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## zhbgv()

subroutine zhbgv | ( | character | jobz,
|  | character | uplo,
|  | integer | n,
|  | integer | ka,
|  | integer | kb,
|  | complex*16, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | complex*16, dimension( ldbb, * ) | bb,
|  | integer | ldbb,
|  | double precision, dimension( * ) | w,
|  | complex*16, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | complex*16, dimension( * ) | work,
|  | double precision, dimension( * ) | rwork,
|  | integer | info )

ZHBGV

Download ZHBGV + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
      !> of a complex generalized Hermitian-definite banded eigenproblem, of
      !> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
      !> and banded, and B is also positive definite.
      !>

Parameters

  [in]

  JOBZ

      !>          JOBZ is CHARACTER*1
      !>          = 'N':  Compute eigenvalues only;
      !>          = 'V':  Compute eigenvalues and eigenvectors.
      !>

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangles of A and B are stored;
      !>          = 'L':  Lower triangles of A and B are stored.
      !>

  [in]

  N

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

  [in]

  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.
      !>

  [in]

  KB

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

  [in,out]

  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 contents of AB are destroyed.
      !>

  [in]

  LDAB

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

  [in,out]

  BB

      !>          BB is COMPLEX*16 array, dimension (LDBB, N)
      !>          On entry, the upper or lower triangle of the Hermitian band
      !>          matrix B, stored in the first kb+1 rows of the array.  The
      !>          j-th column of B is stored in the j-th column of the array BB
      !>          as follows:
      !>          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
      !>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
      !>
      !>          On exit, the factor S from the split Cholesky factorization
      !>          B = S**H*S, as returned by ZPBSTF.
      !>

  [in]

  LDBB

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

  [out]

  W

      !>          W is DOUBLE PRECISION array, dimension (N)
      !>          If INFO = 0, the eigenvalues in ascending order.
      !>

  [out]

  Z

      !>          Z is COMPLEX*16 array, dimension (LDZ, N)
      !>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
      !>          eigenvectors, with the i-th column of Z holding the
      !>          eigenvector associated with W(i). The eigenvectors are
      !>          normalized so that Z**H*B*Z = I.
      !>          If JOBZ = 'N', then Z is not referenced.
      !>

  [in]

  LDZ

      !>          LDZ is INTEGER
      !>          The leading dimension of the array Z.  LDZ >= 1, and if
      !>          JOBZ = 'V', LDZ >= N.
      !>

  [out]

  WORK

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

  [out]

  RWORK

      !>          RWORK is DOUBLE PRECISION array, dimension (3*N)
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value
      !>          > 0:  if INFO = i, and i is:
      !>             <= N:  the algorithm failed to converge:
      !>                    i off-diagonal elements of an intermediate
      !>                    tridiagonal form did not converge to zero;
      !>             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
      !>                    returned INFO = i: B is not positive definite.
      !>                    The factorization of B could not be completed and
      !>                    no eigenvalues or eigenvectors were computed.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.