demo + utils venv
This commit is contained in:
d3m1g0d
@@ -0,0 +1,717 @@
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"""
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Low-level LAPACK functions (:mod:`scipy.linalg.lapack`)
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=======================================================
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This module contains low-level functions from the LAPACK library.
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The `*gegv` family of routines have been removed from LAPACK 3.6.0
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and have been deprecated in SciPy 0.17.0. They will be removed in
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a future release.
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.. versionadded:: 0.12.0
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.. note::
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The common ``overwrite_<>`` option in many routines, allows the
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input arrays to be overwritten to avoid extra memory allocation.
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However this requires the array to satisfy two conditions
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which are memory order and the data type to match exactly the
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order and the type expected by the routine.
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As an example, if you pass a double precision float array to any
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``S....`` routine which expects single precision arguments, f2py
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will create an intermediate array to match the argument types and
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overwriting will be performed on that intermediate array.
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Similarly, if a C-contiguous array is passed, f2py will pass a
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FORTRAN-contiguous array internally. Please make sure that these
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details are satisfied. More information can be found in the f2py
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documentation.
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.. warning::
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These functions do little to no error checking.
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It is possible to cause crashes by mis-using them,
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so prefer using the higher-level routines in `scipy.linalg`.
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Finding functions
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-----------------
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.. autosummary::
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get_lapack_funcs
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All functions
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-------------
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.. autosummary::
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:toctree: generated/
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sgbsv
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dgbsv
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cgbsv
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zgbsv
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sgbtrf
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dgbtrf
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cgbtrf
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zgbtrf
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sgbtrs
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dgbtrs
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cgbtrs
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zgbtrs
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sgebal
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dgebal
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cgebal
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zgebal
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sgees
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dgees
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cgees
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zgees
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sgeev
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dgeev
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cgeev
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zgeev
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sgeev_lwork
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dgeev_lwork
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cgeev_lwork
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zgeev_lwork
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sgegv
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dgegv
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cgegv
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zgegv
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sgehrd
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dgehrd
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cgehrd
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zgehrd
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sgehrd_lwork
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dgehrd_lwork
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cgehrd_lwork
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zgehrd_lwork
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sgelss
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dgelss
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cgelss
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zgelss
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sgelss_lwork
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dgelss_lwork
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cgelss_lwork
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zgelss_lwork
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sgelsd
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dgelsd
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cgelsd
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zgelsd
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sgelsd_lwork
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dgelsd_lwork
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cgelsd_lwork
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zgelsd_lwork
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sgelsy
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dgelsy
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cgelsy
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zgelsy
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sgelsy_lwork
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dgelsy_lwork
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cgelsy_lwork
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zgelsy_lwork
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sgeqp3
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dgeqp3
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cgeqp3
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zgeqp3
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sgeqrf
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dgeqrf
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cgeqrf
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zgeqrf
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sgerqf
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dgerqf
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cgerqf
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zgerqf
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sgesdd
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dgesdd
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cgesdd
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zgesdd
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sgesdd_lwork
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dgesdd_lwork
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cgesdd_lwork
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zgesdd_lwork
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sgesvd
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dgesvd
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cgesvd
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zgesvd
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sgesvd_lwork
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dgesvd_lwork
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cgesvd_lwork
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zgesvd_lwork
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sgesv
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dgesv
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cgesv
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zgesv
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sgesvx
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dgesvx
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cgesvx
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zgesvx
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sgecon
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dgecon
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cgecon
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zgecon
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ssysv
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dsysv
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csysv
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zsysv
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ssysv_lwork
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dsysv_lwork
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csysv_lwork
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zsysv_lwork
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ssysvx
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dsysvx
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csysvx
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zsysvx
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ssysvx_lwork
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dsysvx_lwork
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csysvx_lwork
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zsysvx_lwork
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ssygst
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dsygst
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ssytrd
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dsytrd
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ssytrd_lwork
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dsytrd_lwork
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chetrd
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zhetrd
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chetrd_lwork
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zhetrd_lwork
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chesv
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zhesv
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chesv_lwork
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zhesv_lwork
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chesvx
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zhesvx
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chesvx_lwork
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zhesvx_lwork
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chegst
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zhegst
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sgetrf
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dgetrf
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cgetrf
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zgetrf
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sgetri
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dgetri
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cgetri
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zgetri
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sgetri_lwork
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dgetri_lwork
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cgetri_lwork
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zgetri_lwork
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sgetrs
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dgetrs
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cgetrs
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zgetrs
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sgges
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dgges
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cgges
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zgges
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sggev
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dggev
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cggev
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zggev
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chbevd
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zhbevd
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chbevx
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zhbevx
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cheev
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zheev
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cheevd
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zheevd
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cheevr
