def test_Helmholtz2(SD):
M = 2 * N
kx = 11
points, weights = SD.points_and_weights(M)
uj = np.random.randn(M)
u_hat = np.zeros(M)
u_hat = SD.fst(uj, u_hat)
uj = SD.ifst(u_hat, uj)
A = ADDmat(np.arange(M).astype(np.float))
B = BDDmat(np.arange(M).astype(np.float), SD.quad)
s = slice(0, M - 2)
u1 = np.zeros(M)
u1 = SD.fst(uj, u1)
c = A.matvec(u1) + kx ** 2 * B.matvec(u1)
b = np.zeros(M)
SFTc.Mult_Helmholtz_1D(M, SD.quad == "GL", 1, kx ** 2, u1, b)
assert np.allclose(c, b)
b = np.zeros((M, 4, 4), dtype=np.complex)
u1 = u1.repeat(16).reshape((M, 4, 4)) + 1j * u1.repeat(16).reshape((M, 4, 4))
kx = np.zeros((4, 4)) + kx
SFTc.Mult_Helmholtz_3D_complex(M, SD.quad == "GL", 1.0, kx ** 2, u1, b)
assert np.linalg.norm(b[:, 2, 2].real - c) / (M * 16) < 1e-12
assert np.linalg.norm(b[:, 2, 2].imag - c) / (M * 16) < 1e-12
def test_Helmholtz(ST2):
M = 4 * N
kx = 12
points, weights = ST2.points_and_weights(M)
fj = np.random.randn(M)
f_hat = np.zeros(M)
f_hat = ST2.fst(fj, f_hat)
fj = ST2.ifst(f_hat, fj)
if ST2.__class__.__name__ == "ShenDirichletBasis":
A = ADDmat(np.arange(M).astype(np.float))
B = BDDmat(np.arange(M).astype(np.float), ST2.quad)
s = slice(0, M - 2)
elif ST2.__class__.__name__ == "ShenNeumannBasis":
A = ANNmat(np.arange(M).astype(np.float))
B = BNNmat(np.arange(M).astype(np.float), ST2.quad)
s = slice(1, M - 2)
f_hat = np.zeros(M)
f_hat = ST2.fastShenScalar(fj, f_hat)
u_hat = np.zeros(M)
u_hat[s] = la.spsolve(A.diags() + kx ** 2 * B.diags(), f_hat[s])
u1 = np.zeros(M)
u1 = ST2.ifst(u_hat, u1)
c = A.matvec(u_hat) + kx ** 2 * B.matvec(u_hat)
c2 = np.dot(A.diags().toarray(), u_hat[s]) + kx ** 2 * np.dot(B.diags().toarray(), u_hat[s])
# from IPython import embed; embed()
assert np.allclose(c, f_hat)
assert np.allclose(c[s], c2)
# Multidimensional
f_hat = f_hat.repeat(16).reshape((M, 4, 4)) + 1j * f_hat.repeat(16).reshape((M, 4, 4))
kx = np.zeros((4, 4)) + 12
H = Helmholtz(M, kx, ST2.quad, ST2.__class__.__name__ == "ShenNeumannBasis")
u0_hat = np.zeros((M, 4, 4), dtype=np.complex)
u0_hat = H(u0_hat, f_hat)
u0 = np.zeros((M, 4, 4), dtype=np.complex)
u0 = ST2.ifst(u0_hat, u0)
assert np.linalg.norm(u0[:, 2, 2].real - u1) / (M * 16) < 1e-12
assert np.linalg.norm(u0[:, 2, 2].imag - u1) / (M * 16) < 1e-12
