"""
Low-level BLAS functions (:mod:`scipy.linalg.blas`)
===================================================
This module contains low-level functions from the BLAS library.
.. versionadded:: 0.12.0
.. warning::
These functions do little to no error checking.
It is possible to cause crashes by mis-using them,
so prefer using the higher-level routines in `scipy.linalg`.
Finding functions
-----------------
.. autosummary::
:toctree: generated/
get_blas_funcs
find_best_blas_type
BLAS Level 1 functions
----------------------
.. autosummary::
:toctree: generated/
caxpy
ccopy
cdotc
cdotu
crotg
cscal
csrot
csscal
cswap
dasum
daxpy
dcopy
ddot
dnrm2
drot
drotg
drotm
drotmg
dscal
dswap
dzasum
dznrm2
icamax
idamax
isamax
izamax
sasum
saxpy
scasum
scnrm2
scopy
sdot
snrm2
srot
srotg
srotm
srotmg
sscal
sswap
zaxpy
zcopy
zdotc
zdotu
zdrot
zdscal
zrotg
zscal
zswap
BLAS Level 2 functions
----------------------
.. autosummary::
:toctree: generated/
cgemv
cgerc
cgeru
chemv
ctrmv
csyr
cher
cher2
dgemv
dger
dsymv
dtrmv
dsyr
dsyr2
sgemv
sger
ssymv
strmv
ssyr
ssyr2
zgemv
zgerc
zgeru
zhemv
ztrmv
zsyr
zher
zher2
BLAS Level 3 functions
----------------------
.. autosummary::
:toctree: generated/
cgemm
chemm
cherk
cher2k
csymm
csyrk
csyr2k
dgemm
dsymm
dsyrk
dsyr2k
sgemm
ssymm
ssyrk
ssyr2k
zgemm
zhemm
zherk
zher2k
zsymm
zsyrk
zsyr2k
"""
#
# Author: Pearu Peterson, March 2002
# refactoring by Fabian Pedregosa, March 2010
#
from __future__ import division, print_function, absolute_import
__all__ = ['get_blas_funcs', 'find_best_blas_type']
import numpy as _np
from scipy.linalg import _fblas
try:
from scipy.linalg import _cblas
except ImportError:
_cblas = None
# Expose all functions (only fblas --- cblas is an implementation detail)
empty_module = None
from scipy.linalg._fblas import *
del empty_module
# 'd' will be default for 'i',..
_type_conv = {'f': 's', 'd': 'd', 'F': 'c', 'D': 'z', 'G': 'z'}
# some convenience alias for complex functions
_blas_alias = {'cnrm2': 'scnrm2', 'znrm2': 'dznrm2',
'cdot': 'cdotc', 'zdot': 'zdotc',
'cger': 'cgerc', 'zger': 'zgerc',
'sdotc': 'sdot', 'sdotu': 'sdot',
'ddotc': 'ddot', 'ddotu': 'ddot'}
def find_best_blas_type(arrays=(), dtype=None):
"""Find best-matching BLAS/LAPACK type.
Arrays are used to determine the optimal prefix of BLAS routines.
Parameters
----------
arrays : sequence of ndarrays, optional
Arrays can be given to determine optimal prefix of BLAS
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
-------
prefix : str
BLAS/LAPACK prefix character.
dtype : dtype
Inferred Numpy data type.
prefer_fortran : bool
Whether to prefer Fortran order routines over C order.
"""
dtype = _np.dtype(dtype)
prefer_fortran = False
if arrays:
# use the most generic type in arrays
dtypes = [ar.dtype for ar in arrays]
dtype = _np.find_common_type(dtypes, ())
try:
index = dtypes.index(dtype)
except ValueError:
index = 0
if arrays[index].flags['FORTRAN']:
# prefer Fortran for leading array with column major order
prefer_fortran = True
prefix = _type_conv.get(dtype.char, 'd')
if dtype.char == 'G':
# complex256 -> complex128 (i.e., C long double -> C double)
dtype = _np.dtype('D')
elif dtype.char not in 'fdFD':
dtype = _np.dtype('d')
return prefix, dtype, prefer_fortran
def _get_funcs(names, arrays, dtype,
lib_name, fmodule, cmodule,
fmodule_name, cmodule_name, alias):
"""
Return available BLAS/LAPACK functions.
Used also in lapack.py. See get_blas_funcs for docstring.
"""
funcs = []
unpack = False
dtype = _np.dtype(dtype)
module1 = (cmodule, cmodule_name)
module2 = (fmodule, fmodule_name)
if isinstance(names, str):
names = (names,)
unpack = True
prefix, dtype, prefer_fortran = find_best_blas_type(arrays, dtype)
if prefer_fortran:
module1, module2 = module2, module1
for i, name in enumerate(names):
func_name = prefix + name
func_name = alias.get(func_name, func_name)
func = getattr(module1[0], func_name, None)
module_name = module1[1]
if func is None:
func = getattr(module2[0], func_name, None)
module_name = module2[1]
if func is None:
raise ValueError(
'%s function %s could not be found' % (lib_name, func_name))
func.module_name, func.typecode = module_name, prefix
func.dtype = dtype
func.prefix = prefix # Backward compatibility
funcs.append(func)
if unpack:
return funcs[0]
else:
return funcs
def get_blas_funcs(names, arrays=(), dtype=None):
"""Return available BLAS function objects from names.
Arrays are used to determine the optimal prefix of BLAS routines.
Parameters
----------
names : str or sequence of str
Name(s) of BLAS functions without type prefix.
arrays : sequence of ndarrays, optional
Arrays can be given to determine optimal prefix of BLAS
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 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.
"""
return _get_funcs(names, arrays, dtype,
"BLAS", _fblas, _cblas, "fblas", "cblas",
_blas_alias)