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "NumPy includes the dot product. For 2-dimensional arrays ``np.dot`` performs a matrix-matrix multiplication."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "C = np.dot(A, B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit np.dot(A, B)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "There are different ways to parallelize a matrix-matrix multiplication. Each element of the matrix can be calculated independently."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit \n",
+ "p = len(rc)\n",
+ "# Distribute the elements of the result viewmatrix round robin.\n",
+ "C1h = [[rc[(i * n + j) % p].apply(np.dot, A[i,:], B[:,j]) for j in range(n)] for i in range(n)]\n",
+ "# Wait until the calculation is done\n",
+ "dview.wait()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This, however, produces $n^2$ short tasks and the overhead (latency) is just overwhelming.\n",
+ "\n",
+ "We want to calculate\n",
+ "\n",
+ "$$ C = \\left ( \\begin{array}{cccc}\n",
+ " 4 & 3 & 1 & 6 \\\\\n",
+ " 1 & 2 & 0 & 3 \\\\\n",
+ " 7 & 9 & 2 & 0 \\\\\n",
+ " 2 & 2 & -1 & 4 \\\\\n",
+ " \\end{array}\n",
+ " \\right ) \n",
+ " \\left ( \\begin{array}{cc}\n",
+ " \\frac{1}{12} & \\frac{1}{2} \\\\\n",
+ " \\frac{1}{9} & \\frac{1}{4} \\\\\n",
+ " \\frac{1}{3} & 1 \\\\\n",
+ " \\frac{1}{7} & -\\frac{1}{3}\n",
+ " \\end{array}\n",
+ " \\right ). \n",
+ "$$\n",
+ "\n",
+ "We can split the matrices into tiles. In the above example, we might use a 2 by 2 tile.\n",
+ "\n",
+ "$$ C = \\left ( \\begin{array} {cc}\n",
+ " a_{00} & a_{01} \\\\\n",
+ " a_{10} & a_{11}\n",
+ " \\end{array} \\right )\n",
+ " \\left ( \\begin{array} {c}\n",
+ " b_{00} \\\\\n",
+ " b_{10}\n",
+ " \\end{array} \\right )\n",
+ " = \\left ( \\begin{array} {c}\n",
+ " a_{00} b_{00} + a_{01} b_{10} \\\\\n",
+ " a_{10} b_{00} + a_{11} b_{10}\n",
+ " \\end{array} \\right )\n",
+ " ,\n",
+ "$$\n",
+ "\n",
+ "where, for example, $a_{00}= \\left ( \\begin{array}{cc} 4 & 3 \\\\ 1 & 2 \\end{array} \\right )$. $a_{00}b_{00}$ is a matrix-matrix product and the addition of two matrices of the same shape is defined element by element."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In our example, we have two $n$ by $n$ matrices and we are going to split them in quadrants."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 4096\n",
+ "A = np.random.random([n, n])\n",
+ "B = np.random.random([n, n])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "tdot = %timeit -o np.dot(A,B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "type(n // 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nhalf = n // 2\n",
+ "a00 = A[:nhalf, :nhalf]\n",
+ "a01 = A[:nhalf, nhalf:]\n",
+ "a10 = A[nhalf:, :nhalf]\n",
+ "a11 = A[nhalf:, nhalf:]\n",
+ "b00 = B[:nhalf, :nhalf]\n",
+ "b01 = B[:nhalf, nhalf:]\n",
+ "b10 = B[nhalf:, :nhalf]\n",
+ "b11 = B[nhalf:, nhalf:]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The calculation of the partial results in Python looks very similar to the mathematical description above:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00 = np.dot(a00, b00) + np.dot(a01, b10)\n",
+ "c01 = np.dot(a00, b01) + np.dot(a01, b11)\n",
+ "c10 = np.dot(a10, b00) + np.dot(a11, b10)\n",
+ "c11 = np.dot(a10, b01) + np.dot(a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit -o\n",
+ "c00 = np.dot(a00, b00) + np.dot(a01, b10)\n",
+ "c01 = np.dot(a00, b01) + np.dot(a01, b11)\n",
+ "c10 = np.dot(a10, b00) + np.dot(a11, b10)\n",
+ "c11 = np.dot(a10, b01) + np.dot(a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "_.best / tdot.best"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Hm, this is slower than doing it directly...\n",
+ "\n",
+ "Next we create one view per engine."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "d0 = rc[0]\n",
+ "d1 = rc[1]\n",
+ "d2 = rc[2]\n",
+ "d3 = rc[3]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit d0.apply(lambda A, B : np.dot(A, B), A, B).wait()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00h = d0.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = d1.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = d2.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = d3.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "c00 = c00h.get()\n",
+ "c01 = c01h.get()\n",
+ "c10 = c10h.get()\n",
+ "c11 = c11h.get()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "c00h = d0.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = d1.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = d2.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = d3.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)\n",
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Nothing says, we have to stop at 4 tiles nor do we have to use square tiles. We could also recursively subdivide our tiles.\n",
+ "\n",
+ "The code is not any faster, because our implementation of numpy already blocks the matrices and uses all cores, but it shows the principle."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Slideshow",
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/08_LocalTaskParallel.ipynb b/solutions/08_LocalTaskParallel.ipynb
new file mode 100644
index 0000000..c98ba02
--- /dev/null
+++ b/solutions/08_LocalTaskParallel.ipynb
@@ -0,0 +1,358 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Parallel, Task-Based Computing with Load Balancing on your Local Machine"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our first session [Interactive Parallel Computing on the Local Machine][LocalParallel], we used a direct view to access our engines. This is great as long as we want to do the same task on all engines and don't have many more tasks than engines. If we have many tasks, however, and don't care where each task is executed, the DirectView is not the most convenient view available.\n",
+ "\n",
+ "[LocalParallel]: LocalParallel.ipynb"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rc = Client()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A *direct view* is created by slicing the client. A *load-balanced view* is created by calling rc's method `load_balanced_view()`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "lview = rc.load_balanced_view()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%px import numpy as np\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 4096\n",
+ "A = np.random.random([n, n])\n",
+ "B = np.random.random([n, n])\n",
+ "C = np.dot(A, B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "tnp = %timeit -o A@B"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "a00 = A[:n // 2, :n // 2]\n",
+ "a01 = A[:n // 2, n // 2:]\n",
+ "a10 = A[n // 2:, :n // 2]\n",
+ "a11 = A[n // 2:, n // 2:]\n",
+ "b00 = B[:n // 2, :n // 2]\n",
+ "b01 = B[:n // 2, n // 2:]\n",
+ "b10 = B[n // 2:, :n // 2]\n",
+ "b11 = B[n // 2:, n // 2:]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "c00h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "c00 = c00h.get()\n",
+ "c01 = c01h.get()\n",
+ "c10 = c10h.get()\n",
+ "c11 = c11h.get()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "c00h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b00, a01, b10)\n",
+ "c01h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a00, b01, a01, b11)\n",
+ "c10h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b00, a11, b10)\n",
+ "c11h = lview.apply(lambda a, b, c, d : np.dot(a, b) + np.dot(c, d), a10, b01, a11, b11)\n",
+ "c00h.wait()\n",
+ "c01h.wait()\n",
+ "c10h.wait()\n",
+ "c11h.wait()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compare this time with the one from the [Interactive Parallel Computing on the Local Machine][LocalParallel] where we used a *direct view*. Is it better? Worse? About the same?\n",
+ "\n",
+ "[LocalParallel]: LocalParallel.ipynb#Matrix-Matrix-Multiplication-Using-a-DirectView"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It's probably about the same, so why would we use the *load-balanced view*? For starters, we can throw more tasks at our engines than there are workers. In the previous example, we split our matrices in four blocks. Let's write a function that takes a square matrix with n rows and columns, where n is multiple of threshold, that uses tiles of size threshold."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def BlockMatrixMultiply(A, B, threshold = 256):\n",
+ " \"\"\"Calculates the matrix product of two square matrices of size :math:`n^2` by dividing\n",
+ " matrices into smaller blocks.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " A : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2 \n",
+ " B : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2\n",
+ " threshold: int\n",
+ " Size of blocks\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " output : ndarray\n",
+ " Returns the matrix product of A and B.\n",
+ " \"\"\"\n",
+ " \n",
+ " if threshold > A.shape[0]:\n",
+ " threshold = A.shape[0]\n",
+ " numberOfTiles = A.shape[0] // threshold\n",
+ " C = np.array([[np.sum([np.dot(A[i*threshold:(i+1)*threshold, k*threshold:(k+1)*threshold], \n",
+ " B[k*threshold:(k+1)*threshold, j*threshold:(j+1)*threshold]) \n",
+ " for k in range(numberOfTiles)], axis=0) # Add up all submatrices that belong to tile i,j\n",
+ " for j in range(numberOfTiles)] # Loop over columns of result matrix\n",
+ " for i in range(numberOfTiles)]) # Loop over rows of result matrix\n",
+ "\n",
+ " return C.swapaxes(1,2).reshape(A.shape)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "C1 = BlockMatrixMultiply(A, B, n // 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.allclose(C, C1) # Tests is the difference of all array elements is less than some threshold. Use np.allclose? to get details."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit C=np.dot(A,B)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit BlockMatrixMultiply(A, B, n // 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def BlockMatrixMultiplyLB(A, B, lview, threshold = 256):\n",
+ " \"\"\"Calculates the matrix product of two square matrices of size :math:`n^2` by dividing\n",
+ " matrices into smaller blocks.\n",
+ " \n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " A : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2\n",
+ " B : ndarray\n",
+ " A square matrix of size n**2 where n is a power of 2\n",
+ " threshold: int\n",
+ " Size of blocks\n",
+ " view:\n",
+ " An IPython parallel view\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " output : ndarray\n",
+ " Returns the matrix product of A and B.\n",
+ " \"\"\"\n",
+ " if threshold > A.shape[0]:\n",
+ " threshold = A.shape[0]\n",
+ " n = A.shape[0] // threshold\n",
+ " Ch = [ [lview.apply(lambda a, b, threshold, n, i, j : \n",
+ " np.sum([np.dot(a[:, k*threshold:(k+1)*threshold], \n",
+ " b[k*threshold:(k+1)*threshold,:]) \n",
+ " for k in range(n)], axis=0), # Add up all the matrices that belong to tile i,j\n",
+ " A[i*threshold:(i+1)*threshold,:], B[:,j*threshold:(j+1)*threshold], threshold, n, i, j) # Arguments to lambda\n",
+ " for j in range(n)] # Loop over columns of result matrix\n",
+ " for i in range(n)] # Loop over rows of result matrix\n",
+ "\n",
+ " #lview.wait() # Let's finish all the work that has been started in this view\n",
+ " \n",
+ " # Instead of waiting for the view, we can wait for all our asyncs to finish:\n",
+ " for r in Ch:\n",
+ " for c in r:\n",
+ " c.wait()\n",
+ " \n",
+ " return np.array([[c.get() for c in r] for r in Ch]).swapaxes(1,2).reshape(A.shape)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "C2 = BlockMatrixMultiplyLB(A, B, lview, n // 4) # Creates 16 tasks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.allclose(C, C2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n)\n",
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n // 2) # 4 tasks\n",
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n // 4) # 16 tasks\n",
+ "%timeit BlockMatrixMultiplyLB(A, B, lview, n // 8) # 64 tasks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "BlockMatrixMultiply?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/09_Numba vectorize.ipynb b/solutions/09_Numba vectorize.ipynb
new file mode 100644
index 0000000..131ce5f
--- /dev/null
+++ b/solutions/09_Numba vectorize.ipynb
@@ -0,0 +1,603 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Numba vectorize\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "17 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba offers a decorator `@vectorize` that allows us to generate **fast** [ufuncs](https://numpy.org/doc/stable/reference/ufuncs.html). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numba\n",
+ "import numpy\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A simple trig function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's implement a simple trig function:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import math"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def sinacosb(a, b):\n",
+ " \"\"\"Calculate the product of sin(a) and cos(b)\"\"\"\n",
+ " return math.sin(a) * math.cos(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Passing numpy arrays as arguments"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = 1000000\n",
+ "a = np.ones(n, dtype='int8')\n",
+ "b = 2 * a"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function sinasinb is only defined for scalars, so we have to do something if we want to pass an array."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## numpy.vectorize"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "NumPy provides the function `vectorize`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "npsinacosb = np.vectorize(sinacosb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit npsinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## numba.vectorize"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Dynamic ufuncs"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "usinacosb = numba.vectorize(sinacosb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit usinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function usinacosb is a *dynamic ufunc*. The arguments are determined when the function is called and only then is the function compiled."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Eager compilation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Assume, we know with what kind of arguments a function is called, then numba can generate code as soon as we call numba vectorize. The decorator can take a list of [type specification](https://numba.readthedocs.io/en/stable/reference/types.html#signatures) strings of the form \"f8(f8, f8)\", where the type before the parentheses is the return type and the types within the parentheses are the argument types."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@numba.vectorize(['f8(i8,i8)', 'f4(f4,f4)', 'f8(f8,f8)'], nopython=True)\n",
+ "def usinacosb(a,b):\n",
+ " return math.sin(a) * math.cos(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### target"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If I use eager compilation I can give an addition keyword argument: *target*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "target=\"cpu\": default, run in a single thread on the CPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "target=\"parallel\": run in multiple threads"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "target=\"cuda\": run on a CUDA-capable GPU"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "pusinacosb = numba.vectorize(['f8(i8,i8)', 'f4(f4,f4)', 'f8(f8,f8)', ], nopython=True, target=\"parallel\")(sinacosb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit pusinacosb(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 100_000_000\n",
+ "a = np.ones(n, dtype='int8')\n",
+ "b = 2 * a"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit usinacosb(a, b)\n",
+ "%timeit pusinacosb(a, b) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Exercise: The Mandelbrot set"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The Mandelbrot set is the set of points *c* in the complex plane for which"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$z_{i+1} = z_i^2 + c$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "does not diverge.\n",
+ "\n",
+ "The series diverges if $|z_i|>2$ for any *i*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since it is impracticable to calculate an infinite number of iterations, one usually sets an upper limit for the number of iterations, for example, 20."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Escape time algorithm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A simple implementation of this algorithm is the following:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " p: complex\n",
+ " point in the complex plane\n",
+ " maxtime: int\n",
+ " maximum number of iterations to perform before p is considered in \n",
+ " the Mandelbrot set.\n",
+ " \"\"\"\n",
+ " z = 0j\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Todo:\n",
+ "\n",
+ "1. Generate a grid of size n times m of complex numbers with the real part taken from the interval [-2.2, 1.5] and the imaginary part taken from the interval [-1.5, 1.5]. Hint, numpy.meshgrid can help.\n",
+ "\n",
+ "2. Vectorize escape_time using numba.vectorize and apply it to the array above. Note, the output is an integer.\n",
+ "\n",
+ "3. Visualize the generated array using matplotlib.pyplot.imshow. \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution 1. (c.f. Think Vector)\n",
+ "# Let's take the same ranges for real and imaginary numbers as before\n",
+ "re = numpy.linspace(-2.2, 1, 640)\n",
+ "im = numpy.linspace(-1.2j, 1.2j, 480)\n",
+ "# X and Y will have a shape of (640, 480) with the values taken from re and im.\n",
+ "X, Y = numpy.meshgrid(re, im)\n",
+ "# Finally, add X and Y to get our grid\n",
+ "P = X + Y"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution 2.\n",
+ "escape_time_vec = numba.vectorize(escape_time) \n",
+ "M = escape_time_vec(P, 50)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(M)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%timeit M = escape_time_vec(P, 50)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/10_NumbaIntro.ipynb b/solutions/10_NumbaIntro.ipynb
new file mode 100644
index 0000000..e35b799
--- /dev/null
+++ b/solutions/10_NumbaIntro.ipynb
@@ -0,0 +1,1480 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to Numba's jit compiler\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "17 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba provides a just-in-time (jit) compiler, a decorator `vectorize` that we can use to define `ufunc`s that are fast and flexible, and an interface to CUDA- and ROCm-capable GPUs that allows us to write CUDA kernels in Python! In this notebook, we'll focus on the jit compiler."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Python is an interpreted language"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The Python interpreter parses and executes code when it encounters it. This makes it very flexible but it also precludes many optimizations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "from numba import jit\n",
+ "from matplotlib import pyplot as plt "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## A simple example\n",
+ "Let's start with a simple sum. In Python we may define the sum like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def python_sum(a, start=0):\n",
+ " res = start\n",
+ " for x in a:\n",
+ " res += x\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "When we call `python_sum`, the interpreter goes through it line by line. For each item it has to interpret `res += x` and execute it, i.e., call apropriate C routines that have been compiled for the processor. The only requirements for `a` in this function ar that it is iterable and its elements support the `+` operator. For the following little benchmark, we'll use an `ndarray` of random numbers."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rng = numpy.random.Generator(numpy.random.MT19937())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = rng.uniform(size=10000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_python_sum = %timeit -o python_sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Please calculate the floating point operations per second for `python_sum`. Btw., remember the peak performance of a single core on JUWELS is about 40 GFLOP/s."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "print(f\"python_sum achieves {1e-6 * a.shape[0] / t_python_sum.best:.3f} MFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Compiled languages"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "In compiled languages such as C, C++, Fortran, and Rust a compiler would translate the code once \n",
