def solver_superlu(A):
"""
Return a function for solving a sparse linear system using SuperLU.
Parameters
----------
A : (N, N) array_like
Input.
Returns
-------
solve : callable
To solve the linear system of equations given in `A`, the `solve`
callable should be passed an ndarray of shape (N,).
"""
import scipy.sparse.linalg as spla
_useUmfpack = spla.dsolve.linsolve.useUmfpack
spla.use_solver(useUmfpack=False)
iA = spla.factorized(A)
def solver(b, x0=None):
return iA(b)
spla.use_solver(useUmfpack=_useUmfpack)
return solver,
def solver_umfpack(A):
"""
Return a function for solving a sparse linear system using UMFPACK.
Parameters
----------
A : (N, N) array_like
Input.
Returns
-------
solve : callable
To solve the linear system of equations given in `A`, the `solve`
callable should be passed an ndarray of shape (N,).
"""
import scipy.sparse.linalg as spla
#_useUmfpack = spla.dsolve.linsolve.useUmfpack
spla.use_solver(useUmfpack=True)
A.indptr = A.indptr.astype(np.int64)
A.indices = A.indices.astype(np.int64)
iA = spla.factorized(A)
def solver(b, x0=None):
return iA(b)
#spla.use_solver(useUmfpack=_useUmfpack)
return solver,
def test_solve_long_umfpack(self):
# Solve with UMFPACK: double precision
linalg.use_solver(useUmfpack=True)
a = _to_int64(self.a.astype('d'))
b = self.b
x = linalg.spsolve(a, b)
assert_array_almost_equal(a * x, b)
def test_solve_sparse_rhs(self):
# Solve with UMFPACK: double precision, sparse rhs
linalg.use_solver(useUmfpack=True)
a = self.a.astype('d')
b = csc_matrix(self.b).T
x = linalg.spsolve(a, b)
assert_array_almost_equal(a * x, self.b)
def test_solve_complex_umfpack(self):
# Solve with UMFPACK: double precision complex
linalg.use_solver(useUmfpack=True)
a = self.a.astype('D')
b = self.b
x = linalg.spsolve(a, b)
assert_array_almost_equal(a * x, b)
def __init__(self,engine):
"""Initialize the solver. Load umfpack is available
:param engine: FEM Engine
:type engine: FEM_2D.Engine / FEM_3D.Engine
"""
self.engine = engine
if 'scikits.umfpack' in sys.modules:
sla.use_solver(useUmfpack=True)
def test_factorized_long_umfpack(self):
# Prefactorize (with UMFPACK) matrix for solving with multiple rhs
linalg.use_solver(useUmfpack=True)
a = _to_int64(self.a.astype('d'))
solve = linalg.factorized(a)
x1 = solve(self.b)
assert_array_almost_equal(a * x1, self.b)
x2 = solve(self.b2)
assert_array_almost_equal(a * x2, self.b2)
def test_factorized_without_umfpack(self):
# Prefactorize matrix for solving with multiple rhs
linalg.use_solver(useUmfpack=False)
a = self.a.astype('d')
solve = linalg.factorized(a)
x1 = solve(self.b)
assert_array_almost_equal(a * x1, self.b)
x2 = solve(self.b2)
assert_array_almost_equal(a * x2, self.b2)
def _linear_analysis(self, method, **kwargs):
"""Performs the linear analysis, in which the pressure and flow fields
are computed.
INPUT: method: This can be either 'direct' or 'iterative'
**kwargs
precision: The accuracy to which the ls is to be solved. If not
supplied, machine accuracy will be used. (This only
applies to the iterative solver)
OUTPUT: The maximum, mean, and median pressure change. Moreover,
pressure and flow are modified in-place.
"""
G = self._G
A = self._A.tocsr()
if method == 'direct':
linalg.use_solver(useUmfpack=True)
x = linalg.spsolve(A, self._b)
elif method == 'iterative':
if kwargs.has_key('precision'):
eps = kwargs['precision']
else:
eps = self._eps
AA = smoothed_aggregation_solver(A, max_levels=10, max_coarse=500)
x = abs(AA.solve(self._b, x0=None, tol=eps, accel='cg', cycle='V', maxiter=150))
# abs required, as (small) negative pressures may arise
elif method == 'iterative2':
# Set linear solver
ml = rootnode_solver(A, smooth=('energy', {'degree':2}), strength='evolution' )
M = ml.aspreconditioner(cycle='V')
# Solve pressure system
#x,info = gmres(A, self._b, tol=self._eps, maxiter=50, M=M, x0=self._x)
#x,info = gmres(A, self._b, tol=self._eps/10000000000000, maxiter=50, M=M)
x,info = gmres(A, self._b, tol=self._eps/10000, maxiter=50, M=M)
if info != 0:
print('SOLVEERROR in Solving the Matrix')
pdiff = map(abs, [(p - xx) / p if p > 0 else 0.0
for p, xx in zip(G.vs['pressure'], x)])
maxPDiff = max(pdiff)
meanPDiff = np.mean(pdiff)
medianPDiff = np.median(pdiff)
log.debug(np.nonzero(np.array(pdiff) == maxPDiff)[0])
G.vs['pressure'] = x
G.es['flow'] = [abs(G.vs[edge.source]['pressure'] - \
G.vs[edge.target]['pressure']) * \
edge['conductance'] for edge in G.es]
self._maxPDiff=maxPDiff
self._meanPDiff=meanPDiff
self._medianPDiff=medianPDiff
return maxPDiff, meanPDiff, medianPDiff
def __init__(self,M,C,K,dt):
self.dt = dt
self.tspan = []
self.u = []
self.M = M
self.C = C
self.K = K
self.sys = M + dt*C + (dt**2)*K
if 'scikits.umfpack' in sys.modules:
sla.use_solver(useUmfpack=True)
self.sys.indices = self.sys.indices.astype(np.int64)
self.sys.indptr = self.sys.indptr.astype(np.int64)
self.a0 = self.M.multiply(2) + self.C.multiply(self.dt)
self.a1 = self.dt**2
def __init__(self,M,C,K,dt,alpha,delta):
""" Initialize the Newmark method.
