KSP Solvers Using HIFIR (hifir4py.ksp)¶
Contents¶
Solvers¶
gmres_hif(A, b[, M]) |
HIF-preconditioned (right) restarted GMRES |
gmres(*args, **kw) |
An alias of gmres_hif |
pipit_hifir(A, b, n_null[, M]) |
PIPIT solver for solving the pseudoinverse solution |
pipit(*args, **kw) |
Alias of pipit_hifir |
orth_null(A, n_null, M, leftnull, restart, …) |
Compute multiple (small dimension) null-space components |
Note
gmres_hif is designed for solving consistent systems, in that the
right-hand side is in \(\mathcal{R}(\boldsymbol{A})\). On the other
hand, pipit_hifir is designed for seeking the pseudoinverse
solution of (potentially) inconsistent systems; it is based on a combination
of orth_null and gmres_hif. The users should not call
orth_null in general.
Miscellany¶
GMRES_WorkSpace(n, restart, dtype) |
Workspace class for GMRES solver |
FGMRES_WorkSpace(*args, **kw) |
Workspace buffer for flexible GMRES (FGMRES) |
Note
FGMRES_WorkSpace can also be used in gmres_hif.
Both GMRES_WorkSpace and FGMRES_WorkSpace are optional,
but should be used for getting good performance for sequences of calls of
solvers.
Example Usage¶
Here, we only show the simplest and most straightforward way to use our
HIF-preconditioned GMRES and PIPIT solvers. For advanced usage, refer to
the examples in gmres_hif and pipit_hifir.
HIF-preconditioned GMRES(\(m\))¶
>>> import numpy as np
>>> from scipy.sparse import rand
>>> from hifir4py import *
>>> A = rand(20, 20, 0.5)
>>> b = A.dot(np.ones(20))
>>> x, flag, info = gmres_hif(A, b) # HIF is factorized inside gmres_hif
>>> assert flag == 0, "GMRES failed with flag={}".format(flag)
>>> print("GMRES iterations are {}".format(info["iters"]))
We refer the readers to this more comprehensive example.