+ "and store the results in machine code for a particular processor, but it doesn't translate it \n",
+ "literally, but can look for optimization and map the work optimally to the capabilities of the \n",
+ "processor. That's what makes this much faster but also less flexible. In C++ the sum may be written \n",
+ "like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```cpp\n",
+ "#include <vector>\n",
+ "template <class T>\n",
+ "auto cpp_sum(std::vector<T>& a, T start){\n",
+ " auto res = start;\n",
+ " for (auto x : a){\n",
+ " res += x;\n",
+ " }\n",
+ " return res;\n",
+ "}\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "With C++20 you could get even closer to the functionality of `python_sum`, but this will do for now.\n",
+ "\n",
+ "A part of the assembler code generated for the loop might look something like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```nasm\n",
+ "..B1.14: # Preds ..B1.14 ..B1.13\n",
+ " vaddpd ymm3, ymm3, YMMWORD PTR [rdi+rcx*8] #7.9\n",
+ " vaddpd ymm2, ymm2, YMMWORD PTR [32+rdi+rcx*8] #7.9\n",
+ " vaddpd ymm1, ymm1, YMMWORD PTR [64+rdi+rcx*8] #7.9\n",
+ " vaddpd ymm0, ymm0, YMMWORD PTR [96+rdi+rcx*8] #7.9\n",
+ " add rcx, 16 #6.19\n",
+ " cmp rcx, rax #6.19\n",
+ " jb ..B1.14 # Prob 82% #6.19\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Yes, there are good reasons to love Python (and other higher programming languages).\n",
+ "\n",
+ "Let's run the code:\n",
+ "```\n",
+ "$ ./simple_sum\n",
+ "Sum: 5033.24 in 0.717281 µs. 13941.5 MFLOP. \n",
+ "```\n",
+ "\n",
+ "The function takes about 0.7 µs. This is about 2000 times faster than the interpreted Python loop. \n",
+ "Wouldn't it be great if we could take the Python code in `python_sum` and compile it to machine \n",
+ "code to get some of this speedup?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Compiling a program to machine code involves at least to phases. In the first phase the human readable \n",
+ "program is translated into something that is more palable to a computer such as an \n",
+ "[abstract syntax tree][AST] or [AST][]. Many compilers then perform a first analysis and pattern \n",
+ "matching on the [AST][] before machine specific optimization are applied.\n",
+ "\n",
+ "A popular open source framework for these steps is [LLVM][]. LLVM provides both the language parser, e.g., \n",
+ "clang for C and clang++ for C++ and a toolchain for the language independent optimization steps. The \n",
+ "language parser generates a well defined intermediate representation that can than be optimized. \n",
+ "\n",
+ "[Numba][] uses this infrastructure to optimize a subset of Python to machine code during program \n",
+ "execution. These kind of live compiler are called just-in-time (JIT) compiler. \n",
+ "\n",
+ "[AST]: https://en.wikipedia.org/wiki/Abstract_syntax_tree\n",
+ "[LLVM]: http://llvm.org/\n",
+ "[Numba]: https://numba.pydata.org/"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Python_sum compiled"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's see how well [Numba][] does with the sum. We imported `numba.jit` at the top of the notebook.\n",
+ "The function `jit` returns a `callable`---which makes it usable as a `decorator` as well---that we can \n",
+ "assign to a variable. The variable can then be used just like a regular function:\n",
+ "\n",
+ "[AST]: https://en.wikipedia.org/wiki/Abstract_syntax_tree\n",
+ "[LLVM]: http://llvm.org/\n",
+ "[Numba]: https://numba.pydata.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "numba_sum = jit(python_sum)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 1 numba_sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The first time a \"jitted\" function is called with a specific argument type, numba compiles the code, which takes fairly long. Future calls are much faster:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_jit_sum = %timeit -o numba_sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This is quite an impressive speed up although not quite as fast as the compiled C++ code. Please, \n",
+ "calculate the performance again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "print(f\"Jitted python_sum achieves {1e-6 * a.shape[0] / t_jit_sum.best:.3f} MFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's compare the performance with numpy's `sum`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy_sum = %timeit -o numpy.sum(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "It's a little faster."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"Numpy's sum achieves {1e-6 * a.shape[0] / t_numpy_sum.best:.3f} MFLOP/s\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## A more complex example and nopython\n",
+ "Numba likes simple expressions with simple loops:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def mm(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = rng.uniform(size=(100, 100))\n",
+ "b = rng.uniform(size=(100, 100))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_python_mm = %timeit -o mm(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy_mm = %timeit -o a.dot(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "OK, the Python loop is about 30000 times slower than numpy's `dot` method. Let's see if we can't make this faster using numba. This time, we'll use `jit` as a decorator."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit\n",
+ "def numba_mm(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -n 1 -r 1 numba_mm(a,b) # Warmup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm = %timeit -o numba_mm(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "a = rng.uniform(size=(1000, 1000))\n",
+ "b = rng.uniform(size=(1000, 1000))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm_1000 = %timeit -o numba_mm(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numpy_mm_1000 = %timeit -o a.dot(b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(\"The version of numpy, we used has been compiled against Intel's math kernel library (MKL) and is therefore about %.0f times faster.\" \n",
+ " \"If we used a version that has not been compiled against a fast BLAS library, it would take about the same time as the numba routine.\" \n",
+ " % (t_numba_mm_1000.best / t_numpy_mm_1000.best))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise: prange\n",
+ "Numba can parallelize loops with ``prange``. Import ``prange`` from numba and change the range in row into a prange. You also need to add the arguments ``nopython=True`` and ``parallel=True`` to the jit decorator.\n",
+ "\n",
+ "Rerun and compare.\n",
+ "\n",
+ "**Extra credit:** Look at the changes we did to the matrix-matrix multiplication in the Bottlenecks notebook. Can you include them, too. Does it help? You might want to compare the results of your own calculation with that of numpy. The function ``numpy.allclose`` is useful for that."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution for the first part\n",
+ "from numba import prange\n",
+ "\n",
+ "@jit(nopython=True, parallel=True)\n",
+ "def numba_mm_par(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in prange(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm_par_1000 = %timeit -o numba_mm_par(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution for the extra credit:\n",
+ "@jit(nopython=True, parallel=True)\n",
+ "def numba_mm_kj_par(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in prange(a.shape[0]):\n",
+ " for k in range(a.shape[1]):\n",
+ " for col in range(b.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm_kj_par_1000 = %timeit -o numba_mm_par(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Some other variations\n",
+ "\n",
+ "Let's try some other variations and how they do."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit\n",
+ "def numba_mm2(a,b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " res[row, col] = a[row].dot(b[:,col])\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -r 1 -n 1 numba_mm2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm2_1000 = %timeit -o numba_mm2(a,b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Most of the computation should now be done with numpy, but it's much harder to optimize a dot product than the matrix multiplication. Think back to our discussion about bottlenecks. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit(nopython=True)\n",
+ "def numba_mm3(a, b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " res[row, col] = a[row]@b[:,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit -r 1 -n 1 numba_mm3(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@jit(nopython = True)\n",
+ "def numba_mm4(a, b):\n",
+ " res = numpy.zeros((a.shape[0], b.shape[1]))\n",
+ " for row in range(a.shape[0]):\n",
+ " for col in range(b.shape[1]):\n",
+ " for k in range(a.shape[1]):\n",
+ " res[row, col] += a[row, k] * b[k,col]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_mm4(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_numba_mm4_1000 = %timeit -o numba_mm4(a, b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "20min"
+ ]
+ },
+ "source": [
+ "## Exercise: Mandelbrot with Numba\n",
+ "Now, it's your turn again. Use Numba's jit operator to write a program to calculate the Mandelbrot set."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "def mandelbrot(re_min:float, im_min:float, re_max:float, im_max:float, \n",
+ " width:int, height:int, iter_max:int=50):\n",
+ " \"\"\"Calculate the number of iterations needed to determine for each point *c* in the complex \n",
+ " plain, if the following series diverges.\n",
+ " \n",
+ " .. math::\n",
+ " \n",
+ " z_{i+1} = z_{i}^2 + c\n",
+ " \n",
+ " The series diverges if for any *i* :math:`|z_i| > 2`.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " re_min, im_min: float\n",
+ " lower left corner in the complex plain that is covered\n",
+ " re_max, im_max: float\n",
+ " upper right corner in the complex plain that is coverd\n",
+ " width: int\n",
+ " number of grid points along the real axis\n",
+ " height: int\n",
+ " number of grid points along the imaginary axis\n",
+ " iter_max: int\n",
+ " maximum number of iterations to try\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " res: 2d array of int\n",
+ " 2d array of size (width, height) with the value of *i* that indicates divergence\n",
+ " \"\"\"\n",
+ " dx = (re_max - re_min) / (width - 1)\n",
+ " dy = (im_max - im_min) / (height - 1)\n",
+ " res = numpy.ones((height, width), dtype=int) * iter_max\n",
+ " for j in range(height):\n",
+ " for i in range(width):\n",
+ " z = 0\n",
+ " c = re_min + dx * i + (im_min + dy * j) * 1j\n",
+ " for k in range(iter_max):\n",
+ " z = z * z + c\n",
+ " if abs(z) > 2:\n",
+ " res[j, i] = k\n",
+ " break\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "res = mandelbrot(-2.2, -1.2, 1, 1.2, 640, 480, 50)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(res)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%timeit res = mandelbrot(-2.2, -1.2, 1, 1.2, 640, 480, 50)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Type inference"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As mentioned above, [Numba][]'s jit operator doesn't directly return a compiled function, because \n",
+ "it needs to figure out the type of every variable once a function has been called with specific \n",
+ "arguments. It only compiles a function once for each type of arguments used to call it. The function\n",
+ "signature is then stored in its `signatures` property.\n",
+ "\n",
+ "[Numba]: https://numba.pydata.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.signatures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise: Call numba_sum with an ndarray of type float32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "a_s = rng.uniform(size=10000).astype('f4')\n",
+ "numba_sum(a_s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now there is a second function signature:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.signatures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Numba allows us to look at its type inferrence using "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.inspect_types(signature=numba_sum.signatures[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, this is interesting. If you look at Line 3 of the version called with float32, it still defines\n",
+ "`res` as a double precision number! This will prevent it from vectorizing the loop using single \n",
+ "precision arguments, which potentially cuts performance in half!\n",
+ "\n",
+ "Now, let's see if we can do better."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum(a_s, numpy.float32(0.0))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.signatures"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numba_sum.inspect_types(signature=numba_sum.signatures[2]) # Try adding pretty=True "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now, res is of type `float32`. Let's see if this speeds up things."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit numba_sum(a_s, numpy.float32(0.0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Doesn't look like it. \n",
+ "\n",
+ "Let's dig a little deeper. A speedup would come from the fact that the Skylake-X processor used for \n",
+ "JUWELS Cluster can operate on 16 single precision numbers at once compared to 8 double precision \n",
+ "numbers, but that assumes it's using the right instructions. For that we have to look at the assembler.\n",
+ "\n",
+ "We define a helper function to find instructions in the assembler code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# This function has been borrowed from https://github.com/numba/numba-examples/blob/master/notebooks/simd.ipynb\n",
+ "def find_instr(func, keyword, sig=0, limit=5):\n",
+ " count = 0\n",
+ " for l in func.inspect_asm(func.signatures[sig]).split('\\n'):\n",
+ " if keyword in l:\n",
+ " count += 1\n",
+ " print(l)\n",
+ " if count >= limit:\n",
+ " break\n",
+ " if count == 0:\n",
+ " print('No instructions found')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "find_instr(numba_sum, \"add\", 2, limit=10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The instruction `vaddss` performs an addition of two single precision numbers. It's not vectorized \n",
+ "and uses the smallest register available. For some reason the compilation wasn't done using the best\n",
+ "available instruction set.\n",
+ "\n",
+ "The reason in this case is that we are doing a *reduction*. We are adding up all the values in `a`.\n",
+ "When the compiler vectorizes this, the order of the addition may change. While this is not a problem\n",
+ "if we work with real number, it is a problem for the finite precision math that computers do. The \n",
+ "order of the addition may change the result.\n",
+ "\n",
+ "To allow reordering of operations, we add the option `fastmath=True`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "fast_numba_sum = jit(python_sum, fastmath=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit fast_numba_sum(a_s, numpy.float32(0.0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Now let's look at the assembler again:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "find_instr(fast_numba_sum, \"vaddp\", sig=0, limit=10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This is much better. The `ps` at the end of `vaddps` stands for *packed single precision* indicating \n",
+ "a SIMD instruction. The `ymm` registers used are 256 bits wide, which corresponds to 8 single precision\n",
+ "numbers at a time.\n",
+ "\n",
+ "Skylake-X also has `zmm` registers with a width of 512 bit or 16 single precision numbers, but when\n",
+ "they are used the maximum frequency of the processor is reduced. It can happen that the performance \n",
+ "using `ymm` registers at higher frequency is actually better."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise: Call fast_numba_sum with double precision\n",
+ "\n",
+ "Call `fast_numba_sum` with arguments of type float64 and measure the run time. Compare the result\n",
+ "with the one obtained from `numba_sum`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "#Solution\n",
+ "a = rng.uniform(size=10000).astype('f8')\n",
+ "%timeit fast_numba_sum(a, numpy.float64(0.0))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "find_instr(fast_numba_sum, \"vaddp\", sig=-1, limit=10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"The difference is {fast_numba_sum(a, numpy.float64(0.0)) - numba_sum(a, numpy.float64(0.0))}\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/11_Speeding up your code with Cython.ipynb b/solutions/11_Speeding up your code with Cython.ipynb
new file mode 100644
index 0000000..b951d90
--- /dev/null
+++ b/solutions/11_Speeding up your code with Cython.ipynb
@@ -0,0 +1,1373 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Speeding up your code with Cython"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "<div class=\"dateauthor\">\n",
+ "18 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Cython"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "> “Cython is a language that makes writing C extensions for the Python language as easy as Python itself”"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Cython allows you to write C extensions to Python in a very pythonic manner. In this notebook we'll explore the syntax of Cython and see what kind of speed up we can achieve.\n",
+ "\n",
+ "Cython provides an extension for Jupyter notebooks that makes working with Cython very convenient. If you enter `%load_ext Cython` the `%%cython` magic becomes available."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let us start with something simple. The following function calculates the dot product between two vectors:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def pydot(v, w):\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v = numpy.arange(0, 10000, dtype=int)\n",
+ "w = numpy.arange(0, 10000, dtype=int)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit a = range(10000); b = range(10000)\n",
+ "pydot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "pydot_timing = %timeit -o pydot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Elementwise access to NumPy arrays can in the meantime be just as fast as access for lists.\n",
+ "\n",
+ "Now let us invoke Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "def dot(v, w):\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit a = range(10000); b = range(10000)\n",
+ "dot(a, b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot1_timing = %timeit -o dot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can check what Cython does by invoking the cell magic with the option `-a`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "def dot(v, w):\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This produces an annotated listing. The darker the yellow, the more Python code is in that line. You can click on each line to see the C code that was generated for it. Go ahead and explore.\n",
+ "\n",
+ "There are many references to Python objects and functions. Basically, you only save the overhead of interpreting. Let's see if we can do a little better."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Declaring types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The arguments `v` and `w` are very general. If we know, however, that we are only going to pass ndarrays of integers, we can be more specific:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy\n",
+ "cimport numpy\n",
+ "\n",
+ "def dot(numpy.ndarray[numpy.int_t, ndim = 1] v, numpy.ndarray[numpy.int_t, ndim = 1] w):\n",
+ " cdef long res = 0\n",
+ " if len(v) == len(w) and len(v) > 0:\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "I also added ``cdef long res = 0``. This declares a C variable. C variables are not visible to a Python program. Here this doesn't matter since res is only used within the function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot2_timing = %timeit -o dot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note that ``cdef long res = 0`` is white. It's translated directly into C. `len(v)` is a Python call. It can be pulled out and assigned to an integer variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "\n",
+ "def dot(np.ndarray[np.int_t, ndim = 1] v, np.ndarray[np.int_t, ndim = 1] w):\n",
+ " cdef long res = 0\n",
+ " cdef int n = 0\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " for i in range(0, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot3_timing = %timeit -o dot(v, w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you look at line 10, you'll notice that there are some bounds checks, but they are unnecessary since we check the bounds beforehand already. Let's do away with them."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Skipping checks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot4_timing = %timeit -o dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can dispense of wraparound a[-1]->a[len(a)-1], too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False)\n",
