def solve(self, flag):
start = timer()
A = self.get_laplace_matrix();
b = self.get_source_vector();
if flag == 1:
A += self.get_neuman_penalty_matrix();
b += self.get_neuman_vector();
bc = DirichletBC(self.space, self.pde.dirichlet)
elif flag == 2:
A += self.get_neuman_penalty_matrix();
A += self.get_dirichlet_penalty_matrix();
b += self.get_neuman_vector();
b += self.get_dirichlet_vector();
bc = None;
elif flag == 3:
b += self.get_laplace_dirichlet_vector();
bc = DirichletBC(self.space, self.pde.dirichlet)
elif flag == 4:
A += self.get_neuman_penalty_matrix();
b -= self.get_laplace_neuman_vector();
b += self.get_neuman_vector();
bc = None;
end = timer()
print("Construct linear system time:", end - start)
if bc is not None:
AD, b = bc.apply(A, b)
else:
if flag == 4:
gdof = self.space.number_of_global_dofs()
isBdDof = self.space.boundary_dof()
x = np.zeros((gdof,), dtype=np.float)
ipoints = self.space.interpolation_points()
# the length of ipoints and isBdDof maybe different
idx, = np.nonzero(isBdDof)
x[idx[0]] = self.pde.dirichlet(ipoints[idx[0]])
b -= A@x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[idx[0]] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1-bdIdx, 0, gdof, gdof)
AD = T@A@T + Tbd
b[idx[0]] = x[idx[0]]
else:
AD = A
start = timer()
self.uh[:] = spsolve(AD, b)
end = timer()
print("Solve time:", end-start)
self.recover_grad()
self.recover_laplace()
def solveDirect_mumps(self, b, factorize):
"""
Use solve instead of this interface.
:param numpy.ndarray b: the right hand side
:param bool factorize: if you want to factorize and store factors
:rtype: numpy.ndarray
:return: x
"""
if factorize and self.dsolve is None:
self.mctx = mumps.DMumpsContext()
self.mctx.set_icntl(14, 60)
# self.mctx.set_silent()
self.mctx.set_centralized_sparse(self.A)
self.mctx.run(job=4)
def mdsolve(rhs):
x = rhs.copy()
self.mctx.set_rhs(x)
self.mctx.run(job=3)
return x
self.dsolve = mdsolve
if len(b.shape) == 1 or b.shape[1] == 1:
# Just one RHS
if factorize:
X = self.dsolve(b)
else:
X = mumps.spsolve(self.A, b)
else:
# Multiple RHSs
X = np.empty_like(b)
for i in range(b.shape[1]):
if factorize:
X[:, i] = self.dsolve(b[:, i])
else:
X[:, i] = mumps.spsolve(self.A, b[:, i])
return X
def solveDirect_mumps(self, b, factorize):
"""
Use solve instead of this interface.
:param numpy.ndarray b: the right hand side
:param bool factorize: if you want to factorize and store factors
:rtype: numpy.ndarray
:return: x
"""
if factorize and self.dsolve is None:
self.mctx = mumps.DMumpsContext()
self.mctx.set_icntl(14, 60)
# self.mctx.set_silent()
self.mctx.set_centralized_sparse(self.A)
self.mctx.run(job=4)
def mdsolve(rhs):
x = rhs.copy()
self.mctx.set_rhs(x)
self.mctx.run(job=3)
return x
self.dsolve = mdsolve
if len(b.shape) == 1 or b.shape[1] == 1:
# Just one RHS
if factorize:
X = self.dsolve(b)
else:
X = mumps.spsolve(self.A, b)
else:
# Multiple RHSs
X = np.empty_like(b)
for i in range(b.shape[1]):
if factorize:
X[:,i] = self.dsolve(b[:,i])
else:
X[:,i] = mumps.spsolve(self.A,b[:,i])
return X
def active_set_solver(dmodel,
uh,
gh,
maxit=5000,
dirichlet=None,
solver='direct'):
space = uh.space
start = timer()
A = dmodel.get_left_matrix()
b = dmodel.get_right_vector()
end = timer()
print("Construct linear system time:", end - start)
if dirichlet is not None:
AD, b = dirichlet.apply(A, b)
AD = AD.tolil()
start = timer()
lam = space.function()
gdof = space.number_of_global_dofs()
I = np.ones(gdof, dtype=np.bool)
k = 0
while k < maxit:
print(k)
k += 1
I0 = I.copy()
I[:] = (lam + gh - uh > 0)
if np.all(I == I0) & (k > 1):
break
M = AD.copy()
F = b.copy()
idx, = np.nonzero(I)
M[idx, :] = 0
M[idx, idx] = 1
F[idx] = gh[idx]
if solver is 'direct':
uh[:] = spsolve(M.tocsr(), F)
elif solver is 'amg':
ml = pyamg.ruge_stuben_solver(M.tocsr())
uh[:] = ml.solve(F, tol=1e-12, accel='cg').reshape(-1)
lam[:] = AD @ uh - b
end = timer()
print("Solve time:", end - start)
return A, b
def linear_operator(self, r):
tgdof = self.tensorspace.number_of_global_dofs()
vgdof = self.vectorspace.number_of_global_dofs()
gdof = tgdof + vgdof
gdim = self.tensorspace.geo_dimension()
r0 = r[0:tgdof]
r1 = r[tgdof:]
u0 = r0/self.D
u1 = np.zeros(vgdof, dtype=np.float)
r2 = r1 - self.B@u0
for i in range(3):
