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DGBBRD(3F)							    DGBBRD(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DGBBRD(	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

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

PURPOSE    [Toc]    [Back]

     DGBBRD 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) DOUBLE PRECISION 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






DGBBRD(3F)							    DGBBRD(3F)



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

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

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

     Q	     (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE	PRECISION array, dimension (2*max(M,N))

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


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DGBBRD(	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

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

PURPOSE    [Toc]    [Back]

     DGBBRD 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) DOUBLE PRECISION 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






DGBBRD(3F)							    DGBBRD(3F)



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

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

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

     Q	     (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE	PRECISION array, dimension (2*max(M,N))

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


									PPPPaaaaggggeeee 2222
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