def main():
for n in N:
err = str(n)
err7 = str(n)
Z[0] = n
HS = Helmholtz(n, sqrt(K2 + 2.0 / nu / dt), "GC", False)
BS = Biharmonic(n,
-nu * dt / 2.,
1. + nu * dt * K2,
-(K2 + nu * dt / 2. * K4),
quad="GC",
solver="cython")
BS2 = Biharmonic(n,
-nu * dt / 2.,
1. + nu * dt * K2,
-(K2 + nu * dt / 2. * K4),
quad="GC",
solver="scipy")
fb = random.random((Z[0], Z[1], Z[2] // 2 + 1)) + random.random(
(Z[0], Z[1], Z[2] // 2 + 1)) * 1j
fb[-4:] = 0
ub = zeros((Z[0], Z[1], Z[2] // 2 + 1), dtype=complex)
#sleep(0.5)
t0 = time()
for m in range(M):
ub = BS(ub, fb)
t1 = (time() - t0) / M / Z[1:].prod()
t0 = time()
for m in range(M):
ub = BS2(ub, fb)
t7 = (time() - t0) / M / Z[1:].prod()
#cProfile.runctx("for m in range(M): ub = BS(ub, fb)", globals(), locals(), "res1.stats")
#ps = pstats.Stats("res1.stats")
#for key, val in iteritems(ps.stats):
#if "Solve_Biharmonic" in key[2]:
#results = val[3]/M/Z[1:].prod()
#break
#t1 = results
err += " & {:2.2e} ({:2.2f}) ".format(
t1, 0 if n == N[0] else t1 / t11 / 2.)
err += " & {:2.2e} ({:2.2f}) ".format(
t7, 0 if n == N[0] else t7 / t71 / 2.)
t11 = t1
t71 = t7
fh = random.random((Z[0], Z[1], Z[2] // 2 + 1)) + random.random(
(Z[0], Z[1], Z[2] // 2 + 1)) * 1j
fh[-2:] = 0
uh = zeros((Z[0], Z[1], Z[2] // 2 + 1), dtype=complex)
#sleep(0.5)
t0 = time()
for m in range(M):
uh = HS(uh, fh)
t2 = (time() - t0) / M / Z[1:].prod()
#cProfile.runctx("for m in range(M): uh = HS(uh, fh)", globals(), locals(), "res.stats")
#ps = pstats.Stats("res.stats")
#for key, val in iteritems(ps.stats):
#if "Solve_Helmholtz" in key[2]:
#results = val[3]/M/Z[1:].prod()
#break
#t2 = results
err += "& {:2.2e} ({:2.2f}) \\\ ".format(
t2, 0 if n == N[0] else t2 / t22 / 2.)
t22 = t2
print(err)
N = array([64, 128, 256])
Z = array([0, 200, 1800, 5400])
M = 100
print("\hline")
print("z & " + " & ".join([str(n) for n in N]) + " \\\ ")
print("\hline")
for z in Z:
err = str(z)
for n in N:
errb = 0
errs = 0
vb = zeros(n)
sb = zeros(n)
ss = zeros(n)
BH = Biharmonic(n, -nu * dt / 2., 1. + nu * dt * z**2,
-(z**2 + nu * dt / 2. * z**4), "GC", "cython")
SH = Biharmonic(n, -nu * dt / 2., 1. + nu * dt * z**2,
-(z**2 + nu * dt / 2. * z**4), "GC", "scipy")
for m in range(M):
u = random.random(n)
u[-4:] = 0
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 += " \\\ "
SD = ShenBiharmonicBasis("GC", True)
points, weights = SD.points_and_weights(N)
uj = np.array([u.subs(x, j) for j in points], dtype=float)
fj = np.array([f.subs(x, j) for j in points], dtype=float) # Get f on quad points
#uj_hat = np.zeros(N)
#uj_hat = SD.fst(uj, uj_hat)
#uj = SD.ifst(uj_hat, uj)
#fj_hat = np.zeros(N)
#fj_hat = SD.fst(fj, fj_hat)
