def _steadystate_LU_liouvillian(L, ss_args, has_mkl=0):
"""Creates modified Liouvillian for LU based SS methods.
"""
perm = None
perm2 = None
rev_perm = None
n = int(np.sqrt(L.shape[0]))
form = 'csr'
if has_mkl:
L = L.data + sp.csr_matrix(
(ss_args['weight']*np.ones(n), (np.zeros(n), [nn * (n + 1)
for nn in range(n)])),
shape=(n ** 2, n ** 2))
else:
form = 'csc'
L = L.data.tocsc() + sp.csc_matrix(
(ss_args['weight']*np.ones(n), (np.zeros(n), [nn * (n + 1)
for nn in range(n)])),
shape=(n ** 2, n ** 2))
if settings.debug:
old_band = sp_bandwidth(L)[0]
old_pro = sp_profile(L)[0]
logger.debug('Orig. NNZ: %i' % L.nnz)
if ss_args['use_rcm']:
logger.debug('Original bandwidth: %i' % old_band)
if ss_args['use_wbm']:
if settings.debug:
logger.debug('Calculating Weighted Bipartite Matching ordering...')
_wbm_start = time.time()
perm = weighted_bipartite_matching(L)
_wbm_end = time.time()
L = sp_permute(L, perm, [], form)
ss_args['info']['perm'].append('wbm')
ss_args['info']['wbm_time'] = _wbm_end-_wbm_start
if settings.debug:
wbm_band = sp_bandwidth(L)[0]
logger.debug('WBM bandwidth: %i' % wbm_band)
if ss_args['use_rcm']:
if settings.debug:
logger.debug('Calculating Reverse Cuthill-Mckee ordering...')
_rcm_start = time.time()
perm2 = reverse_cuthill_mckee(L)
_rcm_end = time.time()
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, form)
ss_args['info']['perm'].append('rcm')
ss_args['info']['rcm_time'] = _rcm_end-_rcm_start
if settings.debug:
rcm_band = sp_bandwidth(L)[0]
rcm_pro = sp_profile(L)[0]
logger.debug('RCM bandwidth: %i' % rcm_band)
logger.debug('Bandwidth reduction factor: %f' %
(old_band/rcm_band))
logger.debug('Profile reduction factor: %f' %
(old_pro/rcm_pro))
L.sort_indices()
return L, perm, perm2, rev_perm, ss_args
def _steadystate_power_liouvillian(L, ss_args, has_mkl=0):
"""Creates modified Liouvillian for power based SS methods.
"""
perm = None
perm2 = None
rev_perm = None
n = L.shape[0]
if ss_args['solver'] == 'mkl':
L = L.data - (1e-15) * sp.eye(n, n, format='csr')
kind = 'csr'
else:
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
kind = 'csc'
if settings.debug:
old_band = sp_bandwidth(L)[0]
old_pro = sp_profile(L)[0]
logger.debug('Original bandwidth: %i' % old_band)
logger.debug('Original profile: %i' % old_pro)
if ss_args['use_wbm']:
if settings.debug:
logger.debug('Calculating Weighted Bipartite Matching ordering...')
_wbm_start = time.time()
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore",
"qutip graph functions are deprecated",
DeprecationWarning,
)
perm = weighted_bipartite_matching(L)
_wbm_end = time.time()
L = sp_permute(L, perm, [], kind)
ss_args['info']['perm'].append('wbm')
ss_args['info']['wbm_time'] = _wbm_end - _wbm_start
if settings.debug:
wbm_band = sp_bandwidth(L)[0]
wbm_pro = sp_profile(L)[0]
logger.debug('WBM bandwidth: %i' % wbm_band)
logger.debug('WBM profile: %i' % wbm_pro)
if ss_args['use_rcm']:
if settings.debug:
logger.debug('Calculating Reverse Cuthill-Mckee ordering...')
ss_args['info']['perm'].append('rcm')
_rcm_start = time.time()
perm2 = sp.csgraph.reverse_cuthill_mckee(L)
_rcm_end = time.time()
ss_args['info']['rcm_time'] = _rcm_end - _rcm_start
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, kind)
if settings.debug:
new_band = sp_bandwidth(L)[0]
new_pro = sp_profile(L)[0]
logger.debug('RCM bandwidth: %i' % new_band)
logger.debug('Bandwidth reduction factor: %f' %
(old_band / new_band))
logger.debug('RCM profile: %i' % new_pro)
logger.debug('Profile reduction factor: %f' % (old_pro / new_pro))
L.sort_indices()
return L, perm, perm2, rev_perm, ss_args
def _steadystate_power_liouvillian(L, ss_args, has_mkl=0):
"""Creates modified Liouvillian for power based SS methods.
"""
perm = None
perm2 = None
rev_perm = None
n = L.shape[0]
if ss_args['solver'] == 'mkl':
L = L.data - (1e-15) * sp.eye(n, n, format='csr')
kind = 'csr'
else:
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
kind = 'csc'
orig_nnz = L.nnz
if settings.debug:
old_band = sp_bandwidth(L)[0]
old_pro = sp_profile(L)[0]
logger.debug('Original bandwidth: %i' % old_band)
logger.debug('Original profile: %i' % old_pro)
if ss_args['use_wbm']:
if settings.debug:
logger.debug('Calculating Weighted Bipartite Matching ordering...')
