You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1040 lines
16 KiB
Python
1040 lines
16 KiB
Python
"""
|
|
Low-level LAPACK functions (:mod:`scipy.linalg.lapack`)
|
|
=======================================================
|
|
|
|
This module contains low-level functions from the LAPACK library.
|
|
|
|
The `*gegv` family of routines have been removed from LAPACK 3.6.0
|
|
and have been deprecated in SciPy 0.17.0. They will be removed in
|
|
a future release.
|
|
|
|
.. versionadded:: 0.12.0
|
|
|
|
.. note::
|
|
|
|
The common ``overwrite_<>`` option in many routines, allows the
|
|
input arrays to be overwritten to avoid extra memory allocation.
|
|
However this requires the array to satisfy two conditions
|
|
which are memory order and the data type to match exactly the
|
|
order and the type expected by the routine.
|
|
|
|
As an example, if you pass a double precision float array to any
|
|
``S....`` routine which expects single precision arguments, f2py
|
|
will create an intermediate array to match the argument types and
|
|
overwriting will be performed on that intermediate array.
|
|
|
|
Similarly, if a C-contiguous array is passed, f2py will pass a
|
|
FORTRAN-contiguous array internally. Please make sure that these
|
|
details are satisfied. More information can be found in the f2py
|
|
documentation.
|
|
|
|
.. warning::
|
|
|
|
These functions do little to no error checking.
|
|
It is possible to cause crashes by mis-using them,
|
|
so prefer using the higher-level routines in `scipy.linalg`.
|
|
|
|
Finding functions
|
|
-----------------
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
get_lapack_funcs
|
|
|
|
All functions
|
|
-------------
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
sgbsv
|
|
dgbsv
|
|
cgbsv
|
|
zgbsv
|
|
|
|
sgbtrf
|
|
dgbtrf
|
|
cgbtrf
|
|
zgbtrf
|
|
|
|
sgbtrs
|
|
dgbtrs
|
|
cgbtrs
|
|
zgbtrs
|
|
|
|
sgebal
|
|
dgebal
|
|
cgebal
|
|
zgebal
|
|
|
|
sgecon
|
|
dgecon
|
|
cgecon
|
|
zgecon
|
|
|
|
sgeequ
|
|
dgeequ
|
|
cgeequ
|
|
zgeequ
|
|
|
|
sgeequb
|
|
dgeequb
|
|
cgeequb
|
|
zgeequb
|
|
|
|
sgees
|
|
dgees
|
|
cgees
|
|
zgees
|
|
|
|
sgeev
|
|
dgeev
|
|
cgeev
|
|
