def pde_imp_mg_py(size_h, size_t, init, time, nums, eps, chk):
"""Evolve the PDE using implicit scheme, multigrid and Python"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
mats, mat_us, mat_dl_facs, ints = [], [], [], []
temp, j = n, 0
while True:
a_u = -scipy.sparse.triu(a, k=1, format="csr")
a_dl = scipy.sparse.tril(a.transpose(), k=0, format="csc")
a_dl_fac = scipy.sparse.linalg.splu(a_dl, permc_spec="NATURAL")
mats.append(a)
mat_us.append(a_u)
mat_dl_facs.append(a_dl_fac)
j += 1
if j >= len(nums):
break
temp //= 2
i = utils.mat_int(temp)
ints.append(i)
a = i.transpose().dot(a.dot(i))
ctr = 0
for i in range(m):
u, temp = solve_mg(mats, mat_us, mat_dl_facs, ints, nums, u, u, eps,
chk)
ctr += temp
u = u.reshape((n - 1, n - 1))
return u, ctr
def pde_imp_cg_c(size_h, size_t, init, time, eps):
"""Evolve the PDE using implicit scheme, conjugate gradient and C"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
ctr = exts.pde_imp_cg_wrapper(a.data, a.indices, a.indptr, u, eps, m)
u = u.reshape((n - 1, n - 1))
return u, ctr
def pde_imp_cho_c(size_h, size_t, init, time):
"""Evolve the PDE using implicit scheme, Cholesky decomposition and C"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
ctr = exts.pde_imp_cho_wrapper(a.data, a.indices, a.indptr, u, n - 1, m)
u = u.reshape((n - 1, n - 1))
return u, ctr
def pde_exp(size_h, size_t, init, time):
"""Evolve the PDE with explicit scheme and Python SuperLU binding"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye - dt / dx**2 * lap
for i in range(m):
u = a.dot(u)
u = u.reshape((n - 1, n - 1))
return u
def pde_imp(size_h, size_t, init, time):
"""Evolve the PDE with implicit scheme and Python SuperLU binding"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
a_fac = scipy.sparse.linalg.splu(a.transpose())
for i in range(m):
u = a_fac.solve(u)
u = u.reshape((n - 1, n - 1))
return u
def pde_imp_cg_py(size_h, size_t, init, time, eps):
"""Evolve the PDE using implicit scheme, conjugate gradient and Python"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
ctr = 0
for i in range(m):
u, temp = solve_cg(a, u, u, eps)
ctr += temp
u = u.reshape((n - 1, n - 1))
return u, ctr
def pde_cn(size_h, size_t, init, time):
"""Evolve the PDE with Crank-Nicolson scheme and Python SuperLU binding"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye - dt / dx**2 / 2.0 * lap
b = eye + dt / dx**2 / 2.0 * lap
b_fac = scipy.sparse.linalg.splu(b.transpose())
for i in range(m):
u = a.dot(u)
u = b_fac.solve(u)
u = u.reshape((n - 1, n - 1))
return u
def pde_imp_gs_py(size_h, size_t, init, time, eps, chk):
"""Evolve the PDE using implicit scheme, Gauss-Seidel and Python"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
a_u = -scipy.sparse.triu(a, k=1, format="csr")
a_dl = scipy.sparse.tril(a.transpose(), k=0, format="csc")
a_dl_fac = scipy.sparse.linalg.splu(a_dl, permc_spec="NATURAL")
ctr = 0
for i in range(m):
u, temp = solve_gs(a, a_u, a_dl_fac, u, u, eps, chk)
ctr += temp
u = u.reshape((n - 1, n - 1))
return u, ctr
def pde_imp_mg_c(size_h, size_t, init, time, num, eps, chk):
"""Evolve the PDE using implicit scheme, multigrid and C"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
num = numpy.array(num, dtype=numpy.int32)
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
datas, inds, ptrs = [], [], []
datas.append(a.data)
inds.append(a.indices)
ptrs.append(a.indptr)
temp = n
for j in range(len(num) - 1):
temp //= 2
i = utils.mat_int(temp)
datas.append(i.data)
inds.append(i.indices)
ptrs.append(i.indptr)
ctr = exts.pde_imp_mg_wrapper(n, datas, inds, ptrs, u, num, eps, chk, m)
u = u.reshape((n - 1, n - 1))
return u, ctr
def pde_imp_cho_py(size_h, size_t, init, time):
"""Evolve the PDE using implicit scheme, Cholesky decomposition and Python"""
n, m, u, t = size_h, size_t, init, time
u = u.flatten()
dx, dt = 1.0 / n, t / m
lap = utils.mat_lap(n)
eye = scipy.sparse.eye((n - 1)**2).tocsr()
a = eye + dt / dx**2 * lap
a = a.todia()
ab = numpy.zeros((n, (n - 1)**2))
ab[0] = a.diagonal(k=0)
ab[1, :-1] = a.diagonal(k=1)
ab[n - 1, :1 - n] = a.diagonal(k=n - 1)
l = scipy.linalg.cholesky_banded(ab, lower=True)
l_t = numpy.zeros((n, (n - 1)**2))
for i in range(n):
l_t[n - i - 1, i:] = l[i, :(n - 1)**2 - i]
ctr = 0
for i in range(m):
u = scipy.linalg.solve_banded((n - 1, 0), l, u)
u = scipy.linalg.solve_banded((0, n - 1), l_t, u)
ctr += 1
u = u.reshape((n - 1, n - 1))
return u, ctr