从稀疏矩阵的行创建稀疏对角矩阵

Question

我在Python/Scipy中处理相当大的矩阵.我需要从大矩阵(加载到coo_matrix)中提取行并将它们用作对角元素.目前我以下列方式做到这一点:

import numpy as np
from scipy import sparse

def computation(A):
  for i in range(A.shape[0]):
    diag_elems = np.array(A[i,:].todense())
    ith_diag = sparse.spdiags(diag_elems,0,A.shape[1],A.shape[1], format = "csc")
    #...

#create some random matrix
A = (sparse.rand(1000,100000,0.02,format="csc")*5).astype(np.ubyte)
#get timings
profile.run('computation(A)')

我从profile输出中看到的是,大部分时间是get_csr_submatrix在提取时被函数消耗的diag_elems.这让我觉得我使用了初始数据的低效稀疏表示或从稀疏矩阵中提取行的错误方法.您能否建议一种更好的方法从稀疏矩阵中提取行并以对角线形式表示？

编辑

以下变体从行提取中消除了瓶颈(注意,简单的更改'csc'为csr不够,A[i,:]必须同时替换A.getrow(i)).然而,主要问题是如何省略materialization(.todense())并从行的稀疏表示创建对角矩阵.

import numpy as np
from scipy import sparse

def computation(A):
  for i in range(A.shape[0]):
    diag_elems = np.array(A.getrow(i).todense())
    ith_diag = sparse.spdiags(diag_elems,0,A.shape[1],A.shape[1], format = "csc")
    #...

#create some random matrix
A = (sparse.rand(1000,100000,0.02,format="csr")*5).astype(np.ubyte)
#get timings
profile.run('computation(A)')

如果我直接从1行CSR矩阵创建DIAgonal矩阵,如下所示:

diag_elems = A.getrow(i)
ith_diag = sparse.spdiags(diag_elems,0,A.shape[1],A.shape[1])

那么我既不能指定format="csc"参数,也不能转换ith_diags为CSC格式:

Traceback (most recent call last):
   File "<stdin>", line 1, in <module>
  File "/usr/local/lib/python2.6/profile.py", line 70, in run
    prof = prof.run(statement)
  File "/usr/local/lib/python2.6/profile.py", line 456, in run
    return self.runctx(cmd, dict, dict)
  File "/usr/local/lib/python2.6/profile.py", line 462, in runctx
    exec cmd in globals, locals
  File "<string>", line 1, in <module>
  File "<stdin>", line 4, in computation
  File "/usr/local/lib/python2.6/site-packages/scipy/sparse/construct.py", line 56, in spdiags
    return dia_matrix((data, diags), shape=(m,n)).asformat(format)
  File "/usr/local/lib/python2.6/site-packages/scipy/sparse/base.py", line 211, in asformat
    return getattr(self,'to' + format)()
  File "/usr/local/lib/python2.6/site-packages/scipy/sparse/dia.py", line 173, in tocsc
    return self.tocoo().tocsc()
  File "/usr/local/lib/python2.6/site-packages/scipy/sparse/coo.py", line 263, in tocsc
    data    = np.empty(self.nnz, dtype=upcast(self.dtype))
  File "/usr/local/lib/python2.6/site-packages/scipy/sparse/sputils.py", line 47, in upcast
    raise TypeError,'no supported conversion for types: %s' % args
TypeError: no supported conversion for types: object`

Answer 1

这是我想出的：

def computation(A):
    for i in range(A.shape[0]):
        idx_begin = A.indptr[i]
        idx_end = A.indptr[i+1]
        row_nnz = idx_end - idx_begin
        diag_elems = A.data[idx_begin:idx_end]
        diag_indices = A.indices[idx_begin:idx_end]
        ith_diag = sparse.csc_matrix((diag_elems, (diag_indices, diag_indices)),shape=(A.shape[1], A.shape[1]))
        ith_diag.eliminate_zeros()

Python 分析器显示为 1.464 秒，而之前为 5.574 秒。它利用定义稀疏矩阵的底层密集数组（indptr、索引、数据）。这是我的速成课程： A.indptr[i]:A.indptr[i+1] 定义密集数组中的哪些元素对应于第 i 行中的非零值。A.data 是 A 的非零值的密集一维数组，A.indptr 是这些值所在的列。

我会做更多的测试，以确保这与以前的效果相同。我只检查了几个案例。