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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 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( * )



     #include <sunperf.h>

     void dgbbrd(char vect, int m, int n, int ncc,
                int kl, int ku, double *dab, int ldab, double *d,
               double  *e,  double  *q,  int ldq, double *pt, int
               ldpt, double *dc, int ldc,
                int *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) 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,j-
               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)   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 other-
               wise.

     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 ille-
               gal value.

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