Contents


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, double *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 reduction.

     LDAB (input)
               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)
               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 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)
               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 ille-
               gal value.