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"""
Low-level BLAS functions (:mod:`scipy.linalg.blas`)
===================================================
This module contains low-level functions from the BLAS library.
.. versionadded:: 0.12.0
.. note::
The common ``overwrite_<>`` option in many routines, allows the
input arrays to be overwritten to avoid extra memory allocation.
However this requires the array to satisfy two conditions
which are memory order and the data type to match exactly the
order and the type expected by the routine.
As an example, if you pass a double precision float array to any
``S....`` routine which expects single precision arguments, f2py
will create an intermediate array to match the argument types and
overwriting will be performed on that intermediate array.
Similarly, if a C-contiguous array is passed, f2py will pass a
FORTRAN-contiguous array internally. Please make sure that these
details are satisfied. More information can be found in the f2py
documentation.
.. warning::
These functions do little to no error checking.
It is possible to cause crashes by mis-using them,
so prefer using the higher-level routines in `scipy.linalg`.
Finding functions
-----------------
.. autosummary::
:toctree: generated/
get_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/
sgbmv
sgemv
sger
ssbmv
sspr
sspr2
ssymv
ssyr
ssyr2
stbmv
stpsv
strmv
strsv
dgbmv
dgemv
dger
dsbmv
dspr
dspr2
dsymv
dsyr
dsyr2
dtbmv
dtpsv
dtrmv
dtrsv
cgbmv
cgemv
cgerc
cgeru
chbmv
chemv
cher
cher2
chpmv
chpr
chpr2
ctbmv
ctbsv
ctpmv
ctpsv
ctrmv
ctrsv
csyr
zgbmv
zgemv
zgerc
zgeru
zhbmv
zhemv
zher
zher2
zhpmv
zhpr
zhpr2
ztbmv
ztbsv
ztpmv
ztrmv
ztrsv
zsyr
BLAS Level 3 functions
----------------------
.. autosummary::
:toctree: generated/
sgemm
ssymm
ssyr2k
ssyrk
strmm
strsm
dgemm
dsymm
dsyr2k
dsyrk
dtrmm
dtrsm
cgemm
chemm
cher2k
cherk
csymm
csyr2k
csyrk
ctrmm
ctrsm
zgemm
zhemm
zher2k
zherk
zsymm
zsyr2k
zsyrk
ztrmm
ztrsm
"""
#
# 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.
Examples
--------
>>> import scipy.linalg.blas as bla
>>> a = np.random.rand(10,15)
>>> b = np.asfortranarray(a) # Change the memory layout order
>>> bla.find_best_blas_type((a,))
('d', dtype('float64'), False)
>>> bla.find_best_blas_type((a*1j,))
('z', dtype('complex128'), False)
>>> bla.find_best_blas_type((b,))
('d', dtype('float64'), True)
"""
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.
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)