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dgbbrd(3P)		    Sun Performance Library		    dgbbrd(3P)

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

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

       CHARACTER * 1 VECT
       INTEGER M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
       DOUBLE  PRECISION  AB(LDAB,*),  D(*),   E(*),   Q(LDQ,*),   PT(LDPT,*),
       C(LDC,*), WORK(*)

       SUBROUTINE DGBBRD_64(VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ,
	     PT, LDPT, C, LDC, WORK, INFO)

       CHARACTER * 1 VECT
       INTEGER*8 M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
       DOUBLE	PRECISION   AB(LDAB,*),	  D(*),	 E(*),	Q(LDQ,*),  PT(LDPT,*),
       C(LDC,*), WORK(*)

   F95 INTERFACE
       SUBROUTINE GBBRD(VECT, M, [N], [NCC], KL, KU, AB, [LDAB], D, E, Q,
	      [LDQ], PT, [LDPT], C, [LDC], [WORK], [INFO])

       CHARACTER(LEN=1) :: VECT
       INTEGER :: M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
       REAL(8), DIMENSION(:) :: D, E, WORK
       REAL(8), DIMENSION(:,:) :: AB, Q, PT, C

       SUBROUTINE GBBRD_64(VECT, M, [N], [NCC], KL, KU, AB, [LDAB], D, E,
	      Q, [LDQ], PT, [LDPT], C, [LDC], [WORK], [INFO])

       CHARACTER(LEN=1) :: VECT
       INTEGER(8) :: M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
       REAL(8), DIMENSION(:) :: D, E, WORK
       REAL(8), DIMENSION(:,:) :: AB, Q, PT, C

   C INTERFACE
       #include <sunperf.h>

       void dgbbrd(char vect, int m, int n, int ncc, int kl,  int  ku,	double
		 *ab, int ldab, double *d, double *e, double *q, int ldq, dou‐
		 ble *pt, int ldpt, double *c, int ldc, int *info);

       void dgbbrd_64(char vect, long m, long n, long ncc, long kl,  long  ku,
		 double	 *ab, long ldab, double *d, double *e, double *q, long
		 ldq, double *pt, long ldpt, double *c, long ldc, long *info);

PURPOSE
       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
       VECT (input)
		 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) The number of rows of the matrix A.  M >= 0.

       N (input) The number of columns of the matrix A.	 N >= 0.

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

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

       KU (input)
		 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,j-ku)<=i<=min(m,j+kl).   On
		 exit,	A is overwritten by values generated during the reduc‐
		 tion.

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

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

       E (output)
		 DOUBLE PRECISION array, dimension(min(M,N)-1) The superdiago‐
		 nal 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)
		 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)
		 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)
		 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)
		 = 0:  successful exit.
		 < 0:  if INFO = -i, the i-th argument had an illegal value.

				  6 Mar 2009			    dgbbrd(3P)
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