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dgetrf

```
NAME
DGETRF - compute an LU factorization of a general M-by-N
matrix A using partial pivoting with row interchanges

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

INTEGER        INFO, LDA, M, N

INTEGER        IPIV( * )

DOUBLE         PRECISION A( LDA, * )

PURPOSE
DGETRF 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 algo-
rithm.

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) DOUBLE PRECISION 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 fac-
torization 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.
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