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# LAPACK-3

## 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

```NAME
LAPACK-3  -  computes  an LU factorization of a general m-by-n matrix A
using partial pivoting with row interchanges

SYNOPSIS
SUBROUTINE ZGETF2( M, N, A, LDA, IPIV, INFO )

INTEGER        INFO, LDA, M, N

INTEGER        IPIV( * )

COMPLEX*16     A( LDA, * )

PURPOSE
ZGETF2 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 2 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 = -k, the k-th argument had an illegal value
> 0: if INFO = k, U(k,k) 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)
```