+ "@cython.wraparound(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = v[0] * w[0]\n",
+ " for i in range(1, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot5_timing = %timeit -o dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Adding compiler option\n",
+ "### Cython magic"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython --compile-args=-O2 --compile-args=-march=native --force\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False)\n",
+ "@cython.wraparound(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = 0\n",
+ " for i in range(0, n):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Sometimes we need (or want) to pass some options to the compiler. The cython magic can take compile-args and link-args that are passed to the underlying compiler. Later, we'll show you how to integrate all of this in a setup.py script to compile your extension outside of a notebook.\n",
+ "\n",
+ "The [documentation shows you, which options can be passed to the magic command](https://cython.readthedocs.io/en/latest/src/userguide/source_files_and_compilation.html#compiling-with-a-jupyter-notebook)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot5a_timing = %timeit -o -r 13 dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Adding OpenMP"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since Cython generates compiled Python extensions, we can release the GIL and run things in parallel if we don't make calls to the Python API.\n",
+ "\n",
+ "As we've seen our inner loop is free of any Python calls (the annotated code is white). Since OpenMP supports reductions, we can parallelize the loop using Cython's ``prange``. Within ``prange`` we have to explicitely release the GIL by setting ``nogil=True``. We also need to pass the compiler and linker flags for OpenMP."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython --compile-args=-fopenmp --compile-args=-O2 --compile-args=-march=native --link-args=-fopenmp --force\n",
+ "import numpy as np\n",
+ "cimport numpy as np\n",
+ "cimport cython\n",
+ "from cython.parallel import parallel, prange\n",
+ "\n",
+ "@cython.boundscheck(False)\n",
+ "@cython.wraparound(False)\n",
+ "def dot(np.ndarray[np.int64_t, ndim = 1] v, np.ndarray[np.int64_t, ndim = 1] w):\n",
+ " cdef long res\n",
+ " cdef int i\n",
+ " cdef int n\n",
+ " n = len(v)\n",
+ " if n > 0 and n == len(w):\n",
+ " res = v[0] * w[0]\n",
+ " for i in prange(1, n, nogil=True):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "dot6_timing = %timeit -o dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Our data set is too small to benefit from parallelization. The overhead due to starting multiple threads is too large for this problem size."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Function declaration with def, cdef, and cpdef"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In short, functions defined using **def** are visible from Python and treated like Python functions even within Cython. Functions defined with **cdef** are C functions and are not visible from Python at all. Functions declared with **cpdef** are C functions that can be called efficiently from within Cython but also have a Python wrapper so they can be accessed from Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "#### Exercise\n",
+ "* Define a function `add` in Cython using `cdef` that takes two float values as arguments and returns the sum. \n",
+ "* Try calling it from outside Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Write your function here"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "# Solution\n",
+ "cdef add(float a, float b):\n",
+ " return a + b"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "add(1.1415, 2.0) # -> NameError: name 'add' is not defined"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "\n",
+ "Now use cpdef instead."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Copy the function from above and use cpdef instead of cdef"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "# Solution\n",
+ "cpdef add(float a, float b):\n",
+ " return a + b"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "add(1.1415, 2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Building a Cython extension outside of a notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "So far we have used IPython and the Cython magic to build and test our extension within a notebook. Once we are satisfied and want to put our extension in production, we want to be able to build the extension without IPython. The recommended way to do that is to use `distutils` and a `setup.py` file."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### A simple setup.py file"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```python\n",
+ "from distutils.core import setup\n",
+ "from Cython.Build import cythonize\n",
+ "setup(name=\"Sum of integers\",\n",
+ " ext_modules=cythonize(\"sum.pyx\"),\n",
+ " zip_safe=False\n",
+ " )\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Adding compiler options "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "To add compiler options, for example, to compile with OpenMP, we need to set up an Extension first. Then, we use the Extension instead of the file name in the setup function. Our new setup.py file now looks like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```python\n",
+ "from distutils.core import setup\n",
+ "from distutils.extension import Extension\n",
+ "from Cython.Build import cythonize\n",
+ "\n",
+ "ext_modules = [\n",
+ " Extension(\"sum\",\n",
+ " [\"sum.pyx\"],\n",
+ " extra_compile_args = [\"-fopenmp\"],\n",
+ " extra_link_args = [\"-fopenmp\"]\n",
+ " )\n",
+ "]\n",
+ "setup(name=\"Sum of integers\",\n",
+ " ext_modules=cythonize(ext_modules),\n",
+ " zip_safe=False\n",
+ " )\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercise:** Take the Cython code that defines dot using `prange` in [Adding OpenMP](#Adding-OpenMP) and write it to `dot.pyx` using the `%%writefile` magic. Make sure to comment out the `cython magic`. Take the above code for setup.py and copy it into a file called `setup.py`. Change the setup.py code to build a module named dot and use `dot.pyx`. Then build the extension in a terminal window with the command. **Note:** Make sure our environment is loaded `source hpcpy20`.\n",
+ "\n",
+ "```bash\n",
+ "python setup.py build_ext --inplace\n",
+ "```\n",
+ "\n",
+ "If the build fails with `#include \"numpy/arrayobject.h\" not found`, you need to add the include path for numpy. Luckily, numpy has a function for that: `numpy.get_include()`. Add the include path to the extra_compile_args. Include paths are added using `-I/path/to/be/included`. Since `setup.py` is a Python script you can call `numpy.get_include()` in the script and don't have to hardcode the path.\n",
+ "\n",
+ "Write a test program that loads and tests the extension. Add a doc string to the dot function and include an example section like this:\n",
+ "\n",
+ "```python\n",
+ "def dot(...):\n",
+ "\"\"\" Add description and parameters ...\n",
+ "\n",
+ "Examples\n",
+ "--------\n",
+ ">>> import numpy\n",
+ ">>> from dot import dot\n",
+ ">>> v = numpy.arange(0, 10, dtype=int)\n",
+ ">>> w = numpy.arange(0, 10, dtype=int)\n",
+ ">>> print(dot(v, w))\n",
+ "285\n",
+ "\n",
+ "\"\"\"\n",
+ "```\n",
+ "\n",
+ "Rebuild the extension and run [doctest](https://docs.python.org/3.6/library/doctest.html) (`python -m doctest -v dot.pyx`). Without `-v` only failed tests are reported."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Comparison with Numba"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Numba, can generate fast functions, too."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import int64, jit\n",
+ "@jit(nopython=True)\n",
+ "def udot(v, w):\n",
+ " res = 0\n",
+ " for i in range(0, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import int64, jit\n",
+ "@jit(nopython=False)\n",
+ "def udotg(v, w):\n",
+ " res = 0\n",
+ " for i in range(0, len(v)):\n",
+ " res += v[i] * w[i]\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numbadot_timing = %timeit -o udot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "numbadotg_timing = %timeit -o udotg(v,w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit a = range(10000); b = range(10000)\n",
+ "udotg(a,b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "npdot_timing = %timeit -o np.dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "tunits = {'ns':10**-9, 'us':10**-6, 'ms':10**-3, 's':1.0}\n",
+ "timers = [pydot_timing, dot1_timing, dot2_timing, dot3_timing, dot4_timing, dot5_timing, \n",
+ " dot6_timing, numbadot_timing, numbadotg_timing, npdot_timing]\n",
+ "times = np.array([t.best for t in timers])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(12,6))\n",
+ "plt.subplot(1,2,1)\n",
+ "plt.bar(np.arange(len(times)) + 1, times * 1e6)\n",
+ "plt.ylabel(u\"µs\")\n",
+ "plt.xticks([1, 2, 3, 4, 5, 6, 7, 8, 9, 10],[\"Python\", \"Cython\", \"types1\", \"types2\", \"bounds\", \"wraparound\", \"parallel\", \n",
+ " \"Numba\", \"NumbaG\", \"np.dot\"], rotation=45)\n",
+ "plt.subplot(1,2,2)\n",
+ "plt.bar(np.arange(2, len(times[2:]) + 2) + 1, times[2:] * 1e6)\n",
+ "plt.ylabel(u\"µs\")\n",
+ "plt.xticks([3, 4, 5, 6, 7, 8, 9, 10],[\"types1\", \"types2\", \"bounds\", \"wraparound\", \"parallel\", \n",
+ " \"Numba\", \"NumbaG\", \"np.dot\"], rotation=45)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Finally, let's compare the performance for a larger data set. Remember the last version of our dot function uses OpenMP."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "v = np.arange(10000000, dtype=int)\n",
+ "w = np.arange(10000000, dtype=int)\n",
+ "%timeit -n 1 pydot(v,w)\n",
+ "%timeit dot(v,w)\n",
+ "%timeit udot(v,w)\n",
+ "%timeit np.dot(v,w)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Cython and classes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Sometimes, we want to do more than just wrap a function. We might want an efficient data type that implements some operators, for example. For this Cython allows us to declare classes just like in Python:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "class Point:\n",
+ " \"\"\"A simple class representing a point in the x-y plane.\"\"\"\n",
+ " def __init__(self, x, y):\n",
+ " self.x = x\n",
+ " self.y = y\n",
+ " def __repr__(self):\n",
+ " return \"(%.1f, %.1f)\" % (self.x, self.y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "p = Point(0,1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Extension types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "There is a second type of classes called *[extension types](http://cython.readthedocs.io/en/latest/src/userguide/extension_types.html)*. An extension type stores its members and methods in a C struct instead of a Python dictionary. This makes them more efficient but also more restrictive. Let's look at an example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython\n",
+ "from math import sqrt,asin,pi\n",
+ "\n",
+ "cpdef double rad2deg(double alpha):\n",
+ " return 180 * alpha / pi\n",
+ "\n",
+ "cdef class Point:\n",
+ " \"\"\"A point in 2d.\"\"\"\n",
+ " cdef double x, y\n",
+ "\n",
+ " cdef double distance2origin(Point self):\n",
+ " return sqrt(self.x * self.x + self.y * self.y)\n",
+ " \n",
+ " cdef alpha(Point self):\n",
+ " return asin(self.y / self.distance2origin())\n",
+ " \n",
+ " def __cinit__(self, t_x, t_y):\n",
+ " self.x = t_x\n",
+ " self.y = t_y\n",
+ " \n",
+ " def __repr__(self):\n",
+ " return \"(r=%.2f, alpha=%.2f°)\" % (self.distance2origin(), rad2deg(self.alpha()))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The first thing to note is the definition using `cdef class`. It's the reason extension types are also referred to as cdef classes. We can define functions that are only visible to C using `cdef` and Python functions using `def` (or both at once with `cpdef`). For functions defined with `cdef`, we need to give the type of self as well as a return type.\n",
+ "\n",
+ "We can use the new class as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "p = Point(0.5, 1)\n",
+ "print(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Try which methods of Point you can call."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "# No regular member functions can be called, but __cinit__ and __repr__ are used under the hood \n",
+ "# when initializing and printing a point."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Cython Tutorial at SciPy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The following video is from a half-day tutorial on Cython."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import YouTubeVideo\n",
+ "YouTubeVideo(\"gMvkiQ-gOW8\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/12_Writing your own Python bindings.ipynb b/solutions/12_Writing your own Python bindings.ipynb
new file mode 100644
index 0000000..7c51169
--- /dev/null
+++ b/solutions/12_Writing your own Python bindings.ipynb
@@ -0,0 +1,1549 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Writing language bindings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div class=\"dateauthor\">\n",
+ "18 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Why bindings?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* Use existing optimized code as a library\n",
+ "* Avoid overhead of calling a binary via `popen` and communication via pipes\n",
+ "* Cleaner code"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Python is often used as a \"glue language\" that combines calls to compiled programs and libraries to get the job done. Many libraries provide Python bindings that allows you to call them from Python. Numpy, for example, can call vendor-optimized routines to perform linear algebra operation near peak machine performance, but others don't.\n",
+ "\n",
+ "Python also allows you to call other programs from within Python and pipe the in- and output. This often requires conversion of data, for example, into text and back, which can result in a lot of overhead.\n",
+ "\n",
+ "These are just two cases, when you might want to write your own Python bindings."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "There are wrapper programs such as [swig](http://www.swig.org/), [sip](https://www.riverbankcomputing.com/software/sip/intro), or [binder](http://cppbinder.readthedocs.io/en/latest/) that can help you generate bindings, but you will frequently need to tune the generated wrappers.\n",
+ "\n",
+ "In this notebook we'll use [cffi](https://cffi.readthedocs.io/en/latest/) to wrap a single function with simple data types. We use [Cython][] to wrap more complex C/C++ functions and even C++ classes and compare this with [PyBind11](https://pybind11.readthedocs.io/en/latest/). Finally we use [f2py](https://docs.scipy.org/doc/numpy/f2py/) to generate bindings for a Fortran code and compare it to wrapping the same Fortran code with [Cython][].\n",
+ "\n",
+ "[Cython]: http://cython.org"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Preparations\n",
+ "\n",
+ "Before we can look at the bindings, we need to build our libraries. Open a terminal, switch to the tutorial directory and run\n",
+ "\n",
+ "```bash\n",
+ "./build.sh\n",
+ "```\n",
+ "\n",
+ "Wait until the build has finished and then continue with this notebook.\n",
+ "\n",
+ "**Tip:** You can open a terminal from within JupyterLab by going to File->New->Terminal. To get the right environment in a terminal `source hpcpy20` in the tutorial directory."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Ctypes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "While ``ctypes`` is a Python standard module it is not very convenient and I'm not going to talk about it. You can look at the [documentation](https://docs.python.org/3/library/ctypes.html) instead if you want to learn more."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Foreign function interface"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's start with a simple function signature. This function is in declared in a header file ``text_stats.h`` and it's part of the library ``libtext_stats.so``."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```c\n",
+ "/** Counts the occurences of a string in a file.\n",
+ " * \n",
+ " * @param filename name of file to open\n",
+ " * @param word string to look for in file\n",
+ " *\n",
+ " * @return number of occurences of word in file with filename\n",
+ " */\n",
+ "int word_frequency(char* filename, char* word);\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A quick way to access this function is to use the module ``cffi``."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Foreign function interface\n",
+ "### Calling word_frequency from Python"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import cffi"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ffi = cffi.FFI()\n",
+ "ffi.cdef(\"\"\"\n",
+ " int word_frequency(char* filename, char* word);\n",
+ "\"\"\") # The definition is the same as in the header file.\n",
+ "\n",
+ "TS = ffi.dlopen(\"./code/text_stats/build/libtext_stats.so\")\n",
+ "wc = TS.word_frequency(b\"test.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "What if word_frequency had been written Fortran?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ "function word_frequency(filename, word)\n",
+ " implicit none\n",
+ " character(len=*), intent(in) :: filename\n",
+ " character(len=*), intent(in) :: word\n",
+ " integer :: word_frequency\n",
+ " ...\n",
+ "end function word_frequency\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can access Fortran functions almost like C functions. The exact function name may differ, though. The default symbol \n",
+ "when compiled with ifort or gfortran is ``word_frequency_``. This can be changed with the option `-fno-underscoring` (gcc) or `-assume nounderscore` (Intel).\n",
+ "\n",
+ "On JUWELS, we are using the Intel Fortran compiler ifort. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "Use the terminal that you used earlier to run `build.sh` or open a new one. Make sure you are in the \n",
+ "tutorial directory. Source `hpcpy20` using `source hpcpy20`. Change into code/textstats/ and compile \n",
+ "the file word_frequency.F90 with the following command:\n",
+ "\n",
+ "```bash\n",
+ "ifort word_frequency.F90 -shared -O2 -o build/libwf.so -fPIC\n",
+ "```\n",
+ "\n",
+ "```bash\n",
+ "nm build/libwf.so | grep word_frequency\n",
+ "```\n",
+ "\n",
+ "to check the symbol.\n",
+ "\n",
+ "Change the cell below to use libwf.so instead of libtext_stats.so. Don't forget to adjust the function declaration.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ffi = cffi.FFI()\n",
+ "ffi.cdef(\"\"\"\n",
+ " int word_frequency(char* filename, char* word);\n",
+ "\"\"\") # The definition is the same as in the header file.\n",
+ "\n",
+ "TS = ffi.dlopen(\"./code/text_stats/build/libtext_stats.so\")\n",
+ "wc = TS.word_frequency(b\"test.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution (with underscore)\n",
+ "ffi = cffi.FFI()\n",
+ "ffi.cdef(\"\"\"\n",
+ " int word_frequency_(char* filename, char* word);\n",
+ "\"\"\") # The definition is the same as in the header file.\n",
+ "\n",
+ "TS = ffi.dlopen(\"./code/text_stats/build/libwf.so\")\n",
+ "wc = TS.word_frequency_(b\"test.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you compiled the library with the option `-assume nounderscore`, you could use the original declaration without underscore with libwf.so.\n",
+ "\n",
+ "**Note**: There is no way to *reload* a library using cffi."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution if compiled with ifort and -assume nounderscore (or gfortran and -fno-underscoring)\n",
+ "ffi = cffi.FFI()\n",
+ "ffi.cdef(\"\"\"\n",
+ " int word_frequency(char* filename, char* word);\n",
+ "\"\"\") # The definition is the same as in the header file.\n",
+ "\n",
+ "TS = ffi.dlopen(\"./code/text_stats/build/libwf.so\")\n",
+ "wc = TS.word_frequency(b\"test.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## ISO_C_BINDING"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Fortran 2003 improved the interoperability between Fortran and C with the `iso_c_binding`. It provides data kinds that are C compatible and the `bind` attribute. The function definition can be changed to"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ "function word_frequency(filename, word) bind(C)\n",
+ " use iso_c_binding\n",
+ " implicit none\n",
+ " character(kind=c_char, len=1), intent(in) :: filename\n",
+ " character(kind=c_char, len=1), intent(in) :: word\n",
