def test_n2(self):
"""
Test matrix for n = 2
"""
D1 = np.array([[0.0, 0.0], \
[0.0, 0.0]])
D2 = spectral_diff_matrix(2)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n2_shifted(self):
"""
Test matrix for n = 2, with xmin and xmax set.
"""
D1 = np.array([[0.0, 0.0], \
[0.0, 0.0]])
D2 = spectral_diff_matrix(2, xmin=-2.1, xmax=3.7)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n3_shifted(self):
"""
Test matrix for n = 3, with xmin and xmax set.
"""
x = 0.625448056632489
D1 = np.array([[0, x, -x], \
[-x, 0, x], \
[x, -x, 0]])
D2 = spectral_diff_matrix(3, xmin=-2.1, xmax=3.7)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n4(self):
"""
Test matrix for n = 4
"""
D1 = np.array([[0, 0.5, 0, -0.5], \
[-0.5, 0, 0.5, 0], \
[0, -0.5, 0, 0.5], \
[0.5, 0,-0.5, 0]])
D2 = spectral_diff_matrix(4)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n3(self):
"""
Test matrix for n = 3
"""
x = 0.577350269189626
D1 = np.array([[0, x, -x], \
[-x, 0, x], \
[x, -x, 0]])
D2 = spectral_diff_matrix(3)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n4_shifted(self):
"""
Test matrix for n = 4, with xmin and xmax set.
"""
x = 0.541653905791344
D1 = np.array([[0, x, 0, -x], \
[-x, 0, x, 0], \
[0, -x, 0, x], \
[x, 0, -x, 0]])
D2 = spectral_diff_matrix(4, xmin=-2.1, xmax=3.7)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n5(self):
"""
Test matrix for n = 5
"""
e = 0.85065080835204
f = 0.525731112119134
D1 = np.array([[0, e, -f, f, -e], \
[-e, 0, e, -f, f], \
[f, -e, 0, e, -f], \
[-f, f, -e, 0, e], \
[e, -f, f, -e, 0]])
D2 = spectral_diff_matrix(5)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_n5_shifted(self):
"""
Test matrix for n = 5, with xmin and xmax set.
"""
e = 0.921516665616892
f = 0.569528620550711
D1 = np.array([[0, e, -f, f, -e], \
[-e, 0, e, -f, f], \
[f, -e, 0, e, -f], \
[-f, f, -e, 0, e], \
[e, -f, f, -e, 0]])
D2 = spectral_diff_matrix(5, xmin=-2.1, xmax=3.7)
np.testing.assert_allclose(D1, D2, rtol=1e-13, atol=1e-13)
def test_random(self):
"""
Do a bunch of tests for random xmin and xmax.
"""
for n in range(1, 10):
for whichrand in range(10):
xmin = np.random.rand() * 20 - 10
xmax = xmin + np.random.rand() * 20
D = spectral_diff_matrix(n, xmin=xmin, xmax=xmax)
# Check that the diagonal entries are all 0:
for j in range(n):
self.assertLess(np.abs(D[j, j]), 1e-14)
# Check that the row and column sums are all 0
self.assertLess(np.max(np.abs(np.sum(D, axis=0))), 1e-11)
self.assertLess(np.max(np.abs(np.sum(D, axis=1))), 1e-11)
def test_Fourier(self):
"""
Confirm that the derivative of a sin/cos is computed exactly.
"""
xmin = -3.4
xmax = -0.7
L = xmax - xmin
for nphi in range(11, 21, 2):
D = spectral_diff_matrix(nphi, xmin=xmin, xmax=xmax)
for n in range(0, int(np.floor(nphi / 2)) - 1):
for phase in [0, 0.3]:
phi = np.linspace(xmin, xmax, nphi, endpoint=False)
x = np.sin(n * phi * 2 * np.pi / L + phase)
dx = (n * 2 * np.pi / L) * np.cos(n * phi * 2 * np.pi / L +
phase)
np.testing.assert_allclose(np.matmul(D, x),
dx,
rtol=1e-12,
atol=1e-12)