zgeev
|
|
|
|
sgeev_lwork
|
|
dgeev_lwork
|
|
cgeev_lwork
|
|
zgeev_lwork
|
|
|
|
sgegv
|
|
dgegv
|
|
cgegv
|
|
zgegv
|
|
|
|
sgehrd
|
|
dgehrd
|
|
cgehrd
|
|
zgehrd
|
|
|
|
sgehrd_lwork
|
|
dgehrd_lwork
|
|
cgehrd_lwork
|
|
zgehrd_lwork
|
|
|
|
sgejsv
|
|
dgejsv
|
|
|
|
sgels
|
|
dgels
|
|
cgels
|
|
zgels
|
|
|
|
sgels_lwork
|
|
dgels_lwork
|
|
cgels_lwork
|
|
zgels_lwork
|
|
|
|
sgelsd
|
|
dgelsd
|
|
cgelsd
|
|
zgelsd
|
|
|
|
sgelsd_lwork
|
|
dgelsd_lwork
|
|
cgelsd_lwork
|
|
zgelsd_lwork
|
|
|
|
sgelss
|
|
dgelss
|
|
cgelss
|
|
zgelss
|
|
|
|
sgelss_lwork
|
|
dgelss_lwork
|
|
cgelss_lwork
|
|
zgelss_lwork
|
|
|
|
sgelsy
|
|
dgelsy
|
|
cgelsy
|
|
zgelsy
|
|
|
|
sgelsy_lwork
|
|
dgelsy_lwork
|
|
cgelsy_lwork
|
|
zgelsy_lwork
|
|
|
|
sgeqp3
|
|
dgeqp3
|
|
cgeqp3
|
|
zgeqp3
|
|
|
|
sgeqrf
|
|
dgeqrf
|
|
cgeqrf
|
|
zgeqrf
|
|
|
|
sgeqrf_lwork
|
|
dgeqrf_lwork
|
|
cgeqrf_lwork
|
|
zgeqrf_lwork
|
|
|
|
sgeqrfp
|
|
dgeqrfp
|
|
cgeqrfp
|
|
zgeqrfp
|
|
|
|
sgeqrfp_lwork
|
|
dgeqrfp_lwork
|
|
cgeqrfp_lwork
|
|
zgeqrfp_lwork
|
|
|
|
sgerqf
|
|
dgerqf
|
|
cgerqf
|
|
zgerqf
|
|
|
|
sgesdd
|
|
dgesdd
|
|
cgesdd
|
|
zgesdd
|
|
|
|
sgesdd_lwork
|
|
dgesdd_lwork
|
|
cgesdd_lwork
|
|
zgesdd_lwork
|
|
|
|
sgesv
|
|
dgesv
|
|
cgesv
|
|
zgesv
|
|
|
|
sgesvd
|
|
dgesvd
|
|
cgesvd
|
|
zgesvd
|
|
|
|
sgesvd_lwork
|
|
dgesvd_lwork
|
|
cgesvd_lwork
|
|
zgesvd_lwork
|
|
|
|
sgesvx
|
|
dgesvx
|
|
cgesvx
|
|
zgesvx
|
|
|
|
sgetrf
|
|
dgetrf
|
|
cgetrf
|
|
zgetrf
|
|
|
|
sgetc2
|
|
dgetc2
|
|
cgetc2
|
|
zgetc2
|
|
|
|
sgetri
|
|
dgetri
|
|
cgetri
|
|
zgetri
|
|
|
|
sgetri_lwork
|
|
dgetri_lwork
|
|
cgetri_lwork
|
|
zgetri_lwork
|
|
|
|
sgetrs
|
|
dgetrs
|
|
cgetrs
|
|
zgetrs
|
|
|
|
sgesc2
|
|
dgesc2
|
|
cgesc2
|
|
zgesc2
|
|
|
|
sgges
|
|
dgges
|
|
cgges
|
|
zgges
|
|
|
|
sggev
|
|
dggev
|
|
cggev
|
|
zggev
|
|
|
|
sgglse
|
|
dgglse
|
|
cgglse
|
|
zgglse
|
|
|
|
sgglse_lwork
|
|
dgglse_lwork
|
|
cgglse_lwork
|
|
zgglse_lwork
|
|
|
|
sgtsv
|
|
dgtsv
|
|
cgtsv
|
|
zgtsv
|
|
|
|
sgtsvx
|
|
dgtsvx
|
|
cgtsvx
|
|
zgtsvx
|
|
|
|
chbevd
|
|
zhbevd
|
|
|
|
chbevx
|
|
zhbevx
|
|
|
|
checon
|
|
zhecon
|
|
|
|
cheequb
|
|
zheequb
|
|
|
|
cheev
|
|
zheev
|
|
|
