451 lines
10 KiB
Python
451 lines
10 KiB
Python
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"""
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Low-level BLAS functions (:mod:`scipy.linalg.blas`)
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===================================================
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This module contains low-level functions from the BLAS library.
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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_blas_funcs
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find_best_blas_type
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BLAS Level 1 functions
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----------------------
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.. autosummary::
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:toctree: generated/
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caxpy
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ccopy
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cdotc
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cdotu
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crotg
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cscal
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csrot
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csscal
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cswap
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dasum
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daxpy
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dcopy
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ddot
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dnrm2
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drot
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drotg
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drotm
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drotmg
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dscal
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dswap
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dzasum
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dznrm2
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icamax
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idamax
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isamax
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izamax
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sasum
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saxpy
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scasum
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scnrm2
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scopy
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sdot
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snrm2
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srot
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srotg
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srotm
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srotmg
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sscal
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sswap
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zaxpy
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zcopy
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zdotc
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zdotu
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zdrot
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zdscal
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zrotg
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zscal
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zswap
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BLAS Level 2 functions
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----------------------
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.. autosummary::
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:toctree: generated/
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sgbmv
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sgemv
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sger
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ssbmv
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sspr
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sspr2
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ssymv
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ssyr
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ssyr2
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stbmv
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stpsv
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strmv
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strsv
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dgbmv
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dgemv
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dger
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dsbmv
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dspr
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dspr2
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dsymv
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dsyr
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dsyr2
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dtbmv
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dtpsv
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dtrmv
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dtrsv
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cgbmv
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cgemv
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cgerc
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cgeru
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chbmv
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chemv
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cher
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cher2
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chpmv
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chpr
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chpr2
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ctbmv
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ctbsv
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ctpmv
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ctpsv
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ctrmv
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ctrsv
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csyr
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zgbmv
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zgemv
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zgerc
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zgeru
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zhbmv
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zhemv
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zher
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zher2
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zhpmv
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zhpr
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zhpr2
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ztbmv
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ztbsv
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ztpmv
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ztrmv
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ztrsv
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zsyr
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BLAS Level 3 functions
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----------------------
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.. autosummary::
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:toctree: generated/
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sgemm
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ssymm
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ssyr2k
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ssyrk
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strmm
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strsm
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dgemm
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dsymm
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dsyr2k
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dsyrk
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dtrmm
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dtrsm
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cgemm
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chemm
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cher2k
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cherk
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csymm
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csyr2k
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csyrk
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ctrmm
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ctrsm
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zgemm
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zhemm
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zher2k
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zherk
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zsymm
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zsyr2k
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zsyrk
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ztrmm
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ztrsm
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"""
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#
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# Author: Pearu Peterson, March 2002
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# refactoring by Fabian Pedregosa, March 2010
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#
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__all__ = ['get_blas_funcs', 'find_best_blas_type']
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import numpy as _np
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import functools
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from scipy.linalg import _fblas
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try:
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from scipy.linalg import _cblas
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except ImportError:
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_cblas = None
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# Expose all functions (only fblas --- cblas is an implementation detail)
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empty_module = None
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from scipy.linalg._fblas import *
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del empty_module
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# all numeric dtypes '?bBhHiIlLqQefdgFDGO' that are safe to be converted to
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# single precision float : '?bBhH!!!!!!ef!!!!!!'
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# double precision float : '?bBhHiIlLqQefdg!!!!'
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# single precision complex : '?bBhH!!!!!!ef!!F!!!'
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# double precision complex : '?bBhHiIlLqQefdgFDG!'
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_type_score = {x: 1 for x in '?bBhHef'}
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_type_score.update({x: 2 for x in 'iIlLqQd'})
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# Handle float128(g) and complex256(G) separately in case non-Windows systems.
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# On Windows, the values will be rewritten to the same key with the same value.
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_type_score.update({'F': 3, 'D': 4, 'g': 2, 'G': 4})
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# Final mapping to the actual prefixes and dtypes
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_type_conv = {1: ('s', _np.dtype('float32')),
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2: ('d', _np.dtype('float64')),
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3: ('c', _np.dtype('complex64')),
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4: ('z', _np.dtype('complex128'))}
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# some convenience alias for complex functions
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_blas_alias = {'cnrm2': 'scnrm2', 'znrm2': 'dznrm2',
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'cdot': 'cdotc', 'zdot': 'zdotc',
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'cger': 'cgerc', 'zger': 'zgerc',
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'sdotc': 'sdot', 'sdotu': 'sdot',
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'ddotc': 'ddot', 'ddotu': 'ddot'}
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def find_best_blas_type(arrays=(), dtype=None):
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"""Find best-matching BLAS/LAPACK type.
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Arrays are used to determine the optimal prefix of BLAS routines.
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Parameters
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----------
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arrays : sequence of ndarrays, optional
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Arrays can be given to determine optimal prefix of BLAS
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routines. If not given, double-precision routines will be
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used, otherwise the most generic type in arrays will be used.
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dtype : str or dtype, optional
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Data-type specifier. Not used if `arrays` is non-empty.
