def _get_solver(M,
sparse=False,
lstsq=False,
sym_pos=True,
cholesky=True,
permc_spec='MMD_AT_PLUS_A'):
"""
Given solver options, return a handle to the appropriate linear system
solver.
Parameters
----------
M : 2D array
As defined in [4] Equation 8.31
sparse : bool (default = False)
True if the system to be solved is sparse. This is typically set
True when the original ``A_ub`` and ``A_eq`` arrays are sparse.
lstsq : bool (default = False)
True if the system is ill-conditioned and/or (nearly) singular and
thus a more robust least-squares solver is desired. This is sometimes
needed as the solution is approached.
sym_pos : bool (default = True)
True if the system matrix is symmetric positive definite
Sometimes this needs to be set false as the solution is approached,
even when the system should be symmetric positive definite, due to
numerical difficulties.
cholesky : bool (default = True)
True if the system is to be solved by Cholesky, rather than LU,
decomposition. This is typically faster unless the problem is very
small or prone to numerical difficulties.
permc_spec : str (default = 'MMD_AT_PLUS_A')
Sparsity preservation strategy used by SuperLU. Acceptable values are:
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering.
See SuperLU documentation.
Returns
-------
solve : function
Handle to the appropriate solver function
"""
try:
if sparse:
if lstsq:
def solve(r, sym_pos=False):
return sps.linalg.lsqr(M, r)[0]
elif cholesky:
solve = cholmod(M)
else:
if has_umfpack and sym_pos:
solve = sps.linalg.factorized(M)
else: # factorized doesn't pass permc_spec
solve = sps.linalg.splu(M, permc_spec=permc_spec).solve
else:
if lstsq: # sometimes necessary as solution is approached
def solve(r):
return sp.linalg.lstsq(M, r)[0]
elif cholesky:
L = sp.linalg.cho_factor(M)
def solve(r):
return sp.linalg.cho_solve(L, r)
else:
# this seems to cache the matrix factorization, so solving
# with multiple right hand sides is much faster
def solve(r, sym_pos=sym_pos):
return sp.linalg.solve(M, r, sym_pos=sym_pos)
# There are many things that can go wrong here, and it's hard to say
# what all of them are. It doesn't really matter: if the matrix can't be
# factorized, return None. get_solver will be called again with different
# inputs, and a new routine will try to factorize the matrix.
except KeyboardInterrupt:
raise
except Exception:
return None
return solve
def _get_solver(M, sparse=False, lstsq=False, sym_pos=True,
cholesky=True, permc_spec='MMD_AT_PLUS_A'):
"""
Given solver options, return a handle to the appropriate linear system
solver.
Parameters
----------
M : 2D array
As defined in [4] Equation 8.31
sparse : bool (default = False)
True if the system to be solved is sparse. This is typically set
True when the original ``A_ub`` and ``A_eq`` arrays are sparse.
lstsq : bool (default = False)
True if the system is ill-conditioned and/or (nearly) singular and
thus a more robust least-squares solver is desired. This is sometimes
needed as the solution is approached.
sym_pos : bool (default = True)
True if the system matrix is symmetric positive definite
Sometimes this needs to be set false as the solution is approached,
even when the system should be symmetric positive definite, due to
numerical difficulties.
cholesky : bool (default = True)
True if the system is to be solved by Cholesky, rather than LU,
decomposition. This is typically faster unless the problem is very
small or prone to numerical difficulties.
permc_spec : str (default = 'MMD_AT_PLUS_A')
Sparsity preservation strategy used by SuperLU. Acceptable values are:
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering.
See SuperLU documentation.
Returns
-------
solve : function
Handle to the appropriate solver function
"""
try:
if sparse:
if lstsq:
def solve(r, sym_pos=False):
return sps.linalg.lsqr(M, r)[0]
elif cholesky:
solve = cholmod(M)
else:
if has_umfpack and sym_pos:
solve = sps.linalg.factorized(M)
else: # factorized doesn't pass permc_spec
solve = sps.linalg.splu(M, permc_spec=permc_spec).solve
else:
if lstsq: # sometimes necessary as solution is approached
def solve(r):
return sp.linalg.lstsq(M, r)[0]
elif cholesky:
L = sp.linalg.cho_factor(M)
def solve(r):
return sp.linalg.cho_solve(L, r)
else:
# this seems to cache the matrix factorization, so solving
# with multiple right hand sides is much faster
def solve(r, sym_pos=sym_pos):
return sp.linalg.solve(M, r, sym_pos=sym_pos)
# There are many things that can go wrong here, and it's hard to say
# what all of them are. It doesn't really matter: if the matrix can't be
# factorized, return None. get_solver will be called again with different
# inputs, and a new routine will try to factorize the matrix.
except KeyboardInterrupt:
raise
except Exception:
return None
return solve
