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""" 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::
get_lapack_funcs
All functions -------------
.. autosummary:: :toctree: generated/
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
ssygst dsygst
ssytrd dsytrd
ssytrd_lwork dsytrd_lwork
chetrd zhetrd
chetrd_lwork zhetrd_lwork
chesv zhesv
chesv_lwork zhesv_lwork
chesvx zhesvx
chesvx_lwork zhesvx_lwork
chegst zhegst
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
""" # # Author: Pearu Peterson, March 2002 #
# Backward compatibility:
# Backward compatibility
# Expose all functions (only flapack --- clapack is an implementation detail)
LAPACK 3.6.0 in favor of the `*ggev` family of routines. The corresponding wrappers will be removed from SciPy in a future release."""
# Modyfy _flapack in this scope so the deprecation warnings apply to # functions returned by get_lapack_funcs.
# some convenience alias for complex functions 'corghr': 'cunghr', 'zorghr': 'zunghr', 'corghr_lwork': 'cunghr_lwork', 'zorghr_lwork': 'zunghr_lwork', 'corgqr': 'cungqr', 'zorgqr': 'zungqr', 'cormqr': 'cunmqr', 'zormqr': 'zunmqr', 'corgrq': 'cungrq', 'zorgrq': 'zungrq', }
"""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.
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))
""" "LAPACK", _flapack, _clapack, "flapack", "clapack", _lapack_alias)
""" 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
""" raise ValueError('') raise ValueError("Internal work array size computation failed: " "%d" % (info,))
# Single-precision routine -- take next fp value to work # around possible truncation in LAPACK code lwork = _np.nextafter(lwork, _np.inf, dtype=_np.float32)
raise ValueError("Too large work array required -- computation cannot " "be performed with standard 32-bit LAPACK.") return lwork |