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

```
CGEQRF(3F)							    CGEQRF(3F)

```

### NAME[Toc][Back]

```     CGEQRF - compute a	QR factorization of a complex M-by-N matrix A
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

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

### PURPOSE[Toc][Back]

```     CGEQRF computes a QR factorization	of a complex M-by-N matrix A:  A = Q *
R.

```

### 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
above the diagonal	of the array contain the min(M,N)-by-N upper
trapezoidal matrix	R (R is	upper triangular if m >= n); the
elements below the	diagonal, with the array TAU, represent	the
unitary matrix Q as a product of min(m,n) 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/output)	COMPLEX	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,N).  For optimum
performance LWORK >= N*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(1) H(2) .	. . H(k), where	k = min(m,n).

Page 1

CGEQRF(3F)							    CGEQRF(3F)

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; v(i+1:m) is stored	on exit	in A(i+1:m,i), and tau in
TAU(i).
CGEQRF(3F)							    CGEQRF(3F)

```

### NAME[Toc][Back]

```     CGEQRF - compute a	QR factorization of a complex M-by-N matrix A
```

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDA, LWORK, M, N

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

### PURPOSE[Toc][Back]

```     CGEQRF computes a QR factorization	of a complex M-by-N matrix A:  A = Q *
R.

```

### 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
above the diagonal	of the array contain the min(M,N)-by-N upper
trapezoidal matrix	R (R is	upper triangular if m >= n); the
elements below the	diagonal, with the array TAU, represent	the
unitary matrix Q as a product of min(m,n) 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/output)	COMPLEX	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,N).  For optimum
performance LWORK >= N*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(1) H(2) .	. . H(k), where	k = min(m,n).

Page 1

CGEQRF(3F)							    CGEQRF(3F)

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; v(i+1:m) is stored	on exit	in A(i+1:m,i), 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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