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Returns
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-------
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prefix : str
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BLAS/LAPACK prefix character.
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dtype : dtype
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Inferred Numpy data type.
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prefer_fortran : bool
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Whether to prefer Fortran order routines over C order.
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Examples
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--------
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>>> import scipy.linalg.blas as bla
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>>> a = np.random.rand(10,15)
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>>> b = np.asfortranarray(a) # Change the memory layout order
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>>> bla.find_best_blas_type((a,))
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('d', dtype('float64'), False)
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>>> bla.find_best_blas_type((a*1j,))
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('z', dtype('complex128'), False)
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>>> bla.find_best_blas_type((b,))
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('d', dtype('float64'), True)
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"""
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dtype = _np.dtype(dtype)
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max_score = _type_score.get(dtype.char, 5)
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prefer_fortran = False
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if arrays:
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# In most cases, single element is passed through, quicker route
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if len(arrays) == 1:
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max_score = _type_score.get(arrays[0].dtype.char, 5)
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prefer_fortran = arrays[0].flags['FORTRAN']
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else:
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# use the most generic type in arrays
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scores = [_type_score.get(x.dtype.char, 5) for x in arrays]
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max_score = max(scores)
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ind_max_score = scores.index(max_score)
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# safe upcasting for mix of float64 and complex64 --> prefix 'z'
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if max_score == 3 and (2 in scores):
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max_score = 4
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if arrays[ind_max_score].flags['FORTRAN']:
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# prefer Fortran for leading array with column major order
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prefer_fortran = True
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# Get the LAPACK prefix and the corresponding dtype if not fall back
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# to 'd' and double precision float.
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prefix, dtype = _type_conv.get(max_score, ('d', _np.dtype('float64')))
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return prefix, dtype, prefer_fortran
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def _get_funcs(names, arrays, dtype,
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lib_name, fmodule, cmodule,
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fmodule_name, cmodule_name, alias):
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"""
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Return available BLAS/LAPACK functions.
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Used also in lapack.py. See get_blas_funcs for docstring.
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"""
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funcs = []
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unpack = False
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dtype = _np.dtype(dtype)
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module1 = (cmodule, cmodule_name)
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module2 = (fmodule, fmodule_name)
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if isinstance(names, str):
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names = (names,)
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unpack = True
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prefix, dtype, prefer_fortran = find_best_blas_type(arrays, dtype)
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if prefer_fortran:
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module1, module2 = module2, module1
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for name in names:
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func_name = prefix + name
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func_name = alias.get(func_name, func_name)
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func = getattr(module1[0], func_name, None)
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module_name = module1[1]
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if func is None:
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func = getattr(module2[0], func_name, None)
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module_name = module2[1]
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if func is None:
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raise ValueError(
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'%s function %s could not be found' % (lib_name, func_name))
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func.module_name, func.typecode = module_name, prefix
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func.dtype = dtype
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func.prefix = prefix # Backward compatibility
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funcs.append(func)
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if unpack:
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return funcs[0]
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else:
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return funcs
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def _memoize_get_funcs(func):
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"""
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Memoized fast path for _get_funcs instances
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"""
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memo = {}
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func.memo = memo
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@functools.wraps(func)
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def getter(names, arrays=(), dtype=None):
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key = (names, dtype)
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for array in arrays:
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# cf. find_blas_funcs
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key += (array.dtype.char, array.flags.fortran)
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try:
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value = memo.get(key)
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except TypeError:
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# unhashable key etc.
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key = None
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value = None
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if value is not None:
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return value
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value = func(names, arrays, dtype)
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if key is not None:
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memo[key] = value
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return value
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return getter
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@_memoize_get_funcs
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def get_blas_funcs(names, arrays=(), dtype=None):
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"""Return available BLAS function objects from names.
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Arrays are used to determine the optimal prefix of BLAS routines.
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Parameters
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----------
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names : str or sequence of str
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Name(s) of BLAS functions without type prefix.
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arrays : sequence of ndarrays, optional
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Arrays can be given to determine optimal prefix of BLAS
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routines. If not given, double-precision routines will be
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used, otherwise the most generic type in arrays will be used.
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dtype : str or dtype, optional
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Data-type specifier. Not used if `arrays` is non-empty.
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Returns
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-------
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|
|
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 BLAS, 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.
|
||
|
|
The code and the dtype are stored in attributes `typecode` and `dtype`
|
||
|
|
of the returned functions.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import scipy.linalg as LA
|
||
|
|
>>> a = np.random.rand(3,2)
|
||
|
|
>>> x_gemv = LA.get_blas_funcs('gemv', (a,))
|
||
|
|
>>> x_gemv.typecode
|
||
|
|
'd'
|
||
|
|
>>> x_gemv = LA.get_blas_funcs('gemv',(a*1j,))
|
||
|
|
>>> x_gemv.typecode
|
||
|
|
'z'
|
||
|
|
|
||
|
|
"""
|
||
|
|
return _get_funcs(names, arrays, dtype,
|
||
|
|
"BLAS", _fblas, _cblas, "fblas", "cblas",
|
||
|
|
_blas_alias)
|