从稀疏矩阵的行创建一个稀疏对角矩阵

Question

我在Python/Scipy中处理相当大的矩阵。我需要从大矩阵（它被加载到coo_matrix）中提取行并将它们用作对角元素。目前，我这样做，以下列方式：

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输出看到的是，大部分的时间由get_csr_submatrix功能而提取diag_elems消耗。这使我认为我使用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。你能否提出一种更好的方法从稀疏矩阵中提取一行并以对角线形式表示它？

EDIT

以下变体从行提取去除瓶颈（注意，简单改变'csc'到csr不充分，A[i,:]必须A.getrow(i)被替换以及）。然而，主要问题是如何省略实现（.todense()）并根据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)') 

如果创建从直接1-行CSR矩阵对角矩阵，如下所示：

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

然后我既不能指定format="csc"参数，也不转换ith_diags到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分析器说1.464秒比5.574秒前。它利用了定义稀疏矩阵的底层密集数组（indptr，indices，data）。这是我的速成教程：A.indptr [i]：A.indptr [i + 1]定义密集阵列中的哪些元素对应于第i行中的非零值。 A.data是非零密集的一维数组，A和A.indptr的值是这些值的列。

我会做一些更多的测试，以便非常确定这和以前一样。我只检查了几个案例。