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zheevr
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chegv
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zhegv
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chegvd
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zhegvd
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chegvx
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zhegvx
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slarf
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dlarf
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clarf
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zlarf
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slarfg
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dlarfg
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clarfg
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zlarfg
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slartg
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dlartg
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clartg
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zlartg
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slasd4
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dlasd4
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slaswp
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dlaswp
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claswp
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zlaswp
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slauum
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dlauum
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clauum
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zlauum
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spbsv
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dpbsv
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cpbsv
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zpbsv
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spbtrf
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dpbtrf
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cpbtrf
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zpbtrf
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spbtrs
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dpbtrs
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cpbtrs
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zpbtrs
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sposv
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dposv
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cposv
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zposv
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sposvx
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dposvx
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cposvx
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zposvx
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spocon
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dpocon
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cpocon
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zpocon
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spotrf
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dpotrf
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cpotrf
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zpotrf
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spotri
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dpotri
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cpotri
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zpotri
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spotrs
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dpotrs
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cpotrs
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zpotrs
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crot
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zrot
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strsyl
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dtrsyl
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ctrsyl
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ztrsyl
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strtri
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dtrtri
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ctrtri
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ztrtri
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strtrs
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dtrtrs
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ctrtrs
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ztrtrs
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spftrf
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dpftrf
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cpftrf
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zpftrf
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spftri
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dpftri
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cpftri
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zpftri
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spftrs
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dpftrs
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cpftrs
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zpftrs
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cunghr
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zunghr
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cungqr
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zungqr
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cungrq
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zungrq
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cunmqr
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zunmqr
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cunmrz
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zunmrz
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cunmrz_lwork
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zunmrz_lwork
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sgtsv
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dgtsv
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cgtsv
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zgtsv
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sptsv
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dptsv
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cptsv
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zptsv
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slamch
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dlamch
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sorghr
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dorghr
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sorgqr
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dorgqr
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sorgrq
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dorgrq
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sormqr
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dormqr
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sormrz
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dormrz
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sormrz_lwork
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dormrz_lwork
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ssbev
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dsbev
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ssbevd
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dsbevd
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ssbevx
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dsbevx
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sstebz
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dstebz
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sstemr
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dstemr
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ssterf
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dsterf
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sstein
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dstein
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sstev
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dstev
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ssyev
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dsyev
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ssyevd
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dsyevd
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ssyevr
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dsyevr
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ssygv
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dsygv
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ssygvd
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dsygvd
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ssygvx
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dsygvx
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ssfrk
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dsfrk
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chfrk
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zhfrk
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stfsm
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dtfsm
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ctfsm
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ztfsm
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stpttf
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dtpttf
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ctpttf
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ztpttf
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stfttp
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dtfttp
|
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ctfttp
|
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ztfttp
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||||
|
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stfttr
|
||||
dtfttr
|
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ctfttr
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||||
ztfttr
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strttf
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dtrttf
|
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ctrttf
|
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ztrttf
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stpttr
|
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dtpttr
|
||||
ctpttr
|
||||
ztpttr
|
||||
|
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strttp
|
||||
dtrttp
|
||||
ctrttp
|
||||
ztrttp
|
||||
|
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stfsm
|
||||
dtfsm
|
||||
ctfsm
|
||||
dtfsm
|
||||
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stzrzf
|
||||
dtzrzf
|
||||
ctzrzf
|
||||
ztzrzf
|
||||
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stzrzf_lwork
|
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dtzrzf_lwork
|
||||
ctzrzf_lwork
|
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ztzrzf_lwork
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slange
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dlange
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clange
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zlange
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ilaver
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"""
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#
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# Author: Pearu Peterson, March 2002
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#
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from __future__ import division, print_function, absolute_import
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__all__ = ['get_lapack_funcs']
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import numpy as _np
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from .blas import _get_funcs
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# Backward compatibility:
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from .blas import find_best_blas_type as find_best_lapack_type
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from scipy.linalg import _flapack
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try:
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from scipy.linalg import _clapack
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except ImportError:
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_clapack = None
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# Backward compatibility
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from scipy._lib._util import DeprecatedImport as _DeprecatedImport
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clapack = _DeprecatedImport("scipy.linalg.blas.clapack", "scipy.linalg.lapack")
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flapack = _DeprecatedImport("scipy.linalg.blas.flapack", "scipy.linalg.lapack")
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# Expose all functions (only flapack --- clapack is an implementation detail)
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empty_module = None
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from scipy.linalg._flapack import *
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del empty_module
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_dep_message = """The `*gegv` family of routines has been deprecated in
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||||
LAPACK 3.6.0 in favor of the `*ggev` family of routines.
