MATLAB Function Reference

dmperm

Dulmage-Mendelsohn decomposition

Syntax

p = dmperm(A)
[p,q,r] = dmperm(A)
[p,q,r,s] = dmperm(A)

Description

If A is a reducible matrix, the linear system Ax = b can be solved by permuting A to a block upper triangular form, with irreducible diagonal blocks, and then performing block backsubstitution. Only the diagonal blocks of the permuted matrix need to be factored, saving fill and arithmetic in the blocks above the diagonal.

p = dmperm(A) returns a row permutation p so that if A has full column rank, A(p,:) is square with nonzero diagonal. This is also called a maximum matching.

[p,q,r] = dmperm(A) 當 A 是平方矩陣(square matrix)時，求得橫列排列(row permutation) p 和直行排列(column permutation) q ，使得 A(p,q) is in block upper triangular form。所得的第三個輸出引數 r 代表區塊(block)的邊界： A(p,q) 中第 k 個區塊的邊界的索引值為 r(k):r(k+1)-1。

[p,q,r,s] = dmperm(A), 當 A 不是平方矩陣(square matrix)時， 求出 p 和 q 、索引值 r 和 s ，使得 A(p,q) 是 block upper triangular。而且區塊的邊界為 (r(i):r(i+1)-1, s(i):s(i+1)-1)。

In graph theoretic terms, the diagonal blocks correspond to strong Hall components of the adjacency graph of A.

dlmwrite

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