+ " integer :: word_frequency\n",
+ " ...\n",
+ "end function word_frequency\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, the name of the function will always be `word_frequency`. `bind` takes as optional argument the name under which the function should be known to C: bind(c, name=\"wf\") would let us call the function as `wf(filename, word)` from C (and Python).\n",
+ "\n",
+ "To learn more about [CFFI](https://bitbucket.org/cffi/cffi) look at it's [documentation](https://cffi.readthedocs.io/en/latest/)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Cython"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext cython"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Cython generates C code that is compiled to an extension. It can trivially call C (and even C++) \n",
+ "functions, which we can use to write Python bindings. But first an annotated example of a \"normal\"\n",
+ "cython module. The following code will make the function `cysum` available to Cython and Python:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -a\n",
+ "import numpy\n",
+ "cimport numpy # Make C-style calls available\n",
+ "cimport cython\n",
+ "@cython.boundscheck(False) # Turn off boundary checks for array access.\n",
+ "# Functions defined with `def` are visible from Python and Cython\n",
+ "def cysum(numpy.ndarray[numpy.float_t, ndim=1] a): # Define the input type as 1d ndarray of floats\n",
+ " \"\"\"Sum up the elements of a.\n",
+ " \n",
+ " Paramters\n",
+ " ---------\n",
+ " a : ndarray\n",
+ " array to sum over\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " res: float\n",
+ " sum of the elements of a\n",
+ " \"\"\"\n",
+ " cdef float res = 0.0; # Define a C-only variable using `cdef`\n",
+ " cdef int n = len(a)\n",
+ " for i in range(n):\n",
+ " res += a[i]\n",
+ " return res\n",
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's wrap `word_frequency` using cython. We need to pass compile and link arguments to the call as described in [Adding compiler options][CompilerOptions].\n",
+ "\n",
+ "[CompilerOptions]: ./Speeding%20up%20your%20code%20with%20Cython.ipynb#Adding-compiler-options\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -I code/text_stats -L code/text_stats/build -l text_stats\n",
+ "cdef extern from \"text_stats.h\":\n",
+ " cpdef int word_frequency(char* filename, char* word)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "word_frequency(b\"text.txt\", b\"you\") # Need to use byte type in Python 3."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note** Unfortunately, this doesn't work the way it's supposed to. Although `-L` should add the path to the library to the search path of the linker, the linker still doesn't find the library. To make it work, I added the path to libtext_stats.so to the `LD_LIBRARY_PATH` when the kernel is loaded."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Adapting types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The function `word_frequency` takes bytes instead of strings because the C function uses char\\*, which is mapped to bytes in Python 3. We would want a Python function that takes strings, though. We can do this by calling our C function from a Python function within Cython and take care of the argument conversion ourselves."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Cython\n",
+ "cdef extern from \"text_stats.h\":\n",
+ " cdef int word_frequency(char* filename, char* word)\n",
+ " \n",
+ "def wordfrequency(filename, word):\n",
+ " \"\"\"Counts the occurences of a string in a file.\"\"\"\n",
+ " # We first need to decode the strings\n",
+ " filenameb = filename.encode('UTF-8')\n",
+ " wordb = word.encode('UTF-8')\n",
+ " # Now we can convert them to C strings\n",
+ " cdef char* filenamec = filenameb\n",
+ " cdef char* wordc = wordb\n",
+ " # And finally pass them to our C function\n",
+ " return word_frequency(filenamec, wordc)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The function wordfrequency takes two Python strings and encodes them to get the proper byte representation that is then passed to the original C function. A complete implementation with doc string and compiler arguments can look like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -I code/text_stats -L code/text_stats/build -ltext_stats\n",
+ "cdef extern from \"text_stats.h\":\n",
+ " cdef int word_frequency(char* filename, char* word)\n",
+ " \n",
+ "def wordfrequency(filename, word):\n",
+ " \"\"\"Counts the occurences of a string in a file.\n",
+ "\n",
+ " Paramters\n",
+ " ---------\n",
+ " filename: string\n",
+ " name of file to open\n",
+ " word: string\n",
+ " string to look for in file\n",
+ "\n",
+ " Returns\n",
+ " -------\n",
+ " ct: int \n",
+ " number of occurences of word in file with filename\n",
+ " \"\"\"\n",
+ " # We first need to decode the strings\n",
+ " filenameb = filename.encode('UTF-8')\n",
+ " wordb = word.encode('UTF-8')\n",
+ " # Now we can convert them to C strings\n",
+ " cdef char* filenamec = filenameb\n",
+ " cdef char* wordc = wordb\n",
+ " # And finally pass them to our C function\n",
+ " return word_frequency(filenamec, wordc)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "wordfrequency(\"text.txt\", \"you\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Wrapping Fortran"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can do almost the same thing as above, to wrap the Fortran function `word_frequency`. We don't have a header file, so we skip that part:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -Lcode/text_stats/build -lwf\n",
+ "cdef extern:\n",
+ " cdef int word_frequency_(char* filename, char* word)\n",
+ " \n",
+ "def wordfrequency2(filename, word):\n",
+ " \"\"\"Counts the occurences of a string in a file.\"\"\"\n",
+ " # We first need to decode the strings\n",
+ " filenameb = filename.encode('UTF-8')\n",
+ " wordb = word.encode('UTF-8')\n",
+ " # Now we can convert them to C strings\n",
+ " cdef char* filenamec = filenameb\n",
+ " cdef char* wordc = wordb\n",
+ " # And finally pass them to our C function\n",
+ " return word_frequency_(filenamec, wordc)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "wordfrequency2(\"text.txt\", \"you\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If we cannot/don't want to change our original source code by adding `bind` for example or using the kinds from iso_c_binding or we don't have access to the source code in the first place, we can write a wrapper in Fortran that includes the binding. Look [here](http://www.fortran90.org/src/best-practices.html#interfacing-with-c) for an example."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Wrapping C++"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can use Cython to wrap C++ as well. Let's start with a simple 3d point class."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```c++\n",
+ "#pragma once\n",
+ "\n",
+ "#include <vector>\n",
+ "\n",
+ "class Point3D{\n",
+ "public:\n",
+ " Point3D(const double x, const double y, const double z);\n",
+ " Point3D(const std::vector<double> r);\n",
+ " void translate(const double dx, const double dy, const double dz);\n",
+ " void translate(const std::vector<double> dr);\n",
+ " const std::vector<double> coordinates();\n",
+ "private:\n",
+ " double _x, _y, _z;\n",
+ "};\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "For starters, I'm only going to wrap `Point3D(x, y, z)`, `translate(dx, dy, dz)`, and `coordinates()`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Cython needs to know that we are dealing with C++ now. Usually, this is added to the setup.py or .pxd file, but it can be done in a notebook cell, too. That's what the second line in the following cell is doing.\n",
+ "\n",
+ "First, you need to import the header and then define the functions that should be made available to Cython. Since these are methods of a class, you define that too using the **cppclass** keyword.\n",
+ "\n",
+ "An important part of C++ is the standard library. Cython comes with a number of prepared wrappers, for example, for std::vector. These are imported from libcpp."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -Icode/point -Lcode/point/build -lpoint\n",
+ "# distutils: language = c++\n",
+ "from libcpp.vector cimport vector\n",
+ "\n",
+ "cdef import from \"point3d.h\":\n",
+ " cdef cppclass Point3D:\n",
+ " Point3D(double x, double y, double z)\n",
+ " void translate(double dx, double dy, double dz)\n",
+ " vector[double] coordinates()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As before, so far these functions are only available to Cython. To make them available to Python, you have to write a wrapper. There are two new functions that are used to deal with classes: initialization is done in \\_\\_cinit\\_\\_ and there's a corresponding destructor function called \\_\\_dealloc\\_\\_."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "By convention a pointer to the object called `thisptr` is kept as part of the wrapper object."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython -Icode/point -Lcode/point/build -lpoint\n",
+ "# distutils: language = c++\n",
+ "from libcpp.vector cimport vector\n",
+ "\n",
+ "cdef import from \"point3d.h\":\n",
+ " cdef cppclass Point3D:\n",
+ " Point3D(double x, double y, double z)\n",
+ " void translate(double dx, double dy, double dz)\n",
+ " vector[double] coordinates()\n",
+ " \n",
+ "cdef class PyPoint3D: # This is an extension type (aka cdef class)\n",
+ " cdef Point3D *thisptr\n",
+ " \n",
+ " def __cinit__(self, double x, double y, double z):\n",
+ " self.thisptr = new Point3D(x, y, z)\n",
+ " \n",
+ " def __dealloc__(self):\n",
+ " del self.thisptr"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "You can now construct an object of type PyPoint3D, which keeps a reference to it's copy of Point3D."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "origin = PyPoint3D(0,0,0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, let's wrap the two functions as well."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%cython --compile-args=-Icode/point --link-args=-Lcode/point/build --link-args=-lpoint\n",
+ "# distutils: language = c++\n",
+ "from libcpp.vector cimport vector\n",
+ "\n",
+ "cdef import from \"point3d.h\":\n",
+ " cdef cppclass Point3D:\n",
+ " Point3D(double x, double y, double zwf)\n",
+ " void translate(double dx, double dy, double dz)\n",
+ " vector[double] coordinates()\n",
+ " \n",
+ "cdef class PyPoint3D:\n",
+ " cdef Point3D *thisptr\n",
+ " \n",
+ " def __cinit__(self, x, y, z):\n",
+ " self.thisptr = new Point3D(x, y, z)\n",
+ " \n",
+ " def __dealloc__(self):\n",
+ " del self.thisptr\n",
+ " \n",
+ " def translate(self, dx, dy, dz):\n",
+ " \"\"\"Move this point by (dx, dy, dz).\n",
+ " \n",
+ " Paramters\n",
+ " ---------\n",
+ " dx : float\n",
+ " shift along x-axis\n",
+ " dy : float\n",
+ " shift along y-axis\n",
+ " dz : float\n",
+ " shift along z-axis\n",
+ " \"\"\"\n",
+ " self.thisptr.translate(dx, dy, dz)\n",
+ " \n",
+ " def coordinates(self):\n",
+ " \"\"\"Get the coordinates of this point.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " r : list\n",
+ " coordinates of this point.\n",
+ " \"\"\"\n",
+ " return self.thisptr.coordinates()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, let's construct a point, shift it and return its coordinates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_point_cython = %timeit -o p = PyPoint3D(1,1,1); p.translate(-0.5, -0.5, -0.5);p.coordinates()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## PyBind11"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A powerful alternative to Cython for writing bindings for C++ code is PyBind11. In contrast to Cython, which adds some additional keywords to Python, PyBind11 is a header-only library that make Python types available in C++ and allows you to write Python bindings in C++. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's start with the `word_frequency` example again. This is the PyBind11 code that wraps this function:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```c++\n",
+ "#include <pybind11/pybind11.h>\n",
+ "\n",
+ "extern \"C\" {\n",
+ " #include <text_stats.h>\n",
+ "}\n",
+ "\n",
+ "namespace py = pybind11; // This is purely for convenience\n",
+ "\n",
+ "PYBIND11_MODULE(text_stats, m){\n",
+ " m.doc() = \"Some functions that provide statistical information about a text.\";\n",
+ " m.def(\"word_frequency\", &word_frequency, R\"doc(Counts the occurences of a string in a file.\n",
+ "\n",
+ "Paramters\n",
+ "---------\n",
+ "filename: string\n",
+ " name of file to open\n",
+ "word: string\n",
+ " string to look for in file\n",
+ "\n",
+ "Returns\n",
+ "-------\n",
+ "ct: int \n",
+ " number of occurences of word in file with filename \n",
+ ")doc\");\n",
+ "\n",
+ "}\n",
+ "\n",
+ "```\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Compiling the extension"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This code can be compiled like this:\n",
+ "\n",
+ "```bash\n",
+ "icpc -O3 -shared -fpic -std=c++14 `python3-config --includes` -I/p/project/training2020/packages/lib/python3.8/site-packages/pybind11/include -I code/text_stats `python3-config --cflags --ldflags` code/text_stats/text_stats_bind.cpp -o text_stats.so -L code/text_stats/build -ltext_stats\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "!icpc -O3 -shared -fpic -std=c++14 `python3-config --includes` -I/p/project/training2020/packages/lib/python3.8/site-packages/pybind11/include -I code/text_stats code/text_stats/text_stats_bind.cpp -o text_stats.so `python3-config --cflags --ldflags` -L code/text_stats/build -ltext_stats "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Using the extension"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import text_stats"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "text_stats.word_frequency(\"text.txt\", \"you\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note that we didn't have to convert our string at all. It's done automatically by PyBind11."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Wrapping a class with Pybind11"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "PyBind11 can deal with classes, too. The following code wraps the Point3D class:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "```c++\n",
+ "#include <vector>\n",
+ "#include <pybind11/pybind11.h>\n",
+ "#include <pybind11/stl.h>\n",
+ "#include <point3d.h>\n",
+ "\n",
+ "namespace py = pybind11; // This is purely for convenience\n",
+ "\n",
+ "PYBIND11_MODULE(points, m){\n",
+ " m.doc() = \"A collection of functions and objects to deal with 3D points.\";\n",
+ "\n",
+ " py::class_<Point3D>(m, \"Point3D\")\n",
+ " .def(py::init<double, double, double>())\n",
+ " .def(py::init<std::vector<double>>())\n",
+ " .def(\"translate\", (void (Point3D::*)(double, double, double)) &Point3D::translate,\n",
+ " R\"doc(Move this point by (dx, dy, dz).\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " dx : float\n",
+ " shift along x-axis\n",
+ " dy : float\n",
+ " shift along y-axis\n",
+ " dz : float\n",
+ " shift along z-axis\n",
+ " )doc\")\n",
+ " .def(\"coordinates\", &Point3D::coordinates,\n",
+ " R\"doc(Get the coordinates of this point.\n",
+ " \n",
+ " Returns\n",
+ " -------\n",
+ " r : list\n",
+ " coordinates of this point.\n",
+ " )doc\")\n",
+ " .def(\"rotate\", &Point3D::rotate, R\"doc(Rotates this point about x, y, and z\n",
+ " \n",
+ " The rotation is performed as if this point was first rotated by alpha around the x-axis, \n",
+ " then rotated by beta around the y-axis, and finally rotated by gamma around the z-axis.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " alpha: float\n",
+ " rotation around x-axis in rad\n",
+ " beta: float \n",
+ " rotation arounx y-axis in rad\n",
+ " gamma: float \n",
+ " rotation around z-axis in rad\n",
+ " )doc\");\n",
+ "}\n",
+ "\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## F2Py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The methods to wrap Fortran that we looked at so far relied on Fortran's C interface/compatibility. For Fortran 77/90/95 code you can also use `f2py` to generate bindings in a very convenient way. F2Py is distributed together with NumPy."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In Fortran, you can use a module to store the points."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ "! points.f90\n",
+ "module points\n",
+ "implicit none\n",
+ "\n",
+ "real, allocatable, dimension(:) :: x\n",
+ "real, allocatable, dimension(:) :: y\n",
+ "real, allocatable, dimension(:) :: z\n",
+ "\n",
+ "contains\n",
+ " subroutine init(N)\n",
+ " integer, intent(in) :: N\n",
+ " \n",
+ " allocate(x(N))\n",
+ " allocate(y(N))\n",
+ " allocate(z(N))\n",
+ " \n",
+ " end subroutine init\n",
+ "\n",
+ " subroutine coordinates(idx, tx, ty, tz)\n",
+ " integer, intent(inout) :: idx\n",
+ " real, intent(out) :: tx\n",
+ " real, intent(out) :: ty\n",
+ " real, intent(out) :: tz\n",
+ " tx = x(idx)\n",
+ " ty = y(idx)\n",
+ " tz = z(idx)\n",
+ " end subroutine coordinates\n",
+ "\n",
+ " ...\n",
+ " \n",
+ " subroutine finalize\n",
+ " deallocate (x, y, z)\n",
+ " end subroutine finalize\n",
+ " \n",
+ "end module points\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note**: Remember that you can use '!' to call programs as if you were doing it from the terminal."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "numpy.__file__"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "!f2py -c code/point/points.f90 -m points_f"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from points_f import points"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "points.init(1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "points.set(1, 1.0, 1.0, 1.0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "points.translate(1, -0.5, -0.5, -0.5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x, y, z = points.coordinates(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Note that f2py honors the intent defined in the Fortran module. The subroutine coordinates takes one input value idx and has three \"return arguments\" tx, ty, tz that contain the coordinates of the particle idx. F2py converts this into a Python function that takes one argument and returns a tuple with three values."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Wrapping F77"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Fortran 77 doesn't know anything about intents nor modules, so how can we use f2py to generate nice Python bindings to older Fortran code?\n",
+ "\n",
+ "In Fortran 77, the translate function might be written like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```Fortran\n",
+ " subroutine translate(idx, dx, dy, dz, x, y, z, N)\n",
+ " implicit none\n",
+ " integer idx, N\n",
+ " real*8 dx, dy, dz\n",
+ " real*8 x(N), y(N), z(N)\n",
+ " x(idx) = x(idx) + dx\n",
+ " y(idx) = y(idx) + dy\n",
+ " z(idx) = z(idx) + dz\n",
+ " end subroutine translate\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### cf2py comments for better bindings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can use f2py comments to add the intents like this:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Fortran\n",
+ " subroutine translate(idx, dx, dy, dz, x, y, z, N)\n",
+ " implicit none\n",
+ " integer idx, N\n",
+ " real*8 dx, dy, dz\n",
+ " real*8 x(N), y(N), z(N)\n",
+ "cf2py intent(in) idx, N\n",
+ "cf2py intent(in) dx, dy, dz\n",
+ "cf2py intent(in,out) x, y, z\n",
+ "cf2py depend(N) x, y, z\n",
+ " x(idx) = x(idx) + dx\n",
+ " y(idx) = y(idx) + dy\n",
+ " z(idx) = z(idx) + dz\n",
+ " end subroutine translate\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The Fortran compiler will ignore the comments, but f2py will use them to generate the proper wrapper."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Although f2py is part of NumPy, little work has been done on it to improve support for modern Fortran. This will hopefully [change](https://www.youtube.com/watch?v=56M40Y2jl9Y)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/13_Introduction to Dask.ipynb b/solutions/13_Introduction to Dask.ipynb
new file mode 100644
index 0000000..4a2f3f9
--- /dev/null
+++ b/solutions/13_Introduction to Dask.ipynb
@@ -0,0 +1,797 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to Dask\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Olav Zimmermann\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Dask implements flexible **intra- and inter-node parallel execution based on a task model**. It features data structures that 'feel' like ordinary numpy ndarrys or pandas dataframes but under the hood have been enabled to work on **distributed data**.\n",
