如何并行scipy稀疏矩阵乘法

Question

我有一个scipy.sparse.csr_matrix格式的大型稀疏矩阵X,我想用一个利用并行性的numpy数组W来乘以它.经过一些研究后,我发现我需要在多处理中使用Array,以避免在进程之间复制X和W(例如:如何在Python多处理中将Pool.map与Array(共享内存)结合起来？并将共享的只读数据复制到Python多处理的不同过程？).这是我最近的尝试

import multiprocessing 
import numpy 
import scipy.sparse 
import time 

def initProcess(data, indices, indptr, shape, Warr, Wshp):
    global XData 
    global XIndices 
    global XIntptr 
    global Xshape 

    XData = data 
    XIndices = indices 
    XIntptr = indptr 
    Xshape = shape 

    global WArray
    global WShape 

    WArray = Warr     
    WShape = Wshp 

def dot2(args):
    rowInds, i = args     

    global XData 
    global XIndices
    global XIntptr 
    global Xshape 

    data = numpy.frombuffer(XData, dtype=numpy.float)
    indices = numpy.frombuffer(XIndices, dtype=numpy.int32)
    indptr = numpy.frombuffer(XIntptr, dtype=numpy.int32)
    Xr = scipy.sparse.csr_matrix((data, indices, indptr), shape=Xshape)

    global WArray
    global WShape 
    W = numpy.frombuffer(WArray, dtype=numpy.float).reshape(WShape)

    return Xr[rowInds[i]:rowInds[i+1], :].dot(W)

def getMatmat(X): 
    numJobs = multiprocessing.cpu_count()
    rowInds = numpy.array(numpy.linspace(0, X.shape[0], numJobs+1), numpy.int)

    #Store the data in X as RawArray objects so we can share it amoung processes
    XData = multiprocessing.RawArray("d", X.data)
    XIndices = multiprocessing.RawArray("i", X.indices)
    XIndptr = multiprocessing.RawArray("i", X.indptr)

    def matmat(W): 
        WArray = multiprocessing.RawArray("d", W.flatten())
        pool = multiprocessing.Pool(processes=multiprocessing.cpu_count(), initializer=initProcess, initargs=(XData, XIndices, XIndptr, X.shape, WArray, W.shape)) 
        params = [] 

        for i in range(numJobs): 
            params.append((rowInds, i))

        iterator = pool.map(dot2, params)
        P = numpy.zeros((X.shape[0], W.shape[1])) 

        for i in range(numJobs): 
            P[rowInds[i]:rowInds[i+1], :] = iterator[i]

        return P   

    return matmat 

if __name__ == '__main__':
    #Create a random sparse matrix X and a random dense one W     
    X = scipy.sparse.rand(10000, 8000, 0.1)
    X = X.tocsr()
    W = numpy.random.rand(8000, 20)

    startTime = time.time()
    A = getMatmat(X)(W)
    parallelTime = time.time()-startTime 

    startTime = time.time()
    B = X.dot(W)
    nonParallelTime = time.time()-startTime 

    print(parallelTime, nonParallelTime)

但是输出类似于:(4.431,0.165)表示并行版本比非并行乘法慢得多.

我相信在将大数据复制到进程的类似情况下可能会导致减速,但这不是这种情况,因为我使用Array来存储共享变量(除非它发生在numpy.frombuffer或创建csr_matrix时,但后来我找不到直接分享csr_matrix的方法.速度慢的另一个可能原因是每个过程返回每个矩阵乘法的大结果,但是我不确定是否可以解决这个问题.

有人能看到我错在哪里吗？谢谢你的帮助!

更新:我不能确定,但​​我认为在进程之间共享大量数据并不是那么高效,理想情况下我应该使用多线程(尽管全局解释器锁(GIL)非常难以实现).解决这个问题的一种方法是使用Cython发布GIL(参见http://docs.cython.org/src/userguide/parallelism.html),尽管许多numpy函数需要通过GIL.