|
cheev_lwork
|
|
zheev_lwork
|
|
|
|
cheevd
|
|
zheevd
|
|
|
|
cheevd_lwork
|
|
zheevd_lwork
|
|
|
|
cheevr
|
|
zheevr
|
|
|
|
cheevr_lwork
|
|
zheevr_lwork
|
|
|
|
cheevx
|
|
zheevx
|
|
|
|
cheevx_lwork
|
|
zheevx_lwork
|
|
|
|
chegst
|
|
zhegst
|
|
|
|
chegv
|
|
zhegv
|
|
|
|
chegv_lwork
|
|
zhegv_lwork
|
|
|
|
chegvd
|
|
zhegvd
|
|
|
|
chegvx
|
|
zhegvx
|
|
|
|
chegvx_lwork
|
|
zhegvx_lwork
|
|
|
|
chesv
|
|
zhesv
|
|
|
|
chesv_lwork
|
|
zhesv_lwork
|
|
|
|
chesvx
|
|
zhesvx
|
|
|
|
chesvx_lwork
|
|
zhesvx_lwork
|
|
|
|
chetrd
|
|
zhetrd
|
|
|
|
chetrd_lwork
|
|
zhetrd_lwork
|
|
|
|
chetrf
|
|
zhetrf
|
|
|
|
chetrf_lwork
|
|
zhetrf_lwork
|
|
|
|
chfrk
|
|
zhfrk
|
|
|
|
slamch
|
|
dlamch
|
|
|
|
slange
|
|
dlange
|
|
clange
|
|
zlange
|
|
|
|
slarf
|
|
dlarf
|
|
clarf
|
|
zlarf
|
|
|
|
slarfg
|
|
dlarfg
|
|
clarfg
|
|
zlarfg
|
|
|
|
slartg
|
|
dlartg
|
|
clartg
|
|
zlartg
|
|
|
|
slasd4
|
|
dlasd4
|
|
|
|
slaswp
|
|
dlaswp
|
|
claswp
|
|
zlaswp
|
|
|
|
slauum
|
|
dlauum
|
|
clauum
|
|
zlauum
|
|
|
|
sorcsd
|
|
dorcsd
|
|
sorcsd_lwork
|
|
dorcsd_lwork
|
|
|
|
sorghr
|
|
dorghr
|
|
sorghr_lwork
|
|
dorghr_lwork
|
|
|
|
sorgqr
|
|
dorgqr
|
|
|
|
sorgrq
|
|
dorgrq
|
|
|
|
sormqr
|
|
dormqr
|
|
|
|
sormrz
|
|
dormrz
|
|
|
|
sormrz_lwork
|
|
dormrz_lwork
|
|
|
|
spbsv
|
|
dpbsv
|
|
cpbsv
|
|
zpbsv
|
|
|
|
spbtrf
|
|
dpbtrf
|
|
cpbtrf
|
|
zpbtrf
|
|
|
|
spbtrs
|
|
dpbtrs
|
|
cpbtrs
|
|
zpbtrs
|
|
|
|
spftrf
|
|
dpftrf
|
|
cpftrf
|
|
zpftrf
|
|
|
|
spftri
|
|
dpftri
|
|
cpftri
|
|
zpftri
|
|
|
|
spftrs
|
|
dpftrs
|
|
cpftrs
|
|
zpftrs
|
|
|
|
spocon
|
|
dpocon
|
|
cpocon
|
|
zpocon
|
|
|
|
spstrf
|
|
dpstrf
|
|
cpstrf
|
|
zpstrf
|
|
|
|
spstf2
|
|
dpstf2
|
|
cpstf2
|
|
zpstf2
|
|
|
|
sposv
|
|
dposv
|
|
cposv
|
|
zposv
|
|
|
|
sposvx
|
|
dposvx
|
|
cposvx
|
|
zposvx
|
|
|
|
spotrf
|
|
dpotrf
|
|
cpotrf
|
|
zpotrf
|
|
|
|
spotri
|
|
dpotri
|
|
cpotri
|
|
zpotri
|
|
|
|
spotrs
|
|
dpotrs
|
|
cpotrs
|
|
zpotrs
|
|
|
|
sppcon
|
|
dppcon
|
|
cppcon
|
|
zppcon
|
|
|
|
sppsv
|
|
dppsv
|
|
cppsv
|
|
zppsv
|
|
|
|
spptrf
|
|
dpptrf
|
|
cpptrf
|
|
zpptrf
|
|
|
|
spptri
|
|
dpptri
|
|
cpptri
|
|
zpptri
|
|
|
|
spptrs
|
|
dpptrs
|
|
cpptrs
