高效行标准化矩阵 [英] Efficiently Row Standardize a Matrix

问题描述

我需要一种行标准化稀疏矩阵的有效方法.

I need an efficient way to row standardize a sparse matrix.

给予

W = matrix([[0, 1, 0, 1, 0, 0, 0, 0, 0],
            [1, 0, 1, 0, 1, 0, 0, 0, 0],
            [0, 1, 0, 0, 0, 1, 0, 0, 0],
            [1, 0, 0, 0, 1, 0, 1, 0, 0],
            [0, 1, 0, 1, 0, 1, 0, 1, 0],
            [0, 0, 1, 0, 1, 0, 0, 0, 1],
            [0, 0, 0, 1, 0, 0, 0, 1, 0],
            [0, 0, 0, 0, 1, 0, 1, 0, 1],
            [0, 0, 0, 0, 0, 1, 0, 1, 0]])
row_sums = W.sum(1)

我需要生产...

W2 = matrix([[0.  , 0.5 , 0.  , 0.5 , 0.  , 0.  , 0.  , 0.  , 0.  ],
             [0.33, 0.  , 0.33, 0.  , 0.33, 0.  , 0.  , 0.  , 0.  ],
             [0.  , 0.5 , 0.  , 0.  , 0.  , 0.5 , 0.  , 0.  , 0.  ],
             [0.33, 0.  , 0.  , 0.  , 0.33, 0.  , 0.33, 0.  , 0.  ],
             [0.  , 0.25, 0.  , 0.25, 0.  , 0.25, 0.  , 0.25, 0.  ],
             [0.  , 0.  , 0.33, 0.  , 0.33, 0.  , 0.  , 0.  , 0.33],
             [0.  , 0.  , 0.  , 0.5 , 0.  , 0.  , 0.  , 0.5 , 0.  ],
             [0.  , 0.  , 0.  , 0.  , 0.33, 0.  , 0.33, 0.  , 0.33],
             [0.  , 0.  , 0.  , 0.  , 0.  , 0.5 , 0.  , 0.5 , 0.  ]]) 

在哪里

for i in range(9):
    W2[i] = W[i]/row_sums[i]

我想找到一种无需循环(即向量化)并使用Scipy.sparse矩阵的方法. W可能会大到1000万x 1000万.

I'd like to find a way to do this without loops (i.e. Vectorized) and using Scipy.sparse matrices. W could be as large at 10mil x 10mil.

推荐答案

带有一些矩阵代数

>>> cc
<9x9 sparse matrix of type '<type 'numpy.int32'>'
    with 24 stored elements in Compressed Sparse Row format>
>>> ccd = sparse.spdiags(1./cc.sum(1).T, 0, *cc.shape)
>>> ccn = ccd * cc
>>> np.round(ccn.todense(), 2)
array([[ 0.  ,  0.5 ,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.33,  0.  ,  0.33,  0.  ,  0.33,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ],
       [ 0.33,  0.  ,  0.  ,  0.  ,  0.33,  0.  ,  0.33,  0.  ,  0.  ],
       [ 0.  ,  0.25,  0.  ,  0.25,  0.  ,  0.25,  0.  ,  0.25,  0.  ],
       [ 0.  ,  0.  ,  0.33,  0.  ,  0.33,  0.  ,  0.  ,  0.  ,  0.33],
       [ 0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.33,  0.  ,  0.33,  0.  ,  0.33],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,  0.5 ,  0.  ]])
>>> ccn
<9x9 sparse matrix of type '<type 'numpy.float64'>'
    with 24 stored elements in Compressed Sparse Row format>

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