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.

New in version 0.12.0.

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

get_lapack_funcs

All functions

sgbsv
dgbsv
cgbsv
zgbsv
sgbtrf
dgbtrf
cgbtrf
zgbtrf
sgbtrs
dgbtrs
cgbtrs
zgbtrs
sgebal
dgebal
cgebal
zgebal
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
sgelss
dgelss
cgelss
zgelss
sgelss_lwork
dgelss_lwork
cgelss_lwork
zgelss_lwork
sgelsd
dgelsd
cgelsd
zgelsd
sgelsd_lwork
dgelsd_lwork
cgelsd_lwork
zgelsd_lwork
sgelsy
dgelsy
cgelsy
zgelsy
sgelsy_lwork
dgelsy_lwork
cgelsy_lwork
zgelsy_lwork
sgeqp3
dgeqp3
cgeqp3
zgeqp3
sgeqrf
dgeqrf
cgeqrf
zgeqrf
sgerqf
dgerqf
cgerqf
zgerqf
sgesdd
dgesdd
cgesdd
zgesdd
sgesdd_lwork
dgesdd_lwork
cgesdd_lwork
zgesdd_lwork
sgesvd
dgesvd
cgesvd
zgesvd
sgesvd_lwork
dgesvd_lwork
cgesvd_lwork
zgesvd_lwork
sgesv
dgesv
cgesv
zgesv
sgesvx
dgesvx
cgesvx
zgesvx
sgecon
dgecon
cgecon
zgecon
ssysv
dsysv
csysv
zsysv
ssysv_lwork
dsysv_lwork
csysv_lwork
zsysv_lwork
ssysvx
dsysvx
csysvx
zsysvx
ssysvx_lwork
dsysvx_lwork
csysvx_lwork
zsysvx_lwork
ssytrd
dsytrd
ssytrd_lwork
dsytrd_lwork
chetrd
zhetrd
chetrd_lwork
zhetrd_lwork
chesv
zhesv
chesv_lwork
zhesv_lwork
chesvx
zhesvx
chesvx_lwork
zhesvx_lwork
sgetrf
dgetrf
cgetrf
zgetrf
sgetri
dgetri
cgetri
zgetri
sgetri_lwork
dgetri_lwork
cgetri_lwork
zgetri_lwork
sgetrs
dgetrs
cgetrs
zgetrs
sgges
dgges
cgges
zgges
sggev
dggev
cggev
zggev
chbevd
zhbevd
chbevx
zhbevx
cheev
zheev
cheevd
zheevd
cheevr
zheevr
chegv
zhegv
chegvd
zhegvd
chegvx
zhegvx
slarf
dlarf
clarf
zlarf
slarfg
dlarfg
clarfg
zlarfg
slartg
dlartg
clartg
zlartg
slasd4
dlasd4
slaswp
dlaswp
claswp
zlaswp
slauum
dlauum
clauum
zlauum
spbsv
dpbsv
cpbsv
zpbsv
spbtrf
dpbtrf
cpbtrf
zpbtrf
spbtrs
dpbtrs
cpbtrs
zpbtrs
sposv
dposv
cposv
zposv
sposvx
dposvx
cposvx
zposvx
spocon
dpocon
cpocon
zpocon
spotrf
dpotrf
cpotrf
zpotrf
spotri
dpotri
cpotri
zpotri
spotrs
dpotrs
cpotrs
zpotrs
crot
zrot
strsyl
dtrsyl
ctrsyl
ztrsyl
strtri
dtrtri
ctrtri
ztrtri
strtrs
dtrtrs
ctrtrs
ztrtrs
cunghr
zunghr
cungqr
zungqr
cungrq
zungrq
cunmqr
zunmqr
sgtsv
dgtsv
cgtsv
zgtsv
sptsv
dptsv
cptsv
zptsv
slamch
dlamch
sorghr
dorghr
sorgqr
dorgqr
sorgrq
dorgrq
sormqr
dormqr
ssbev
dsbev
ssbevd
dsbevd
ssbevx
dsbevx
sstebz
dstebz
sstemr
dstemr
ssterf
dsterf
sstein
dstein
sstev
dstev
ssyev
dsyev
ssyevd
dsyevd
ssyevr
dsyevr
ssygv
dsygv
ssygvd
dsygvd
ssygvx
dsygvx
slange
dlange
clange
zlange
ilaver

Module Contents

Functions

get_lapack_funcs(names,arrays=tuple,dtype=None) Return available LAPACK function objects from names.
_compute_lwork(routine,*args,**kwargs) Round floating-point lwork returned by lapack to integer.
get_lapack_funcs(names, arrays=tuple, dtype=None)

Return available LAPACK function objects from names.

Arrays are used to determine the optimal prefix of LAPACK routines.

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.
funcs : list
List containing the found function(s).

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.

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))
_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.

>>> 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