# Ubuntu Feisty 7.04 manual page repository

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` `

### 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  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,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(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).

```
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