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

```
SGELQF(3F)							    SGELQF(3F)

```

### NAME[Toc][Back]

```     SGELQF - compute an LQ factorization of a real M-by-N matrix A
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

REAL		A( LDA,	* ), TAU( * ), WORK( LWORK )
```

### PURPOSE[Toc][Back]

```     SGELQF computes an	LQ factorization of a real 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) REAL 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
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) REAL array, dimension (min(M,N))
The scalar	factors	of the elementary reflectors (see Further
Details).

WORK    (workspace/output)	REAL 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(k) . . . H(2) H(1), where	k = min(m,n).

Each H(i) has the form

Page 1

SGELQF(3F)							    SGELQF(3F)

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

where tau is a real scalar, and v is a real vector	with
v(1:i-1) =	0 and v(i) = 1;	v(i+1:n) is stored on exit in A(i,i+1:n), and
tau in TAU(i).
SGELQF(3F)							    SGELQF(3F)

```

### NAME[Toc][Back]

```     SGELQF - compute an LQ factorization of a real M-by-N matrix A
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

REAL		A( LDA,	* ), TAU( * ), WORK( LWORK )
```

### PURPOSE[Toc][Back]

```     SGELQF computes an	LQ factorization of a real 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) REAL 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
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) REAL array, dimension (min(M,N))
The scalar	factors	of the elementary reflectors (see Further
Details).

WORK    (workspace/output)	REAL 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(k) . . . H(2) H(1), where	k = min(m,n).

Each H(i) has the form

Page 1

SGELQF(3F)							    SGELQF(3F)

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

where tau is a real scalar, and v is a real vector	with
v(1:i-1) =	0 and v(i) = 1;	v(i+1:n) is stored on exit in A(i,i+1:n), 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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