使用 MKL BLAS 时，scipy 是否支持稀疏矩阵乘法的多线程？

根据 MKL BLAS 文档 “所有矩阵-矩阵运算（第 3 级）都针对密集和稀疏 BLAS 进行线程化。”http://software.intel.com/en-us/articles/parallelism-in-the-intel-math-kernel-library http://software.intel.com/en-us/articles/parallelism-in-the-intel-math-kernel-library

我用 MKL BLAS 构建了 Scipy。使用下面的测试代码，我看到了密集矩阵乘法的预期多线程加速，但不是稀疏矩阵乘法。 Scipy 是否有任何更改以启用多线程稀疏操作？

# test dense matrix multiplication
from numpy import *
import time    
x = random.random((10000,10000))
t1 = time.time()
foo = dot(x.T, x)
print time.time() - t1

# test sparse matrix multiplication
from scipy import sparse
x = sparse.rand(10000,10000)
t1 = time.time()
foo = dot(x.T, x)
print time.time() - t1

据我所知，答案是否定的。但是，您可以围绕 MKL 稀疏乘法例程构建自己的包装器。您询问了两个稀疏矩阵的乘法。下面是我用来将一个稀疏矩阵乘以一个稠密向量的一些包装器代码，因此它应该不难适应（请参阅 mkl_cspblas_dcsrgemm 的英特尔 MKL 参考）。另外，请注意 scipy 数组的存储方式：默认为 coo，但 csr （或 csc）可能是更好的选择。我选择了csr，但MKL支持大多数类型（只需调用适当的例程）。

据我所知，scipy 的默认值和 MKL 都是多线程的。通过改变OMP_NUM_THREADS我可以看到性能上的差异。

要使用下面的功能，如果您有最新版本的 MKL，只需确保您有LD_LIBRARY_PATHS设置为包含相关的 MKL 目录。对于旧版本，您需要构建一些特定的库。我的信息来自python 中的 IntelMKL https://software.intel.com/en-us/articles/using-intel-mkl-in-your-python-programs

def SpMV_viaMKL( A, x ):
 """
 Wrapper to Intel's SpMV
 (Sparse Matrix-Vector multiply)
 For medium-sized matrices, this is 4x faster
 than scipy's default implementation
 Stephen Becker, April 24 2014
 [email protected] /cdn-cgi/l/email-protection
 """

 import numpy as np
 import scipy.sparse as sparse
 from ctypes import POINTER,c_void_p,c_int,c_char,c_double,byref,cdll
 mkl = cdll.LoadLibrary("libmkl_rt.so")

 SpMV = mkl.mkl_cspblas_dcsrgemv
 # Dissecting the "cspblas_dcsrgemv" name:
 # "c" - for "c-blas" like interface (as opposed to fortran)
 #    Also means expects sparse arrays to use 0-based indexing, which python does
 # "sp"  for sparse
 # "d"   for double-precision
 # "csr" for compressed row format
 # "ge"  for "general", e.g., the matrix has no special structure such as symmetry
 # "mv"  for "matrix-vector" multiply

 if not sparse.isspmatrix_csr(A):
     raise Exception("Matrix must be in csr format")
 (m,n) = A.shape

 # The data of the matrix
 data    = A.data.ctypes.data_as(POINTER(c_double))
 indptr  = A.indptr.ctypes.data_as(POINTER(c_int))
 indices = A.indices.ctypes.data_as(POINTER(c_int))

 # Allocate output, using same conventions as input
 nVectors = 1
 if x.ndim is 1:
    y = np.empty(m,dtype=np.double,order='F')
    if x.size != n:
        raise Exception("x must have n entries. x.size is %d, n is %d" % (x.size,n))
 elif x.shape[1] is 1:
    y = np.empty((m,1),dtype=np.double,order='F')
    if x.shape[0] != n:
        raise Exception("x must have n entries. x.size is %d, n is %d" % (x.size,n))
 else:
    nVectors = x.shape[1]
    y = np.empty((m,nVectors),dtype=np.double,order='F')
    if x.shape[0] != n:
        raise Exception("x must have n entries. x.size is %d, n is %d" % (x.size,n))

 # Check input
 if x.dtype.type is not np.double:
    x = x.astype(np.double,copy=True)
 # Put it in column-major order, otherwise for nVectors > 1 this FAILS completely
 if x.flags['F_CONTIGUOUS'] is not True:
    x = x.copy(order='F')

 if nVectors == 1:
    np_x = x.ctypes.data_as(POINTER(c_double))
    np_y = y.ctypes.data_as(POINTER(c_double))
    # now call MKL. This returns the answer in np_y, which links to y
    SpMV(byref(c_char("N")), byref(c_int(m)),data ,indptr, indices, np_x, np_y ) 
 else:
    for columns in xrange(nVectors):
        xx = x[:,columns]
        yy = y[:,columns]
        np_x = xx.ctypes.data_as(POINTER(c_double))
        np_y = yy.ctypes.data_as(POINTER(c_double))
        SpMV(byref(c_char("N")), byref(c_int(m)),data,indptr, indices, np_x, np_y ) 

 return y