833 lines
13 KiB
Python
833 lines
13 KiB
Python
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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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:toctree: generated/
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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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sgecon
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dgecon
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cgecon
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zgecon
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sgeequ
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dgeequ
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cgeequ
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zgeequ
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sgeequb
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dgeequb
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cgeequb
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zgeequb
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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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sgels
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dgels
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cgels
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zgels
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sgels_lwork
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dgels_lwork
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cgels_lwork
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zgels_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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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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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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sgesv
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dgesv
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cgesv
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zgesv
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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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sgesvx
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dgesvx
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cgesvx
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zgesvx
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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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sgglse
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dgglse
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cgglse
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zgglse
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sgglse_lwork
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dgglse_lwork
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cgglse_lwork
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zgglse_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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chbevd
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zhbevd
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chbevx
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zhbevx
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checon
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zhecon
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cheequb
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zheequb
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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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chegst
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zhegst
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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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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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chetrd
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zhetrd
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chetrd_lwork
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zhetrd_lwork
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chetrf
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zhetrf
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chetrf_lwork
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zhetrf_lwork
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chfrk
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zhfrk
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slamch
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dlamch
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slange
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dlange
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clange
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zlange
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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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sorghr
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dorghr
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sorghr_lwork
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dorghr_lwork
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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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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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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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spocon
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dpocon
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cpocon
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zpocon
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spstrf
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dpstrf
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cpstrf
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zpstrf
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spstf2
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dpstf2
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cpstf2
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zpstf2
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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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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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sptsv
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dptsv
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cptsv
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zptsv
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crot
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zrot
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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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ssfrk
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dsfrk
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sstebz
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dstebz
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sstein
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dstein
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sstemr
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dstemr
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sstemr_lwork
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dstemr_lwork
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ssterf
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dsterf
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sstev
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dstev
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ssycon
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dsycon
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csycon
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zsycon
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ssyconv
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dsyconv
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csyconv
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zsyconv
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ssyequb
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dsyequb
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csyequb
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zsyequb
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ssyev
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dsyev
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ssyevd
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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
|