# Ubuntu Feisty 7.04 manual page repository

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

` `

### NAME

```        ZGEQRF - compute a QR factorization of a complex M-by-N matrix A
```

### SYNOPSIS

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

INTEGER        INFO, LDA, LWORK, M, N

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

### PURPOSE

```        ZGEQRF  computes a QR factorization of a complex M-by-N matrix A: A = Q
* R.
```

### 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
above the diagonal of the array contain the min(M,N)-by-N upper
trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
elements  below the diagonal, with the array TAU, represent the
unitary matrix Q as a product of min(m,n) 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)
WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
mum  performance  LWORK >= N*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(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i), and tau  in
TAU(i).

```
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