:param M: The mass matrix.
:type M: CSC Matrix
:param C: [description]
:type C: CSC Matrix
:param K: [description]
:type K: CSC Matrix
:param dt: Time-step
:type dt: float
:param alpha: Alpha parameter (Newmark's Method)
:type alpha: float
:param delta: Delta parameter (Newmark's Method)
:type delta: float
"""
self.alpha = alpha
self.delta = delta
self.dt = dt
self.a0 = 1/(alpha*(dt**2))
self.a1 = delta/(alpha*dt)
self.a2 = 1/(alpha*dt)
self.a3 = 1/(2*alpha) - 1
self.a4 = delta/alpha - 1
self.a5 = (dt/2) * ((delta/alpha)-2)
self.a6 = dt*(1-delta)
self.a7 = delta*dt
self.tspan = []
self.u = []
self.M = M
self.C = C
self.Keff = K + M.multiply(self.a0) + C.multiply(self.a1)
if 'scikits.umfpack' in sys.modules:
sla.use_solver(useUmfpack=True)
self.Keff.indices = self.Keff.indices.astype(int)
self.Keff.indptr = self.Keff.indptr.astype(int)
#Initial conditions
self.u0 = np.zeros(M.shape[0])
self.du0 = np.zeros(M.shape[0])
self.ddu0 = np.zeros(M.shape[0])
def solve(self, method):
"""Solves the linear system A x = b for the vector of unknown pressures
x, either using a direct solver (obsolete) or an iterative GMRES solver. From the
pressures, the flow field is computed.
INPUT: method: This can be either 'direct' or 'iterative2'
OUTPUT: None - G is modified in place.
G_final.pkl & G_final.vtp: are save as output
sampledict.pkl: is saved as output
"""
b = self._b
A = self._A
G = self._G
htt2htd = self._P.tube_to_discharge_hematocrit
A = self._A.tocsr()
if method == 'direct':
linalg.use_solver(useUmfpack=True)
x = linalg.spsolve(A, b)
elif method == 'iterative2':
ml = rootnode_solver(A, smooth=('energy', {'degree':2}), strength='evolution' )
M = ml.aspreconditioner(cycle='V')
# Solve pressure system
x,info = gmres(A, self._b, tol=1000*self._eps, maxiter=200, M=M)
if info != 0:
print('ERROR in Solving the Matrix')
print(info)
G.vs['pressure'] = x
G.es['flow'] = [abs(G.vs[edge.source]['pressure'] - G.vs[edge.target]['pressure']) * \
edge['conductance'] for edge in G.es]
#Default Units - mmHg for pressure
G.vs['pressure'] = [v['pressure']/self._scalingFactor for v in G.vs]
if self._withRBC:
G.es['v']=[e['htd']/e['htt']*e['flow']/(0.25*np.pi*e['diameter']**2) for e in G.es]
else:
G.es['v']=[e['flow']/(0.25*np.pi*e['diameter']**2) for e in G.es]
def test_origen_against_CRAM_lambdify(xs_tape9, time, nuclide, phi, umfpack, alpha_as_He4=False):
e_complex = CRAM_matrix_exp_lambdify()
lambdify_desc = 'CRAM lambdify UMFPACK' if umfpack else 'CRAM lambdify SuperLU'
logger.info("Running %s %s at time=%s, nuclide=%s, phi=%s", lambdify_desc,
xs_tape9, time, nuclide, phi)
logger.info('-'*80)
alpha_part = '_alpha_as_He4' if alpha_as_He4 else ''
npzfilename = os.path.join('data', os.path.splitext(os.path.basename(xs_tape9))[0] + '_' +
str(phi) + alpha_part + '.npz')
nucs, mat = load_sparse_csr(npzfilename)
assert mat.shape[1] == len(nucs)
b = initial_vector(nuclide, nucs)
use_solver(useUmfpack=umfpack)
CRAM_lambdify_time, CRAM_lambdify_res = time_func(e_complex, -mat*float(time), b)
CRAM_lambdify_res = np.asarray(CRAM_lambdify_res)
logger.info("%s runtime: %s", lambdify_desc, CRAM_lambdify_time)
return CRAM_lambdify_time, CRAM_lambdify_res
def _linear_analysis(self, method, **kwargs):
"""Performs the linear analysis, in which the pressure and flow fields
are computed.
INPUT: method: This can be either 'direct' or 'iterative'
**kwargs
precision: The accuracy to which the ls is to be solved. If not
supplied, machine accuracy will be used. (This only
applies to the iterative solver)
OUTPUT: The maximum, mean, and median pressure change. Moreover,
pressure and flow are modified in-place.