+ "While the task based scheduling enables parallel execution of even highly irregular computation pipelines, the distributed data structures make dask also an interesting choice for processing of data volumes that are larger than main memory.\n",
+ "\n",
+ "Among the distinctive features of dask is peer-to-peer data sharing between workers, and high resilience provided by nanny processes that can restart failing workers.\n",
+ "\n",
+ "Dask has been developed by Continuum Analytics, the company that also developed Numba etc."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.delayed "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`dask.delayed` can be used to formulate arbitrary task graphs. \n",
+ "\n",
+ "It can either be employed as a decorator `@delayed` (not show in this tutorial) or as a wrapper function `dask.delayed(func)`. \n",
+ "This function marks a function to be scheduled by Dask. Delayed functions will be evaluated lazily, e.g. not before their result is needed. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "This is similar in spirit to other lazy evaluation schemes in python (e.g. `eval()`, `lambda` or `concurrent.futures`) and also similar to other task frameworks such as tensorflow. \n",
+ "\n",
+ "As dask.delayed works on the level of individual functions, the user remains in control which functions will be evaluated eagerly and which ones lazily. Although Dask has a sophisticated scheduler for lazy task evaluation, eager evaluation can be preferable in some situations, e.g. for functions that control routing in the task graph, such as functions calculating data used in `if-`statements."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We first do some settings:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import warnings\n",
+ "warnings.filterwarnings('ignore')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The next cell implements some dummy functions and builds a simple pipeline with some data dependencies."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import random\n",
+ "from time import sleep\n",
+ "from dask import delayed\n",
+ "\n",
+ "def input_task(myinput):\n",
+ " #sleep(random.random() / 2)\n",
+ " sleep(0.5)\n",
+ "input_task=delayed(input_task)\n",
+ "\n",
+ "def common_task():\n",
+ " #sleep(random.random() / 2 + 2.5)\n",
+ " sleep(3)\n",
+ "common_task=delayed(common_task)\n",
+ "\n",
+ "def mapitem_task(item, common):\n",
+ " #sleep(random.random() * 4)\n",
+ " sleep(2)\n",
+ "mapitem_task=delayed(mapitem_task)\n",
+ "\n",
+ "def summarize_task(intermediates):\n",
+ " #sleep(random.random() *2)\n",
+ " sleep(1)\n",
+ "summarize_task=delayed(summarize_task)\n",
+ "\n",
+ "## taskgraph\n",
+ "\n",
+ "prepared = [input_task(i) for i in range(8)]\n",
+ "common_data=common_task()\n",
+ "intermediates=[mapitem_task(item,common_data) for item in prepared]\n",
+ "dlresult=summarize_task(intermediates)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Try to think about it ahead of running the next cells:\n",
+ "- What is the minimal wall time possible?\n",
+ "- How many tasks does the task graph have for range(8) in prepared?\n",
+ "- How many inputs could you process maximally in the same time it takes for 8 inputs?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Poll",
+ "Solution"
+ ]
+ },
+ "source": [
+ "Poll:\n",
+ "- minimal walltime: A) 3s B) 4s C) 6s D) 6.5s\n",
+ "- how many tasks in task graph: A) 1 B) 8 C) 16 D) 18 \n",
+ "- max tasks in the same time as 8 tasks: A) 8 B) 24 C) 48 D) 96"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The task graph generated by `dask` can be visualized (don't try this for large graphs!)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import graphviz\n",
+ "dlresult.visualize(format='svg')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The computation of any of the tasks is delayed until the execution is triggered by an explicit command to compute dlresult upon which the individual tasks are scheduled according to the dependency structure."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%time dlresult.compute()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "- How close to optimal is the observed scheduling?\n",
+ "- What is the largest number of inputs you can process under 8 seconds? Why?\n",
+ "- Change the program in a way that enables you to estimate how much overhead per task is incurred by Dask."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Poll"
+ ]
+ },
+ "source": [
+ "Poll: \n",
+ "- largest number of inputs you can process under 8 seconds: A) 12 B) 24 C) 48 D) 96\n",
+ "- task overhead per task: A) 100µs B) 200µs C) 1ms D) 2ms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## (Semi)structured data processing tasks with dask (bag, dataframe, array)\n",
+ "\n",
+ "Dask supports three datatypes that allow for structured and semi-structured computation patterns:\n",
+ "\n",
+ "- The slowest, most general data structure is **`dask.bag`** which implements parallel list processing. \n",
+ "- **`dask.dataframe`** is a faster structure that can be used like a tiled Pandas dataframe. \n",
+ "- Similarly **`dask.array`** works like a tiled `numpy.ndarray`. \n",
+ "\n",
+ "While some restrictions apply, an important subset of Panda's/NumPy's functions are available for [**`dask.dataframe`**](http://dask.pydata.org/en/latest/dataframe-api.html) and [**`dask.array`**](http://dask.pydata.org/en/latest/array-api.html), respectively and typically have the identical interfaces."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.bag\n",
+ "\n",
+ "A **dask.bag** can contain arbitrary data items (including complex types). Dask bags are processed in chunks called partitions. Setting the number of partitions allows to adapt processing to the number of CPUs and the amount of RAM available. \n",
+ "\n",
+ "Typical ways to generate a bag are:\n",
+ "\n",
+ "- `from_sequence(seq)` (where *seq* is an iterable, such as a list)\n",
+ "- `read_text(fn_or_glob)` (where *fn_or_glob* is either a filename or a glob string, creates one partition per file)\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from operator import add\n",
+ "import dask.bag as db"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "l=[x for x in range(1000000)]\n",
+ "s= db.from_sequence(l,npartitions=4) # you can manually set the number of partitions\n",
+ "mysum=s.fold(add) # fold performs a parallel reduction "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "mysum.visualize()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%time result=mysum.compute()\n",
+ "result=mysum.compute\n",
+ "result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%time r=list(s.filter(lambda x: x % 2 == 0).map(lambda x: x * 1.2))\n",
+ "r[:5] #note: apparently no type coercion!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "(The syntax is kind of unfortunate since Python is moving away from filter and map to list comprehensions and generator expressions.)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Exercise:**\n",
+ "\n",
+ "Code the same operations without dask, i.e. using a) just python and b) using numpy and measure the runtime of the calculations. \n",
+ "\n",
+ "Conclusions? "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "## Solutions:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "First let's use timeit on the dask bag to have a more reliable time estimate:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "s= db.from_sequence(l,npartitions=4)\n",
+ "r=list(s.filter(lambda x: x % 2 == 0).map(lambda x: x*1.2))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "Python has map and filter functions too, which allows for a functional programming pattern very similar to the dask bag code:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "funclist=list(map(lambda x: x * 1.2,filter(lambda x: x % 2 == 0,l)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "Of course we can also write this as a simple loop:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "looplist=[]\n",
+ "for x in l:\n",
+ " if x%2==0:\n",
+ " looplist.append(x*1.2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "A more concise (and very pythonic) way to write this loop is a list comprehension:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "complist=[x*1.2 for x in l if x %2 ==0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "Finally one can also write this using numpy:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit import numpy as np\n",
+ "arr=np.array(l)\n",
+ "out2=(arr[arr%2==0]*1.2).tolist()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.dataframe\n",
+ "\n",
+ "**`dask.dataframe`** behaves like a distributed [Pandas](https://pandas.pydata.org/pandas-docs/stable/) DataFrame. It also uses Pandas functionality under the hood, such as Pandas' fast `read_csv`-method. However, only a small part of the large Pandas functionality is [available](http://dask.pydata.org/en/latest/dataframe-api.html)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import dask.dataframe as dd\n",
+ "df = dd.read_csv(\"data/iris.csv\") # not a reasonably sized task (too small!)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "h=df.groupby(df.Name).SepalLength.mean()\n",
+ "h.compute()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.array\n",
+ "\n",
+ "**`dask.dataframe`** is the distributed equivalent of numpy ndarray."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import dask.array as da\n",
+ "x = da.ones((5, 15), chunks=(5, 5))\n",
+ "x.dask"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x.visualize()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "## numpy or dask.array?\n",
+ "\n",
+ "Despite the sophisticated parallelization, the general rule applies,\n",
+ "that numpy arrays are faster and should be therefore preferred over dask arrays for normal computation if the arrays fit into main memory.\n",
+ "However, Dask allows for many optimizations. Apart from a sophisticated user-tweakable optimizer the chunking can be changed for different workloads.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%timeit\n",
+ "x_np = np.random.normal(10, 0.1, size=(10000,3000))\n",
+ "y_np = x_np.transpose()\n",
+ "result=x_np.dot(y_np)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from dask.diagnostics import ProgressBar\n",
+ "import dask.array as da"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "x_dask = da.random.normal(10, 0.1, size=(10000,3000), chunks=(5000,3000)) # using as many chunks as CPU cores is good for random number calculation\n",
+ "x_rechunked=x_dask.rechunk((1000,3000)) # larger chunks are no longer better for dot product calculation\n",
+ "y_dask = x_rechunked.transpose()\n",
+ "result=x_dask.dot(y_dask)\n",
+ "#with ProgressBar():\n",
+ "%timeit result.compute(scheduler=\"threads\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## dask.distributed\n",
+ "\n",
+ "`dask.distributed` extends `dask` to distributed computing on several nodes."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "`dask.distributed` features a sophisticated **web-based monitoring** based on the package `bokeh`. See **Dashboard** when you started the client above that shows the address and port of the web server."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "### dask.distributed working with schedulers\n",
+ "There are external packages like `dask.jobqueue` that allow dask to work on top of scheduling systems such as Sun Grid Engine, Slurm, Torque etc. (For details read the docs [(link)](https://jobqueue.dask.org/en/latest/index.html).)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "## dask and other packages\n",
+ "\n",
+ "### dask on sparse data\n",
+ "Dask does currently not support sparse matrix formats directly but dask's chunks can work with any in-memory array representation that follows the `numpy.ndarray` API. One such library is `sparse` [(link)](https://sparse.pydata.org/en/stable/), written by the main dask developer, Matthew Rocklin, but it only supports coordinate list layout (COO) for sparse matrices. Note that the `scipy.sparse` format, which additionally supports compressed sparse row (CSR) and compressed sparse column (CSC) layouts, does not follow the `numpy.ndarray` API but the `numpy.matrix` API and hence is not compatible with dask. Therefore even the popular dask-ML package for machine learning suggests to convert scipy sparse matrices (e.g. from sklearn outputs) to dense matrices. There are some other projects such as `Sparsity` [(link)](https://sparsity.readthedocs.io/en/latest/) that have goals similar to `sparse` but are much younger."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "### x-array project \n",
+ "The [x-array](http://xarray.pydata.org/en/stable/) project provides an n-dimensional equivalent of a Pandas DataFrame and can employ dask for distributed processing. This project was originally developed for applications in the Earth sciences. It provides, e.g. a convenient in-memory representation of netCDF files."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "### Multi-GPU processing with Rapids and dask\n",
+ "\n",
+ "Rapids [(link)](https://rapids.ai/) is an open source project supported by nVidia that provides several libraries GPU data science and data analytics project.\n",
+ "cuDF, one of the Rapids libraries, is a single-GPU library that implements a subset of the pandas dataframe functionality on GPUs.\n",
+ "Using dask-cuDF [(link)](https://github.com/rapidsai/cudf/tree/main/python/dask_cudf) allows for scaling cuDF to multiple (nVidia) GPUs, both single and multi-node."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/14_Introduction to MPI.ipynb b/solutions/14_Introduction to MPI.ipynb
new file mode 100644
index 0000000..8f41493
--- /dev/null
+++ b/solutions/14_Introduction to MPI.ipynb
@@ -0,0 +1,1787 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to MPI\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "MPI (Message Passing Interface) is the most used protocol for communicating between processes. It doesn't matter if the processes that want to talk to each other are on the same or different nodes (i.e., computers). In this tutorial, we'll use `mpi4py` to learn about MPI and its API.\n",
+ "\n",
+ "An MPI program can run on a single computer/node with one or more processes that share memory or on multiple computers that are connected to each other via some network (not shown)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Communicators"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "MPI processes talk to each other via communicators. The global communicator `MPI.COMM_WORLD` connects all MPI processes. Each process has a unique *rank* within `MPI.COMM_WORLD`. The process with `rank=0` is usually called the root process. MPI processes can participate in different communicators and may have a different rank in these communicators."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Point to point communication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Sending messages from one MPI task to another is the foundation of MPI. Messages consist of some meta information such as the *source* and the *destination*, a *tag* that identifies the message, the *data type*, and the *count* of data items and the actual data.\n",
+ "\n",
+ "For each `Send` there has to be a matching `Recv`. This means that the meta information has to fit (including the tag). There are some wildcards and some additional commands that make this more flexible.\n",
+ "\n",
+ "Sending and receiving can be blocking or non-blocking. In the latter case, the flow of the program continuous after the call. In the former the program waits until the message has been transmitted. There is a very real danger for deadlocks here!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Collective communication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Collective calls are performed by all ranks of a communicator and thus *must* be called by all ranks. Examples for collective calls are `Bcast`, `Scatter`, `Gather`, and `Allreduce`. We'll look at some collective calls later in the notebook."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "You could implement collective calls yourself using `Send` and `Recv`, but using the provided collective calls makes your code easier to read and allows vendors to optimize MPI for their platform. For example, in the picture above all the calls share the bandwidth of rank 0. One could use a tree-like pattern to balance the network load instead."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You can find more information about MPI at http://materials.jeremybejarano.com/MPIwithPython/index.html, the documentation of mpi4py at https://mpi4py.readthedocs.io/en/stable/ (take a look at the tutorials), and the API reference at https://mpi4py.bitbucket.io/apiref/index.html."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "from matplotlib import pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Starting the engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Note, this is only needed to run MPI programs from a Jupyter notebook.**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can use ipyparallel to run MPI from a notebook. To do that, we need to start some IPython engines. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Click on the ``+``-sign at the top of the Files tab on the left to start a new launcher. In the launcher click on Terminal. A terminal will open as a new tab. Grab the tab and pull it to the right to have the terminal next to your notebook.\n",
+ "\n",
+ "**Note**: The terminal does not have the same modules loaded as the notebook. To fix that type `source hpcpy20`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Next start the ipcontroller: `ipcontroller &`. After that we can launch 4 MPI tasks with 12 threads each like this\n",
+ "\n",
+ "```bash\n",
+ "export OMP_NUM_THREADS=12\n",
+ "srun -n 4 -c 12 --ntasks-per-node 4 ipengine start\n",
+ "```\n",
+ "\n",
+ "**Note**, you can can start the controller and the engines in separate terminals. That will keep the output separate."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Connecting to the engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next, we want to connect to the engines:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client\n",
+ "rc = Client()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "rc.ids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Next, we need to create a view and activate it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "view = rc[:]\n",
+ "view.activate()\n",
+ "view.block = True"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Setting up for MPI"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We are now ready to use MPI with our IPython notebook.\n",
+ "\n",
+ "We will use the cell magic ``%%px`` and the line magic ``%px`` to execute commands on all the engines. So, whenenver you see ``%%px`` the cell is executed on *all* the engines, but not in the process that controls your notebook!\n",
+ "\n",
+ "**Note**: Everything that appears *after* ``%%px`` and ``%px`` would be part of a regular mpi4py program."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px from mpi4py import MPI # Import and initialize MPI on the engines\n",
+ "#from mpi4py import MPI # Import and initialize MPI in the notebook "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%px import numpy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Importing MPI initializes the MPI and sets up the default communicator `COMM_WORLD`, which includes all processes involved in this MPI program.\n",
+ "\n",
+ "Using `COMM_WORLD`, each process can determine its *rank* and the total number of ranks available:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm = MPI.COMM_WORLD\n",
+ "rank = comm.Get_rank()\n",
+ "size = comm.Get_size()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "print(\"I'm %d of %d. Resistance is futile.\" % (rank + 1, size))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Point to point"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can send messages from one rank to another. \n",
+ "\n",
+ "The sender will use `Send` and the receiver a corresponding `Recv`. To get the doc string, you can run"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%px --target 0 \n",
+ "help(MPI.Comm.Send)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The `buf` argument needs to implement the [buffer protocol](https://docs.python.org/3/c-api/buffer.html). This is true, for example, for numpy arrays, but not for primitive types such as float. That's the reason we use `numpy.ones` and `numpy.zeros` of size 1 below.\n",
+ "\n",
+ "The following exercises will only work if more than one process is available."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "import sys\n",
