def test_BDNmat(S1S2):
S1, S2 = S1S2
f_hat = np.zeros(N)
fj = np.random.random(N)
f_hat = S2.fst(fj, f_hat)
fj = S2.ifst(f_hat, fj)
if S1.__class__.__name__ == "ShenNeumannBasis":
B = BNDmat(np.arange(N).astype(np.float), S1.quad)
else:
B = BDNmat(np.arange(N).astype(np.float), S1.quad)
f_hat = S2.fst(fj, f_hat)
u2 = B.matvec(f_hat)
u0 = np.zeros(N)
u0 = S1.fastShenScalar(fj, u0)
assert np.allclose(u0, u2)
# Multidimensional version
fj = fj.repeat(16).reshape((N, 4, 4)) + 1j * fj.repeat(16).reshape((N, 4, 4))
f_hat = f_hat.repeat(16).reshape((N, 4, 4)) + 1j * f_hat.repeat(16).reshape((N, 4, 4))
u0 = np.zeros((N, 4, 4), dtype=np.complex)
u0 = S1.fastShenScalar(fj, u0)
u2 = B.matvec(f_hat)
assert np.linalg.norm(u2 - u0) / (N * 16) < 1e-12
def test_Mult_Div():
SD = ShenDirichletBasis("GC")
SN = ShenDirichletBasis("GC")
Cm = CNDmat(np.arange(N).astype(np.float))
Bm = BNDmat(np.arange(N).astype(np.float), "GC")
uk = np.random.randn((N)) + np.random.randn((N)) * 1j
vk = np.random.randn((N)) + np.random.randn((N)) * 1j
wk = np.random.randn((N)) + np.random.randn((N)) * 1j
b = np.zeros(N, dtype=np.complex)
uk0 = np.zeros(N, dtype=np.complex)
vk0 = np.zeros(N, dtype=np.complex)
wk0 = np.zeros(N, dtype=np.complex)
uk0 = SD.fst(uk, uk0)
uk = SD.ifst(uk0, uk)
uk0 = SD.fst(uk, uk0)
vk0 = SD.fst(vk, vk0)
vk = SD.ifst(vk0, vk)
vk0 = SD.fst(vk, vk0)
wk0 = SD.fst(wk, wk0)
wk = SD.ifst(wk0, wk)
wk0 = SD.fst(wk, wk0)
SFTc.Mult_Div_1D(N, 7, 7, uk0[: N - 2], vk0[: N - 2], wk0[: N - 2], b[1 : N - 2])
uu = Cm.matvec(uk0)
uu += 1j * 7 * Bm.matvec(vk0) + 1j * 7 * Bm.matvec(wk0)
# from IPython import embed; embed()
assert np.allclose(uu, b)
uk0 = uk0.repeat(4 * 4).reshape((N, 4, 4)) + 1j * uk0.repeat(4 * 4).reshape((N, 4, 4))
vk0 = vk0.repeat(4 * 4).reshape((N, 4, 4)) + 1j * vk0.repeat(4 * 4).reshape((N, 4, 4))
wk0 = wk0.repeat(4 * 4).reshape((N, 4, 4)) + 1j * wk0.repeat(4 * 4).reshape((N, 4, 4))
b = np.zeros((N, 4, 4), dtype=np.complex)
m = np.zeros((4, 4)) + 7
n = np.zeros((4, 4)) + 7
SFTc.Mult_Div_3D(N, m, n, uk0[: N - 2], vk0[: N - 2], wk0[: N - 2], b[1 : N - 2])
uu = Cm.matvec(uk0)
uu += 1j * 7 * Bm.matvec(vk0) + 1j * 7 * Bm.matvec(wk0)
assert np.allclose(uu, b)
