def test_Mult_CTD(SD):
C = CTDmat(np.arange(N).astype(np.float))
B = BTTmat(np.arange(N).astype(np.float), SD.quad)
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
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)
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_CTD_1D(N, vk0, wk0, bv, bw)
cv = C.matvec(vk0)
cw = C.matvec(wk0)
cv /= B.dd
cw /= B.dd
assert np.allclose(cv, bv)
assert np.allclose(cw, bw)
def test_CTDmat(SDST):
SD, ST = SDST
Cm = CTDmat(np.arange(N).astype(np.float))
fj = np.random.randn(N)
# project to ST
f_hat = np.zeros(N)
f_hat = SD.fst(fj, f_hat)
fj = SD.ifst(f_hat, fj)
# Check if ST.fcs(f') equals Cm*SD.fst(f)
f_hat = SD.fst(fj, f_hat)
cs = Cm.matvec(f_hat)
df = np.zeros(N)
df = SD.fastChebDerivative(fj, df)
cs2 = np.zeros(N)
cs2 = ST.fastChebScalar(df, cs2)
# from IPython import embed; embed()
assert np.allclose(cs, cs2)
# Multidimensional version
f_hat = f_hat.repeat(4 * 4).reshape((N, 4, 4)) + 1j * f_hat.repeat(4 * 4).reshape((N, 4, 4))
df = df.repeat(4 * 4).reshape((N, 4, 4)) + 1j * df.repeat(4 * 4).reshape((N, 4, 4))
cs = Cm.matvec(f_hat)
cs2 = np.zeros((N, 4, 4), dtype=np.complex)
cs2 = ST.fastChebScalar(df, cs2)
assert np.allclose(cs, cs2)