"""
G = self._G
A = self._A.tocsr()
if method == 'direct':
linalg.use_solver(useUmfpack=True)
x = linalg.spsolve(A, self._b)
elif method == 'iterative':
if kwargs.has_key('precision'):
eps = kwargs['precision']
else:
eps = self._eps
AA = smoothed_aggregation_solver(A, max_levels=10, max_coarse=500)
x = abs(
AA.solve(self._b,
x0=None,
tol=eps,
accel='cg',
cycle='V',
maxiter=150))
# abs required, as (small) negative pressures may arise
elif method == 'iterative2':
# Set linear solver
ml = rootnode_solver(A,
smooth=('energy', {
'degree': 2
}),
strength='evolution')
M = ml.aspreconditioner(cycle='V')
# Solve pressure system
#x,info = gmres(A, self._b, tol=self._eps, maxiter=50, M=M, x0=self._x)
#x,info = gmres(A, self._b, tol=self._eps/10000000000000, maxiter=50, M=M)
x, info = gmres(A, self._b, tol=self._eps / 10000, maxiter=50, M=M)
if info != 0:
print('SOLVEERROR in Solving the Matrix')
pdiff = map(abs, [(p - xx) / p if p > 0 else 0.0
for p, xx in zip(G.vs['pressure'], x)])
maxPDiff = max(pdiff)
meanPDiff = np.mean(pdiff)
medianPDiff = np.median(pdiff)
log.debug(np.nonzero(np.array(pdiff) == maxPDiff)[0])
G.vs['pressure'] = x
G.es['flow'] = [abs(G.vs[edge.source]['pressure'] - \
G.vs[edge.target]['pressure']) * \
edge['conductance'] for edge in G.es]
self._maxPDiff = maxPDiff
self._meanPDiff = meanPDiff
self._medianPDiff = medianPDiff
return maxPDiff, meanPDiff, medianPDiff
def _steadystate_iterative(L, ss_args):
"""
Iterative steady state solver using the GMRES, LGMRES, or BICGSTAB
algorithm and a sparse incomplete LU preconditioner.
"""
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
if settings.debug:
print('Starting '+ss_args['method']+' solver...')
dims = L.dims[0]
n = prod(L.dims[0][0])
b = np.zeros(n ** 2)
b[0] = ss_args['weight']
L, perm, perm2, rev_perm, ss_args = _steadystate_LU_liouvillian(L, ss_args)
if np.any(perm):
b = b[np.ix_(perm,)]
if np.any(perm2):
b = b[np.ix_(perm2,)]
use_solver(assumeSortedIndices=True, useUmfpack=ss_args['use_umfpack'])
if ss_args['M'] is None and ss_args['use_precond']:
ss_args['M'], ss_args = _iterative_precondition(L, n, ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
# Select iterative solver type
_iter_start = time.time()
if ss_args['method'] == 'iterative-gmres':
v, check = gmres(L, b, tol=ss_args['tol'], M=ss_args['M'],
x0=ss_args['x0'], restart=ss_args['restart'],
maxiter=ss_args['maxiter'], callback=_iter_count)
elif ss_args['method'] == 'iterative-lgmres':
v, check = lgmres(L, b, tol=ss_args['tol'], M=ss_args['M'],
x0=ss_args['x0'], maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-bicgstab':
v, check = bicgstab(L, b, tol=ss_args['tol'], M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'], callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
_iter_end = time.time()
ss_args['info']['iter_time'] = _iter_end - _iter_start
if 'precond_time' in ss_args['info'].keys():
ss_args['info']['solution_time'] = (ss_args['info']['iter_time'] +
ss_args['info']['precond_time'])
ss_args['info']['iterations'] = ss_iters['iter']
ss_args['info']['residual_norm'] = la.norm(b - L*v, np.inf)
if settings.debug:
print('Number of Iterations:', ss_iters['iter'])
print('Iteration. time:', _iter_end - _iter_start)
if check > 0:
raise Exception("Steadystate error: Did not reach tolerance after " +
str(ss_args['maxiter']) + " steps." +
"\nResidual norm: " +
str(ss_args['info']['residual_norm']))
elif check < 0:
raise Exception(
"Steadystate error: Failed with fatal error: " + str(check) + ".")
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
data = vec2mat(v)
data = 0.5 * (data + data.conj().T)
if ss_args['return_info']:
return Qobj(data, dims=dims, isherm=True), ss_args['info']
else:
return Qobj(data, dims=dims, isherm=True)
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
if settings.has_mkl and ss_args['method'] == 'power':
has_mkl = 1
else:
has_mkl = 0
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(L,
ss_args, has_mkl)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2,)]
# Do preconditioning
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres', 'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(L, int(np.sqrt(n)), ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
if settings.has_mkl:
lu = mkl_splu(L)
else:
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz+U_nnz)/orig_nnz))
it = 0
_tol = max(ss_args['tol']/10, 1e-15) # Should make this user accessible
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
v, check = gmres(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'], restart=ss_args['restart'],
maxiter=ss_args['maxiter'], callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
v, check = lgmres(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'], maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
v, check = bicgstab(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'], callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
v = v / la.norm(v, np.inf)
it += 1
if ss_args['method'] == 'power' and settings.has_mkl:
lu.delete()
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L*v)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_direct_sparse(L, ss_args):
"""
Direct solver that uses scipy sparse matrices
"""
if settings.debug:
print('Starting direct LU solver...')