#fj = SD.ifst(fj_hat, fj)
solver = Biharmonic(N, a, b, c, quad=SD.quad, solver="cython")
solver2 = Biharmonic(N, a, b, c, quad=SD.quad)
f_hat = np.zeros(N)
f_hat = SD.fastShenScalar(fj, f_hat)
u_hat = np.zeros(N)
u_hat2 = np.zeros(N)
from time import time
t0 = time()
u_hat = solver(u_hat, f_hat)
t1 = time()
u_hat2 = solver2(u_hat2, f_hat)
t2 = time()
print "cython / scipy ", t1-t0, t2-t1
def test_ABBmat(SB):
M = 6 * N
u = sin(6 * pi * x)**2
f = u.diff(x, 2)
points, weights = SB.points_and_weights(M)
uj = np.array([u.subs(x, h) for h in points], dtype=np.float)
fj = np.array([f.subs(x, h) for h in points], dtype=np.float)
A = ABBmat(np.arange(M).astype(np.float))
f_hat = np.zeros(M)
f_hat = SB.fastShenScalar(fj, f_hat)
u_hat = np.zeros(M)
u_hat[:-4] = la.spsolve(A.diags(), f_hat[:-4])
u0 = np.zeros(M)
u0 = SB.ifst(u_hat, u0)
assert np.allclose(u0, uj)
u1 = np.zeros(M)
u1 = SB.fst(uj, u1)
c = A.matvec(u1)
assert np.allclose(c, f_hat, 1e-6, 1e-6)
# Multidimensional
f_hat = (f_hat.repeat(16).reshape(
(M, 4, 4)) + 1j * f_hat.repeat(16).reshape((M, 4, 4)))
u1 = (u1.repeat(16).reshape((M, 4, 4)) + 1j * u1.repeat(16).reshape(
(M, 4, 4)))
c = A.matvec(u1)
assert np.allclose(c, f_hat, 1e-6, 1e-6)
B = BBBmat(np.arange(M).astype(np.float), SB.quad)
u0 = np.random.randn(M)
u0_hat = np.zeros(M)
u0_hat = SB.fst(u0, u0_hat)
u0 = SB.ifst(u0_hat, u0)
b = np.zeros(M)
k = 2.
b = A.matvec(u0_hat) - k**2 * B.matvec(u0_hat)
AA = A.diags().toarray() - k**2 * B.diags().toarray()
z0_hat = np.zeros(M)
z0_hat[:-4] = solve(AA, b[:-4])
z0 = np.zeros(M)
z0 = SB.ifst(z0_hat, z0)
assert np.allclose(z0, u0)
k = np.ones(M) * 2
k = k.repeat(16).reshape((M, 4, 4))
k2 = k**2
u0_hat = u0_hat.repeat(16).reshape(
(M, 4, 4)) + 1j * u0_hat.repeat(16).reshape((M, 4, 4))
u0 = u0.repeat(16).reshape((M, 4, 4))
b = A.matvec(u0_hat) - k**2 * B.matvec(u0_hat)
alfa = np.ones((M, 4, 4))
BH = Biharmonic(M, 0, alfa[0], -k2[0], SB.quad, "cython")
z0_hat = np.zeros((M, 4, 4), dtype=np.complex)
z0_hat = BH(z0_hat, b)
z0 = np.zeros((M, 4, 4))
z0 = SB.ifst(z0_hat.real, z0)
#from IPython import embed; embed()
assert np.allclose(z0, u0)
N = array([64, 128, 256])
Z = array([0, 200, 1800, 5400])
M = 100
print("\hline")
print("z & " + " & ".join([str(n) for n in N]) + " \\\ ")
print("\hline")
for z in Z:
err = str(z)
for n in N:
errb = 0
errs = 0
vb = zeros(n)
sb = zeros(n)
ss = zeros(n)
BH = Biharmonic(n, -nu*dt/2., 1.+nu*dt*z**2, -(z**2+nu*dt/2.*z**4), "GC", "cython")
SH = Biharmonic(n, -nu*dt/2., 1.+nu*dt*z**2, -(z**2+nu*dt/2.*z**4), "GC", "scipy")
for m in range(M):
u = random.random(n)
u[-4:] = 0
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)