def test_splu_solve(self):
# Prefactorize (with UMFPACK) matrix for solving with multiple rhs
a = self.a.astype('d')
lu = um.splu(a)
x1 = lu.solve(self.b)
assert_allclose(a * x1, self.b)
x2 = lu.solve(self.b2)
assert_allclose(a * x2, self.b2)
def test_splu_solve(self):
# Prefactorize (with UMFPACK) matrix for solving with multiple rhs
a = self.a.astype('d')
lu = um.splu(a)
x1 = lu.solve(self.b)
assert_allclose(a*x1, self.b)
x2 = lu.solve(self.b2)
assert_allclose(a*x2, self.b2)
def test_splu_solve_int64(self):
# Prefactorize (with UMFPACK) matrix with int64 indices for solving with
# multiple rhs
a = _to_int64(self.a.astype('d'))
lu = um.splu(a)
x1 = lu.solve(self.b)
assert_allclose(a * x1, self.b)
x2 = lu.solve(self.b2)
assert_allclose(a * x2, self.b2)
def lu_factorize(self):
## 重新做LU分解
self.B = self.A[:, self.idxB]
self.etas = []
self.eta_count = 0
if LINEAR_SOLVER_TYPE == LinearSolver.SUPERLU:
self.invB = splinalg.splu(self.B)
else:
self.invB = umfpack.splu(self.B)
def test_splu_solve_int64(self):
# Prefactorize (with UMFPACK) matrix with int64 indices for solving with
# multiple rhs
a = _to_int64(self.a.astype('d'))
lu = um.splu(a)
x1 = lu.solve(self.b)
assert_allclose(a*x1, self.b)
x2 = lu.solve(self.b2)
assert_allclose(a*x2, self.b2)
def test_splu_solve_sparse(self):
# Prefactorize (with UMFPACK) matrix for solving with multiple rhs
A = self.a.astype('d')
lu = um.splu(A)
b = csc_matrix(self.b.reshape(self.b.shape[0], 1))
b2 = csc_matrix(self.b2.reshape(self.b2.shape[0], 1))
B = hstack((b, b2))
X = lu.solve_sparse(B)
assert dense_norm(((A * X) - B).todense()) < 1e-14
assert_allclose((A * X).todense(), B.todense())
def test_splu_solve_sparse(self):
# Prefactorize (with UMFPACK) matrix for solving with multiple rhs
A = self.a.astype('d')
lu = um.splu(A)
b = csc_matrix(self.b.reshape(self.b.shape[0], 1))
b2 = csc_matrix(self.b2.reshape(self.b2.shape[0], 1))
B = hstack((b, b2))
X = lu.solve_sparse(B)
assert dense_norm(((A*X) - B).todense()) < 1e-14
assert_allclose((A*X).todense(), B.todense())
def pagerank_umf(G, personal_vec):
M = nx.to_scipy_sparse_matrix(G,
nodelist=G.nodes(),
weight='weight',
dtype=float)
S = scipy.array(M.sum(axis=1)).flatten()
S[S != 0] = 1.0 / S[S != 0]
Q = scipy.sparse.spdiags(S.T, 0, *M.shape, format='csr')
M = Q * M
alpha = 0.85
A = scipy.sparse.eye(M.shape[0]) - alpha * M
LU = umfpack.splu(A)
ppr_mat = []
for i in range(personal_vec.shape[1]):
pr = LU.solve(personal_vec[:, i])
pr = linalg.spsolve(A, personal_vec[:, i])
ppr_mat.append(pr)
def test_splu_lu(self):
A = csc_matrix([[1,2,0,4],[1,0,0,1],[1,0,2,1],[2,2,1,0.]])
lu = um.splu(A)
Pr = np.zeros((4, 4))
Pr[lu.perm_r, np.arange(4)] = 1
Pr = csc_matrix(Pr)
Pc = np.zeros((4, 4))
Pc[np.arange(4), lu.perm_c] = 1
Pc = csc_matrix(Pc)
R = csc_matrix((4, 4))
R.setdiag(lu.R)
A2 = (R * Pr.T * (lu.L * lu.U) * Pc.T).A
assert_allclose(A2, A.A, atol=1e-13)
def test_splu_lu(self):
A = csc_matrix([[1, 2, 0, 4], [1, 0, 0, 1], [1, 0, 2, 1],
[2, 2, 1, 0.]])
lu = um.splu(A)
Pr = np.zeros((4, 4))
Pr[lu.perm_r, np.arange(4)] = 1
Pr = csc_matrix(Pr)
Pc = np.zeros((4, 4))
Pc[np.arange(4), lu.perm_c] = 1
Pc = csc_matrix(Pc)
R = csc_matrix((4, 4))
R.setdiag(lu.R)
A2 = (R * Pr.T * (lu.L * lu.U) * Pc.T).A
assert_allclose(A2, A.A, atol=1e-13)
def Solve(self, A, b, reuse_factorisation=False):
"""Solves the linear system of equations"""
if not issparse(A):
raise ValueError("Linear system is not of sparse type")
if A.shape == (0,0) and b.shape[0] == 0:
warn("Empty linear system!!! Nothing to solve!!!")
return np.copy(b)
self.reuse_factorisation = reuse_factorisation
if self.solver_type != "direct" and self.reuse_factorisation is True:
warn("Re-using factorisation for non-direct solvers is not possible. The pre-conditioner is going to be reused instead")
# DECIDE IF THE SOLVER TYPE IS APPROPRIATE FOR THE PROBLEM
if self.switcher_message is False and self.dont_switch_solver is False:
# PREFER PARDISO OR MUMPS OVER AMG IF AVAILABLE
if self.has_pardiso:
self.solver_type = "direct"
self.solver_subtype = "pardiso"
elif self.has_mumps:
self.solver_type = "direct"
self.solver_subtype = "mumps"
elif b.shape[0] > 100000 and self.has_amg_solver:
self.solver_type = "amg"
self.solver_subtype = "gmres"
print('Large system of equations. Switching to algebraic multigrid solver')
self.switcher_message = True
# elif mesh.points.shape[0]*MainData.nvar > 50000 and MainData.C < 4:
# self.solver_type = "direct"
# self.solver_subtype = "MUMPS"
# print 'Large system of equations. Switching to MUMPS solver'
elif b.shape[0] > 70000 and self.geometric_discretisation=="hex" and self.has_amg_solver:
self.solver_type = "amg"
self.solver_subtype = "gmres"
print('Large system of equations. Switching to algebraic multigrid solver')
self.switcher_message = True
else:
self.solver_type = "direct"
self.solver_subtype = "umfpack"
if self.solver_type == 'direct':
# CALL DIRECT SOLVER
if self.solver_subtype=='umfpack' and self.has_umfpack:
if A.dtype != np.float64:
A = A.astype(np.float64)
if self.solver_context_manager is None:
if self.reuse_factorisation is False:
sol = spsolve(A,b,permc_spec='MMD_AT_PLUS_A',use_umfpack=True)
# from scikits import umfpack
# sol = umfpack.spsolve(A, b)
else:
from scikits import umfpack
lu = umfpack.splu(A)
sol = lu.solve(b)
self.solver_context_manager = lu
else:
sol = self.solver_context_manager.solve(b)
elif self.solver_subtype=='mumps' and self.has_mumps:
from mumps.mumps_context import MUMPSContext
t_solve = time()
A = A.tocoo()
# False means non-symmetric - Do not change it to True. True means symmetric pos def
# which is not the case for electromechanics
if self.solver_context_manager is None:
context = MUMPSContext((A.shape[0], A.row, A.col, A.data, False), verbose=False)
context.analyze()
context.factorize()
sol = context.solve(rhs=b)
if self.reuse_factorisation:
self.solver_context_manager = context
else:
sol = self.solver_context_manager.solve(rhs=b)
print("MUMPS solver time is {}".format(time() - t_solve))
return sol
elif self.solver_subtype == "pardiso" and self.has_pardiso:
# NOTE THAT THIS PARDISO SOLVER AUTOMATICALLY SAVES THE RIGHT FACTORISATION
import pypardiso
from pypardiso.scipy_aliases import pypardiso_solver as ps
A = A.tocsr()
t_solve = time()
sol = pypardiso.spsolve(A,b)
if self.reuse_factorisation is False:
ps.remove_stored_factorization()
ps.free_memory()
print("Pardiso solver time is {}".format(time() - t_solve))
else:
# FOR 'super_lu'
if A.dtype != np.float64:
A = A.astype(np.float64)
A = A.tocsc()
if self.solver_context_manager is None:
if self.reuse_factorisation is False:
sol = spsolve(A,b,permc_spec='MMD_AT_PLUS_A',use_umfpack=True)
else:
lu = splu(A)
sol = lu.solve(b)
self.solver_context_manager = lu
else:
sol = self.solver_context_manager.solve(b)
elif self.solver_type == "iterative":
# CALL ITERATIVE SOLVER
if self.solver_subtype == "gmres":
sol = gmres(A,b,tol=self.iterative_solver_tolerance)[0]
if self.solver_subtype == "lgmres":
sol = lgmres(A,b,tol=self.iterative_solver_tolerance)[0]
elif self.solver_subtype == "bicgstab":
sol = bicgstab(A,b,tol=self.iterative_solver_tolerance)[0]
else:
sol = cg(A,b,tol=self.iterative_solver_tolerance)[0]
# PRECONDITIONED ITERATIVE SOLVER - CHECK
# P = spilu(A.tocsc(), drop_tol=1e-5)
# M_x = lambda x: P.solve(x)
# m = A.shape[1]
# n = A.shape[0]
# M = LinearOperator((n * m, n * m), M_x)
# sol = cg(A, b, tol=self.iterative_solver_tolerance, M=M)[0]
elif self.solver_type == "amg":
if self.has_amg_solver is False:
raise ImportError('Algebraic multigrid solver was not found. Please install it using "pip install pyamg"')
from pyamg import ruge_stuben_solver, rootnode_solver, smoothed_aggregation_solver
if A.dtype != b.dtype:
# DOWN-CAST
b = b.astype(A.dtype)
if not isspmatrix_csr(A):
A = A.tocsr()
t_solve = time()
if self.iterative_solver_tolerance > 1e-9:
self.iterative_solver_tolerance = 1e-10
# AMG METHOD
amg_func = None
if self.preconditioner_type=="smoothed_aggregation":
# THIS IS TYPICALLY FASTER BUT THE TOLERANCE NEED TO BE SMALLER, TYPICALLY 1e-10
amg_func = smoothed_aggregation_solver
elif self.preconditioner_type == "ruge_stuben":
amg_func = ruge_stuben_solver
elif self.preconditioner_type == "rootnode":
amg_func = rootnode_solver
else:
amg_func = rootnode_solver
ml = amg_func(A)
# ml = amg_func(A, smooth=('energy', {'degree':2}), strength='evolution' )
# ml = amg_func(A, max_levels=3, diagonal_dominance=True)
# ml = amg_func(A, coarse_solver=spsolve)
# ml = amg_func(A, coarse_solver='cholesky')
if self.solver_context_manager is None:
# M = ml.aspreconditioner(cycle='V')
M = ml.aspreconditioner()
if self.reuse_factorisation:
self.solver_context_manager = M
else:
M = self.solver_context_manager
# EXPLICIT CALL TO KYROLOV SOLVERS WITH AMG PRECONDITIONER
# sol, info = bicgstab(A, b, M=M, tol=self.iterative_solver_tolerance)
# sol, info = cg(A, b, M=M, tol=self.iterative_solver_tolerance)
# sol, info = gmres(A, b, M=M, tol=self.iterative_solver_tolerance)
# IMPLICIT CALL TO KYROLOV SOLVERS WITH AMG PRECONDITIONER
residuals = []
sol = ml.solve(b, tol=self.iterative_solver_tolerance, accel=self.solver_subtype, residuals=residuals)
print("AMG solver time is {}".format(time() - t_solve))
elif self.solver_type == "petsc" and self.has_petsc:
if self.solver_subtype != "gmres" and self.solver_subtype != "minres" and self.solver_subtype != "cg":
self.solver_subtype == "cg"
if self.iterative_solver_tolerance < 1e-9:
self.iterative_solver_tolerance = 1e-7
from petsc4py import PETSc
t_solve = time()
pA = PETSc.Mat().createAIJ(size=A.shape, csr=(A.indptr, A.indices, A.data))
pb = PETSc.Vec().createWithArray(b)
ksp = PETSc.KSP()
ksp.create(PETSc.COMM_WORLD)
# ksp.create()
ksp.setType(self.solver_subtype)
ksp.setTolerances(atol=self.iterative_solver_tolerance,
rtol=self.iterative_solver_tolerance)
# ILU
ksp.getPC().setType('icc')
# CREATE INITIAL GUESS
psol = PETSc.Vec().createWithArray(np.ones(b.shape[0]))
# SOLVE
ksp.setOperators(pA)
ksp.setFromOptions()
ksp.solve(pb, psol)
sol = psol.getArray()
