# dgetrf2.f man page

dgetrf2.f

## Synopsis

### Functions/Subroutines

recursive subroutine dgetrf2 (M, N, A, LDA, IPIV, INFO)
DGETRF2

## Function/Subroutine Documentation

### recursive subroutine dgetrf2 (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO)

DGETRF2

Purpose:

``` DGETRF2 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 recursive version of the algorithm. It divides
the matrix into four submatrices:

[  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ]  with n1 = min(m,n)/2
[  A21 | A22  ]       n2 = n-n1

[ A11 ]
The subroutine calls itself to factor [ --- ],
[ A12 ]
[ A12 ]
do the swaps on [ --- ], solve A12, update A22,
[ A22 ]

then calls itself to factor A22 and do the swaps on A21.```
Parameters:

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A.  N >= 0.```

A

```          A is 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

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

IPIV

```          IPIV is 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

```          INFO is 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.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

June 2016

Definition at line 115 of file dgetrf2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dgetrf2(3) is an alias of dgetrf2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK