# Ubuntu Feisty 7.04 manual page repository

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Provided by: lapack3-doc_3.0.20000531a-6ubuntu3_all

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### NAME

```        ZGELQF - compute an LQ factorization of a complex M-by-N matrix A
```

### SYNOPSIS

```        SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER        INFO, LDA, LWORK, M, N

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

### PURPOSE

```        ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L
* Q.
```

### 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, the  elements  on  and
below the diagonal of the array contain the m-by-min(m,n) lower
trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
elements  above the diagonal, with the array TAU, represent the
unitary matrix Q as a product  of  elementary  reflectors  (see
Further  Details).   LDA     (input) INTEGER The leading dimen‐
sion 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)
WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
mum performance LWORK >= M*NB, where NB is the  optimal  block‐
size.

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
The matrix Q is represented as a product of elementary reflectors

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(1:i-1)
=  0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and
tau in TAU(i).

```
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