diff --git a/pySDC/helpers/spectral_helper.py b/pySDC/helpers/spectral_helper.py
index cd175bb738722db435eaf0649bec825ed073b5d0..d74aab8733f256272f0cb99a5ea6e1fd13fe3a34 100644
--- a/pySDC/helpers/spectral_helper.py
+++ b/pySDC/helpers/spectral_helper.py
@@ -194,8 +194,9 @@ class ChebychevHelper(SpectralHelper1D):
x0 (float): Coordinate of left boundary. Note that only -1 is currently implented
x1 (float): Coordinate of right boundary. Note that only +1 is currently implented
"""
- assert x0 == -1
- assert x1 == 1
+ # need linear transformation y = ax + b with a = (x1-x0)/2 and b = (x1+x0)/2
+ self.lin_trf_fac = (x1 - x0) / 2
+ self.lin_trf_off = (x1 + x0) / 2
super().__init__(*args, x0=x0, x1=x1, **kwargs)
self.transform_type = transform_type
@@ -214,7 +215,7 @@ class ChebychevHelper(SpectralHelper1D):
Returns:
numpy.ndarray: 1D grid
'''
- return self.xp.cos(np.pi / self.N * (self.xp.arange(self.N) + 0.5))
+ return self.lin_trf_fac * self.xp.cos(np.pi / self.N * (self.xp.arange(self.N) + 0.5)) + self.lin_trf_off
def get_wavenumbers(self):
"""Get the domain in spectral space"""
@@ -306,7 +307,7 @@ class ChebychevHelper(SpectralHelper1D):
(n / (2 * (self.xp.arange(self.N) + 1)))[1::2]
* (-1) ** (self.xp.arange(self.N // 2))
/ (np.append([1], self.xp.arange(self.N // 2 - 1) + 1))
- )
+ ) * self.lin_trf_fac
else:
raise NotImplementedError(f'This function allows to integrate only from x=0, you attempted from x={lbnd}.')
return S
@@ -327,7 +328,7 @@ class ChebychevHelper(SpectralHelper1D):
D[k, j] = 2 * j * ((j - k) % 2)
D[0, :] /= 2
- return self.sparse_lib.csc_matrix(self.xp.linalg.matrix_power(D, p))
+ return self.sparse_lib.csc_matrix(self.xp.linalg.matrix_power(D, p)) / self.lin_trf_fac**p
def get_norm(self, N=None):
'''
@@ -565,7 +566,7 @@ class UltrasphericalHelper(ChebychevHelper):
xp = self.xp
N = self.N
l = p
- return 2 ** (l - 1) * factorial(l - 1) * sp.diags(xp.arange(N - l) + l, offsets=l)
+ return 2 ** (l - 1) * factorial(l - 1) * sp.diags(xp.arange(N - l) + l, offsets=l) / self.lin_trf_fac**p
def get_S(self, lmbda):
"""
@@ -647,8 +648,10 @@ class UltrasphericalHelper(ChebychevHelper):
Returns:
sparse integration matrix
"""
- return self.sparse_lib.diags(1 / (self.xp.arange(self.N - 1) + 1), offsets=-1) @ self.get_basis_change_matrix(
- p_out=1, p_in=0
+ return (
+ self.sparse_lib.diags(1 / (self.xp.arange(self.N - 1) + 1), offsets=-1)
+ @ self.get_basis_change_matrix(p_out=1, p_in=0)
+ * self.lin_trf_fac
)
def get_integration_constant(self, u_hat, axis):
diff --git a/pySDC/tests/test_helpers/test_spectral_helper_1d_chebychev.py b/pySDC/tests/test_helpers/test_spectral_helper_1d_chebychev.py
index 37a1ee7175e1a77946adcc5701c08b7c161314da..5052e5908c086b3e1db51506f06409b7723108cb 100644
--- a/pySDC/tests/test_helpers/test_spectral_helper_1d_chebychev.py
+++ b/pySDC/tests/test_helpers/test_spectral_helper_1d_chebychev.py
@@ -79,7 +79,7 @@ def test_differentiation_matrix(N):
from pySDC.helpers.spectral_helper import ChebychevHelper
cheby = ChebychevHelper(N)
- x = np.cos(np.pi / N * (np.arange(N) + 0.5))
+ x = cheby.get_1dgrid()
coeffs = np.random.random(N)
norm = cheby.get_norm()
@@ -91,6 +91,36 @@ def test_differentiation_matrix(N):
assert np.allclose(exact, du)
+@pytest.mark.base
+@pytest.mark.parametrize('N', [4, 7, 32])
+@pytest.mark.parametrize('x0', [-1, 0])
+@pytest.mark.parametrize('x1', [0.789, 1])
+@pytest.mark.parametrize('p', [1, 2])
+def test_differentiation_non_standard_domain_size(N, x0, x1, p):
+ import numpy as np
+ import scipy
+ from pySDC.helpers.spectral_helper import ChebychevHelper
+
+ cheby = ChebychevHelper(N, x0=x0, x1=x1)
+ x = cheby.get_1dgrid()
+ assert all(x > x0)
+ assert all(x < x1)
+
+ coeffs = np.random.random(N)
+ u = np.polynomial.Chebyshev(coeffs)(x)
+ u_hat = cheby.transform(u)
+ du_exact = np.polynomial.Chebyshev(coeffs).deriv(p)(x)
+ du_hat_exact = cheby.transform(du_exact)
+
+ D = cheby.get_differentiation_matrix(p)
+
+ du_hat = D @ u_hat
+ du = cheby.itransform(du_hat)
+
+ assert np.allclose(du_hat_exact, du_hat), np.linalg.norm(du_hat_exact - du_hat)
+ assert np.allclose(du, du_exact), np.linalg.norm(du_exact - du)
+
+
@pytest.mark.base
@pytest.mark.parametrize('N', [4, 32])
def test_integration_matrix(N):
@@ -121,7 +151,8 @@ def test_transform(N, d, transform_type):
cheby = ChebychevHelper(N, transform_type=transform_type)
u = np.random.random((d, N))
norm = cheby.get_norm()
- x = cheby.get_1dgrid()
+ x = (cheby.get_1dgrid() * cheby.lin_trf_fac + cheby.lin_trf_off) * cheby.lin_trf_fac + cheby.lin_trf_off
+ x = (cheby.get_1dgrid() - cheby.lin_trf_off) / cheby.lin_trf_fac
itransform = cheby.itransform(u, axis=-1).real
@@ -370,15 +401,3 @@ def test_tau_method2D_diffusion(nz, nx, bc_val, plotting=False):
assert np.allclose(
polys[i](z), sol[0, i, :]
), f'Solution is incorrectly transformed back to real space at x={x[i]}'
-
-
-if __name__ == '__main__':
- test_differentiation_matrix(4, 'T2U')
- # test_transform(6, 1, 'fft')
- # test_tau_method('T2U', -1.0, N=4, bc_val=3.0)
- # test_tau_method2D('T2T', -1, nx=2**7, nz=2**6, bc_val=4.0, plotting=True)
- # test_integration_matrix(5, 'T2U')
- # test_integration_matrix2D(2**0, 2**2, 'T2U', 'z')
- # test_differentiation_matrix2D(2**7, 2**7, 'T2U', 'mixed')
- # test_integration_BC(6)
- # test_filter(12, 2, 5, 'T2U')
diff --git a/pySDC/tests/test_helpers/test_spectral_helper_1d_ultraspherical.py b/pySDC/tests/test_helpers/test_spectral_helper_1d_ultraspherical.py
index d5ba10afbf18fab9eb031bd68c35597bb6601106..22d5fb5001d524918b7e2ebab8abd340fbc15080 100644
--- a/pySDC/tests/test_helpers/test_spectral_helper_1d_ultraspherical.py
+++ b/pySDC/tests/test_helpers/test_spectral_helper_1d_ultraspherical.py
@@ -21,6 +21,37 @@ def test_differentiation_matrix(N, p):
assert np.allclose(exact, du)
+@pytest.mark.base
+@pytest.mark.parametrize('N', [4, 7, 32])
+@pytest.mark.parametrize('x0', [-1, 0])
+@pytest.mark.parametrize('x1', [0.789, 1])
+@pytest.mark.parametrize('p', [1, 2])
+def test_differentiation_non_standard_domain_size(N, x0, x1, p):
+ import numpy as np
+ import scipy
+ from pySDC.helpers.spectral_helper import UltrasphericalHelper
+
+ helper = UltrasphericalHelper(N, x0=x0, x1=x1)
+ x = helper.get_1dgrid()
+ assert all(x > x0)
+ assert all(x < x1)
+
+ coeffs = np.random.random(N)
+ u = np.polynomial.Chebyshev(coeffs)(x)
+ u_hat = helper.transform(u)
+ du_exact = np.polynomial.Chebyshev(coeffs).deriv(p)(x)
+ du_hat_exact = helper.transform(du_exact)
+
+ D = helper.get_differentiation_matrix(p)
+ Q = helper.get_basis_change_matrix(p_in=p, p_out=0)
+
+ du_hat = Q @ D @ u_hat
+ du = helper.itransform(du_hat)
+
+ assert np.allclose(du_hat_exact, du_hat), np.linalg.norm(du_hat_exact - du_hat)
+ assert np.allclose(du, du_exact), np.linalg.norm(du_exact - du)
+
+
@pytest.mark.base
@pytest.mark.parametrize('N', [4, 7, 32])
def test_integration(N):
@@ -94,9 +125,3 @@ def test_poisson_problem(N, deg, Dirichlet_recombination):
assert np.allclose(u_hat[deg + 3 :], 0)
assert np.allclose(u_exact, u)
-
-
-if __name__ == '__main__':
- # test_differentiation_matrix(6, 2)
- test_poisson_problem(6, 1, True)
- # test_integration()