EVOLUTION-MANAGER

Edit File: lapack.py

""" 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 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 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 sgetri dgetri cgetri zgetri sgetri_lwork dgetri_lwork cgetri_lwork zgetri_lwork sgetrs dgetrs cgetrs zgetrs sgges dgges cgges zgges sggev dggev cggev zggev sgglse dgglse cgglse zgglse sgglse_lwork dgglse_lwork cgglse_lwork zgglse_lwork sgtsv dgtsv cgtsv zgtsv chbevd zhbevd chbevx zhbevx checon zhecon cheequb zheequb cheev zheev cheevd zheevd cheevr zheevr chegst zhegst chegv zhegv chegvd zhegvd chegvx zhegvx 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 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 sptsv dptsv cptsv zptsv 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 ssyevd dsyevd ssyevr dsyevr ssygst dsygst ssygv dsygv ssygvd dsygvd ssygvx dsygvx 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 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 stpqrt dtpqrt ctpqrt ztpqrt stpmqrt dtpmqrt ctpmqrt ztpmqrt cunmrz zunmrz cunmrz_lwork zunmrz_lwork ilaver """ # # Author: Pearu Peterson, March 2002 # from __future__ import division, print_function, absolute_import import numpy as _np from .blas import _get_funcs, _memoize_get_funcs from scipy.linalg import _flapack try: from scipy.linalg import _clapack except ImportError: _clapack = None # Backward compatibility from .blas import find_best_blas_type as find_best_lapack_type 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) # Modyfy _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', } @_memoize_get_funcs def get_lapack_funcs(names, arrays=(), dtype=None): """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)) """ return _get_funcs(names, arrays, dtype, "LAPACK", _flapack, _clapack, "flapack", "clapack", _lapack_alias) _int32_max = _np.iinfo(_np.int32).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) 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) else: return tuple(_check_work_float(x.real, dtype) for x in ret[:-1]) def _check_work_float(value, 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 value < 0 or value > _int32_max: raise ValueError("Too large work array required -- computation cannot " "be performed with standard 32-bit LAPACK.") return value