dims = L.dims[0]
n = prod(L.dims[0][0])
b = np.zeros(n ** 2, dtype=complex)
b[0] = ss_args['weight']
L, perm, perm2, rev_perm, ss_args = _steadystate_LU_liouvillian(L, ss_args)
if np.any(perm):
b = b[np.ix_(perm,)]
if np.any(perm2):
b = b[np.ix_(perm2,)]
use_solver(assumeSortedIndices=True, useUmfpack=ss_args['use_umfpack'])
ss_args['info']['permc_spec'] = ss_args['permc_spec']
ss_args['info']['drop_tol'] = ss_args['drop_tol']
ss_args['info']['diag_pivot_thresh'] = ss_args['diag_pivot_thresh']
ss_args['info']['fill_factor'] = ss_args['fill_factor']
ss_args['info']['ILU_MILU'] = ss_args['ILU_MILU']
if not ss_args['use_umfpack']:
# Use superLU solver
orig_nnz = L.nnz
_direct_start = time.time()
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
v = lu.solve(b)
_direct_end = time.time()
ss_args['info']['solution_time'] = _direct_end-_direct_start
if (settings.debug or ss_args['return_info']) and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
ss_args['info']['l_nnz'] = L_nnz
ss_args['info']['u_nnz'] = U_nnz
ss_args['info']['lu_fill_factor'] = (L_nnz+U_nnz)/L.nnz
if settings.debug:
print('L NNZ:', L_nnz, ';', 'U NNZ:', U_nnz)
print('Fill factor:', (L_nnz+U_nnz)/orig_nnz)
else:
# Use umfpack solver
_direct_start = time.time()
v = spsolve(L, b)
_direct_end = time.time()
ss_args['info']['solution_time'] = _direct_end-_direct_start
if (not ss_args['use_umfpack']) and ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
data = vec2mat(v)
data = 0.5 * (data + data.conj().T)
if ss_args['return_info']:
return Qobj(data, dims=dims, isherm=True), ss_args['info']
else:
return Qobj(data, dims=dims, isherm=True)
import cPickle
import numpy as np
import scipy as sp
import scipy.io as sio
import scipy.sparse as sparse
import scipy.optimize as opt
# umfpack disabled due to bug in scipy
# http://mail.scipy.org/pipermail/scipy-user/2009-December/023625.html
#try:
#import scikits.umfpack as um
#HAS_UMFPACK = True
#except:
#HAS_UMFPACK = False
HAS_UMFPACK = False
from scipy.sparse.linalg import spsolve, use_solver
use_solver(useUmfpack=False)
from utils import dec2base, base2dec
import ConfigParser
def get_config_file():
"""Get the location and name of the config file for specifying
the data cache dir. You can call this to find out where to put your
config.
"""
if sys.platform.startswith('win'):
cfname = '~/pyentropy.cfg'
else:
cfname = '~/.pyentropy.cfg'
return os.path.expanduser(cfname)
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
mtol = ss_args['mtol']
if mtol is None:
mtol = max(0.1*tol, 1e-15)
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
if ss_args['solver'] == 'mkl' and ss_args['method'] == 'power':
has_mkl = 1
else:
has_mkl = 0
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(L,
ss_args,
has_mkl)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2,)]
# Do preconditioning
if ss_args['solver'] == 'scipy':
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres',
'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(L, int(np.sqrt(n)),
ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
if ss_args['solver'] == 'mkl':
lu = mkl_splu(L, max_iter_refine=ss_args['max_iter_refine'],
scaling_vectors=ss_args['scaling_vectors'],
weighted_matching=ss_args['weighted_matching'])
else:
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz+U_nnz)/orig_nnz))
it = 0
# FIXME: These atol keyword except checks can be removed once scipy 1.1
# is a minimum requirement
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
check = 0
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
try:
v, check = gmres(L, v, tol=mtol, atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = gmres(L, v, tol=mtol,
M=ss_args['M'], x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
try:
v, check = lgmres(L, v, tol=mtol, atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = lgmres(L, v, tol=mtol,
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
try:
v, check = bicgstab(L, v, tol=mtol, atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = bicgstab(L, v, tol=mtol,
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
if check > 0:
raise Exception("{} failed to find solution in "
"{} iterations.".format(ss_args['method'],
check))
if check < 0:
raise Exception("Breakdown in {}".format(ss_args['method']))
v = v / la.norm(v, np.inf)
it += 1
if ss_args['method'] == 'power' and ss_args['solver'] == 'mkl':
lu.delete()
if ss_args['return_info']:
ss_args['info']['max_iter_refine'] = ss_args['max_iter_refine']
ss_args['info']['scaling_vectors'] = ss_args['scaling_vectors']
ss_args['info']['weighted_matching'] = ss_args['weighted_matching']
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L*v, np.inf)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = v[::rhoss.shape[0]+1]
data = v / np.sum(trow)
else:
data = data / la.norm(v)
data = dense2D_to_fastcsr_fmode(vec2mat(data),
rhoss.shape[0],
rhoss.shape[0])
rhoss.data = 0.5 * (data + data.H)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = prod(rhoss.shape)
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
L.sort_indices()
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
if settings.debug:
old_band = sp_bandwidth(L)[0]
logger.debug('Original bandwidth: %i' % old_band)
perm = reverse_cuthill_mckee(L)
rev_perm = np.argsort(perm)
L = sp_permute(L, perm, perm, 'csc')
v = v[np.ix_(perm, )]
if settings.debug:
new_band = sp_bandwidth(L)[0]
logger.debug('RCM bandwidth: %i' % new_band)
logger.debug('Bandwidth reduction factor: %f' %
round(old_band / new_band, 2))
_power_start = time.time()
# Get LU factors
lu = splu(L,
permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz + U_nnz) / orig_nnz))
it = 0
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
v = lu.solve(v)
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' + str(maxiter) +
' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end - _power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L * v, np.inf)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_iterative(L, ss_args):
"""
Iterative steady state solver using the GMRES, LGMRES, or BICGSTAB
algorithm and a sparse incomplete LU preconditioner.
