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zgetrf2.f(3) LAPACK zgetrf2.f(3)

NAME

zgetrf2.f

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

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Tue Nov 14 2017 Version 3.8.0