zhbgst(3S)

NAME
     ZHBGST - reduce 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, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZHBGST reduces a complex Hermitian-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**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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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