"""
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
if settings.debug:
logger.debug('Starting %s solver.' % ss_args['method'])
dims = L.dims[0]
n = int(np.sqrt(L.shape[0]))
b = np.zeros(n ** 2)
b[0] = ss_args['weight']
L, perm, perm2, rev_perm, ss_args = _steadystate_LU_liouvillian(L, ss_args)
if np.any(perm):
b = b[np.ix_(perm,)]
if np.any(perm2):
b = b[np.ix_(perm2,)]
use_solver(assumeSortedIndices=True)
if ss_args['M'] is None and ss_args['use_precond']:
ss_args['M'], ss_args = _iterative_precondition(L, n, ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
# Select iterative solver type
_iter_start = time.time()
# FIXME: These atol keyword except checks can be removed once scipy 1.1
# is a minimum requirement
if ss_args['method'] == 'iterative-gmres':
try:
v, check = gmres(L, b, tol=ss_args['tol'], atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = gmres(L, b, tol=ss_args['tol'],
M=ss_args['M'], x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-lgmres':
try:
v, check = lgmres(L, b, tol=ss_args['tol'], atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = lgmres(L, b, tol=ss_args['tol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-bicgstab':
try:
v, check = bicgstab(L, b, tol=ss_args['tol'],
atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = bicgstab(L, b, tol=ss_args['tol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
_iter_end = time.time()
ss_args['info']['iter_time'] = _iter_end - _iter_start
if 'precond_time' in ss_args['info'].keys():
ss_args['info']['solution_time'] = (ss_args['info']['iter_time'] +
ss_args['info']['precond_time'])
else:
ss_args['info']['solution_time'] = ss_args['info']['iter_time']
ss_args['info']['iterations'] = ss_iters['iter']
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(b - L*v, np.inf)
if settings.debug:
logger.debug('Number of Iterations: %i' % ss_iters['iter'])
logger.debug('Iteration. time: %f' % (_iter_end - _iter_start))
if check > 0:
raise Exception("Steadystate error: Did not reach tolerance after " +
str(ss_args['maxiter']) + " steps." +
"\nResidual norm: " +
str(ss_args['info']['residual_norm']))
elif check < 0:
raise Exception(
"Steadystate error: Failed with fatal error: " + str(check) + ".")
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
data = vec2mat(v)
data = 0.5 * (data + data.conj().T)
if ss_args['return_info']:
return Qobj(data, dims=dims, isherm=True), ss_args['info']
else:
return Qobj(data, dims=dims, isherm=True)
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
print('Starting iterative inverse-power method solver...')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = prod(rhoss.shape)
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
L.sort_indices()
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('Original bandwidth:', old_band)
perm = reverse_cuthill_mckee(L)
rev_perm = np.argsort(perm)
L = sp_permute(L, perm, perm, 'csc')
v = v[np.ix_(perm,)]
if settings.debug:
new_band = sp_bandwidth(L)[0]
print('RCM bandwidth:', new_band)
print('Bandwidth reduction factor:', round(old_band/new_band, 2))
# Get LU factors
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
print('L NNZ:', L_nnz, ';', 'U NNZ:', U_nnz)
print('Fill factor:', (L_nnz+U_nnz)/orig_nnz)
_power_start = time.time()
it = 0
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
v = lu.solve(v)
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if settings.debug:
print('Number of iterations:', it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_iterative(L, ss_args):
"""
Iterative steady state solver using the GMRES, LGMRES, or BICGSTAB
algorithm and a sparse incomplete LU preconditioner.
"""
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
if settings.debug:
logger.debug('Starting %s solver.' % ss_args['method'])
dims = L.dims[0]
n = prod(L.dims[0][0])
b = np.zeros(n**2)
b[0] = ss_args['weight']
L, perm, perm2, rev_perm, ss_args = _steadystate_LU_liouvillian(L, ss_args)
if np.any(perm):
b = b[np.ix_(perm, )]
if np.any(perm2):
b = b[np.ix_(perm2, )]
use_solver(assumeSortedIndices=True, useUmfpack=ss_args['use_umfpack'])
if ss_args['M'] is None and ss_args['use_precond']:
ss_args['M'], ss_args = _iterative_precondition(L, n, ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
# Select iterative solver type
_iter_start = time.time()
if ss_args['method'] == 'iterative-gmres':
v, check = gmres(L,
b,
tol=ss_args['tol'],
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-lgmres':
v, check = lgmres(L,
b,
tol=ss_args['tol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-bicgstab':
v, check = bicgstab(L,
b,
tol=ss_args['tol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
_iter_end = time.time()
ss_args['info']['iter_time'] = _iter_end - _iter_start
if 'precond_time' in ss_args['info'].keys():
ss_args['info']['solution_time'] = (ss_args['info']['iter_time'] +
ss_args['info']['precond_time'])
ss_args['info']['iterations'] = ss_iters['iter']
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(b - L * v, np.inf)
if settings.debug:
logger.debug('Number of Iterations: %i' % ss_iters['iter'])
logger.debug('Iteration. time: %f' % (_iter_end - _iter_start))
if check > 0:
raise Exception("Steadystate error: Did not reach tolerance after " +
str(ss_args['maxiter']) + " steps." +
"\nResidual norm: " +
str(ss_args['info']['residual_norm']))
elif check < 0:
raise Exception("Steadystate error: Failed with fatal error: " +
str(check) + ".")
