ZHBGST (3lapack)

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, * )

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.