zhbgvd.f(3)

NAME
zhbgvd.f -

SYNOPSIS

  Functions/Subroutines
subroutine zhbgvd (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHBGST

Function/Subroutine Documentation

  subroutine zhbgvd (characterJOBZ, characterUPLO, integerN, integerKA, integerKB, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

ZHBGST

Purpose:

     ZHBGVD 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.  If eigenvectors are
     desired, it uses a divide and conquer algorithm.
     The divide and conquer algorithm makes very mild assumptions about
     floating point arithmetic. It will work on machines with a guard
     digit in add/subtract, or on those binary machines without guard
     digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
     Cray-2. It could conceivably fail on hexadecimal or decimal machines
     without guard digits, but we know of none.

Parameters:
    JOBZ

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

    UPLO

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

    LDAB

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

    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.

    LDBB

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

    W

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

    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.

    LDZ

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

    WORK

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO=0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If N <= 1,               LWORK >= 1.
              If JOBZ = 'N' and N > 1, LWORK >= N.
              If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal sizes of the WORK, RWORK and
              IWORK arrays, returns these values as the first entries of
              the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
              On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.

    LRWORK

              LRWORK is INTEGER
              The dimension of array RWORK.
              If N <= 1,               LRWORK >= 1.
              If JOBZ = 'N' and N > 1, LRWORK >= N.
              If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
              If LRWORK = -1, then a workspace query is assumed; the
              routine only calculates the optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    IWORK

              IWORK is INTEGER array, dimension (MAX(1,LIWORK))
              On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.

    LIWORK

              LIWORK is INTEGER
              The dimension of array IWORK.
              If JOBZ = 'N' or N <= 1, LIWORK >= 1.
              If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
              If LIWORK = -1, then a workspace query is assumed; the
              routine only calculates the optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    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.

Date:
    November 2011

Contributors:
    Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 251 of file zhbgvd.f.

Author

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