|
|
zpptrs
|
|
|
|
sptsv
|
|
dptsv
|
|
cptsv
|
|
zptsv
|
|
|
|
sptsvx
|
|
dptsvx
|
|
cptsvx
|
|
zptsvx
|
|
|
|
spttrf
|
|
dpttrf
|
|
cpttrf
|
|
zpttrf
|
|
|
|
spttrs
|
|
dpttrs
|
|
cpttrs
|
|
zpttrs
|
|
|
|
spteqr
|
|
dpteqr
|
|
cpteqr
|
|
zpteqr
|
|
|
|
crot
|
|
zrot
|
|
|
|
ssbev
|
|
dsbev
|
|
|
|
ssbevd
|
|
dsbevd
|
|
|
|
ssbevx
|
|
dsbevx
|
|
|
|
ssfrk
|
|
dsfrk
|
|
|
|
sstebz
|
|
dstebz
|
|
|
|
sstein
|
|
dstein
|
|
|
|
sstemr
|
|
dstemr
|
|
|
|
sstemr_lwork
|
|
dstemr_lwork
|
|
|
|
ssterf
|
|
dsterf
|
|
|
|
sstev
|
|
dstev
|
|
|
|
ssycon
|
|
dsycon
|
|
csycon
|
|
zsycon
|
|
|
|
ssyconv
|
|
dsyconv
|
|
csyconv
|
|
zsyconv
|
|
|
|
ssyequb
|
|
dsyequb
|
|
csyequb
|
|
zsyequb
|
|
|
|
ssyev
|
|
dsyev
|
|
|
|
ssyev_lwork
|
|
dsyev_lwork
|
|
|
|
ssyevd
|
|
dsyevd
|
|
|
|
ssyevd_lwork
|
|
dsyevd_lwork
|
|
|
|
ssyevr
|
|
dsyevr
|
|
|
|
ssyevr_lwork
|
|
dsyevr_lwork
|
|
|
|
ssyevx
|
|
dsyevx
|
|
|
|
ssyevx_lwork
|
|
dsyevx_lwork
|
|
|
|
ssygst
|
|
dsygst
|
|
|
|
ssygv
|
|
dsygv
|
|
|
|
ssygv_lwork
|
|
dsygv_lwork
|
|
|
|
ssygvd
|
|
dsygvd
|
|
|
|
ssygvx
|
|
dsygvx
|
|
|
|
ssygvx_lwork
|
|
dsygvx_lwork
|
|
|
|
ssysv
|
|
dsysv
|
|
csysv
|
|
zsysv
|
|
|
|
ssysv_lwork
|
|
dsysv_lwork
|
|
csysv_lwork
|
|
zsysv_lwork
|
|
|
|
ssysvx
|
|
dsysvx
|
|
csysvx
|
|
zsysvx
|
|
|
|
ssysvx_lwork
|
|
dsysvx_lwork
|
|
csysvx_lwork
|
|
zsysvx_lwork
|
|
|
|
ssytf2
|
|
dsytf2
|
|
csytf2
|
|
zsytf2
|
|
|
|
ssytrd
|
|
dsytrd
|
|
|
|
ssytrd_lwork
|
|
dsytrd_lwork
|
|
|
|
ssytrf
|
|
dsytrf
|
|
csytrf
|
|
zsytrf
|
|
|
|
ssytrf_lwork
|
|
dsytrf_lwork
|
|
csytrf_lwork
|
|
zsytrf_lwork
|
|
|
|
stbtrs
|
|
dtbtrs
|
|
ctbtrs
|
|
ztbtrs
|
|
|
|
stfsm
|
|
dtfsm
|
|
ctfsm
|
|
ztfsm
|
|
|
|
stfttp
|
|
dtfttp
|
|
ctfttp
|
|
ztfttp
|
|
|
|
stfttr
|
|
dtfttr
|
|
ctfttr
|
|
ztfttr
|
|
|
|
stgsen
|
|
dtgsen
|
|
ctgsen
|
|
ztgsen
|
|
|
|
stpttf
|
|
dtpttf
|
|
ctpttf
|
|
ztpttf
|
|
|
|
stpttr
|
|
dtpttr
|
|
ctpttr
|
|
ztpttr
|
|
|
|
strsyl
|
|
dtrsyl
|
|
ctrsyl
|
|
ztrsyl
|
|
|
|
strtri
|
|
dtrtri
|
|
ctrtri
|
|
ztrtri
|
|
|
|
strtrs
|
|
dtrtrs
|
|
ctrtrs
|
|
ztrtrs
|
|
|
|
strttf
|
|
dtrttf
|
|
ctrttf
|
|
ztrttf
|
|
|
|
strttp
|
|
dtrttp
|
|
ctrttp
|
|
ztrttp
|
|
|
|
