.TH CGETC2 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CGETC2 - an LU factorization, using complete pivoting, of the n-by-n matrix A .SH SYNOPSIS .TP 19 SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO ) .TP 19 .ti +4 INTEGER INFO, LDA, N .TP 19 .ti +4 INTEGER IPIV( * ), JPIV( * ) .TP 19 .ti +4 COMPLEX A( LDA, * ) .SH PURPOSE CGETC2 computes an LU factorization, using 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. .br This is a level 1 BLAS version of the algorithm. .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 A (input/output) COMPLEX array, dimension (LDA, N) On entry, the n-by-n matrix 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, giving a nonsingular perturbed system. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1, N). .TP 8 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). .TP 8 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). .TP 8 INFO (output) INTEGER = 0: successful exit .br > 0: if INFO = k, U(k, k) is likely to produce overflow if one tries to solve for x in Ax = b. So U is perturbed to avoid the overflow. .SH FURTHER DETAILS Based on contributions by .br Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden. .br