SYNOPSIS

SUBROUTINE DGETC2(

N, A, LDA, IPIV, JPIV, INFO )

    

INTEGER INFO, LDA, N

    

INTEGER IPIV( * ), JPIV( * )

    

DOUBLE PRECISION A( LDA, * )

PURPOSE

DGETC2 computes an LU factorization with complete pivoting of the n-by-n matrix A. The factorization has the form A = P * L * U * Q, where P and Q are permutation matrices, L is lower triangular with unit diagonal elements and U is upper triangular.
This is the Level 2 BLAS algorithm.

ARGUMENTS

N (input) INTEGER

The order of the matrix A. N >= 0.

A (input/output) DOUBLE PRECISION array, dimension (LDA, N)

On entry, the n-by-n matrix A to be factored. On exit, the factors L and U from the factorization A = P*L*U*Q; the unit diagonal elements of L are not stored. If U(k, k) appears to be less than SMIN, U(k, k) is given the value of SMIN, i.e., giving a nonsingular perturbed system.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).

IPIV (output) INTEGER array, dimension(N).

The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).

JPIV (output) INTEGER array, dimension(N).

The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).

INFO (output) INTEGER

= 0: successful exit
> 0: if INFO = k, U(k, k) is likely to produce owerflow if we try to solve for x in Ax = b. So U is perturbed to avoid the overflow.

FURTHER DETAILS

Based on contributions by

   Bo Kagstrom and Peter Poromaa, Department of Computing Science,
   Umea University, S-901 87 Umea, Sweden.