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NAME
     zhbgst - reduce a complex Hermitian-definite banded general-
     ized  eigenproblem  A*x  = lambda*B*x to standard form C*y =
     lambda*y,

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

     CHARACTER UPLO, VECT

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

     DOUBLE PRECISION RWORK( * )

     COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X(  LDX,
               * )



     #include <sunperf.h>

     void zhbgst(char vect, char uplo, int n,  int  ka,  int  kb,
               doublecomplex  *zab,  int ldab, doublecomplex *bb,
               int ldbb, doublecomplex *zx, int ldx, int *info) ;

PURPOSE
     ZHBGST reduces a complex Hermitian-definite banded  general-
     ized 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**H*S by  ZPBSTF,
     using  a split Cholesky factorization. A is overwritten by C
     = X**H*A*X, where X = S**(-1)*Q and Q is  a  unitary  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)   COMPLEX*16    array,    dimension
               (LDAB,N)
               On entry, the upper or lower triangle of the  Her-
               mitian  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**H*A*X,  stored
               in the same format as A.

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

     BB        (input) COMPLEX*16 array, dimension (LDBB,N)
               The banded factor S from the split  Cholesky  fac-
               torization  of B, as returned by ZPBSTF, 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) COMPLEX*16 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) COMPLEX*16 array, dimension (N)

     RWORK     (workspace) DOUBLE PRECISION array, dimension (N)

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

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