u1[:] = spsolve(self.SL, r2 - self.SU@u1, permc_spec="NATURAL")
r3 = r2 - (self.SL@u1 + self.SU@u1)
for i in range(gdim):
u1[i::gdim] = [email protected](self.PI.transpose()@r3[i::gdim], tol=1e-8, accel='cg')
for i in range(3):
u1[:] = spsolve(self.SUT, r2 - self.SLT@u1, permc_spec="NATURAL")
return np.r_[u0 + self.B.transpose()@u1, -u1]
def solve(self):
mesh = self.mesh
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
itype = mesh.itype
ftype = mesh.ftype
A = self.get_left_matrix()
b = self.get_right_vector()
x = np.r_[self.uh, self.ph] #把self.uh,self.ph组合在一起
b = b - A @ x
# Modify matrix
bdIdx = np.zeros((A.shape[0], ), dtype=itype)
bdIdx[NE] = 1
Tbd = spdiags(bdIdx, 0, A.shape[0], A.shape[1])
T = spdiags(1 - bdIdx, 0, A.shape[0], A.shape[1])
AD = T @ A @ T + Tbd
scipy.sparse.save_npz('AD.npz', AD)
b[NE] = self.ph[0]
with open("b.csv", "w", newline="") as datacsv:
csvwriter = csv.writer(datacsv, dialect=("excel"))
csvwriter.writerow(['b'])
csvwriter.writerows([b])
# solve
x[:] = spsolve(AD, b)
# solve
from mumps import DMumpsContext
ctx = DMumpsContext()
if ctx.myid == 0:
ctx.set_centralized_sparse(AD.tocoo())
x = b.copy()
ctx.set_rhs(x)
ctx.set_silent()
ctx.run(job=6)
self.uh[:] = x[:NE]
self.ph[:] = x[NE:]
print('ph', self.ph)
print('pI', self.pI)
return x
def solve(self):
tgdof = self.tensorspace.number_of_global_dofs()
vgdof = self.vectorspace.number_of_global_dofs()
gdof = tgdof + vgdof
start = timer()
M, B = self.get_left_matrix()
b = self.get_right_vector()
A = bmat([[M, B.transpose()], [B, None]]).tocsr()
bb = np.r_[np.zeros(tgdof), b]
end = timer()
print("Construct linear system time:", end - start)
start = timer()
x = spsolve(A, bb)
end = timer()
print("Solve time:", end-start)
self.sh[:] = x[0:tgdof]
self.uh[:] = x[tgdof:]
def solve1(a, L, uh, dirichlet=None, neuman=None, solver='cg'):
space = a.space
start = timer()
A = a.get_matrix()
b = L.get_vector()
end = timer()
print("Construct linear system time:", end - start)
if neuman is not None:
b += neuman.get_vector()
if dirichlet is not None:
AD, b = dirichlet.apply(A, b)
else:
AD = A
# print("The condtion number is: ", np.linalg.cond(AD.todense()))
if solver is 'cg':
start = timer()
D = AD.diagonal()
M = spdiags(1 / D, 0, AD.shape[0], AD.shape[1])
uh[:], info = cg(AD, b, tol=1e-14, M=M)
end = timer()
print(info)
elif solver is 'amg':
start = timer()
ml = pyamg.ruge_stuben_solver(AD)
uh[:] = ml.solve(b, tol=1e-12, accel='cg').reshape((-1, ))
end = timer()
print(ml)
elif solver is 'direct':
start = timer()
uh[:] = spsolve(AD, b)
end = timer()
else:
print("We don't support solver: " + solver)
print("Solve time:", end - start)
return A
def solve(self):
mesh = self.mesh
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
itype = mesh.itype
ftype = mesh.ftype
A = self.get_left_matrix()
b = self.get_right_vector()
x = np.r_[self.uh, self.ph] #把self.uh,self.ph组合在一起
b = b - A @ x
# Modify matrix
bdIdx = np.zeros((A.shape[0], ), dtype=itype)
bdIdx[NE] = 1
Tbd = spdiags(bdIdx, 0, A.shape[0], A.shape[1])
T = spdiags(1 - bdIdx, 0, A.shape[0], A.shape[1])
AD = T @ A @ T + Tbd
b[NE] = self.ph[0]
K = AD.todense()
# solve
x[:] = spsolve(AD, b)
# solve
from mumps import DMumpsContext
ctx = DMumpsContext()
if ctx.myid == 0:
ctx.set_centralized_sparse(AD.tocoo())
x = b.copy()
ctx.set_rhs(x)
ctx.set_silent()
ctx.run(job=6)
self.uh[:] = x[:NE]
self.ph[:] = x[NE:]
print('ph', self.ph)
print('pI', self.pI)
return x
def solve(dmodel, uh, dirichlet=None, solver='direct'):
space = uh.space
start = timer()
A = dmodel.get_left_matrix()
b = dmodel.get_right_vector()
end = timer()
print("Construct linear system time:", end - start)
if dirichlet is not None:
AD, b = dirichlet.apply(A, b)
else:
AD = A
if solver is 'cg':
start = timer()
D = AD.diagonal()
M = spdiags(1 / D, 0, AD.shape[0], AD.shape[1])
uh[:], info = cg(AD, b, tol=1e-14, M=M)
end = timer()
print(info)
elif solver is 'amg':
start = timer()
ml = pyamg.ruge_stuben_solver(AD)
uh[:] = ml.solve(b, tol=1e-12, accel='cg').reshape(-1)
end = timer()
print(ml)
elif solver is 'direct':
start = timer()
uh[:] = spsolve(AD, b)
end = timer()
else:
raise ValueError("We don't support solver `{}`! ".format(solver))
print("Solve time:", end - start)
return AD, b