ZHBGST(3)                  MathKeisan LAPACK routine                 ZHBGST(3)



NAME
       ZHBGST  -  a complex Hermitian-definite banded generalized 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, * )

PURPOSE
       ZHBGST reduces a complex Hermitian-definite banded  generalized  eigen-
       problem   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 Hermitian 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 factorization 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 illegal value.



 LAPACK routine (version 3.1)    November 2006                       ZHBGST(3)