# zgeqlf.f(3) [centos man page]

```zgeqlf.f(3)							      LAPACK							       zgeqlf.f(3)

NAME
zgeqlf.f -

SYNOPSIS
Functions/Subroutines
subroutine zgeqlf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQLF

Function/Subroutine Documentation
subroutine zgeqlf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( *
)WORK, integerLWORK, integerINFO)
ZGEQLF

Purpose:

ZGEQLF computes a QL factorization of a complex M-by-N matrix A:
A = Q * L.

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 A.
On exit,
if m >= n, the lower triangle of the subarray
A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
if m <= n, the elements on and below the (n-m)-th
superdiagonal contain the M-by-N lower trapezoidal matrix L;
the remaining elements, with the array TAU, represent the
unitary matrix Q as a product of elementary reflectors
(see Further Details).

LDA

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

TAU

TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.  LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(k) . . . H(2) H(1), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with
v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 139 of file zgeqlf.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zgeqlf.f(3)```

## Check Out this Related Man Page

```ZGEQLF(l)								 )								 ZGEQLF(l)

NAME
ZGEQLF - compute a QL factorization of a complex M-by-N matrix A

SYNOPSIS
SUBROUTINE ZGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER	  INFO, LDA, LWORK, M, N

COMPLEX*16	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
ZGEQLF computes a QL factorization of a complex M-by-N matrix A: A = Q * L.

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*16 array, dimension (LDA,N)
On  entry,  the	M-by-N	matrix A.  On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower
triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L;
the  remaining  elements,  with	the  array  TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further
Details).  LDA	  (input) INTEGER The leading dimension of the array A.  LDA >= max(1,M).

TAU     (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).

WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.  LWORK >= max(1,N).  For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of  the  WORK  array,  returns  this
value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors

Q = H(k) . . . H(2) H(1), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v'

where  tau  is a complex scalar, and v is a complex vector with v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-
k+i-1,n-k+i), and tau in TAU(i).

LAPACK version 3.0						   15 June 2000 							 ZGEQLF(l)```
Man Page