Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  reduces  a  complex  Hermitian-definite banded generalized eigenproblem A*x =
       lambda*B*x to standard form C*y = lambda*y,

SYNOPSIS

       SUBROUTINE CHBGST( 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

           REAL           RWORK( * )

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

PURPOSE

       CHBGST 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 CPBSTF, 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 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 array, dimension (LDBB,N)
                The banded factor S from the split Cholesky factorization of
                B, as returned by CPBSTF, 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 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 array, dimension (N)

        RWORK   (workspace) REAL array, dimension (N)

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

 LAPACK routine (version 3.2.2)             April 2011                            CHBGST(3lapack)