_wbm_start = time.time()
perm = weighted_bipartite_matching(L)
_wbm_end = time.time()
L = sp_permute(L, perm, [], kind)
ss_args['info']['perm'].append('wbm')
ss_args['info']['wbm_time'] = _wbm_end-_wbm_start
if settings.debug:
wbm_band = sp_bandwidth(L)[0]
wbm_pro = sp_profile(L)[0]
logger.debug('WBM bandwidth: %i' % wbm_band)
logger.debug('WBM profile: %i' % wbm_pro)
if ss_args['use_rcm']:
if settings.debug:
logger.debug('Calculating Reverse Cuthill-Mckee ordering...')
ss_args['info']['perm'].append('rcm')
_rcm_start = time.time()
perm2 = reverse_cuthill_mckee(L)
_rcm_end = time.time()
ss_args['info']['rcm_time'] = _rcm_end-_rcm_start
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, kind)
if settings.debug:
new_band = sp_bandwidth(L)[0]
new_pro = sp_profile(L)[0]
logger.debug('RCM bandwidth: %i' % new_band)
logger.debug('Bandwidth reduction factor: %f'
% (old_band/new_band))
logger.debug('RCM profile: %i' % new_pro)
logger.debug('Profile reduction factor: %f'
% (old_pro/new_pro))
L.sort_indices()
return L, perm, perm2, rev_perm, ss_args
def _steadystate_power_liouvillian(L, ss_args):
"""Creates modified Liouvillian for power based SS methods.
"""
perm = None
perm2 = None
rev_perm = None
n = L.shape[0]
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
orig_nnz = L.nnz
if settings.debug:
old_band = sp_bandwidth(L)[0]
old_pro = sp_profile(L)[0]
logger.debug('Original bandwidth: %i' % old_band)
logger.debug('Original profile: %i' % old_pro)
if ss_args['use_wbm']:
if settings.debug:
logger.debug('Calculating Weighted Bipartite Matching ordering...')
_wbm_start = time.time()
perm = weighted_bipartite_matching(L)
_wbm_end = time.time()
L = sp_permute(L, perm, [], 'csc')
ss_args['info']['perm'].append('wbm')
ss_args['info']['wbm_time'] = _wbm_end - _wbm_start
if settings.debug:
wbm_band = sp_bandwidth(L)[0]
wbm_pro = sp_profile(L)[0]
logger.debug('WBM bandwidth: %i' % wbm_band)
logger.debug('WBM profile: %i' % wbm_pro)
if ss_args['use_rcm']:
if settings.debug:
logger.debug('Calculating Reverse Cuthill-Mckee ordering...')
ss_args['info']['perm'].append('rcm')
_rcm_start = time.time()
perm2 = reverse_cuthill_mckee(L)
_rcm_end = time.time()
ss_args['info']['rcm_time'] = _rcm_end - _rcm_start
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, 'csc')
if settings.debug:
new_band = sp_bandwidth(L)[0]
new_pro = sp_profile(L)[0]
logger.debug('RCM bandwidth: %i' % new_band)
logger.debug('Bandwidth reduction factor: %f' %
(old_band / new_band))
logger.debug('RCM profile: %i' % new_pro)
logger.debug('Profile reduction factor: %f' % (old_pro / new_pro))
L.sort_indices()
return L, perm, perm2, rev_perm, ss_args
def _steadystate_LU_liouvillian(L, ss_args):
"""Creates modified Liouvillian for LU based SS methods.
"""
perm = None
perm2 = None
rev_perm = None
dims = L.dims[0]
n = prod(L.dims[0][0])
L = L.data.tocsc() + sp.csc_matrix(
(ss_args['weight']*np.ones(n), (np.zeros(n), [nn * (n + 1)
for nn in range(n)])),
shape=(n ** 2, n ** 2))
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('NNZ:', L.nnz)
if ss_args['use_rcm']:
print('Original bandwidth:', old_band)
if ss_args['use_wbm']:
if settings.debug:
print('Calculating Weighted Bipartite Matching ordering...')
_wbm_start = time.time()
perm = weighted_bipartite_matching(L)
_wbm_end = time.time()
L = sp_permute(L, perm, [], 'csc')
ss_args['info']['perm'].append('wbm')
ss_args['info']['wbm_time'] = _wbm_end-_wbm_start
if settings.debug:
wbm_band = sp_bandwidth(L)[0]
print('WBM bandwidth:', wbm_band)
if ss_args['use_rcm']:
if settings.debug:
print('Calculating Reverse Cuthill-Mckee ordering...')