Answer 1

你最好的选择是使用 Cython 降级到 C。这样您就可以击败 GIL 并使用 OpenMP。我对多重处理速度较慢并不感到惊讶——那里有很多开销。

这是 CSparse 稀疏矩阵的简单包装器 OpenMP 包装器 - python 中的向量乘积代码。

在我的笔记本电脑上，它的运行速度比 scipy 快一点。但我没有那么多核心。代码（包括 setup.py 脚本和 C 头文件和内容）位于以下要点中： https: //gist.github.com/rmcgibbo/6019670

我怀疑，如果你真的希望并行代码更快（在我的笔记本电脑上，即使使用 4 个线程，它也只比单线程 scipy 快 20% 左右），你需要比我更仔细地考虑并行性发生在哪里做到了，注意缓存局部性。

# psparse.pyx

#-----------------------------------------------------------------------------
# Imports
#-----------------------------------------------------------------------------
cimport cython
cimport numpy as np
import numpy as np
import scipy.sparse
from libc.stddef cimport ptrdiff_t
from cython.parallel import parallel, prange

#-----------------------------------------------------------------------------
# Headers
#-----------------------------------------------------------------------------

ctypedef int csi

ctypedef struct cs:
    # matrix in compressed-column or triplet form
    csi nzmax       # maximum number of entries
    csi m           # number of rows
    csi n           # number of columns
    csi *p          # column pointers (size n+1) or col indices (size nzmax)
    csi *i          # row indices, size nzmax
    double *x       # numerical values, size nzmax
    csi nz          # # of entries in triplet matrix, -1 for compressed-col

cdef extern csi cs_gaxpy (cs *A, double *x, double *y) nogil
cdef extern csi cs_print (cs *A, csi brief) nogil

assert sizeof(csi) == 4

#-----------------------------------------------------------------------------
# Functions
#-----------------------------------------------------------------------------

@cython.boundscheck(False)
def pmultiply(X not None, np.ndarray[ndim=2, mode='fortran', dtype=np.float64_t] W not None):
    """Multiply a sparse CSC matrix by a dense matrix

    Parameters
    ----------
    X : scipy.sparse.csc_matrix
        A sparse matrix, of size N x M
    W : np.ndarray[dtype=float564, ndim=2, mode='fortran']
        A dense matrix, of size M x P. Note, W must be contiguous and in
        fortran (column-major) order. You can ensure this using
        numpy's `asfortranarray` function.

    Returns
    -------
    A : np.ndarray[dtype=float64, ndim=2, mode='fortran']
        A dense matrix, of size N x P, the result of multiplying X by W.

    Notes
    -----
    This function is parallelized over the columns of W using OpenMP. You
    can control the number of threads at runtime using the OMP_NUM_THREADS
    environment variable. The internal sparse matrix code is from CSPARSE, 
    a Concise Sparse matrix package. Copyright (c) 2006, Timothy A. Davis.
    http://www.cise.ufl.edu/research/sparse/CSparse, licensed under the
    GNU LGPL v2.1+.

    References
    ----------
    .. [1] Davis, Timothy A., "Direct Methods for Sparse Linear Systems
    (Fundamentals of Algorithms 2)," SIAM Press, 2006. ISBN: 0898716136
    """
    if X.shape[1] != W.shape[0]:
        raise ValueError('matrices are not aligned')

    cdef int i
    cdef cs csX
    cdef np.ndarray[double, ndim=2, mode='fortran'] result
    cdef np.ndarray[csi, ndim=1, mode = 'c'] indptr  = X.indptr
    cdef np.ndarray[csi, ndim=1, mode = 'c'] indices = X.indices
    cdef np.ndarray[double, ndim=1, mode = 'c']    data = X.data

    # Pack the scipy data into the CSparse struct. This is just copying some
    # pointers.
    csX.nzmax = X.data.shape[0]
    csX.m = X.shape[0]
    csX.n = X.shape[1]
    csX.p = &indptr[0]
    csX.i = &indices[0]
    csX.x = &data[0]
    csX.nz = -1  # to indicate CSC format

    result = np.zeros((X.shape[0], W.shape[1]), order='F', dtype=np.double)
    for i in prange(W.shape[1], nogil=True):
        # X is in fortran format, so we can get quick access to each of its
        # columns
        cs_gaxpy(&csX, &W[0, i], &result[0, i])

    return result

它从 CSparse 调用一些 C。

// src/cs_gaxpy.c

#include "cs.h"
/* y = A*x+y */
csi cs_gaxpy (const cs *A, const double *x, double *y)
{
  csi p, j, n, *Ap, *Ai ;
  double *Ax ;
  if (!CS_CSC (A) || !x || !y) return (0) ;       /* check inputs */
  n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
  for (j = 0 ; j < n ; j++)
    {
      for (p = Ap [j] ; p < Ap [j+1] ; p++)
        {
      y [Ai [p]] += Ax [p] * x [j] ;
        }
    }
  return (1) ;
}