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
data = vec2mat(v)
data = 0.5 * (data + data.conj().T)
if ss_args['return_info']:
return Qobj(data, dims=dims, isherm=True), ss_args['info']
else:
return Qobj(data, dims=dims, isherm=True)
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(
L, ss_args)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2, )]
# Do preconditioning
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres', 'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(
L, int(np.sqrt(n)), ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
lu = splu(L,
permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz + U_nnz) / orig_nnz))
it = 0
_tol = np.max(ss_args['tol'] / 10,
1e-15) # Should make this user accessible
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
v, check = gmres(L,
v,
tol=_tol,
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
v, check = lgmres(L,
v,
tol=_tol,
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
v, check = bicgstab(L,
v,
tol=_tol,
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' + str(maxiter) +
' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end - _power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L * v)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_direct_sparse(L, ss_args):
"""
Direct solver that uses scipy sparse matrices
"""
if settings.debug:
logger.debug('Starting direct LU solver.')
dims = L.dims[0]
n = int(np.sqrt(L.shape[0]))
b = np.zeros(n**2, dtype=complex)
b[0] = ss_args['weight']
L, perm, perm2, rev_perm, ss_args = _steadystate_LU_liouvillian(L, ss_args)
if np.any(perm):
b = b[np.ix_(perm, )]
if np.any(perm2):
b = b[np.ix_(perm2, )]
use_solver(assumeSortedIndices=True, useUmfpack=ss_args['use_umfpack'])
ss_args['info']['permc_spec'] = ss_args['permc_spec']
ss_args['info']['drop_tol'] = ss_args['drop_tol']
ss_args['info']['diag_pivot_thresh'] = ss_args['diag_pivot_thresh']
ss_args['info']['fill_factor'] = ss_args['fill_factor']
ss_args['info']['ILU_MILU'] = ss_args['ILU_MILU']
if not ss_args['use_umfpack']:
# Use superLU solver
orig_nnz = L.nnz
_direct_start = time.time()
lu = splu(L,
permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
v = lu.solve(b)
_direct_end = time.time()
ss_args['info']['solution_time'] = _direct_end - _direct_start
if (settings.debug or ss_args['return_info']) and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
ss_args['info']['l_nnz'] = L_nnz
ss_args['info']['u_nnz'] = U_nnz
ss_args['info']['lu_fill_factor'] = (L_nnz + U_nnz) / L.nnz
if settings.debug:
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz + U_nnz) / orig_nnz))
else:
# Use umfpack solver
_direct_start = time.time()
v = spsolve(L, b)
_direct_end = time.time()
ss_args['info']['solution_time'] = _direct_end - _direct_start
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(b - L * v)
if (not ss_args['use_umfpack']) and ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
data = vec2mat(v)
data = 0.5 * (data + data.conj().T)
if ss_args['return_info']:
return Qobj(data, dims=dims, isherm=True), ss_args['info']
else:
return Qobj(data, dims=dims, isherm=True)
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
mtol = ss_args['mtol']
if mtol is None:
mtol = max(0.1 * tol, 1e-15)
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
if ss_args['solver'] == 'mkl' and ss_args['method'] == 'power':
has_mkl = 1
else:
has_mkl = 0
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(
L, ss_args, has_mkl)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2, )]
# Do preconditioning
if ss_args['solver'] == 'scipy':
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres',
'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(
L, int(np.sqrt(n)), ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
if ss_args['solver'] == 'mkl':
lu = mkl_splu(L,
max_iter_refine=ss_args['max_iter_refine'],
scaling_vectors=ss_args['scaling_vectors'],
weighted_matching=ss_args['weighted_matching'])
else:
lu = splu(L,
permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz + U_nnz) / orig_nnz))
it = 0
# FIXME: These atol keyword except checks can be removed once scipy 1.1
# is a minimum requirement
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
check = 0
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
try:
v, check = gmres(L,
v,
tol=mtol,
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = gmres(L,
v,
tol=mtol,
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
try:
v, check = lgmres(L,
v,
tol=mtol,
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = lgmres(L,
v,
tol=mtol,
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
try:
v, check = bicgstab(L,
v,
tol=mtol,
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = bicgstab(L,
v,
tol=mtol,
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
if check > 0:
raise Exception("{} failed to find solution in "
"{} iterations.".format(ss_args['method'], check))
if check < 0:
raise Exception("Breakdown in {}".format(ss_args['method']))
v = v / la.norm(v, np.inf)
it += 1
if ss_args['method'] == 'power' and ss_args['solver'] == 'mkl':
lu.delete()
if ss_args['return_info']:
ss_args['info']['max_iter_refine'] = ss_args['max_iter_refine']
ss_args['info']['scaling_vectors'] = ss_args['scaling_vectors']
ss_args['info']['weighted_matching'] = ss_args['weighted_matching']
if it >= maxiter:
raise Exception('Failed to find steady state after ' + str(maxiter) +
' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end - _power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L * v, np.inf)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
# normalise according to type of problem
if sflag:
trow = v[::rhoss.shape[0] + 1]
data = v / np.sum(trow)
else:
data = data / la.norm(v)
data = dense2D_to_fastcsr_fmode(vec2mat(data), rhoss.shape[0],
rhoss.shape[0])
rhoss.data = 0.5 * (data + data.H)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_iterative(L, ss_args):
"""
Iterative steady state solver using the GMRES, LGMRES, or BICGSTAB
algorithm and a sparse incomplete LU preconditioner.
