def test_Mult_CTD(quad):
SD = ShenDirichletBasis(N, quad=quad)
SD.plan(N, 0, np.complex, {})
C = inner_product((SD.CT, 0), (SD, 1))
B = inner_product((SD.CT, 0), (SD.CT, 0))
vk = np.random.randn((N))+np.random.randn((N))*1j
wk = np.random.randn((N))+np.random.randn((N))*1j
bv = np.zeros(N, dtype=np.complex)
bw = np.zeros(N, dtype=np.complex)
vk0 = np.zeros(N, dtype=np.complex)
wk0 = np.zeros(N, dtype=np.complex)
cv = np.zeros(N, dtype=np.complex)
cw = np.zeros(N, dtype=np.complex)
vk0 = SD.forward(vk, vk0)
vk = SD.backward(vk0, vk)
vk0 = SD.forward(vk, vk0)
wk0 = SD.forward(wk, wk0)
wk = SD.backward(wk0, wk)
wk0 = SD.forward(wk, wk0)
LUsolve.Mult_CTD_1D(N, vk0, wk0, bv, bw)
cv = np.zeros_like(vk0)
cw = np.zeros_like(wk0)
cv = C.matvec(vk0, cv)
cw = C.matvec(wk0, cw)
cv /= B[0]
cw /= B[0]
assert np.allclose(cv, bv)
assert np.allclose(cw, bw)
def test_Helmholtz_matvec(quad):
M = 2*N
SD = ShenDirichletBasis(M, quad=quad)
kx = 11
uj = np.random.randn(M)
u_hat = np.zeros(M)
u_hat = SD.forward(uj, u_hat)
uj = SD.backward(u_hat, uj)
B = inner_product((SD, 0), (SD, 0))
A = inner_product((SD, 0), (SD, 2))
AB = HelmholtzCoeff(M, 1, kx**2, SD.quad)
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)
#LUsolve.Mult_Helmholtz_1D(M, SD.quad=="GL", 1, kx**2, u1, b)
b = AB.matvec(u1, b)
#from IPython import embed; embed()
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((1, 4, 4))+kx
#LUsolve.Mult_Helmholtz_3D_complex(M, SD.quad=="GL", 1.0, kx**2, u1, b)
AB = HelmholtzCoeff(M, 1, kx**2, SD.quad)
b = AB.matvec(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_Mult_Div():
SD = ShenDirichletBasis(N, "GC")
SN = ShenNeumannBasis(N, "GC")
SD.plan(N, 0, np.complex, {})
SN.plan(N, 0, np.complex, {})
Cm = inner_product((SN, 0), (SD, 1))
Bm = inner_product((SN, 0), (SD, 0))
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.forward(uk, uk0)
uk = SD.backward(uk0, uk)
uk0 = SD.forward(uk, uk0)
vk0 = SD.forward(vk, vk0)
vk = SD.backward(vk0, vk)
vk0 = SD.forward(vk, vk0)
wk0 = SD.forward(wk, wk0)
wk = SD.backward(wk0, wk)
wk0 = SD.forward(wk, wk0)
LUsolve.Mult_Div_1D(N, 7, 7, uk0[:N - 2], vk0[:N - 2], wk0[:N - 2],
b[1:N - 2])
uu = np.zeros_like(uk0)
v0 = np.zeros_like(vk0)
w0 = np.zeros_like(wk0)
uu = Cm.matvec(uk0, uu)
uu += 1j * 7 * Bm.matvec(vk0, v0) + 1j * 7 * Bm.matvec(wk0, w0)
#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
LUsolve.Mult_Div_3D(N, m, n, uk0[:N - 2], vk0[:N - 2], wk0[:N - 2],
b[1:N - 2])
uu = np.zeros_like(uk0)
v0 = np.zeros_like(vk0)
w0 = np.zeros_like(wk0)
uu = Cm.matvec(uk0, uu)
uu += 1j * 7 * Bm.matvec(vk0, v0) + 1j * 7 * Bm.matvec(wk0, w0)
assert np.allclose(uu, b)
def test_Mult_CTD_3D(quad):
SD = ShenDirichletBasis(N, quad=quad)
SD.plan((N, 4, 4), 0, np.complex, {})
C = inner_product((SD.CT, 0), (SD, 1))
B = inner_product((SD.CT, 0), (SD.CT, 0))
vk = np.random.random((N, 4, 4))+np.random.random((N, 4, 4))*1j
wk = np.random.random((N, 4, 4))+np.random.random((N, 4, 4))*1j
bv = np.zeros((N, 4, 4), dtype=np.complex)
bw = np.zeros((N, 4, 4), dtype=np.complex)
