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man pages->IRIX man pages -> complib/sgbbrd (3)
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Contents

SGBBRD(3F)							    SGBBRD(3F)

NAME[Toc][Back]

SGBBRD - reduce a real general m-by-n band	matrix A to upper bidiagonal
form B by an orthogonal transformation

SYNOPSIS[Toc][Back]

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

CHARACTER	VECT

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

REAL		AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), PT(	LDPT,
* ), Q(	LDQ, * ), WORK(	* )

PURPOSE[Toc][Back]

SGBBRD reduces a real general m-by-n band matrix A	to upper bidiagonal
form B by an orthogonal 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) REAL 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,jku)<=i<=min(m,j+kl).
On exit, A is overwritten by	values
generated during the reduction.

Page 1

SGBBRD(3F)							    SGBBRD(3F)

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) REAL array, dimension (LDQ,M)
If	VECT = 'Q' or 'B', the m-by-m orthogonal 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) REAL array, dimension (LDPT,N)
If	VECT = 'P' or 'B', the n-by-n orthogonal 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) REAL 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) REAL array, dimension (2*max(M,N))

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

NAME[Toc][Back]

SGBBRD - reduce a real general m-by-n band	matrix A to upper bidiagonal
form B by an orthogonal transformation

SYNOPSIS[Toc][Back]

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

CHARACTER	VECT

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

REAL		AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), PT(	LDPT,
* ), Q(	LDQ, * ), WORK(	* )

PURPOSE[Toc][Back]

SGBBRD reduces a real general m-by-n band matrix A	to upper bidiagonal
form B by an orthogonal 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) REAL 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,jku)<=i<=min(m,j+kl).
On exit, A is overwritten by	values
generated during the reduction.

Page 1

SGBBRD(3F)							    SGBBRD(3F)

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) REAL array, dimension (LDQ,M)
If	VECT = 'Q' or 'B', the m-by-m orthogonal 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) REAL array, dimension (LDPT,N)
If	VECT = 'P' or 'B', the n-by-n orthogonal 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) REAL 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) REAL array, dimension (2*max(M,N))

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

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