"""
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
if settings.debug:
logger.debug('Starting %s solver.' % ss_args['method'])
dims = L.dims[0]
n = int(np.sqrt(L.shape[0]))
b = np.zeros(n**2)
b[0] = ss_args['weight']
L, perm, perm2, rev_perm, ss_args = _steadystate_LU_liouvillian(L, ss_args)
if np.any(perm):
b = b[np.ix_(perm, )]
if np.any(perm2):
b = b[np.ix_(perm2, )]
use_solver(assumeSortedIndices=True)
if ss_args['M'] is None and ss_args['use_precond']:
ss_args['M'], ss_args = _iterative_precondition(L, n, ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
# Select iterative solver type
_iter_start = time.time()
# FIXME: These atol keyword except checks can be removed once scipy 1.1
# is a minimum requirement
extra = {"callback_type": 'legacy'} if scipy.__version__ >= "1.4" else {}
if ss_args['method'] == 'iterative-gmres':
try:
v, check = gmres(L,
b,
tol=ss_args['tol'],
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count,
**extra)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = gmres(L,
b,
tol=ss_args['tol'],
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-lgmres':
try:
v, check = lgmres(L,
b,
tol=ss_args['tol'],
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = lgmres(L,
b,
tol=ss_args['tol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'iterative-bicgstab':
try:
v, check = bicgstab(L,
b,
tol=ss_args['tol'],
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = bicgstab(L,
b,
tol=ss_args['tol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
_iter_end = time.time()
ss_args['info']['iter_time'] = _iter_end - _iter_start
if 'precond_time' in ss_args['info'].keys():
ss_args['info']['solution_time'] = (ss_args['info']['iter_time'] +
ss_args['info']['precond_time'])
else:
ss_args['info']['solution_time'] = ss_args['info']['iter_time']
ss_args['info']['iterations'] = ss_iters['iter']
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(b - L * v, np.inf)
if settings.debug:
logger.debug('Number of Iterations: %i' % ss_iters['iter'])
logger.debug('Iteration. time: %f' % (_iter_end - _iter_start))
if check > 0:
raise Exception("Steadystate error: Did not reach tolerance after " +
str(ss_args['maxiter']) + " steps." +
"\nResidual norm: " +
str(ss_args['info']['residual_norm']))
elif check < 0:
raise Exception("Steadystate error: Failed with fatal error: " +
str(check) + ".")
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
data = vec2mat(v)
data = 0.5 * (data + data.conj().T)
if ss_args['return_info']:
return Qobj(data, dims=dims, isherm=True), ss_args['info']
else:
return Qobj(data, dims=dims, isherm=True)
def solve(self, method, **kwargs):
"""Solves the linear system A x = b for the vector of unknown pressures
x, either using a direct solver or an iterative AMG solver. From the
pressures, the flow field is computed.
INPUT: method: This can be either 'direct' or 'iterative'
**kwargs
precision: The accuracy to which the ls is to be solved. If not
supplied, machine accuracy will be used.
maxiter: The maximum number of iterations. The default value for
the iterative solver is 250.
OUTPUT: None - G is modified in place.
"""
b = self._b
G = self._G
htt2htd = self._P.tube_to_discharge_hematocrit
A = self._A.tocsr()
if method == 'direct':
linalg.use_solver(useUmfpack=True)
x = linalg.spsolve(A, b)
elif method == 'iterative':
if kwargs.has_key('precision'):
eps = kwargs['precision']
else:
eps = self._eps
if kwargs.has_key('maxiter'):
maxiter = kwargs['maxiter']
else:
maxiter = 250
AA = pyamg.smoothed_aggregation_solver(A, max_levels=10, max_coarse=500)
x = abs(AA.solve(self._b, x0=None, tol=eps, accel='cg', cycle='V', maxiter=maxiter))
# abs required, as (small) negative pressures may arise
elif method == 'iterative2':
# Set linear solver
ml = rootnode_solver(A, smooth=('energy', {'degree':2}), strength='evolution' )
M = ml.aspreconditioner(cycle='V')
# Solve pressure system
x,info = gmres(A, self._b, tol=self._eps, maxiter=50, M=M)
if info != 0:
print('ERROR in Solving the Matrix')
G.vs['pressure'] = x
self._x = x
conductance = self._conductance
G.es['flow'] = [abs(G.vs[edge.source]['pressure'] - \
G.vs[edge.target]['pressure']) * \
conductance[i] for i, edge in enumerate(G.es)]
for v in G.vs:
v['pressure']=v['pressure']/vgm.units.scaling_factor_du('mmHg',G['defaultUnits'])
if self._withRBC:
for e in G.es:
dischargeHt = min(htt2htd(e['htt'], e['diameter'], self._invivo), 1.0)
e['v']=dischargeHt/e['htt']*e['flow']/(0.25*np.pi*e['diameter']**2)
else:
for e in G.es:
e['v']=e['flow']/(0.25*np.pi*e['diameter']**2)
#Convert 'pBC' from default Units to mmHg
pBCneNone=G.vs(pBC_ne=None).indices
if 'diamCalcEff' in G.es.attribute_names():
del(G.es['diamCalcEff'])
if 'effResistance' in G.es.attribute_names():
del(G.es['effResistance'])
if 'conductance' in G.es.attribute_names():
del(G.es['conductance'])
if 'resistance' in G.es.attribute_names():
del(G.es['resistance'])
G.vs[pBCneNone]['pBC']=np.array(G.vs[pBCneNone]['pBC'])*(1/vgm.units.scaling_factor_du('mmHg',G['defaultUnits']))
vgm.write_pkl(G, 'G_final.pkl')
vgm.write_vtp(G, 'G_final.vtp',False)
#Write Output
sampledict={}
for eprop in ['flow', 'v']:
if not eprop in sampledict.keys():
sampledict[eprop] = []
sampledict[eprop].append(G.es[eprop])
for vprop in ['pressure']:
if not vprop in sampledict.keys():
sampledict[vprop] = []
sampledict[vprop].append(G.vs[vprop])
g_output.write_pkl(sampledict, 'sampledict.pkl')
def run_transmute_test(data,
degree,
prec,
time,
*,
expr=None,
plot=True,
_print=False,
run_all=True,
use_cache=True,
thetas=None,
alphas=None,
alpha0=None):
"""
Run transmute test on the data
If run_all=True, runs the test on all forms of the exponential. Otherwise,
only use part_frac_complex (the fastest).
