---
name: "cgetrf"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cgetrf/3lapack"
---

# cgetrf(3lapack)

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

## NAME

CGETRF - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

## SYNOPSIS

- SUBROUTINE CGETRF(

  M, N, A, LDA, IPIV, INFO )

- INTEGER

  INFO, LDA, M, N

- INTEGER

  IPIV( \* )

- COMPLEX

  A( LDA, \* )

## PURPOSE

CGETRF 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 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.