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

```
CGBBRD(3F)							    CGBBRD(3F)

```

### NAME[Toc][Back]

```     CGBBRD - reduce a complex general m-by-n band matrix A to real upper
bidiagonal	form B by a unitary transformation
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CGBBRD(	VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
LDPT, C, LDC, WORK, RWORK, INFO	)

CHARACTER	VECT

INTEGER	INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

REAL		D( * ),	E( * ),	RWORK( * )

COMPLEX	AB( LDAB, * ), C( LDC, * ), PT(	LDPT, *	), Q( LDQ, *
), WORK( * )
```

### PURPOSE[Toc][Back]

```     CGBBRD reduces a complex general m-by-n band matrix A to real upper
bidiagonal	form B by a unitary transformation: Q' * A * P = B.

The routine computes B, and optionally forms Q or P', or computes Q'*C
for a given matrix	C.

```

### ARGUMENTS[Toc][Back]

```     VECT    (input) CHARACTER*1
Specifies whether or not the matrices Q and P' are	to be formed.
= 'N': do not form	Q or P';
= 'Q': form Q only;
= 'P': form P' only;
= 'B': form both.

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.

NCC     (input) INTEGER
The number	of columns of the matrix C.  NCC >= 0.

KL	     (input) INTEGER
The number	of subdiagonals	of the matrix A. KL >= 0.

KU	     (input) INTEGER
The number	of superdiagonals of the matrix	A. KU >= 0.

AB	     (input/output) COMPLEX array, dimension (LDAB,N)
On	entry, the m-by-n band matrix A, stored	in rows	1 to KL+KU+1.
The j-th column of	A is stored in the j-th	column of the array AB
as	follows:  AB(ku+1+i-j,j) = A(i,j) for max(1,j

Page 1

CGBBRD(3F)							    CGBBRD(3F)

ku)<=i<=min(m,j+kl).  On exit, A is overwritten by	values
generated during the reduction.

LDAB    (input) INTEGER
The leading dimension of the array	A. LDAB	>= KL+KU+1.

D	     (output) REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.

E	     (output) REAL array, dimension (min(M,N)-1)
The superdiagonal elements	of the bidiagonal matrix B.

Q	     (output) COMPLEX array, dimension (LDQ,M)
If	VECT = 'Q' or 'B', the m-by-m unitary matrix Q.	 If VECT = 'N'
or	'P', the array Q is not	referenced.

LDQ     (input) INTEGER
The leading dimension of the array	Q.  LDQ	>= max(1,M) if VECT =
'Q' or 'B'; LDQ >=	1 otherwise.

PT	     (output) COMPLEX array, dimension (LDPT,N)
If	VECT = 'P' or 'B', the n-by-n unitary matrix P'.  If VECT =
'N' or 'Q', the array PT is not referenced.

LDPT    (input) INTEGER
The leading dimension of the array	PT.  LDPT >= max(1,N) if VECT
= 'P' or 'B'; LDPT	>= 1 otherwise.

C	     (input/output) COMPLEX array, dimension (LDC,NCC)
On	entry, an m-by-ncc matrix C.  On exit, C is overwritten	by
Q'*C.  C is not referenced	if NCC = 0.

LDC     (input) INTEGER
The leading dimension of the array	C.  LDC	>= max(1,M) if NCC >
0;	LDC >= 1 if NCC	= 0.

WORK    (workspace) COMPLEX array,	dimension (max(M,N))

RWORK   (workspace) REAL array, dimension (max(M,N))

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
CGBBRD(3F)							    CGBBRD(3F)

```

### NAME[Toc][Back]

```     CGBBRD - reduce a complex general m-by-n band matrix A to real upper
bidiagonal	form B by a unitary transformation
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CGBBRD(	VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
LDPT, C, LDC, WORK, RWORK, INFO	)

CHARACTER	VECT

INTEGER	INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

REAL		D( * ),	E( * ),	RWORK( * )

COMPLEX	AB( LDAB, * ), C( LDC, * ), PT(	LDPT, *	), Q( LDQ, *
), WORK( * )
```

### PURPOSE[Toc][Back]

```     CGBBRD reduces a complex general m-by-n band matrix A to real upper
bidiagonal	form B by a unitary transformation: Q' * A * P = B.

The routine computes B, and optionally forms Q or P', or computes Q'*C
for a given matrix	C.

```

### ARGUMENTS[Toc][Back]

```     VECT    (input) CHARACTER*1
Specifies whether or not the matrices Q and P' are	to be formed.
= 'N': do not form	Q or P';
= 'Q': form Q only;
= 'P': form P' only;
= 'B': form both.

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.

NCC     (input) INTEGER
The number	of columns of the matrix C.  NCC >= 0.

KL	     (input) INTEGER
The number	of subdiagonals	of the matrix A. KL >= 0.

KU	     (input) INTEGER
The number	of superdiagonals of the matrix	A. KU >= 0.

AB	     (input/output) COMPLEX array, dimension (LDAB,N)
On	entry, the m-by-n band matrix A, stored	in rows	1 to KL+KU+1.
The j-th column of	A is stored in the j-th	column of the array AB
as	follows:  AB(ku+1+i-j,j) = A(i,j) for max(1,j

Page 1

CGBBRD(3F)							    CGBBRD(3F)

ku)<=i<=min(m,j+kl).  On exit, A is overwritten by	values
generated during the reduction.

LDAB    (input) INTEGER
The leading dimension of the array	A. LDAB	>= KL+KU+1.

D	     (output) REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.

E	     (output) REAL array, dimension (min(M,N)-1)
The superdiagonal elements	of the bidiagonal matrix B.

Q	     (output) COMPLEX array, dimension (LDQ,M)
If	VECT = 'Q' or 'B', the m-by-m unitary matrix Q.	 If VECT = 'N'
or	'P', the array Q is not	referenced.

LDQ     (input) INTEGER
The leading dimension of the array	Q.  LDQ	>= max(1,M) if VECT =
'Q' or 'B'; LDQ >=	1 otherwise.

PT	     (output) COMPLEX array, dimension (LDPT,N)
If	VECT = 'P' or 'B', the n-by-n unitary matrix P'.  If VECT =
'N' or 'Q', the array PT is not referenced.

LDPT    (input) INTEGER
The leading dimension of the array	PT.  LDPT >= max(1,N) if VECT
= 'P' or 'B'; LDPT	>= 1 otherwise.

C	     (input/output) COMPLEX array, dimension (LDC,NCC)
On	entry, an m-by-ncc matrix C.  On exit, C is overwritten	by
Q'*C.  C is not referenced	if NCC = 0.

LDC     (input) INTEGER
The leading dimension of the array	C.  LDC	>= max(1,M) if NCC >
0;	LDC >= 1 if NCC	= 0.

WORK    (workspace) COMPLEX array,	dimension (max(M,N))

RWORK   (workspace) REAL array, dimension (max(M,N))

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.

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