MATLAB Functions | Help Desk |
colperm
Sparse column permutation based on nonzero count
j = colperm(S)
j = colperm(S)
generates a permutation vector j
such that the columns of S(:,j)
are ordered according to increasing count of nonzero entries. This is sometimes useful as a preordering for LU factorization; in this case use lu(S(:,j))
.
If S
is symmetric, then j
=
colperm(S)
generates a permutation j
so that both the rows and columns of S(j,j)
are ordered according to increasing count of nonzero entries. If S
is positive definite, this is sometimes useful as a preordering for Cholesky factorization; in this case use chol(S(j,j))
.
The algorithm involves a sort on the counts of nonzeros in each column.
The n
-by-n
arrowhead matrix
A = [ones(1,n); ones(n-1,1) speye(n-1,n-1)]has a full first row and column. Its LU factorization,
lu(A)
, is almost completely full. The statement
j = colperm(A)returns
j
=
[2:n
1]
. So A(j,j)
sends the full row and column to the bottom and the rear, and lu(A(j,j))
has the same nonzero structure as A
itself.
On the other hand, the Bucky ball example, B = bucky
,
has exactly three nonzero elements in each row and column, so j = colperm(B)
is the identity permutation and is no help at all for reducing fill-in with subsequent factorizations.
chol
Cholesky factorization
colmmd
Sparse minimum degree ordering
lu
LU matrix factorization
symrcm
Sparse reverse Cuthill-McKee ordering