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## man page of LAPACK-3

### LAPACK-3: computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

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LAPACK-3 - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges## SYNOPSIS

SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) INTEGER INFO, LDA, M, N INTEGER IPIV( * ) COMPLEX*16 A( LDA, * )## PURPOSE

ZGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This is the right-looking Level 3 BLAS version of the algorithm.## ARGUMENTS

M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). IPIV (output) INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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