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

```
DORGRQ(3F)							    DORGRQ(3F)

```

### NAME[Toc][Back]

```     DORGRQ - generate an M-by-N real matrix Q with orthonormal	rows,
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, K, LDA, LWORK, M,	N

DOUBLE		PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
```

### PURPOSE[Toc][Back]

```     DORGRQ generates an M-by-N	real matrix Q with orthonormal rows, which is
defined as	the last M rows	of a product of	K elementary reflectors	of
order N

Q  =	 H(1) H(2) . . . H(k)

as	returned by DGERQF.

```

### ARGUMENTS[Toc][Back]

```     M	     (input) INTEGER
The number	of rows	of the matrix Q. M >= 0.

N	     (input) INTEGER
The number	of columns of the matrix Q. N >= M.

K	     (input) INTEGER
The number	of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.

A	     (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On	entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for	i = 1,2,...,k, as
returned by DGERQF	in the last k rows of its array	argument A.
On	exit, the M-by-N matrix	Q.

LDA     (input) INTEGER
The first dimension of the	array A. LDA >=	max(1,M).

TAU     (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector
H(i), as returned by DGERQF.

WORK    (workspace/output)	DOUBLE PRECISION 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.

Page 1

DORGRQ(3F)							    DORGRQ(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument has an illegal value
DORGRQ(3F)							    DORGRQ(3F)

```

### NAME[Toc][Back]

```     DORGRQ - generate an M-by-N real matrix Q with orthonormal	rows,
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, K, LDA, LWORK, M,	N

DOUBLE		PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
```

### PURPOSE[Toc][Back]

```     DORGRQ generates an M-by-N	real matrix Q with orthonormal rows, which is
defined as	the last M rows	of a product of	K elementary reflectors	of
order N

Q  =	 H(1) H(2) . . . H(k)

as	returned by DGERQF.

```

### ARGUMENTS[Toc][Back]

```     M	     (input) INTEGER
The number	of rows	of the matrix Q. M >= 0.

N	     (input) INTEGER
The number	of columns of the matrix Q. N >= M.

K	     (input) INTEGER
The number	of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.

A	     (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On	entry, the (m-k+i)-th row must contain the vector which
defines the elementary reflector H(i), for	i = 1,2,...,k, as
returned by DGERQF	in the last k rows of its array	argument A.
On	exit, the M-by-N matrix	Q.

LDA     (input) INTEGER
The first dimension of the	array A. LDA >=	max(1,M).

TAU     (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector
H(i), as returned by DGERQF.

WORK    (workspace/output)	DOUBLE PRECISION 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.

Page 1

DORGRQ(3F)							    DORGRQ(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument has an illegal value

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