stzrzf
|
|
dtzrzf
|
|
ctzrzf
|
|
ztzrzf
|
|
|
|
stzrzf_lwork
|
|
dtzrzf_lwork
|
|
ctzrzf_lwork
|
|
ztzrzf_lwork
|
|
|
|
cunghr
|
|
zunghr
|
|
|
|
cunghr_lwork
|
|
zunghr_lwork
|
|
|
|
cungqr
|
|
zungqr
|
|
|
|
cungrq
|
|
zungrq
|
|
|
|
cunmqr
|
|
zunmqr
|
|
|
|
sgeqrt
|
|
dgeqrt
|
|
cgeqrt
|
|
zgeqrt
|
|
|
|
sgemqrt
|
|
dgemqrt
|
|
cgemqrt
|
|
zgemqrt
|
|
|
|
sgttrf
|
|
dgttrf
|
|
cgttrf
|
|
zgttrf
|
|
|
|
sgttrs
|
|
dgttrs
|
|
cgttrs
|
|
zgttrs
|
|
|
|
stpqrt
|
|
dtpqrt
|
|
ctpqrt
|
|
ztpqrt
|
|
|
|
stpmqrt
|
|
dtpmqrt
|
|
ctpmqrt
|
|
ztpmqrt
|
|
|
|
cuncsd
|
|
zuncsd
|
|
|
|
cuncsd_lwork
|
|
zuncsd_lwork
|
|
|
|
cunmrz
|
|
zunmrz
|
|
|
|
cunmrz_lwork
|
|
zunmrz_lwork
|
|
|
|
ilaver
|
|
|
|
"""
|
|
#
|
|
# Author: Pearu Peterson, March 2002
|
|
#
|
|
|
|
import numpy as _np
|
|
from .blas import _get_funcs, _memoize_get_funcs
|
|
from scipy.linalg import _flapack
|
|
from re import compile as regex_compile
|
|
try:
|
|
from scipy.linalg import _clapack
|
|
except ImportError:
|
|
_clapack = None
|
|
|
|
try:
|
|
from scipy.linalg import _flapack_64
|
|
HAS_ILP64 = True
|
|
except ImportError:
|
|
HAS_ILP64 = False
|
|
_flapack_64 = None
|
|
|
|
# Backward compatibility
|
|
from scipy._lib._util import DeprecatedImport as _DeprecatedImport
|
|
clapack = _DeprecatedImport("scipy.linalg.blas.clapack", "scipy.linalg.lapack")
|
|
flapack = _DeprecatedImport("scipy.linalg.blas.flapack", "scipy.linalg.lapack")
|
|
|
|
# Expose all functions (only flapack --- clapack is an implementation detail)
|
|
empty_module = None
|
|
from scipy.linalg._flapack import *
|
|
del empty_module
|
|
|
|
__all__ = ['get_lapack_funcs']
|
|
|
|
_dep_message = """The `*gegv` family of routines has been deprecated in
|
|
LAPACK 3.6.0 in favor of the `*ggev` family of routines.
|
|
The corresponding wrappers will be removed from SciPy in
|
|
a future release."""
|
|
|
|
cgegv = _np.deprecate(cgegv, old_name='cgegv', message=_dep_message)
|
|
dgegv = _np.deprecate(dgegv, old_name='dgegv', message=_dep_message)
|
|
sgegv = _np.deprecate(sgegv, old_name='sgegv', message=_dep_message)
|
|
zgegv = _np.deprecate(zgegv, old_name='zgegv', message=_dep_message)
