SRC/zhbgst.f(3)            Library Functions Manual            SRC/zhbgst.f(3)

NAME
       SRC/zhbgst.f

SYNOPSIS
   Functions/Subroutines
       subroutine zhbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx,
           work, rwork, info)
           ZHBGST

Function/Subroutine Documentation
   subroutine zhbgst (character vect, character uplo, integer n, integer ka,
       integer kb, complex*16, dimension( ldab, * ) ab, integer ldab,
       complex*16, dimension( ldbb, * ) bb, integer ldbb, complex*16,
       dimension( ldx, * ) x, integer ldx, complex*16, dimension( * ) work,
       double precision, dimension( * ) rwork, integer info)
       ZHBGST

       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.
           !>

       Parameters
           VECT

           !>          VECT is CHARACTER*1
           !>          = 'N':  do not form the transformation matrix X;
           !>          = 'V':  form X.
           !>

           UPLO

           !>          UPLO is CHARACTER*1
           !>          = 'U':  Upper triangle of A is stored;
           !>          = 'L':  Lower triangle of A is stored.
           !>

           N

           !>          N is INTEGER
           !>          The order of the matrices A and B.  N >= 0.
           !>

           KA

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

           KB

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

           AB

           !>          AB is 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

           !>          LDAB is INTEGER
           !>          The leading dimension of the array AB.  LDAB >= KA+1.
           !>

           BB

           !>          BB is 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

           !>          LDBB is INTEGER
           !>          The leading dimension of the array BB.  LDBB >= KB+1.
           !>

           X

           !>          X is 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

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

           WORK

           !>          WORK is COMPLEX*16 array, dimension (N)
           !>

           RWORK

           !>          RWORK is DOUBLE PRECISION array, dimension (N)
           !>

           INFO

           !>          INFO is INTEGER
           !>          = 0:  successful exit
           !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 163 of file zhbgst.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/zhbgst.f(3)