man dgetc2 (Fonctions bibliothèques) - compute an LU factorization with complete pivoting of the n-by-n matrix A

NAME

DGETC2 - compute an LU factorization with complete pivoting of the n-by-n matrix A

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.