# zgetrf2.f - Man Page

## Synopsis

### Functions/Subroutines

recursive subroutine **zgetrf2** (M, **N**, A, **LDA**, IPIV, INFO)**ZGETRF2**

## Function/Subroutine Documentation

### recursive subroutine zgetrf2 (integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO)

**ZGETRF2**

**Purpose:**

ZGETRF2 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 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*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

Univ. of Colorado Denver

NAG Ltd.

**Date:**June 2016

Definition at line 115 of file zgetrf2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgetrf2(3) is an alias of zgetrf2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK