def test_Helmholtz2(quad):
M = 2*N
SD = ShenDirichletBasis(M, quad=quad)
kx = 12
uj = np.random.randn(M)
u_hat = np.zeros(M)
u_hat = SD.forward(uj, u_hat)
uj = SD.backward(u_hat, uj)
#from IPython import embed; embed()
A = inner_product((SD, 0), (SD, 2))
B = inner_product((SD, 0), (SD, 0))
u1 = np.zeros(M)
u1 = SD.forward(uj, u1)
c0 = np.zeros_like(u1)
c1 = np.zeros_like(u1)
c = A.matvec(u1, c0)+kx**2*B.matvec(u1, c1)
b = np.zeros(M)
H = Helmholtz(M, kx, SD)
b = H.matvec(u1, b)
#LUsolve.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
H = Helmholtz(M, kx, SD)
b = H.matvec(u1, b)
#LUsolve.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
vb = BH.matvec(u, vb)
sb = BH(sb, vb)
errb += max(abs(sb - u)) / max(abs(u))
###
ss = SH(ss, vb)
errs += max(abs(ss - u)) / max(abs(u))
###
#err += " & {:2.2e} ".format(errb/M)
err += " & {:2.2e} & {:2.2e} ".format(errb / M, errs / M)
err += " \\\ "
print err
print "\hline"
for z in Z:
err = str(z)
for n in N:
errh = 0
vh = zeros(n)
sh = zeros(n)
alfa = sqrt(z**2 + 2.0 / nu / dt)
HS = Helmholtz(n, alfa, "GC")
for m in range(M):
u = random.randn(n)
u[-2:] = 0
vh = HS.matvec(u, vh)
sh = HS(sh, vh)
errh += max(abs(sh - u)) / max(abs(u))
err += " & {:2.2e} ".format(errh / M)
err += " \\\ "
print err