vk0 = np.zeros((N, 4, 4), dtype=np.complex)
wk0 = np.zeros((N, 4, 4), dtype=np.complex)
cv = np.zeros((N, 4, 4), dtype=np.complex)
cw = np.zeros((N, 4, 4), dtype=np.complex)
vk0 = SD.forward(vk, vk0)
vk = SD.backward(vk0, vk)
vk0 = SD.forward(vk, vk0)
wk0 = SD.forward(wk, wk0)
wk = SD.backward(wk0, wk)
wk0 = SD.forward(wk, wk0)
LUsolve.Mult_CTD_3D_ptr(N, vk0, wk0, bv, bw, 0)
cv = np.zeros_like(vk0)
cw = np.zeros_like(wk0)
cv = C.matvec(vk0, cv)
cw = C.matvec(wk0, cw)
cv /= B[0].repeat(np.array(bv.shape[1:]).prod()).reshape(bv.shape)
cw /= B[0].repeat(np.array(bv.shape[1:]).prod()).reshape(bv.shape)
assert np.allclose(cv, bv)
assert np.allclose(cw, bw)
def test_Mult_CTD_3D(quad):
SD = ShenDirichletBasis(N, quad=quad)
SD.plan((N, 4, 4), 0, np.complex, {})
C = inner_product((SD.CT, 0), (SD, 1))
B = inner_product((SD.CT, 0), (SD.CT, 0))
vk = np.random.random((N, 4, 4))+np.random.random((N, 4, 4))*1j
wk = np.random.random((N, 4, 4))+np.random.random((N, 4, 4))*1j
bv = np.zeros((N, 4, 4), dtype=np.complex)
bw = np.zeros((N, 4, 4), dtype=np.complex)
vk0 = np.zeros((N, 4, 4), dtype=np.complex)
wk0 = np.zeros((N, 4, 4), dtype=np.complex)
cv = np.zeros((N, 4, 4), dtype=np.complex)
cw = np.zeros((N, 4, 4), dtype=np.complex)
vk0 = SD.forward(vk, vk0)
vk = SD.backward(vk0, vk)
vk0 = SD.forward(vk, vk0)
wk0 = SD.forward(wk, wk0)
wk = SD.backward(wk0, wk)
wk0 = SD.forward(wk, wk0)
LUsolve.Mult_CTD_3D_ptr(N, vk0, wk0, bv, bw, 0)
cv = np.zeros_like(vk0)
cw = np.zeros_like(wk0)
cv = C.matvec(vk0, cv)
cw = C.matvec(wk0, cw)
cv /= B[0].repeat(np.array(bv.shape[1:]).prod()).reshape(bv.shape)
cw /= B[0].repeat(np.array(bv.shape[1:]).prod()).reshape(bv.shape)
assert np.allclose(cv, bv)
assert np.allclose(cw, bw)
def test_Mult_Div():
SD = ShenDirichletBasis(N, "GC")
SN = ShenNeumannBasis(N, "GC")
SD.plan(N, 0, np.complex, {})
SN.plan(N, 0, np.complex, {})
Cm = inner_product((SN, 0), (SD, 1))
Bm = inner_product((SN, 0), (SD, 0))
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.forward(uk, uk0)
uk = SD.backward(uk0, uk)
uk0 = SD.forward(uk, uk0)
vk0 = SD.forward(vk, vk0)
vk = SD.backward(vk0, vk)
vk0 = SD.forward(vk, vk0)
wk0 = SD.forward(wk, wk0)
wk = SD.backward(wk0, wk)
wk0 = SD.forward(wk, wk0)
LUsolve.Mult_Div_1D(N, 7, 7, uk0[:N-2], vk0[:N-2], wk0[:N-2], b[1:N-2])
uu = np.zeros_like(uk0)
v0 = np.zeros_like(vk0)
w0 = np.zeros_like(wk0)
uu = Cm.matvec(uk0, uu)
uu += 1j*7*Bm.matvec(vk0, v0) + 1j*7*Bm.matvec(wk0, w0)
#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
LUsolve.Mult_Div_3D(N, m, n, uk0[:N-2], vk0[:N-2], wk0[:N-2], b[1:N-2])
uu = np.zeros_like(uk0)
v0 = np.zeros_like(vk0)
w0 = np.zeros_like(wk0)
uu = Cm.matvec(uk0, uu)
uu += 1j*7*Bm.matvec(vk0, v0) + 1j*7*Bm.matvec(wk0, w0)
assert np.allclose(uu, b)
def test_Helmholtz2(quad):
M = 2 * N
SD = ShenDirichletBasis(M, quad=quad, plan=True)
kx = 12
points, weights = SD.points_and_weights(M)
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))
s = SD.slice()
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