|
|
|
|
# Modify _flapack in this scope so the deprecation warnings apply to
|
|
# functions returned by get_lapack_funcs.
|
|
_flapack.cgegv = cgegv
|
|
_flapack.dgegv = dgegv
|
|
_flapack.sgegv = sgegv
|
|
_flapack.zgegv = zgegv
|
|
|
|
# some convenience alias for complex functions
|
|
_lapack_alias = {
|
|
'corghr': 'cunghr', 'zorghr': 'zunghr',
|
|
'corghr_lwork': 'cunghr_lwork', 'zorghr_lwork': 'zunghr_lwork',
|
|
'corgqr': 'cungqr', 'zorgqr': 'zungqr',
|
|
'cormqr': 'cunmqr', 'zormqr': 'zunmqr',
|
|
'corgrq': 'cungrq', 'zorgrq': 'zungrq',
|
|
}
|
|
|
|
|
|
# Place guards against docstring rendering issues with special characters
|
|
p1 = regex_compile(r'with bounds (?P<b>.*?)( and (?P<s>.*?) storage){0,1}\n')
|
|
p2 = regex_compile(r'Default: (?P<d>.*?)\n')
|
|
|
|
|
|
def backtickrepl(m):
|
|
if m.group('s'):
|
|
return ('with bounds ``{}`` with ``{}`` storage\n'
|
|
''.format(m.group('b'), m.group('s')))
|
|
else:
|
|
return 'with bounds ``{}``\n'.format(m.group('b'))
|
|
|
|
|
|
for routine in [ssyevr, dsyevr, cheevr, zheevr,
|
|
ssyevx, dsyevx, cheevx, zheevx,
|
|
ssygvd, dsygvd, chegvd, zhegvd]:
|
|
if routine.__doc__:
|
|
routine.__doc__ = p1.sub(backtickrepl, routine.__doc__)
|
|
routine.__doc__ = p2.sub('Default ``\\1``\n', routine.__doc__)
|
|
else:
|
|
continue
|
|
|
|
del regex_compile, p1, p2, backtickrepl
|
|
|
|
|
|
@_memoize_get_funcs
|
|
def get_lapack_funcs(names, arrays=(), dtype=None, ilp64=False):
|
|
"""Return available LAPACK function objects from names.
|
|
|
|
Arrays are used to determine the optimal prefix of LAPACK routines.
|
|
|
|
Parameters
|
|
----------
|
|
names : str or sequence of str
|
|
Name(s) of LAPACK functions without type prefix.
|
|
|
|
arrays : sequence of ndarrays, optional
|
|
Arrays can be given to determine optimal prefix of LAPACK
|
|
routines. If not given, double-precision routines will be
|
|
used, otherwise the most generic type in arrays will be used.
|
|
|
|
dtype : str or dtype, optional
|
|
Data-type specifier. Not used if `arrays` is non-empty.
|
|
|
|
ilp64 : {True, False, 'preferred'}, optional
|
|
Whether to return ILP64 routine variant.
|
|
Choosing 'preferred' returns ILP64 routine if available, and
|
|
otherwise the 32-bit routine. Default: False
|
|
|
|
Returns
|
|
-------
|
|
funcs : list
|
|
List containing the found function(s).
|
|
|
|
Notes
|
|
-----
|
|
This routine automatically chooses between Fortran/C
|
|
interfaces. Fortran code is used whenever possible for arrays with
|
|
column major order. In all other cases, C code is preferred.
|
|
|
|
In LAPACK, the naming convention is that all functions start with a
|
|
type prefix, which depends on the type of the principal
|
|
matrix. These can be one of {'s', 'd', 'c', 'z'} for the NumPy
|
|
types {float32, float64, complex64, complex128} respectively, and
|
|
are stored in attribute ``typecode`` of the returned functions.
|
|
|
|
Examples
|
|
--------
|
|
Suppose we would like to use '?lange' routine which computes the selected
|
|
norm of an array. We pass our array in order to get the correct 'lange'
|
|
flavor.
