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

```
ZGERQF(3F)							    ZGERQF(3F)

```

### NAME[Toc][Back]

```     ZGERQF - compute an RQ factorization of a complex M-by-N matrix A
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

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

### PURPOSE[Toc][Back]

```     ZGERQF computes an	RQ factorization of a complex M-by-N matrix A:	A = R
* Q.

```

### 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 upper
triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
triangular	matrix R; if m >= n, the elements on and above the
(m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix
R;	the remaining elements,	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)
On	exit, if INFO =	0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  LWORK >=	max(1,M).  For optimum
performance LWORK >= M*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(1)' H(2)'	. . . H(k)', where k = min(m,n).

Page 1

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

```

### NAME[Toc][Back]

```     ZGERQF - compute an RQ factorization of a complex M-by-N matrix A
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

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

### PURPOSE[Toc][Back]

```     ZGERQF computes an	RQ factorization of a complex M-by-N matrix A:	A = R
* Q.

```

### 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 upper
triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
triangular	matrix R; if m >= n, the elements on and above the
(m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix
R;	the remaining elements,	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)
On	exit, if INFO =	0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  LWORK >=	max(1,M).  For optimum
performance LWORK >= M*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(1)' H(2)'	. . . H(k)', where k = min(m,n).

Page 1

ZGERQF(3F)							    ZGERQF(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(nk+i+1:n)
=	0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1))	is stored on exit in
A(m-k+i,1:n-k+i-1), 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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