# print('Converged in', ksp.getIterationNumber(), 'iterations.')
print("Petsc linear iterative solver time is {}".format(time() - t_solve))
else:
warn("{} solver is not available. Default solver is going to be used".format(self.solver_type))
# FOR 'super_lu'
if A.dtype != np.float64:
A = A.astype(np.float64)
A = A.tocsc()
if self.solver_context_manager is None:
if self.reuse_factorisation is False:
sol = spsolve(A,b,permc_spec='MMD_AT_PLUS_A',use_umfpack=True)
else:
lu = splu(A)
sol = lu.solve(b)
self.solver_context_manager = lu
else:
sol = self.solver_context_manager.solve(b)
return sol
def solve_sparse_mat_mat_lu(A, B, solver="petsc"):
"""
Solves AX=B for X
Parameters
----------
A: scipy sparse matrix
NxN Matrix
B: scipy sparse matrix
NxP Matrix
solver: string
Choice of direct solver. "petsc" or "scipy"
Returns
_______
out: scipy sparse matrix
solution X
Notes
_____
Ignores zero columns in B, and hence is faster than the existing scipy implementation
"""
sf = 1.e30 # scaling factor for petsc
assert solver in ["petsc", "scipy"]
if solver == "petsc":
lu_A = get_petsc_ksp(A * sf, pctype="lu", ksptype="preonly", tol=1e-25, max_it=100)
elif solver == "scipy":
lu_A = splu(A)
B = B.tocsc() # Convert to csc to extract columns efficiently
# Create a sparse output matrix by repeatedly applying
# the sparse factorization to solve columns of b.
# Adapted from scipy.sparse.linalg.dsolve.linsolve
ind_of_nonzero_cols = np.unique(B.nonzero()[1])
data_segs = []
row_segs = []
col_segs = []
for j in ind_of_nonzero_cols:
Bj = B[:, j].A.ravel()
if solver == "scipy":
xj = lu_A.solve(Bj)
elif solver == "petsc":
xj = petsc_solve_from_ksp(lu_A, Bj * sf, x=None, tol=1e-5)
w = np.flatnonzero(xj)
segment_length = w.shape[0]
row_segs.append(w)
col_segs.append(np.ones(segment_length, dtype=int) * j)
data_segs.append(np.asarray(xj[w], dtype=A.dtype))
sparse_data = np.concatenate(data_segs)
sparse_row = np.concatenate(row_segs)
sparse_col = np.concatenate(col_segs)
x = csc_matrix((sparse_data, (sparse_row, sparse_col)), shape=B.shape, dtype=B.dtype)
return x
def solve(self, solver="lu", x0=None, tol=1.e-6):
solver = solver.lower()
sf = 1e30
pores = self.network.pores
A = self.csr_solver_matrix
self.solver_matrix.set_csr_singular_rows_to_dirichlet(A)
self.A = A
mass_residual = 1.0
if x0 is not None:
self.sol[:] = x0
if solver == "lu":
lu_A = splu(A)
elif solver == "amg":
ml = pyamg.rootnode_solver(A, max_coarse=10)
elif solver == "petsc":
comm = MPI.COMM_SELF
ksp = get_petsc_ksp(A=A * sf, ksptype="minres", tol=tol, max_it=1000)
petsc_rhs = PETSc.Vec().createWithArray(self.rhs * sf, comm=comm)
elif "trilinos" in solver:
epetra_mat = matrix_scipy_to_epetra(A * sf)
epetra_rhs = vector_numpy_to_epetra(self.rhs * sf)
if "ml" in solver:
epetra_prec = trilinos_ml_prec(epetra_mat)
def inner_loop_solve(tol):
if solver == "lu":
self.sol[:] = lu_A.solve(self.rhs)
elif solver == "amg":
self.sol[:] = ml.solve(b=self.rhs, x0=self.sol, tol=tol, accel='gmres')
elif solver == "petsc":
ksp.setTolerances(rtol=tol)
ksp.setFromOptions()
petsc_sol = PETSc.Vec().createWithArray(self.sol, comm=comm)
ksp.setInitialGuessNonzero(True)
ksp.solve(petsc_rhs, petsc_sol)
self.sol[:] = petsc_sol.getArray()
elif "trilinos" in solver:
epetra_sol = vector_numpy_to_epetra(self.sol)
if "ml" in solver:
x = trilinos_solve(epetra_mat, epetra_rhs, epetra_prec, x=epetra_sol, tol=tol)
else:
x = solve_aztec(epetra_mat, epetra_rhs, x=epetra_sol, tol=tol)
self.sol[:] = x
pores.p_w[:] = self.sol[:] # This side-effect is required for the compute_mass_residual function
pores.p_n[:] = pores.p_w + pores.p_c
count = 0
while (mass_residual > 1e-5) and (count < 100):
count += 1
inner_loop_solve(tol)
mass_residual = self.compute_mass_residual(A, self.rhs, self.sol)
logger.debug("Mass flux residual %e", mass_residual)
if count == 99:
logger.warn("Failed to converge. Residual %e. Falling back to mltrilinos solver", mass_residual)
return self.solve(solver="mltrilinos") # Fall back to reliable solver
tol /= 10.0
if "ml" in solver:
epetra_prec.DestroyPreconditioner();
return np.copy(self.sol)