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## man page of LAPACK-3

### LAPACK-3: computes an LU factorization, using complete pivoting, of the n-by-n matrix A

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## NAME

LAPACK-3 - computes an LU factorization, using complete pivoting, of the n-by-n matrix A## SYNOPSIS

SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO ) INTEGER INFO, LDA, N INTEGER IPIV( * ), JPIV( * ) COMPLEX*16 A( LDA, * )## PURPOSE

ZGETC2 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. This is a level 1 BLAS version of the algorithm.ARGUMENTS

N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) COMPLEX*16 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. 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 overflow if one tries 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. LAPACK auxiliary routine (versionMarch 2011 LAPACK-3(3)

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