"""
nucs, matrix = load_sparse_csr(data)
expr = get_CRAM_from_cache(degree,
prec,
expr=expr,
plot=plot,
use_cache=use_cache)
num, den = fraction(expr)
if not (thetas and alphas and alpha0):
thetas, alphas, alpha0 = thetas_alphas(expr, prec)
part_frac = thetas_alphas_to_expr_real(thetas, alphas, alpha0)
part_frac_complex = thetas_alphas_to_expr_complex(thetas, alphas, alpha0)
# part_frac_complex2 = thetas_alphas_to_expr_complex2(thetas, alphas, alpha0)
e = {}
from ..py_solve import py_solve
py_solve_expm = getattr(py_solve, 'expmI%d' % degree)
e['transmutagen generated C solver'] = lambda m: py_solve_expm(m).T
e['part_frac_complex UMFPACK'] = lambda m: (use_solver(
useUmfpack=True) or lambdify_expr(part_frac_complex)(m))
e['part_frac_complex SuperLU'] = lambda m: (use_solver(
useUmfpack=False) or lambdify_expr(part_frac_complex)(m))
e['scipy.sparse.linalg.expm'] = lambda m: expm(-m)
if run_all:
e['rat_func'] = lambdify_expr(expr)
e['rat_func_horner'] = lambdify_expr(horner(num) / horner(den))
e['part_frac'] = lambdify_expr(part_frac)
# e['part_frac_complex2'] = lambdify_expr(part_frac_complex2)
res = {}
for func in sorted(e):
if _print:
print(func)
arg = -matrix * time
res[func] = time_and_run(e[func], arg, _print=_print)
return res
def solve(self, method, **kwargs):
"""Solves the linear system A x = b for the vector of unknown pressures
x, either using a direct solver (obsolete) or an iterative GMRES solver. From the
pressures, the flow field is computed.
INPUT: method: This can be either 'direct' or 'iterative2'
OUTPUT: None - G is modified in place.
G_final.pkl & G_final.vtp: are save as output
sampledict.pkl: is saved as output
"""
b = self._b
G = self._G
htt2htd = self._P.tube_to_discharge_hematocrit
A = self._A.tocsr()
if method == 'direct':
linalg.use_solver(useUmfpack=True)
x = linalg.spsolve(A, b)
elif method == 'iterative2':
ml = rootnode_solver(A,
smooth=('energy', {
'degree': 2
}),
strength='evolution')
M = ml.aspreconditioner(cycle='V')
# Solve pressure system
#x,info = gmres(A, self._b, tol=self._eps, maxiter=1000, M=M)
x, info = gmres(A, self._b, tol=10 * self._eps, M=M)
if info != 0:
print('ERROR in Solving the Matrix')
print(info)
G.vs['pressure'] = x
self._x = x
conductance = self._conductance
G.es['flow'] = [abs(G.vs[edge.source]['pressure'] - G.vs[edge.target]['pressure']) * \
conductance[i] for i, edge in enumerate(G.es)]
#Default Units - mmHg for pressure
for v in G.vs:
v['pressure'] = v['pressure'] / vgm.units.scaling_factor_du(
'mmHg', G['defaultUnits'])
if self._withRBC:
G.es['v'] = [
e['htd'] / e['htt'] * e['flow'] /
(0.25 * np.pi * e['diameter']**2) for e in G.es
]
else:
G.es['v'] = [
e['flow'] / (0.25 * np.pi * e['diameter']**2) for e in G.es
]
#Convert 'pBC' from default Units to mmHg
pBCneNone = G.vs(pBC_ne=None).indices
G.vs[pBCneNone]['pBC'] = np.array(G.vs[pBCneNone]['pBC']) * (
1 / vgm.units.scaling_factor_du('mmHg', G['defaultUnits']))
vgm.write_pkl(G, 'G_final.pkl')
vgm.write_vtp(G, 'G_final.vtp', False)
#Write Output
sampledict = {}
for eprop in ['flow', 'v']:
if not eprop in sampledict.keys():
sampledict[eprop] = []
sampledict[eprop].append(G.es[eprop])
for vprop in ['pressure']:
if not vprop in sampledict.keys():
sampledict[vprop] = []
sampledict[vprop].append(G.vs[vprop])
g_output.write_pkl(sampledict, 'sampledict.pkl')
