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man pages->IRIX man pages -> complib/zgeqlf (3)
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### Contents

```
ZGEQLF(3F)							    ZGEQLF(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

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

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     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.

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).

Page 1

ZGEQLF(3F)							    ZGEQLF(3F)

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(mk+i+1:m)
=	0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:mk+i-1,n-k+i),
and tau in TAU(i).
ZGEQLF(3F)							    ZGEQLF(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

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

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     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.

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).

Page 1

ZGEQLF(3F)							    ZGEQLF(3F)

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

PPPPaaaaggggeeee 2222```
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