+ "import numpy\n",
+ "comm = MPI.COMM_WORLD\n",
+ "a = numpy.ones(1)\n",
+ "b = numpy.zeros(1)\n",
+ "if (size < 2):\n",
+ " print (\"Warning! Not enough ranks available!\" )\n",
+ "else:\n",
+ " if rank == 0:\n",
+ " print (\"I'm rank zero and I'm sending a datum.\")\n",
+ " comm.Send(a[0], dest = 1) # Default destination is 0!\n",
+ " elif rank == 1:\n",
+ " print (\"I'm rank one and I'm receiving a datum.\")\n",
+ " comm.Recv(b, source = 0) # Default source is 0!\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "**Note**, how we used `rank` to perform different work on the task with rank 0 and the task with rank 1 using if statements. This is a common pattern in MPI programs. The task with rank 0 is often referred to as *root*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Sendrecv"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you need to send data to another rank and receive data from the same rank, combining `Send` and `Recv` command is dangerous and easily leads to deadlocks. Use `Sendrecv` instead."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "a = numpy.ones(1) * rank\n",
+ "b = numpy.ones(1) * rank\n",
+ "if rank == 0:\n",
+ " comm.Sendrecv(a, 1, recvbuf=b, source=1)\n",
+ " print(f\"[{rank}] {b[0]}\")\n",
+ "elif rank == 1:\n",
+ " comm.Sendrecv(a, 0, recvbuf=b, source=0)\n",
+ " print(f\"[{rank}] {b[0]}\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Parallel reduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We'll generate an array of random number on rank 0 and distribute (scatter) it to all ranks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "N = 1000\n",
+ "a_partial = numpy.empty(N)\n",
+ "if rank == 0:\n",
+ " rng = numpy.random.Generator(numpy.random.MT19937())\n",
+ " a = rng.uniform(size=N * size)\n",
+ "else:\n",
+ " a = numpy.empty(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since we are dealing with NumPy arrays, we can use the efficient uppercase versions of the MPI calls. Scatter distributes an array evenly among all nodes. Note, the sendbuf only needs to be allocated on node zero, but the variable must exist everywhere."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm.Scatter(a, a_partial, root = 0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "sum_partial = numpy.sum(a_partial)\n",
+ "total = comm.reduce(sum_partial)\n",
+ "if rank == 0:\n",
+ " print(\"The sum of the random numbers is %f. The average is %f.\" % (total, total / len(a)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Upper vs. lowercase in mpi4py"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "`mpi4py` offers two version of many calls. The first one is written in uppercase. It uses memory buffers, e.g., `np.array`, and maps the call directly to the appropriate C call. The second version is written in lower case and takes arbitrary Python object. The result is given as the return value. Note, that for the uppercase versions all a_partial must have the same size!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "a_all = None\n",
+ "if rank == 0:\n",
+ " a_all = numpy.empty([size, len(a_partial)], dtype='f8')\n",
+ "comm.Gather(a_partial, a_all, root=0)\n",
+ "if rank == 0:\n",
+ " print(type(a_all))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "%timeit comm.Gather(a_partial, a_all, root=0) # Don't use %timeit outside IPython."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The following works independent of the size of a_partial:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "a_all = comm.gather(a_partial)\n",
+ "if rank == 0:\n",
+ " print(type(a_all))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, `a_all` contains a `list` of `np.array`s.\n",
+ "\n",
+ "This second version is convenient, but it is **much** slower:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "%timeit a_all = comm.gather(a_partial)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "It gets worse as arrays get bigger.\n",
+ "\n",
+ "To retrieve the result, we use the `view` again."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "## Remarks\n",
+ "While Jupyter notebooks are a nice way to teach MPI and well tested MPI routines can be quite useful within a notebook, developing MPI code within notebooks can quickly become awkward because mistakes lead to blocking engines. I find it easier to write and test my MPI routines outside Jupyter notebooks and start the program with `mpiexec`/`srun` from the command line.\n",
+ "\n",
+ "For example, you could write the following program and save it to a file:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile helloparallelworld.py\n",
+ "from mpi4py import MPI\n",
+ "import numpy as np\n",
+ "\n",
+ "rank = MPI.COMM_WORLD.Get_rank()\n",
+ "numberOfRanks = MPI.COMM_WORLD.Get_size()\n",
+ "\n",
+ "a = np.zeros(1)\n",
+ "if rank == 0:\n",
+ " print(\"There are %d MPI ranks.\" % numberOfRanks)\n",
+ " a = np.random.random(1)\n",
+ "\n",
+ "print(\"I'm rank %d.\" % rank)\n",
+ "if numberOfRanks < 2:\n",
+ " print(\"Not enough MPI tasks!\")\n",
+ " exit(1)\n",
+ "if rank == 0:\n",
+ " MPI.COMM_WORLD.Send(a, dest=1)\n",
+ "elif rank == 1:\n",
+ " MPI.COMM_WORLD.Recv(a, source=0)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You can then switch to a terminal and execute it as `srun -n 2 --ntasks-per-node 2 python helloparallelworld.py`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercises"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Peak to Peak\n",
+ "Write a program that generates random numbers from a Gaussian distribution and then finds the minimum and maximum number generated.\n",
+ "\n",
+ "a) Generate the random numbers on rank 0 and scatter them. Calculate the maximum and minimum for the partial data for \n",
+ " each rank and send the results back to rank 0. Find the maximum and minimum on rank 0 and compare it with numpy's\n",
+ " `ptp` function.\n",
+ " \n",
+ "b) Generate random numbers at each rank. Calculate the minimum and maximum and use `Reduce` to find the extrema and send \n",
+ " them to rank 0."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "## Solutions:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile mpi_ptp1.py\n",
+ "\n",
+ "from mpi4py import MPI\n",
+ "import numpy as np\n",
+ "\n",
+ "comm=MPI.COMM_WORLD\n",
+ "rank = comm.Get_rank()\n",
+ "numberOfRanks = comm.Get_size()\n",
+ "if numberOfRanks < 2:\n",
+ " print(\"Not enough MPI tasks!\")\n",
+ " exit(1)\n",
+ "\n",
+ "nRnd=10000\n",
+ "part = np.zeros(nRnd)\n",
+ "a=minvals=maxvals=None\n",
+ "if rank == 0:\n",
+ " a = np.random.default_rng().normal(0.0, 1.0, numberOfRanks*nRnd)\n",
+ " maxvals=np.zeros(numberOfRanks)\n",
+ " minvals=np.zeros(numberOfRanks)\n",
+ "comm.Scatter(a,part,0)\n",
+ "comm.Gather(part.max(),maxvals,0)\n",
+ "comm.Gather(part.min(),minvals,0)\n",
+ "if rank == 0:\n",
+ " print(\"np.ptp=%f, mpi_ptp=%f\"%(a.ptp(),max(maxvals)-min(minvals)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile mpi_ptp2.py\n",
+ "\n",
+ "from mpi4py import MPI\n",
+ "import numpy as np\n",
+ "\n",
+ "comm=MPI.COMM_WORLD\n",
+ "rank = comm.Get_rank()\n",
+ "numberOfRanks = comm.Get_size()\n",
+ "if numberOfRanks < 2:\n",
+ " print(\"Not enough MPI tasks!\")\n",
+ " exit(1)\n",
+ "\n",
+ "nRnd=10000\n",
+ "part = np.random.default_rng().normal(0.0, 1.0, nRnd)\n",
+ "minval=part.min()\n",
+ "maxval=part.max()\n",
+ "globmin=np.zeros(1)\n",
+ "globmax=np.zeros(1)\n",
+ "comm.Reduce(minval,globmin,MPI.MIN)\n",
+ "comm.Reduce(maxval,globmax,MPI.MAX)\n",
+ "if rank == 0:\n",
+ " print(\"np.ptp=n.d., mpi_ptp=%f\"%(globmax-globmin))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Domain decomposition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If at least some of the interactions we are dealing with are short ranged, we can often split a system into multiple domains that can be treated independently. These domains don't have to be regular. Sometimes it's better to use [space filling curves](https://en.wikipedia.org/wiki/Space-filling_curve) to split up a problem. In this section, however, we'll look at a regular grid."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "In [Think Vector][TV] we looked at [stencils][TV_Stencils]. In this section, we'll distribute a 2d stencil calculation using a domain decomposition with MPI. \n",
+ "\n",
+ "Remember our system looked something like this (I made it a little wider this time.):\n",
+ "\n",
+ "[TV]: ThinkVector.ipynb\n",
+ "[TV_Stencils]: ThinkVector.ipynb#Stencils"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A = numpy.random.random((10, 30))\n",
+ "A[:,0] = 0\n",
+ "A[:,-1] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(15, 5))\n",
+ "plt.imshow(A)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The system is basically a square grid. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's assume we want to split our system in three parts along the horizontal axis. Each processor get's an equal share of the grid. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "To calculate the value for each point, we need all its neighbors. When we work on the field at the boundary, this includes data from the neighboring domain. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The data from the neighnboring domains is stored as a *halo* to the main domain that the rank is working on. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The data in the halos needs to be transferred from the neighbor(s) and updated after each iterations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "I would recommend using an editor for this exercise. Jupyter Lab comes with an editor that supports syntax highlighting but no auto completion. You can find it under File->New->Text File. The new file will be called `Untitled.txt`. You can change the file name by righ-clicking on the editor tab or right-clicking on the file in the file browser view on the left."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "1. Take the program from the [Stencil][TV_Stencils] and use a 1d domain decomposition as described \n",
+ " above to parallelize the program using MPI over 3 domains using 3 MPI ranks. Construct the grid \n",
+ " in such a way that you can easily divide it into 3 domains. Use [point to point communication](#Point-to-point). The program should run to convergence determined by epsilon just as before.\n",
+ "\n",
+ " Tip: It may be easier to turn the problem by 90° or use Fortran order for the NumPy arrays.\n",
+ " \n",
+ "2. Extend the program from the first part of the exercise to use more than 3 ranks with 1 domain \n",
+ " per rank.\n",
+ "\n",
+ "3. Time the execution of the program from the second part of the exercise.\n",
+ "\n",
+ " a) Keep the size of the system constant and increase the number of ranks/domain, e.g., using 2, \n",
+ " 4, 8, and 16 ranks. How \n",
+ " \n",
+ " b) Keep the size of the domains constant, i.e., the total size is a multiple of the number of \n",
+ " ranks. Again increase the number of ranks\n",
+ "\n",
+ "[TV_Stencils]: ThinkVector.ipynb#Stencils"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile sol_par_stencil.py\n",
+ "# Solution to part 2\n",
+ "import numpy\n",
+ "import matplotlib.pyplot as plt\n",
+ "from mpi4py import MPI\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " comm = MPI.COMM_WORLD\n",
+ " rank = comm.Get_rank()\n",
+ " size = comm.Get_size()\n",
+ "\n",
+ " ny = 20 # Use a grid that's 20 high\n",
+ " nx = ny * size # Make grid `size` times wider\n",
+ "\n",
+ " epsilon = 1e-2\n",
+ " max_iteration = 5000\n",
+ " global_diffAB = numpy.ones(1) * 10 * epsilon\n",
+ "\n",
+ " if rank == 0:\n",
+ " rng = numpy.random.Generator(numpy.random.MT19937())\n",
+ " A = rng.uniform(size=(ny, nx))\n",
+ " A[:,0] = 0\n",
+ " A[:,-1] = 1\n",
+ " # Since we want to split the domain horizontally, it's easier to use Fortran order\n",
+ " A = numpy.asfortranarray(A)\n",
+ " print(A)\n",
+ " else:\n",
+ " A = None\n",
+ "\n",
+ " if rank == 0 or rank == (size - 1):\n",
+ " my_domain = numpy.empty((ny, ny + 1), order='F')\n",
+ " else:\n",
+ " my_domain = numpy.empty((ny, ny + 2), order='F')\n",
+ "\n",
+ " comm.Scatter(A, my_domain)\n",
+ "\n",
+ " if rank > 0:\n",
+ " # Move data, so we have room in the halo\n",
+ " my_domain = numpy.roll(my_domain, 1, axis=1)\n",
+ "\n",
+ " i = 0\n",
+ " while global_diffAB > epsilon and i < max_iteration:\n",
+ " if rank == 0:\n",
+ " print(f\"{i: 4d}: {global_diffAB[0]:.3f}\")\n",
+ " # print(f\"{i: 4d}: {my_domain.strides}\")\n",
+ " # Get column(s) from neighbor\n",
+ " if rank > 0:\n",
+ " # Get column from left neighbor\n",
+ " comm.Sendrecv(my_domain[:,1], dest=rank - 1, recvbuf=my_domain[:,0], source=rank - 1)\n",
+ " if rank < (size - 1):\n",
+ " # Get column from right neighbor\n",
+ " comm.Sendrecv(my_domain[:,-2], dest=rank + 1, recvbuf=my_domain[:,-1], source=rank + 1)\n",
+ " \n",
+ "\n",
+ " # Apply stencil\n",
+ " B = 0.25*(numpy.roll(my_domain, 1,axis=0) + numpy.roll(my_domain, -1, axis=0) + \n",
+ " numpy.roll(my_domain, 1,axis=1) + numpy.roll(my_domain, -1,axis=1))\n",
+ "\n",
+ " # Keep our boundaries at a fixed value\n",
+ " if rank == 0:\n",
+ " B[:, 0] = 0\n",
+ " if rank == (size - 1):\n",
+ " B[:, -1] = 1\n",
+ "\n",
+ " # Calculate local difference\n",
+ " if rank == 0:\n",
+ " diffAB = numpy.linalg.norm(my_domain[:,:-1] - B[:,:-1])\n",
+ " elif rank == (size - 1): \n",
+ " diffAB = numpy.linalg.norm(my_domain[:,1:] - B[:,1:])\n",
+ " else:\n",
+ " diffAB = numpy.linalg.norm(my_domain[:,1:-1] - B[:,1:-1])\n",
+ " my_domain = B.copy(order='A')\n",
+ "\n",
+ " # Calculate global difference\n",
+ " comm.Allreduce(diffAB, global_diffAB)\n",
+ " i += 1\n",
+ "\n",
+ " # Once we are done, collect the result on rank 0\n",
+ " if rank > 0:\n",
+ " A_final = None\n",
+ " comm.Gather(my_domain[:,1: ny + 1], A_final)\n",
+ " else:\n",
+ " A_final = numpy.empty((size, ny, ny))\n",
+ " comm.Gather(my_domain[:, :ny], A_final)\n",
+ " A_final = numpy.vstack(A_final).T\n",
+ " plt.figure(figsize=(15, 5))\n",
+ " plt.imshow(A_final)\n",
+ " plt.savefig(\"final.png\")\n",
+ " \n",
+ "\n",
+ "if __name__ == \"__main__\":\n",
+ " main()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Amdahl's law"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We already talked about a number of ways to parallelize our code, but we haven't discussed how much speedup we might expect from our parallelized code compared to the serial version.\n",
+ "\n",
+ "If we get a profile for our code, we have an idea of how much time the function we parallelized takes, when we run this on a single core. With that information and some assumption, we can estimate the possbile speedup using Amdahl's law."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Assume that the total runtime of a program can be split into a serial and a perfectly parallelizable part."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$t_1 = t_s + t_p$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The runtime for $n$ processors is then"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$t_n = t_s + t_p / n$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "From this, we can calculate the speedup compared to a single core"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{t_1}{t_n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "or"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{t_s + t_p}{t_s + t_p / n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let $f$ be the fraction of the parallelizable part then we can rewrite $s_n$ as"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{t_1}{(1-f)t_1 + ft_1/n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Elimintating $t_1$, we get"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$s_n = \\frac{1}{(1-f) + f/n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Speedup using Amdahl's law"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's plot this vs the number of processors."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def amdahl_speedup(f, n):\n",
+ " return 1.0 / ((1-f) + f / n)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "n = numpy.arange(1, 1000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(5, 2.5), dpi=150)\n",
+ "for f in [0.5, 0.75, 0.8, 0.9, 0.95]:\n",
+ " plt.plot(amdahl_speedup(f, n), label=f\"{f * 100}%\")\n",
+ " plt.legend(); plt.ylim([0, 20]);plt.xlabel('n'); plt.ylabel('s')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Speedup using Amdahl's law"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.figure(figsize=(5, 2.5), dpi=150)\n",
+ "for f in [0.5, 0.75, 0.8, 0.9, 0.95, 0.99]:\n",
+ " plt.plot(amdahl_speedup(f, n), label=f\"{f * 100}%\")\n",
+ " plt.legend(); plt.ylim([0, 100]);plt.xlabel('n'); plt.ylabel('s')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## IPyParallel and MPI"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can use ipyparallel to push data to and pull data from the engines. All the operations that we used in [Interactive Parallel Computing with IPython Parallel][IPCIP] are still available and can be combined with mpi4py.\n",
+ "\n",
+ "[IPCIP]: Interactive%20;Parallel%20;Computing%20;with%20;IPython%20;Parallel.ipynb"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Let's start by creating an array of random numbers and scattering it to all the ranks, i.e., each rank gets some part of the array."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Variables that are defined on the engines can be retrieved through the `view`. To get the variable rank, e.g., you can write"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ranks = view['rank']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Until recently, the ranks were not in any particular order, which can be annoying, but we can get the right order by casting ranks to an ndarray and calling argsort. The result gives us the engines in MPI rank order. Give it a try."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ranksort = numpy.array(ranks).argsort()\n",
+ "rank0 = int(ranksort[0])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# This cell is executed within the notebook. The engines don't know anything about it\n",
+ "rng = numpy.random.Generator(numpy.random.MT19937())\n",
+ "a = np.random.normal(size=100000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# First push the array to the engine with MPI rank 0\n",
+ "%px a = None\n",
+ "view.push({'a':a}, targets=rank0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next, we scatter the data from rank 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "view.scatter('a_partial', a)\n",
+ "view[\"a_partial\"][0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can now calculate the partial sum on each rank and then sum up the partial results using mpi4py's `reduce` function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "sum_partial = np.sum(a_partial)\n",
+ "total = comm.reduce(sum_partial)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Use the view to get the result back into the notebook."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "total = view.pull('total', targets=rank0)\n",
+ "sum_partial = view['sum_partial']\n",
+ "print(\"The sum of the random numbers is %f. The average is %f.\" % (total, total / len(a)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sum_partial"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sum(sum_partial)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/15_Introduction to CuPy.ipynb b/solutions/15_Introduction to CuPy.ipynb
new file mode 100644
index 0000000..1481e68
--- /dev/null
+++ b/solutions/15_Introduction to CuPy.ipynb
@@ -0,0 +1,462 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Introduction to CuPy\n",
+ "<div class=\"dateauthor\">\n",
+ "19 Nov 2020 | Jan H. Meinke\n",
+ "</div>\n",
+ "<img src=\"images/cupy.png\" style=\"float:right\">"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CuPY\n",
+ "### A NumPy-like interface to GPU programming"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "> The best way to program a GPU is to let other people do the work!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "[CuPy][] provides a [NumPy][]-like interface to use and program GPUs.\n",
+ "\n",
+ "[CuPy]: https://cupy.dev/\n",
+ "[NumPy]: https://numpy.org/"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import cupy\n",
+ "N = 2048\n",
+ "A = cupy.random.random((N, N))\n",
+ "B = cupy.random.random((N, N))\n",
+ "C = A@B"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "This cell creates two random arrays of size N by N on the GPU and performs a matrix multiplication using Nvidia's optimized linar algebra library cuBLAS."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "In [Think Vector][TV], you [calculated the Mandelbrot set][TV_Mandelbrot] using [NumPy][] and vectorization. Take either your solution or ours and convert it to [CuPy][]. Visualize the result.\n",
