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NAME
     dsbgst - reduce a real symmetric-definite banded generalized
     eigenproblem  A*x  =  lambda*B*x  to  standard  form  C*y  =
     lambda*y,

SYNOPSIS
     SUBROUTINE DSBGST( VECT, UPLO, N,  KA,  KB,  AB,  LDAB,  BB,
               LDBB, X, LDX, WORK, INFO )

     CHARACTER UPLO, VECT

     INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N

     DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X(
               LDX, * )



     #include <sunperf.h>

     void dsbgst(char vect, char uplo, int n,  int  ka,  int  kb,
               double  *dab, int ldab, double *bb, int ldbb, dou-
               ble *dx, int ldx, int *info) ;

PURPOSE
     DSBGST reduces a real symmetric-definite banded  generalized
     eigenproblem   A*x  =  lambda*B*x   to  standard form  C*y =
     lambda*y, such that C has the same bandwidth as A.

     B must have been previously factorized as S**T*S by  DPBSTF,
     using  a split Cholesky factorization. A is overwritten by C
     = X**T*A*X, where X =  S**(-1)*Q  and  Q  is  an  orthogonal
     matrix chosen to preserve the bandwidth of A.


ARGUMENTS
     VECT      (input) CHARACTER*1
               = 'N':  do not form the transformation matrix X;
               = 'V':  form X.

     UPLO      (input) CHARACTER*1
               = 'U':  Upper triangle of A is stored;
               = 'L':  Lower triangle of A is stored.

     N         (input) INTEGER
               The order of the matrices A and B.  N >= 0.

     KA        (input) INTEGER
               The number of superdiagonals of the  matrix  A  if
               UPLO  = 'U', or the number of subdiagonals if UPLO
               = 'L'.  KA >= 0.

     KB        (input) INTEGER
               The number of superdiagonals of the  matrix  B  if
               UPLO  = 'U', or the number of subdiagonals if UPLO
               = 'L'.  KA >= KB >= 0.

     AB        (input/output) DOUBLE PRECISION  array,  dimension
               (LDAB,N)
               On entry, the upper or lower triangle of the  sym-
               metric  band  matrix  A,  stored in the first ka+1
               rows of the array.  The j-th column of A is stored
               in the j-th column of the array AB as follows:  if
               UPLO = 'U', AB(ka+1+i-j,j) = A(i,j)  for  max(1,j-
               ka)<=i<=j;  if UPLO = 'L', AB(1+i-j,j)    = A(i,j)
               for j<=i<=min(n,j+ka).

               On exit, the transformed matrix  X**T*A*X,  stored
               in the same format as A.

     LDAB      (input) INTEGER
               The leading dimension of the array  AB.   LDAB  >=
               KA+1.

     BB        (input) DOUBLE PRECISION array, dimension (LDBB,N)
               The banded factor S from the split  Cholesky  fac-
               torization  of B, as returned by DPBSTF, stored in
               the first KB+1 rows of the array.

     LDBB      (input) INTEGER
               The leading dimension of the array  BB.   LDBB  >=
               KB+1.

     X         (output) DOUBLE PRECISION array, dimension (LDX,N)
               If VECT = 'V', the n-by-n matrix  X.   If  VECT  =
               'N', the array X is not referenced.

     LDX       (input) INTEGER
               The leading dimension of  the  array  X.   LDX  >=
               max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

     WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
               (2*N)

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

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