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||||
The corresponding wrappers will be removed from SciPy in
|
||||
a future release."""
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||||
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||||
cgegv = _np.deprecate(cgegv, old_name='cgegv', message=_dep_message)
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||||
dgegv = _np.deprecate(dgegv, old_name='dgegv', message=_dep_message)
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sgegv = _np.deprecate(sgegv, old_name='sgegv', message=_dep_message)
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zgegv = _np.deprecate(zgegv, old_name='zgegv', message=_dep_message)
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||||
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||||
# Modyfy _flapack in this scope so the deprecation warnings apply to
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||||
# functions returned by get_lapack_funcs.
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_flapack.cgegv = cgegv
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_flapack.dgegv = dgegv
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_flapack.sgegv = sgegv
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_flapack.zgegv = zgegv
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# some convenience alias for complex functions
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_lapack_alias = {
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'corghr': 'cunghr', 'zorghr': 'zunghr',
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'corghr_lwork': 'cunghr_lwork', 'zorghr_lwork': 'zunghr_lwork',
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||||
'corgqr': 'cungqr', 'zorgqr': 'zungqr',
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||||
'cormqr': 'cunmqr', 'zormqr': 'zunmqr',
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||||
'corgrq': 'cungrq', 'zorgrq': 'zungrq',
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||||
}
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||||
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||||
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||||
def get_lapack_funcs(names, arrays=(), dtype=None):
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"""Return available LAPACK function objects from names.
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||||
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||||
Arrays are used to determine the optimal prefix of LAPACK routines.
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||||
|
||||
Parameters
|
||||
----------
|
||||
names : str or sequence of str
|
||||
Name(s) of LAPACK functions without type prefix.
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||||
|
||||
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.
|
||||
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||||
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)
|
||||
|
||||
|
||||
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
|
||||
|
||||
"""
|
||||
wi = routine(*args, **kwargs)
|
||||
if len(wi) < 2:
|
||||
raise ValueError('')
|
||||
info = wi[-1]
|
||||
if info != 0:
|
||||
raise ValueError("Internal work array size computation failed: "
|
||||
"%d" % (info,))
|
||||
|
||||
lwork = [w.real for w in wi[:-1]]
|
||||
|
||||
dtype = getattr(routine, 'dtype', None)
|
||||
if dtype == _np.float32 or dtype == _np.complex64:
|
||||
# Single-precision routine -- take next fp value to work
|
||||
# around possible truncation in LAPACK code
|
||||
lwork = _np.nextafter(lwork, _np.inf, dtype=_np.float32)
|
||||
|
||||
lwork = _np.array(lwork, _np.int64)
|
||||
if _np.any(_np.logical_or(lwork < 0, lwork > _np.iinfo(_np.int32).max)):
|
||||
raise ValueError("Too large work array required -- computation cannot "
|
||||
"be performed with standard 32-bit LAPACK.")
|
||||
lwork = lwork.astype(_np.int32)
|
||||
if lwork.size == 1:
|
||||
return lwork[0]
|
||||
return lwork
|
||||
Reference in New Issue
Block a user