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)
assert np.allclose(uk[:, 1, 1].imag, uk_hat)
b = np.zeros((N-2, 10, 10), dtype=np.complex)
SFTc.Mult_Helmholtz_3D_complex(N, ST.quad=="GL", 1, alfa**2, uk, b)
assert np.allclose(b[:, 1, 1].real, fk[:-2])
assert np.allclose(b[:, 1, 1].imag, fk[:-2])
return uk_hat
f_hat = fj.copy()
f_hat = ST.fastShenScalar(fj, f_hat)
uk_hat = fj.copy()
uk_hat[:-2] = solve(f_hat)
uq = uk_hat.copy()
uq = ST.ifst(uk_hat, uq)
uqf = uq.copy()
uqf = ST.fst(uq, uqf)
uq0 = uq.copy()
assert np.allclose(ST.ifst(uqf, uq0), uq)
u_exact = np.array([u.subs(x, h) for h in points], dtype=np.float)
plt.figure(); plt.plot(points, [u.subs(x, i) for i in points]); plt.title("U")
plt.figure(); plt.plot(points, uq - u_exact); plt.title("Error")
print "Error = ", np.linalg.norm(uq - u_exact)
#plt.show()