|
|
|
|
>>> import scipy.linalg as LA
|
|
>>> a = np.random.rand(3,2)
|
|
>>> x_lange = LA.get_lapack_funcs('lange', (a,))
|
|
>>> x_lange.typecode
|
|
'd'
|
|
>>> x_lange = LA.get_lapack_funcs('lange',(a*1j,))
|
|
>>> x_lange.typecode
|
|
'z'
|
|
|
|
Several LAPACK routines work best when its internal WORK array has
|
|
the optimal size (big enough for fast computation and small enough to
|
|
avoid waste of memory). This size is determined also by a dedicated query
|
|
to the function which is often wrapped as a standalone function and
|
|
commonly denoted as ``###_lwork``. Below is an example for ``?sysv``
|
|
|
|
>>> import scipy.linalg as LA
|
|
>>> a = np.random.rand(1000,1000)
|
|
>>> b = np.random.rand(1000,1)*1j
|
|
>>> # We pick up zsysv and zsysv_lwork due to b array
|
|
... xsysv, xlwork = LA.get_lapack_funcs(('sysv', 'sysv_lwork'), (a, b))
|
|
>>> opt_lwork, _ = xlwork(a.shape[0]) # returns a complex for 'z' prefix
|
|
>>> udut, ipiv, x, info = xsysv(a, b, lwork=int(opt_lwork.real))
|
|
|
|
"""
|
|
if isinstance(ilp64, str):
|
|
if ilp64 == 'preferred':
|
|
ilp64 = HAS_ILP64
|
|
else:
|
|
raise ValueError("Invalid value for 'ilp64'")
|
|
|
|
if not ilp64:
|
|
return _get_funcs(names, arrays, dtype,
|
|
"LAPACK", _flapack, _clapack,
|
|
"flapack", "clapack", _lapack_alias,
|
|
ilp64=False)
|
|
else:
|
|
if not HAS_ILP64:
|
|
raise RuntimeError("LAPACK ILP64 routine requested, but Scipy "
|
|
"compiled only with 32-bit BLAS")
|
|
return _get_funcs(names, arrays, dtype,
|
|
"LAPACK", _flapack_64, None,
|
|
"flapack_64", None, _lapack_alias,
|
|
ilp64=True)
|
|
|
|
|
|
_int32_max = _np.iinfo(_np.int32).max
|
|
_int64_max = _np.iinfo(_np.int64).max
|
|
|
|
|
|
def _compute_lwork(routine, *args, **kwargs):
|
|
"""
|
|
Round floating-point lwork returned by lapack to integer.
|
|
|
|
Several LAPACK routines compute optimal values for LWORK, which
|
|
they return in a floating-point variable. However, for large
|
|
values of LWORK, single-precision floating point is not sufficient
|
|
to hold the exact value --- some LAPACK versions (<= 3.5.0 at
|
|
least) truncate the returned integer to single precision and in
|
|
some cases this can be smaller than the required value.
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy.linalg import lapack
|
|
>>> n = 5000
|
|
>>> s_r, s_lw = lapack.get_lapack_funcs(('sysvx', 'sysvx_lwork'))
|
|
>>> lwork = lapack._compute_lwork(s_lw, n)
|
|
>>> lwork
|
|
32000
|
|
|
|
"""
|
|
dtype = getattr(routine, 'dtype', None)
|
|
int_dtype = getattr(routine, 'int_dtype', None)
|
|
ret = routine(*args, **kwargs)
|
|
if ret[-1] != 0:
|
|
raise ValueError("Internal work array size computation failed: "
|
|
"%d" % (ret[-1],))
|
|
|
|
if len(ret) == 2:
|
|
return _check_work_float(ret[0].real, dtype, int_dtype)
|
|
else:
|
|
return tuple(_check_work_float(x.real, dtype, int_dtype)
|
|
for x in ret[:-1])
|
|
|
|
|
|
def _check_work_float(value, dtype, int_dtype):
|
|
"""
|
|
Convert LAPACK-returned work array size float to integer,
|
|
carefully for single-precision types.
|
|
"""
|
|
|
|
if dtype == _np.float32 or dtype == _np.complex64:
|
|
# Single-precision routine -- take next fp value to work
|
|
# around possible truncation in LAPACK code
|
|
value = _np.nextafter(value, _np.inf, dtype=_np.float32)
|
|
|
|
value = int(value)
|
|
if int_dtype.itemsize == 4:
|
|
if value < 0 or value > _int32_max:
|
|
raise ValueError("Too large work array required -- computation "
|
|
"cannot be performed with standard 32-bit"
|
|
" LAPACK.")
|
|
elif int_dtype.itemsize == 8:
|
|
if value < 0 or value > _int64_max:
|
|
raise ValueError("Too large work array required -- computation"
|
|
" cannot be performed with standard 64-bit"
|
|
" LAPACK.")
|
|
return value
|