sprank

Purpose

Sparse matrix structural rank.

Synopsis

r = sprank(A)

Description

r = sprank(A) is the structural rank of the matrix A. This is also known as maximum traversal, maximum assignment, and size of a maximum matching in the graph of A.

It is always true that sprank(A) >= rank(A).

Furthermore, in exact arithmetic

sprank(A) == rank(sprand(A))
with probability one.

Examples

The 3-by-3 matrix

A = [ 2    0    1
      0    0    0
      3    0    x ]
has sprank(A) = 2 for any value of x. It also has rank(A) = 2, unless x = 3/2 in which case, rank(A) = 1.

See Also

dmperm, rank

(c) Copyright 1994 by The MathWorks, Inc.