+ "\n",
+ "Tip: If you get an error message when visualizing the results, take a look [below](#CuPy-Arrays).\n",
+ "\n",
+ "[CuPy]: https://cupy.dev/\n",
+ "[NumPy]: https://numpy.org/\n",
+ "[TV]: ThinkVector.ipynb\n",
+ "[TV_Mandelbrot]: ThinkVector.ipynb#Programming-exercise-Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Let's take the same ranges for real and imaginary numbers as above\n",
+ "re = cupy.linspace(-2.2, 1, 640)\n",
+ "im = cupy.linspace(-1.2, 1.2, 480)\n",
+ "# X and Y will have a shape of (640, 480) with the values taken from re and im.\n",
+ "X, Y = cupy.meshgrid(re, im)\n",
+ "\n",
+ "# Finally, add X and Y to get our grid\n",
+ "P = X + Y * 1j\n",
+ "\n",
+ "maxtime = 50\n",
+ "M = cupy.ones_like(P, dtype=int) * maxtime\n",
+ "Z = cupy.zeros_like(P)\n",
+ "\n",
+ "for iter in range(maxtime):\n",
+ " Z = Z * Z + P\n",
+ " mask = cupy.abs(Z) > 2\n",
+ " M[mask] = iter\n",
+ " P[mask] = 0\n",
+ " Z[mask] = 0\n",
+ "\n",
+ "plt.imshow(M.get())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "Compared to the solution for Mandelbrot in Think Vector, I changed 3 things:\n",
+ "\n",
+ "1. Replaced `numpy` with `cupy`\n",
+ "2. Removed `j` from the second `linspace` command and added it instead to construction of P\n",
+ "3. Call `M.get()` to get the data from the GPU, so I can plot them."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## GPU Libraries"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "* cuBLAS\n",
+ "* cuDNN\n",
+ "* cuRand \n",
+ "* cuSolver\n",
+ "* cuSPARSE\n",
+ "* cuFFT\n",
+ "* NCCL "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CuPy is the fastest and easiest way to use Nvidia's GPU libraries."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "a) Time the execution of C=A@B for different matrix sizes, e.g., 256, 512, 1024, 2048, 4096. Calculate the performance in GFLOP/s using gflops = 2e-9 * N ** 3 / t and store the sizes and the times in an ndarray.\n",
+ "\n",
+ "b) Do the same using numpy. How do the numbers compare."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CuPy Arrays"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CuPy arrays live on the GPU. To retrieve them you can use"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "A = cupy.random.random((N, N))\n",
+ "A1_np = A.get()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "A2_np = cupy.asnumpy(A)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The first command only works for GPU arrays, but the second can also be used for a NumPy array. If A is a GPU array, the data will be copied from the CPU to the GPU. If A is a NumPy array, no copy will be made and A2_np becomes a reference to A."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "x = numpy.linspace(0, 1, 10)\n",
+ "x_gpu = cupy.asarray(x) # Copy x to the GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "To transfer data to the GPU use `cupy.asarray`. This doesn't just work with NumPy arrays, but also, for example, with lists."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "### Exercise\n",
+ "Create a 2D array of random number on the GPU. Transfer it to the CPU. Subtract 0.5 from all elements. Copy the result back to the GPU. Clculate the average value of all elements on the GPU and write the result to the screen."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "# Solution\n",
+ "N = 1000\n",
+ "A = cupy.random.random((N, N))\n",
+ "A_np = A.get()\n",
+ "A_np -= 0.5\n",
+ "A = cupy.array(A_np)\n",
+ "print(f\"The average value of the elements is {A.mean()}\") # Should be near 0."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Picking a Device"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CuPy always works on the *current device*. On multi-GPU nodes this can be changed using"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "cupy.cuda.Device(1).use()\n",
+ "A_on_gpu1 = cupy.random.random((N, N))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you need to switch devices regularly, you can use a `with` statement:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "with cupy.cuda.Device(2):\n",
+ " A_on_gpu2 = cupy.random.random((N, N))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note, that you can only access `A_on_gpu2` while device 1 is active. Otherwise, you'll get an error message."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/16_CUDA for Python.ipynb b/solutions/16_CUDA for Python.ipynb
new file mode 100644
index 0000000..fd1566a
--- /dev/null
+++ b/solutions/16_CUDA for Python.ipynb
@@ -0,0 +1,1482 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# Numba and GPUs\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "20 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba supports Nvidia and AMD GPUs. In this course, however, we are going to focus on CUDA capable GPUs from Nvidia. \n",
+ "\n",
+ "Hint: If you are working with an older version of Numba and want to use an already installed CUDA SDK, there are two environment variables that might have to be set to let numba know where it can find the libraries it needs. On JUWELS this it *not* necessary.\n",
+ "\n",
+ "```bash\n",
+ "export NUMBA_NVVM=$CUDA_HOME/nvvm/lib64/libnvvm.so\n",
+ "export NUMBA_LIBDEVICE=$CUDA_HOME/nvvm/libdevice/\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Let's ignore some deprecation warnings\n",
+ "from numba.core.errors import NumbaDeprecationWarning, NumbaPendingDeprecationWarning\n",
+ "import warnings\n",
+ "\n",
+ "warnings.simplefilter('ignore', category=NumbaDeprecationWarning)\n",
+ "warnings.simplefilter('ignore', category=NumbaPendingDeprecationWarning)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Ufunc"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We already learned how to vectorize a function. Remember the Mandelbrot set. We defined a function that returns the number of iterations needed to decide if the algorithm diverges."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import vectorize\n",
+ "\n",
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \"\"\"\n",
+ " z = 0j\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy\n",
+ "x = numpy.linspace(-2, 2, 500)\n",
+ "y = numpy.linspace(-1.5, 1.5, 375)\n",
+ "zr, zc = numpy.meshgrid(x, 1j * y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "escape_time_v = vectorize(\"int64(complex128, int64)\", \n",
+ " target=\"parallel\")(escape_time)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "t_cpu = %timeit -o escape_time_v(zr + zc, 500)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "If you replace `target=\"parallel\"` with `target=\"cuda\"` the function runs on the GPU instead. Give it a try and compare the performance for different sizes of the grid:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "# Your code goes here"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "escape_time_g = vectorize(\"int64(complex128, int64)\", \n",
+ " target=\"cuda\")(escape_time)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "t_gpu = %timeit -o escape_time_g(zr + zc, 500)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CUDA for Python"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Numba allows you to write CUDA programs in Python. \n",
+ "\n",
+ "While a complete introduction to CUDA is beyond the scope of this course---there are other courses for this, for example, GPU Programming with CUDA @ JSC and also many online resources available---here you'll get the nutshell version and some of the differences between CUDA C++ and CUDA Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## CPU vs. GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## CPU vs. GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "CPUs are optimized for latency."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "A CPU tries to execute a given instruction as quickly as possible, i.e., it tries to keep the latency (the time between issuing and executing an instruction) as short as possible. CPUs use caches and a lot of control logic to achieve this goal."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs are optimized for throughput."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## CPU vs. GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "GPUs were (and are) made to display graphics on your screen. It doesn't matter how quickly a GPU can update a single pixel. It's important how quickly it can update all of the pixels on the screen (more than 2 million on an HD display). In addition it often must perform the same operation on a lot of vertices or pixels. \n",
+ "\n",
+ "These two conditions let to a different execution model."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "\n",
+ "## GPU execution model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs use *many* lightweight threads."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs hide latency instead of avoiding it"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "GPUs work best if the problem can me mapped on a grid, but other models are possible."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Kernels"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We can calculate the Mandelbrot set using `escape_time` like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "maxiter = 20\n",
+ "rlim = (-2.2, 1.5)\n",
+ "ilim = (-1.5, 1.5)\n",
+ "nx = 100\n",
+ "ny = 75\n",
+ "\n",
+ "dx = (rlim[1] - rlim[0]) / nx\n",
+ "dy = (ilim[1] - ilim[0]) / ny\n",
+ "\n",
+ "M = numpy.zeros((ny, nx), dtype=int)\n",
+ "\n",
+ "for i in range(ny):\n",
+ " for j in range(nx):\n",
+ " p = rlim[0] + j * dx + (ilim[0] + i * dy) * 1j\n",
+ " M[i, j] = escape_time(p, maxiter)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "plt.imshow(M, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Notice that for every pair (i, j), we calculate the escape time. This makes\n",
+ "\n",
+ "```python\n",
+ " p = rlim[0] + j * dx + (ilim[0] + i * dy) * 1j\n",
+ " M[i, j] = escape_time(p, maxiter)\n",
+ "```\n",
+ "\n",
+ "our kernel that we execute on the grid spanned by the two for loops. It's quite apparent on the image above, where the coordinates for each value are shown in index space."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Threads and blocks and grids, oh my!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The basic unit of execution is a thread. All the threads of a kernel call execute the same code."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Thread blocks"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Threads are organized in blocks. All threads in a block are executed on the same *streaming multiprocessor* (SM, comparable to a core on a CPU). They can share fast *shared memory* and synchronize easily. A thread block is pinned to the SM, i.e., once it was launched on a particular SM it stays there.\n",
+ "\n",
+ "A thread block can have one, two, or three dimensions to make mapping the problem to the thread model easier. The choice is up to the programmer.The maximum dimension of a thread block is 1024x1024x64, where the volume of the thread block (the number of threads in the block) must be 1024 or less."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Grid of thread blocks"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Thread blocks are organized in a grid to cover all the threads needed to solve you problem. A grid can have one, two, or three dimensions. The dimensionality of the grid is in principle independent of the dimensionality of the blocks it contains. The maximum grid dimensions are 2147483647྾65535྾65535 blocks!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Thread ID"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Each thread has an x, y, and z index that can be queried in a kernel."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "``` python\n",
+ "from numba import cuda\n",
+ "\n",
+ "@cuda.jit\n",
+ "def my_kernel:\n",
+ " x,y,z = cuda.grid(3) # use 2 if you only need x, y and 1 for x\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Writing a kernel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "For writing a CUDA kernel, we use `cuda.jit` instead of `jit` as decorator (see above). The kernel can also call other functions that have been decorated with `cuda.jit(device=True)`. A Mandelbrot kernel could look like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import cuda\n",
+ "\n",
+ "escape_time_gpu = cuda.jit(device=True)(escape_time)\n",
+ "\n",
+ "@cuda.jit\n",
+ "def mandelbrot_gpu(M, real_min, real_max, imag_min, imag_max):\n",
+ " \"\"\"Calculate the Mandelbrot set on the GPU.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " M : numpy.ndarray\n",
+ " a two-dimensional integer array that will contain the \n",
+ " escape times for each point.\n",
+ " real_min, real_max: float\n",
+ " minimum and maximums value on the real axis\n",
+ " imag_min, imag_max: float\n",
+ " minimum and maximum value on the imaginary axis\n",
+ " \"\"\"\n",
+ " ny, nx = M.shape\n",
+ " i, j = cuda.grid(2)\n",
+ " \n",
+ " if i < nx and j < ny:\n",
+ " dx = (real_max - real_min) / nx\n",
+ " dy = (imag_max - imag_min) / ny\n",
+ " p = real_min + dx * i + (imag_min + dy * j) * 1j\n",
+ " M[j, i] = escape_time_gpu(p, 20)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Note, that there is no return value. CUDA kernels have to return their result through an argument. In the above kernel, the result will be in M"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Calling a kernel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CUDA needs to know how many blocks and how many threads per block you want to launch. This is called the *launch configuration*. To calculate the Mandelbrot set with of two 1024 by 1024 points with a block size of 32 by 32, we need 1024/32=32 by 1024/32=32 blocks.\n",
+ "\n",
+ "If we want to calculate the set for 1032 by 1032 points, we have to add an extra block. The following lines take care of that:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "M = numpy.zeros((1024, 1024), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0], M.shape[1] // block[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "The launch configuration is passed in square brackets before the function arguments."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit mandelbrot_gpu[grid, block](M, -2.2, 1.2, -1.6, 1.6)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(M, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "If the dimension of your system is not a *multiple of your block size*, you need to add an extra block. The following code snippet takes care of this. (There are other ways to do this, too.)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "M = numpy.zeros((1000, 1000), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0] if M.shape[0] % block[0] == 0 \n",
+ " else M.shape[0] // block[0] + 1,\n",
+ " M.shape[1] // block[1] if M.shape[1] % block[1] == 0 \n",
+ " else M.shape[1] // block[1] + 1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%timeit mandelbrot_gpu[grid, block](M, -2.2, 1.2, -1.6, 1.6)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "plt.imshow(M, interpolation=\"nearest\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Profile the Mandelbrot calculation on the GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "a) Use %timeit to measure the speed of the GPU implementation and compare it to the vectorized version."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "b) The kernel calculates dx and dy for every pixel although it is the same for all of them. Change the kernel so that it takes dx and dy as arguments and calculate dx and dy before you call the kernel. Does this improve the performance?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "@cuda.jit\n",
+ "def mandelbrot_gpu2(M, real_min, real_max, imag_min, imag_max, dx, dy):\n",
+ " \"\"\"Calculate the Mandelbrot set on the GPU.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " M : numpy.ndarray\n",
+ " a two-dimensional integer array that will contain the \n",
+ " escape times for each point.\n",
+ " real_min: float\n",
+ " minimum value on the real axis\n",
+ " imag_min: float\n",
+ " minimum value on the imaginary axis\n",
+ " dx, dy: float\n",
+ " step size along the real and imaginary axes.\n",
+ " \"\"\"\n",
+ " ny, nx = M.shape\n",
+ " i, j = cuda.grid(2)\n",
+ " \n",
+ " if i < nx and j < ny:\n",
+ " p = real_min + dx * i + (imag_min + dy * j) * 1j\n",
+ " M[j, i] = escape_time_gpu(p, 20)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "M = numpy.zeros((1024, 1024), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0], M.shape[1] // block[1])\n",
+ "real_min, real_max = (-2.2, 1.2)\n",
+ "imag_min, imag_max = (-1.6, 1.6)\n",
+ "dx = (real_max - real_min) / M.shape[1]\n",
+ "dy = (imag_max - imag_min) / M.shape[0]\n",
+ "%timeit mandelbrot_gpu2[grid, block](M, -2.2, 1.2, -1.6, 1.6, dx, dy)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "c) Add an additional argument escape_time to the kernel, so that you can time the kernel for different escape time values. Don't forget to add the new argument to the documentation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "@cuda.jit\n",
+ "def mandelbrot_gpu3(M, real_min, real_max, imag_min, imag_max, max_iter=50):\n",
+ " \"\"\"Calculate the Mandelbrot set on the GPU.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " M : numpy.ndarray\n",
+ " a two-dimensional integer array that will contain the \n",
+ " escape times for each point.\n",
+ " real_min, real_max: float\n",
+ " minimum and maximums value on the real axis\n",
+ " imag_min, imag_max: float\n",
+ " minimum and maximum value on the imaginary axis\n",
+ " max_iter: int\n",
+ " maximum number of iterations before we consider this point to be \n",
+ " part of the Mandelbrot set.\n",
+ " \"\"\"\n",
+ " ny, nx = M.shape\n",
+ " i, j = cuda.grid(2)\n",
+ " \n",
+ " if i < nx and j < ny:\n",
+ " dx = (real_max - real_min) / nx\n",
+ " dy = (imag_max - imag_min) / ny\n",
+ " p = real_min + dx * i + (imag_min + dy * j) * 1j\n",
+ " M[j, i] = escape_time_gpu(p, max_iter)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "M = numpy.zeros((1024, 1024), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0], M.shape[1] // block[1])\n",
+ "%timeit mandelbrot_gpu3[grid, block](M, -2.2, 1.2, -1.6, 1.6, 50)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "mandelbrot_gpu3[grid, block](M, -2.2, 1.2, -1.6, 1.6, 50)\n",
+ "plt.imshow(M)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Explicit memory management"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Discrete GPUs have their own memory. Data needs to be transferred from the host and results have to transferred back to the host as necessary. Numba takes care of the memory transfers but it does so in a very conservative way: all data is transferred back to the host after a kernel finished. This behavior can be avoided by [managing memory explicitely](http://numba.pydata.org/numba-doc/latest/cuda/memory.html#data-transfer)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Often, we want to copy an existing array to the GPU. For this we can use `numba.cuda.to_device`. This will allocate memory on the GPU and copy data from the CPU to the GPU, for example,"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "```Python\n",
+ "l = numpy.linspace(0, 10, 100)\n",
+ "d_l = cuda.to_device(l)\n",
+ "# Run kernel\n",
+ "...\n",
+ "# Copy data back\n",
+ "l = d_l.copy_to_host()\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "You can allocate an empty array on the GPU using `numba.cuda.device_array`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "```Python\n",
+ "n = 1000\n",
+ "d_random = cuda.device_array(n)\n",
+ "# Run kernel\n",
+ "...\n",
+ "# Copy data back\n",
+ "myRandom = d_random.copy_to_host()\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Use explicitly managed memory for Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "The M array is transferred to the GPU before the kernel runs. This is not necessary. Use a device array instead. Compare the runtime to the previous version."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "M = cuda.device_array((1024, 1024), dtype=numpy.int32)\n",
+ "block = (32, 32)\n",
+ "grid = (M.shape[0] // block[0], M.shape[1] // block[1])\n",
+ "%timeit mandelbrot_gpu3[grid, block](M, -2.2, 1.2, -1.6, 1.6, 50)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "source": [
+ "This is much faster! Most of the time of running the Mandelbrot program on the GPU is actually spent transferring data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "mandelbrot_gpu3[grid, block](M, -2.2, 1.2, -1.6, 1.6, 50)\n",
