在Julia中,我如何对稀疏矩阵进行列标准化？

Question

如果我使用稀疏(i,j,k)构造函数构造了稀疏矩阵,那么如何对矩阵的列进行归一化(以便每列总和为1)？在创建矩阵之前,我无法有效地规范化条目,因此感谢任何帮助.谢谢!

Answer 1

最简单的方法是按列总和进行广播划分:

julia> A = sprand(4,5,.5)
       A./sum(A,1)
4x5 Array{Float64,2}:
 0.0        0.0989976  0.0        0.0       0.0795486
 0.420754   0.458653   0.0986313  0.0       0.0
 0.0785525  0.442349   0.0        0.856136  0.920451
 0.500693   0.0        0.901369   0.143864  0.0

...但它看起来还没有针对稀疏矩阵进行优化,而是回落到一个完整的矩阵.因此,迭代列的简单循环可以解决问题:

julia> for (col,s) in enumerate(sum(A,1))
         s == 0 && continue # What does a "normalized" column with a sum of zero look like?
         A[:,col] = A[:,col]/s
       end
       A
4x5 sparse matrix with 12 Float64 entries:
    [2, 1]  =  0.420754
    [3, 1]  =  0.0785525
    [4, 1]  =  0.500693
    [1, 2]  =  0.0989976
    [2, 2]  =  0.458653
    [3, 2]  =  0.442349
    [2, 3]  =  0.0986313
    [4, 3]  =  0.901369
    [3, 4]  =  0.856136
    [4, 4]  =  0.143864
    [1, 5]  =  0.0795486
    [3, 5]  =  0.920451

julia> sum(A,1)
1x5 Array{Float64,2}:
 1.0  1.0  1.0  1.0  1.0

这完全在稀疏矩阵内工作并且就地完成(尽管它仍然为每个列切片分配新的稀疏矩阵).