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man pages->IRIX man pages -> complib/cgelq2 (3)
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### Contents

```
CGELQ2(3F)							    CGELQ2(3F)

```

### NAME[Toc][Back]

```     CGELQ2 - compute an LQ factorization of a complex m by n matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CGELQ2(	M, N, A, LDA, TAU, WORK, INFO )

INTEGER	INFO, LDA, M, N

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

### PURPOSE[Toc][Back]

```     CGELQ2 computes an	LQ factorization of a complex m	by n matrix A:	A = L
* 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, the elements on and
below the diagonal	of the array contain the m by min(m,n) lower
trapezoidal matrix	L (L is	lower triangular if m <= n); the
elements above the	diagonal, 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(k)' . . .	H(2)' H(1)', where k = min(m,n).

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(1:i-1) =
0 and v(i)	= 1; conjg(v(i+1:n)) is	stored on exit in A(i,i+1:n), and tau

Page 1

CGELQ2(3F)							    CGELQ2(3F)

in	TAU(i).
CGELQ2(3F)							    CGELQ2(3F)

```

### NAME[Toc][Back]

```     CGELQ2 - compute an LQ factorization of a complex m by n matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CGELQ2(	M, N, A, LDA, TAU, WORK, INFO )

INTEGER	INFO, LDA, M, N

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

### PURPOSE[Toc][Back]

```     CGELQ2 computes an	LQ factorization of a complex m	by n matrix A:	A = L
* 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, the elements on and
below the diagonal	of the array contain the m by min(m,n) lower
trapezoidal matrix	L (L is	lower triangular if m <= n); the
elements above the	diagonal, 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(k)' . . .	H(2)' H(1)', where k = min(m,n).

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(1:i-1) =
0 and v(i)	= 1; conjg(v(i+1:n)) is	stored on exit in A(i,i+1:n), and tau

Page 1

CGELQ2(3F)							    CGELQ2(3F)

in	TAU(i).

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