+ "plt.imshow(M)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Matrix multiplication"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Write a kernel, where each thread calculates one element of the result matrix $C=AB$, where A and B are matrices.\n",
+ "\n",
+ "For the algorithm, you can take a look at Bottlenecks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "@cuda.jit\n",
+ "def mm(A, B, C):\n",
+ " \"\"\"Take two matrices A and B, calculate the matrix product and store it in C.\"\"\"\n",
+ " i, j = cuda.grid(2)\n",
+ " if i < A.shape[0] and j < B.shape[1]:\n",
+ " tmp = 0\n",
+ " for k in range(A.shape[1]):\n",
+ " tmp += A[i, k] * B[k, j]\n",
+ " C[i, j] = tmp"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "A = numpy.random.random((1024, 512))\n",
+ "B = numpy.random.random((512, 256))\n",
+ "C_np = A@B"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "block = (32, 32)\n",
+ "grid = (1024 // 32, 256 // 32)\n",
+ "C = cuda.device_array((1024, 256))\n",
+ "mm[grid, block](A, B, C)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ },
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "C_host = C.copy_to_host()\n",
+ "\n",
+ "numpy.allclose(C_np, C_host)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Using shared memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As you learned in Bottlenecks, the matrix matrix multiplication tends to be memory bandwidth bound. This is true on the GPU, too.\n",
+ "\n",
+ "The way to make it faster is to use faster memory. On a CPU this usually means, dividing the matrix into blocks that fit in cache and hope for the best. On a GPU at lease part of the fast memory is usually programmable. In CUDA this memory is called *shared memory*.\n",
+ "\n",
+ "Shared memory is available to all *threads in a thread block*. Usually, each thread loads data from device memory into shared memory. This is followed by barrier, so that all threads are finished reading. Then the shared memory is reused as often as possible. Another barrier makes sure that all threads are done."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Let's look at an example:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Matrix multiplication with shared memory"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The following function performs a matrix multiplication on the GPU using shared memory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from numba import cuda, float32\n",
+ "# Controls threads per block and shared memory usage.\n",
+ "# The computation will be done on blocks of TPBxTPB elements.\n",
+ "TPB = 16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "@cuda.jit\n",
+ "def fast_matmul(A, B, C):\n",
+ " # Define an array in the shared memory\n",
+ " # The size and type of the arrays must be known at compile time\n",
+ " sA = cuda.shared.array(shape=(TPB, TPB), dtype=float32)\n",
+ " sB = cuda.shared.array(shape=(TPB, TPB), dtype=float32)\n",
+ "\n",
+ " x, y = cuda.grid(2)\n",
+ " tx = cuda.threadIdx.x\n",
+ " ty = cuda.threadIdx.y\n",
+ " bpg = cuda.gridDim.x # blocks per grid\n",
+ "\n",
+ " if x >= C.shape[0] and y >= C.shape[1]:\n",
+ " # Quit if (x, y) is outside of valid C boundary\n",
+ " return\n",
+ "\n",
+ " # Each thread computes one element in the result matrix.\n",
+ " # The dot product is chunked into dot products of TPB-long vectors.\n",
+ " tmp = 0.\n",
+ " for i in range(bpg):\n",
+ " # Preload data into shared memory\n",
+ " sA[tx, ty] = A[x, ty + i * TPB]\n",
+ " sB[tx, ty] = B[tx + i * TPB, y]\n",
+ "\n",
+ " # Wait until all threads finish preloading\n",
+ " cuda.syncthreads()\n",
+ "\n",
+ " # Computes partial product on the shared memory\n",
+ " for j in range(TPB):\n",
+ " tmp += sA[tx, j] * sB[j, ty]\n",
+ "\n",
+ " # Wait until all threads finish computing\n",
+ " cuda.syncthreads()\n",
+ "\n",
+ " C[x, y] = tmp"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "The above example shows most special functions used in CUDA kernels:\n",
+ "\n",
+ "All the cuda specific API is found in numbas cuda module (line 1) \n",
+ "\n",
+ "CUDA kernels are defined like regular Python functions with the added decorator `@cuda.jit` (line 7). The decorator makes sure that the function is compiled for the GPU.\n",
+ "\n",
+ "As mentioned above, CUDA kernels are executed as a grid of blocks of threads. cuda.grid (line 14) returns the global indices of the current thread, e.g., `x, y = cuda.grid(2)` for a two dimensional grid. The argument gives the number of dimensions (1, 2, 3). This function does not exist in CUDA C++.\n",
+ "\n",
+ "In CUDA C++, the programmer usually calculates the global index from the thread index `threadIdx`, the block index `blockIdx`, and the size (dimension) of the block stored in `blockDim`\n",
+ "\n",
+ "```C++\n",
+ "int x = blockIdx.x * blockDim.x + threadIdx.x;\n",
+ "```\n",
+ "\n",
+ "In numba these are available through the cuda module, so that you can rewrite the C++ code above as \n",
+ "\n",
+ "```Python\n",
+ "x = cuda.blockIdx.x * cuda.blockDim.x + cuda.threadIdx.x\n",
+ "```\n",
+ "\n",
+ "In `fast_matmul` these functions are used to get the local index of the thread, which is important to use the shared memory (lines 16--18).\n",
+ "\n",
+ "Shared memory is a programmable cache accessible to all threads within a block. In C++ it is allocated within a kernel as\n",
+ "\n",
+ "```C++\n",
+ "__shared__ float sA[TPB, TPB]; // Allocate a 2D array of floats of size TPB\n",
+ "```\n",
+ "\n",
+ "The cuda module provides shared.array (line 11 & 12) to do the same thing.\n",
+ "\n",
+ "The last function from the cuda module used in `fast_matmul` is cuda.syncthreads(), which implements a barrier for the threads within a block. It corresponds to `__syncthreads()` in CUDA C++.\n",
+ "\n",
+ "These functions cover most kernels."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Not all CUDA features are implemented in Numba. Some missing features are listed at http://numba.pydata.org/numba-doc/dev/cuda/overview.html#missing-cuda-features. Currently they include dynamic parallelism and texture memory."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/17_CUDA and MPI.ipynb b/solutions/17_CUDA and MPI.ipynb
new file mode 100644
index 0000000..f3fefe7
--- /dev/null
+++ b/solutions/17_CUDA and MPI.ipynb
@@ -0,0 +1,735 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "# CUDA for Python and MPI4Py\n",
+ "\n",
+ "<div class=\"dateauthor\">\n",
+ "20 November 2020 | Jan H. Meinke\n",
+ "</div>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "To use MPI in a notebook, we have to use the ipengines again:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Starting the engines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "We can combine ipyparalle and MPI. To do that, we need to start some IPython engines. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Click on the ``+``-sign at the top of the Files tab on the left to start a new launcher. In the launcher click on Terminal. A terminal will open as a new tab. Grab the tab and pull it to the right to have the terminal next to your notebook.\n",
+ "\n",
+ "**Note**: The terminal does not have the same modules loaded as the notebook. To fix that type `source hpcpy20`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Next start the ipcontroller: `ipcontroller &`. After that we can launch 4 MPI tasks with 6 threads each like this\n",
+ "\n",
+ "```bash\n",
+ "export OMP_NUM_THREADS=10\n",
+ "srun -n 4 -c 12 ipengine start\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client\n",
+ "rc = Client()\n",
+ "view = rc[:]\n",
+ "view.activate()\n",
+ "view.block = True"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "# Let's ignore some deprecation warnings\n",
+ "from numba.errors import NumbaDeprecationWarning, NumbaPendingDeprecationWarning\n",
+ "import warnings\n",
+ "\n",
+ "warnings.simplefilter('ignore', category=NumbaDeprecationWarning)\n",
+ "warnings.simplefilter('ignore', category=NumbaPendingDeprecationWarning)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The Kernel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "CUDA kernels cannot make any MPI calls. If you need to pass information from one GPU to another it's done by the main program. Here's a simple example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from ipyparallel import Client\n",
+ "rc = Client()\n",
+ "view = rc[:]\n",
+ "view.activate()\n",
+ "view.block = True"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "CUDA kernels cannot make any MPI calls. If you need to pass information from one GPU to another it's done by the main program. Here's a simple example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "import numpy\n",
+ "import mpi4py.MPI as MPI\n",
+ "from numba import cuda"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Here's a simple kernel that shifts all values in v by a:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "@cuda.jit\n",
+ "def shift(a, v):\n",
+ " \"\"\"Shift all values in v by a.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: float\n",
+ " shift\n",
+ " v: numpy.ndarray\n",
+ " one-dimensional array with values that are to be shifted.\n",
+ " \"\"\"\n",
+ " i = cuda.grid(1)\n",
+ " if i < v.shape[0]:\n",
+ " v[i] += a"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Setting things up"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Now, we set up MPI, and generate random number on rank 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm = MPI.COMM_WORLD\n",
+ "my_rank = comm.Get_rank()\n",
+ "number_of_ranks = comm.Get_size()\n",
+ "N = 1000\n",
+ "a_partial = numpy.empty(N)\n",
+ "if my_rank == 0:\n",
+ " a = numpy.random.random(N * number_of_ranks)\n",
+ "else:\n",
+ " a = numpy.empty(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Since we are dealing with NumPy arrays, we can use the efficient uppercase versions of the MPI calls. Scatter distributes an array evenly among all nodes. Note, the sendbuf only needs to be allocated on node zero, but the variable must exist everywhere."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm.Scatter(a, a_partial, root = 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Setup and call the kernel."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Calling the kernel"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "block = 256\n",
+ "grid = N // block if N % block == 0 else N // block + 1 \n",
+ "\n",
+ "shift[grid, block](-0.5, a_partial)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "Gather works the oposite way to Scatter. Again *a* only needs to have capacity on rank 0."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Collecting the data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "comm.Gather(a_partial, a, root = 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "We generated a uniform distribution between 0 and 1 and then shifted it by -0.5. The mean value should now be close to zero."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "%%px\n",
+ "if my_rank == 0:\n",
+ " print(\"The average of a is %.2f\" % numpy.mean(a)) # Result should be near zero."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Picking a device"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "source": [
+ "As you see from the example above, there's nothing special when using MPI with GPUs. The one thing that might bite you is using *multiple* MPI ranks for *multiple* GPUs on a *single* node. In this case, you might have to tell your MPI rank which GPU to use.\n",
+ "\n",
+ "If you have, for example, 4 GPUs and you know that your scheduler chooses a compact configuration, i.e., rank 0, 1, 2, 3 are on the first node, rank 4, 5, 6, 7 are on the second node, etc., you can use you rank to assign a GPU to your process:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "```python\n",
+ "\n",
+ "cuda.select_device(my_rank % number_of_gpus_per_node)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Shift"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "a) Write the above program to a file. Remember that you can move cells with the arrow buttons above and then merge them. There's a cell magic to write a cell to a file.\n",
+ "\n",
+ "b) Run the program on one node with 4 MPI processes.\n",
+ "\n",
+ "c) Add the cuda.select_device call to the program and run it again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile parallel_shift.py\n",
+ "# Solution for a)\n",
+ "import numpy\n",
+ "import mpi4py.MPI as MPI\n",
+ "from numba import cuda\n",
+ "\n",
+ "@cuda.jit\n",
+ "def shift(a, v):\n",
+ " \"\"\"Shift all values in v by a.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: float\n",
+ " shift\n",
+ " v: numpy.ndarray\n",
+ " one-dimensional array with values that are to be shifted.\n",
+ " \"\"\"\n",
+ " i = cuda.grid(1)\n",
+ " if i < v.shape[0]:\n",
+ " v[i] += a\n",
+ " \n",
+ "\n",
+ "def main():\n",
+ " # Set up for MPI\n",
+ " comm = MPI.COMM_WORLD\n",
+ " my_rank = comm.Get_rank()\n",
+ " number_of_ranks = comm.Get_size()\n",
+ " \n",
+ " # Create an array with N * number_of_ranks elements\n",
+ " N = 1000\n",
+ " a_partial = numpy.empty(N)\n",
+ " if my_rank == 0:\n",
+ " a = numpy.random.random(N * number_of_ranks)\n",
+ " else:\n",
+ " a = numpy.empty(1)\n",
+ " \n",
+ " # Distribute the data across the ranks\n",
+ " comm.Scatter(a, a_partial, root = 0)\n",
+ "\n",
+ " # Set up the launch configuration for the GPU\n",
+ " block = 256\n",
+ " grid = N // block if N % block == 0 else N // block + 1 \n",
+ " shift[grid, block](-0.5, a_partial)\n",
+ " \n",
+ " # Collect the data again on rank 0\n",
+ " comm.Gather(a_partial, a, root = 0) \n",
+ " \n",
+ " if my_rank == 0:\n",
+ " print(\"The average of a is %.2f\" % numpy.mean(a)) # Result should be near zero.\n",
+ " \n",
+ " \n",
+ "if __name__ == \"__main__\":\n",
+ " main()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile parallel_shift_w_selection.py\n",
+ "# Solution for c)\n",
+ "import numpy\n",
+ "import mpi4py.MPI as MPI\n",
+ "from numba import cuda\n",
+ "\n",
+ "@cuda.jit\n",
+ "def shift(a, v):\n",
+ " \"\"\"Shift all values in v by a.\n",
+ " \n",
+ " Parameters\n",
+ " ----------\n",
+ " a: float\n",
+ " shift\n",
+ " v: numpy.ndarray\n",
+ " one-dimensional array with values that are to be shifted.\n",
+ " \"\"\"\n",
+ " i = cuda.grid(1)\n",
+ " if i < v.shape[0]:\n",
+ " v[i] += a\n",
+ " \n",
+ "\n",
+ "def main():\n",
+ " # Set up for MPI\n",
+ " comm = MPI.COMM_WORLD\n",
+ " my_rank = comm.Get_rank()\n",
+ " number_of_ranks = comm.Get_size()\n",
+ " number_of_gpus_per_node = 4\n",
+ " \n",
+ " cuda.select_device(my_rank % number_of_gpus_per_node)\n",
+ " \n",
+ " # Create an array with N * number_of_ranks elements\n",
+ " N = 1000\n",
+ " a_partial = numpy.empty(N)\n",
+ " if my_rank == 0:\n",
+ " a = numpy.random.random(N * number_of_ranks)\n",
+ " else:\n",
+ " a = numpy.empty(1)\n",
+ " \n",
+ " # Distribute the data across the ranks\n",
+ " comm.Scatter(a, a_partial, root = 0)\n",
+ "\n",
+ " # Set up the launch configuration for the GPU\n",
+ " block = 256\n",
+ " grid = N // block if N % block == 0 else N // block + 1 \n",
+ " shift[grid, block](-0.5, a_partial)\n",
+ " \n",
+ " # Collect the data again on rank 0\n",
+ " comm.Gather(a_partial, a, root = 0) \n",
+ " \n",
+ " if my_rank == 0:\n",
+ " print(\"The average of a is %.2f\" % numpy.mean(a)) # Result should be near zero.\n",
+ " \n",
+ " \n",
+ "if __name__ == \"__main__\":\n",
+ " main()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "## Exercise: Multi-GPU Mandelbrot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "source": [
+ "Calculate the Mandelbrot set on multiple GPUs."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "tags": [
+ "Solution"
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "%%writefile multi_gpu_mandelbrot.py\n",
+ "# Solution for calculating the Mandelbrot set on 4 GPUs/node\n",
+ "import numpy\n",
+ "import mpi4py.MPI as MPI\n",
+ "import matplotlib.pyplot as plt\n",
+ "from numba import vectorize, cuda\n",
+ "\n",
+ "@vectorize(\"int64(complex128, int64)\", target=\"cuda\") # Replace cuda with cpu to test w/o GPU\n",
+ "def escape_time(p, maxtime):\n",
+ " \"\"\"Perform the Mandelbrot iteration until it's clear that p diverges\n",
+ " or the maximum number of iterations has been reached.\n",
+ " \"\"\"\n",
+ " z = 0j\n",
+ " for i in range(maxtime):\n",
+ " z = z ** 2 + p\n",
+ " if abs(z) > 2:\n",
+ " return i\n",
+ " return maxtime\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " # Set up for MPI\n",
+ " comm = MPI.COMM_WORLD\n",
+ " my_rank = comm.Get_rank()\n",
+ " number_of_ranks = comm.Get_size()\n",
+ " number_of_gpus_per_node = 4\n",
+ " \n",
+ " # If you want to see if GPU selection makes a difference choose a grid size of 4800 by 6400 and\n",
+ " # measure the time with and without the next line commented out.\n",
+ " cuda.select_device(my_rank % number_of_gpus_per_node)\n",
+ " \n",
+ " maxtime = 50\n",
+ " if my_rank == 0:\n",
+ " limits = (-2.2 - 1.2j, 1 + 1.2j) # lower left, upper right corner of the complex plane\n",
+ " gridsize = (480, 640) # number of rows, number of columns\n",
+ " else:\n",
+ " limits = None\n",
+ " gridsize = None\n",
+ " \n",
+ " # If every rank knows the range to be covered, they could just start, but I only defined them\n",
+ " # on rank 0 so let's broadcast them for this example. We can use the lowercase calls since \n",
+ " # convenience is more relevant than speed since for this part. It's done only once.\n",
+ " global_limit, global_gridsize = comm.bcast([limits, gridsize])\n",
+ " \n",
+ " xall = numpy.linspace(global_limit[0].real, global_limit[1].real, global_gridsize[1])\n",
+ " yall = numpy.linspace(global_limit[0].imag, global_limit[1].imag, global_gridsize[0])\n",
+ "\n",
+ " # There are number_of_rank ranks. Let's split the grid along the y-axis in number_of_rank\n",
+ " # slices\n",
+ " ny = global_gridsize[0] // number_of_ranks\n",
+ " my_y = yall[ny * my_rank: ny * (my_rank + 1)]\n",
+ " X, Y = numpy.meshgrid(xall, my_y)\n",
+ " mesh = X + Y * 1j\n",
+ " my_M = escape_time(mesh, maxtime)\n",
+ " \n",
+ " # Need to allocate space on rank 0 to collect the data\n",
+ " if my_rank == 0:\n",
+ " M = numpy.zeros(global_gridsize) # numpy.empty would work, too, makes it harder to see bugs.\n",
+ " else:\n",
+ " M = None # Don't need to allocate space on the other nodes for M\n",
+ " \n",
+ " comm.Gather(my_M, M)\n",
+ " \n",
+ " if my_rank == 0: # Only rank 0 has the data and should plot the image\n",
+ " plt.imshow(M)\n",
+ " plt.savefig(f\"mandelbrot_{number_of_ranks}_{number_of_gpus_per_node}.png\")\n",
+ " \n",
+ "if __name__ == \"__main__\":\n",
+ " main()\n",
+ " \n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "HPC Python 2020",
+ "language": "python",
+ "name": "hpcpy20"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/solutions/build.sh b/solutions/build.sh
new file mode 100755
index 0000000..9509e2f
--- /dev/null
+++ b/solutions/build.sh
@@ -0,0 +1,19 @@
+#!/bin/bash
+#source hpcpy19
+# Build points
+pushd code/point
+rm -rf build
+mkdir -p build
+cd build
+CC=icc CXX=icpc cmake .. > /dev/null
+make
+popd
+
+# Build text_stats
+pushd code/text_stats
+rm -rf build
+mkdir -p build
+cd build
+CC=icc CXX=icpc cmake .. > /dev/null
+make
+popd
diff --git a/solutions/code b/solutions/code
new file mode 120000
index 0000000..c787d1e
--- /dev/null
+++ b/solutions/code
@@ -0,0 +1 @@
+../code/
\ No newline at end of file
diff --git a/solutions/data b/solutions/data
new file mode 120000
index 0000000..eed2d0b
--- /dev/null
+++ b/solutions/data
@@ -0,0 +1 @@
+../data/
\ No newline at end of file
diff --git a/solutions/hpcpy20 b/solutions/hpcpy20
new file mode 100644
index 0000000..d159b3d
--- /dev/null
+++ b/solutions/hpcpy20
@@ -0,0 +1,20 @@
+#!/bin/bash
+module purge --force
+module load Stages/2020
+module load Intel
+module load ParaStationMPI
+module load Graphviz
+module load SciPy-Stack
+module load numba
+module load dask
+module load mpi4py
+module load CUDA
+module load CMake
+#export NUMBAPRO_NVVM=$CUDA_HOME/nvvm/lib64/libnvvm.so
+#export NUMBAPRO_LIBDEVICE=$CUDA_HOME/nvvm/libdevice
+export LD_LIBRARY_PATH=/p/project/training2020/resources/code/text_stats/build:$LD_LIBRARY_PATH
+export LD_LIBRARY_PATH=/p/project/training2020/resources/code/point/build:$LD_LIBRARY_PATH
+export PYTHONPATH=/p/project/training2020/packages/lib/python3.8/site-packages:$PYTHONPATH
+export PATH=$PATH:/p/project/training2020/packages/bin
+export PS1='π20[\u@\h \W]\$ '
+
diff --git a/solutions/images b/solutions/images
new file mode 120000
index 0000000..e4c5bd0
--- /dev/null
+++ b/solutions/images
@@ -0,0 +1 @@
+../images/
\ No newline at end of file
--
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