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man pages->IRIX man pages -> complib/cgerq2 (3)
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### Contents

```
CGERQ2(3F)							    CGERQ2(3F)

```

### NAME[Toc][Back]

```     CGERQ2 - compute an RQ factorization of a complex m by n matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CGERQ2(	M, N, A, LDA, TAU, WORK, INFO )

INTEGER	INFO, LDA, M, N

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

### PURPOSE[Toc][Back]

```     CGERQ2 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 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 elementary reflectors (see
Further Details).

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

TAU     (output) COMPLEX array, dimension (min(M,N))
The scalar	factors	of the elementary reflectors (see Further
Details).

WORK    (workspace) COMPLEX 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

CGERQ2(3F)							    CGERQ2(3F)

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).
CGERQ2(3F)							    CGERQ2(3F)

```

### NAME[Toc][Back]

```     CGERQ2 - compute an RQ factorization of a complex m by n matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CGERQ2(	M, N, A, LDA, TAU, WORK, INFO )

INTEGER	INFO, LDA, M, N

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

### PURPOSE[Toc][Back]

```     CGERQ2 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 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 elementary reflectors (see
Further Details).

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

TAU     (output) COMPLEX array, dimension (min(M,N))
The scalar	factors	of the elementary reflectors (see Further
Details).

WORK    (workspace) COMPLEX 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

CGERQ2(3F)							    CGERQ2(3F)

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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