def test_TDMA(T):
from scipy.linalg import solve
if T.neumann == True:
B = BNNmat(np.arange(N).astype(np.float), T.quad)
s = slice(1, N - 2)
else:
B = BDDmat(np.arange(N).astype(np.float), T.quad)
s = slice(0, N - 2)
Ba = B.diags().toarray()
f = np.random.random(N)
u = solve(Ba, f[s])
u0 = f.copy()
u0 = T(u0)
assert np.allclose(u0[s], u)
# Again
u0 = f.copy()
u0 = T(u0)
assert np.allclose(u0[s], u)
# Multidimensional version
fc = f.repeat(16).reshape((N, 4, 4))
fc = T(fc)
assert np.allclose(fc[s, 2, 2], u)
fc = f.repeat(16).reshape((N, 4, 4))
fc = T(fc)
assert np.allclose(fc[s, 2, 2], u)
def test_BNNmat(ST):
points, weights = ST.points_and_weights(N)
f_hat = np.zeros(N)
fj = np.random.random(N)
u0 = np.zeros(N)
if ST.__class__.__name__ == "ShenNeumannBasis":
B = BNNmat(np.arange(N).astype(np.float), ST.quad)
f_hat = ST.fst(fj, f_hat)
fj = ST.ifst(f_hat, fj)
u0 = ST.fastShenScalar(fj, u0)
f_hat = ST.fst(fj, f_hat)
elif ST.__class__.__name__ == "ShenDirichletBasis":
B = BDDmat(np.arange(N).astype(np.float), ST.quad)
f_hat = ST.fst(fj, f_hat)
fj = ST.ifst(f_hat, fj)
u0 = ST.fastShenScalar(fj, u0)
f_hat = ST.fst(fj, f_hat)
else:
B = BTTmat(np.arange(N).astype(np.float), ST.quad)
f_hat = ST.fct(fj, f_hat)
fj = ST.ifct(f_hat, fj)
u0 = ST.fastChebScalar(fj, u0)
f_hat = ST.fct(fj, f_hat)
u2 = B.matvec(f_hat)
assert np.allclose(u2, u0)
# Multidimensional version
fj = fj.repeat(16).reshape((N, 4, 4)) + 1j * fj.repeat(16).reshape((N, 4, 4))
u0 = np.zeros((N, 4, 4), dtype=np.complex)
f_hat = np.zeros((N, 4, 4), dtype=np.complex)
if ST.__class__.__name__ in ("ShenNeumannBasis", "ShenDirichletBasis"):
u0 = ST.fastShenScalar(fj, u0)
f_hat = ST.fst(fj, f_hat)
else:
u0 = ST.fastChebScalar(fj, u0)
f_hat = ST.fct(fj, f_hat)
u2 = B.matvec(f_hat)
assert np.allclose(u2, u0)
