zhbgst.f(3)

NAME
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 (characterVECT, characterUPLO, integerN, integerKA, integerKB, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

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.

Date:
    November 2011

Definition at line 165 of file zhbgst.f.

Author

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