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man pages->IRIX man pages -> complib/dgerq2 (3)
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### Contents

```
DGERQ2(3F)							    DGERQ2(3F)

```

### NAME[Toc][Back]

```     DGERQ2 - compute an RQ factorization of a real m by n matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DGERQ2(	M, N, A, LDA, TAU, WORK, INFO )

INTEGER	INFO, LDA, M, N

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

### PURPOSE[Toc][Back]

```     DGERQ2 computes an	RQ factorization of a real 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) DOUBLE PRECISION 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
orthogonal	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) DOUBLE PRECISION array, dimension	(min(M,N))
The scalar	factors	of the elementary reflectors (see Further
Details).

WORK    (workspace) DOUBLE	PRECISION array, dimension (M)

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).

Each H(i) has the form

H(i) = I - tau * v * v'

Page 1

DGERQ2(3F)							    DGERQ2(3F)

where tau is a real scalar, and v is a real vector	with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1;	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).
DGERQ2(3F)							    DGERQ2(3F)

```

### NAME[Toc][Back]

```     DGERQ2 - compute an RQ factorization of a real m by n matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DGERQ2(	M, N, A, LDA, TAU, WORK, INFO )

INTEGER	INFO, LDA, M, N

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

### PURPOSE[Toc][Back]

```     DGERQ2 computes an	RQ factorization of a real 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) DOUBLE PRECISION 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
orthogonal	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) DOUBLE PRECISION array, dimension	(min(M,N))
The scalar	factors	of the elementary reflectors (see Further
Details).

WORK    (workspace) DOUBLE	PRECISION array, dimension (M)

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).

Each H(i) has the form

H(i) = I - tau * v * v'

Page 1

DGERQ2(3F)							    DGERQ2(3F)

where tau is a real scalar, and v is a real vector	with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1;	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```
[ Back ]
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