_rcm_start = time.time()
perm2 = reverse_cuthill_mckee(L)
_rcm_end = time.time()
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, 'csc')
ss_args['info']['perm'].append('rcm')
ss_args['info']['rcm_time'] = _rcm_end-_rcm_start
if settings.debug:
rcm_band = sp_bandwidth(L)[0]
print('RCM bandwidth:', rcm_band)
print('Bandwidth reduction factor:', round(
old_band/rcm_band, 1))
L.sort_indices()
return L, perm, perm2, rev_perm, ss_args
def _steadystate_LU_liouvillian(L, ss_args):
"""Creates modified Liouvillian for LU based SS methods.
"""
perm = None
perm2 = None
rev_perm = None
dims = L.dims[0]
n = prod(L.dims[0][0])
L = L.data.tocsc() + sp.csc_matrix(
(ss_args['weight'] * np.ones(n),
(np.zeros(n), [nn * (n + 1) for nn in range(n)])),
shape=(n**2, n**2))
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('NNZ:', L.nnz)
if ss_args['use_rcm']:
print('Original bandwidth:', old_band)
if ss_args['use_wbm']:
if settings.debug:
print('Calculating Weighted Bipartite Matching ordering...')
_wbm_start = time.time()
perm = weighted_bipartite_matching(L)
_wbm_end = time.time()
L = sp_permute(L, perm, [], 'csc')
ss_args['info']['perm'].append('wbm')
ss_args['info']['wbm_time'] = _wbm_end - _wbm_start
if settings.debug:
wbm_band = sp_bandwidth(L)[0]
print('WBM bandwidth:', wbm_band)
if ss_args['use_rcm']:
if settings.debug:
print('Calculating Reverse Cuthill-Mckee ordering...')
_rcm_start = time.time()
perm2 = reverse_cuthill_mckee(L)
_rcm_end = time.time()
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, 'csc')
ss_args['info']['perm'].append('rcm')
ss_args['info']['rcm_time'] = _rcm_end - _rcm_start
if settings.debug:
rcm_band = sp_bandwidth(L)[0]
print('RCM bandwidth:', rcm_band)
print('Bandwidth reduction factor:', round(old_band / rcm_band, 1))
L.sort_indices()
return L, perm, perm2, rev_perm, ss_args
def _steadystate_iterative(L, ss_args):
"""
Iterative steady state solver using the GMRES or LGMRES algorithm
and a sparse incomplete LU preconditioner.
"""
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 = L.data.tocsc() + sp.csc_matrix(
(ss_args['weight']*np.ones(n), (np.zeros(n), [nn * (n + 1)
for nn in range(n)])),
shape=(n ** 2, n ** 2))
if ss_args['use_wbm']:
perm = weighted_bipartite_matching(L)
L = sp_permute(L, perm, [], 'csc')
b = b[np.ix_(perm,)]
if ss_args['use_rcm']:
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('Original bandwidth ', old_band)
perm2 = reverse_cuthill_mckee(L)
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, 'csc')
b = b[np.ix_(perm2,)]
if settings.debug:
rcm_band = sp_bandwidth(L)[0]
print('RCM bandwidth ', rcm_band)
print('Bandwidth reduction factor:', round(old_band/rcm_band, 1))
L.sort_indices()
if ss_args['M'] is None and ss_args['use_precond']:
ss_args['M'] = _iterative_precondition(L, n, ss_args)
# Select iterative solver type
if ss_args['method'] == 'iterative-gmres':
v, check = gmres(L, b, tol=ss_args['tol'], M=ss_args['M'],
maxiter=ss_args['maxiter'])
elif ss_args['method'] == 'iterative-lgmres':
v, check = lgmres(L, b, tol=ss_args['tol'], M=ss_args['M'],
maxiter=ss_args['maxiter'])
else:
raise Exception("Invalid iterative solver method.")
if check > 0:
raise Exception("Steadystate solver did not reach tolerance after " +
str(check) + " steps.")
elif check < 0:
raise Exception(
"Steadystate solver 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)
return Qobj(data, dims=dims, isherm=True)
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 = L.data.tocsc() + sp.csc_matrix(
(ss_args['weight']*np.ones(n), (np.zeros(n), [nn * (n + 1)
for nn in range(n)])),
shape=(n ** 2, n ** 2))
L.sort_indices()
use_solver(assumeSortedIndices=True, useUmfpack=ss_args['use_umfpack'])
if not ss_args['use_umfpack']:
# Use superLU solver
orig_nnz = L.nnz
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('Original NNZ:', orig_nnz)
if ss_args['use_rcm']:
print('Original bandwidth:', old_band)
if ss_args['use_wbm']:
perm = weighted_bipartite_matching(L)
L = sp_permute(L, perm, [], 'csc')
b = b[np.ix_(perm,)]
if ss_args['use_rcm']:
perm2 = reverse_cuthill_mckee(L)
rev_perm = np.argsort(perm2)
L = sp_permute(L, perm2, perm2, 'csc')
b = b[np.ix_(perm2,)]
if settings.debug:
rcm_band = sp_bandwidth(L)[0]
print('RCM bandwidth:', rcm_band)
print('Bandwidth reduction factor:', round(
old_band/rcm_band, 1))
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)
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)
else:
# Use umfpack solver
v = spsolve(L, b)
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)
return Qobj(data, dims=dims, isherm=True)
