zhpevx.f(3)

NAME
zhpevx.f -

SYNOPSIS

  Functions/Subroutines
subroutine zhpevx (JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

  subroutine zhpevx (characterJOBZ, characterRANGE, characterUPLO, integerN, complex*16, dimension( * )AP, double precisionVL, double precisionVU, integerIL, integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

     ZHPEVX computes selected eigenvalues and, optionally, eigenvectors
     of a complex Hermitian matrix A in packed storage.
     Eigenvalues/vectors can be selected by specifying either a range of
     values or a range of indices for the desired eigenvalues.

Parameters:
    JOBZ

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

    RANGE

              RANGE is CHARACTER*1
              = 'A': all eigenvalues will be found;
              = 'V': all eigenvalues in the half-open interval (VL,VU]
                     will be found;
              = 'I': the IL-th through IU-th eigenvalues will be found.

    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 matrix A.  N >= 0.

    AP

              AP is COMPLEX*16 array, dimension (N*(N+1)/2)
              On entry, the upper or lower triangle of the Hermitian matrix
              A, packed columnwise in a linear array.  The j-th column of A
              is stored in the array AP as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
              On exit, AP is overwritten by values generated during the
              reduction to tridiagonal form.  If UPLO = 'U', the diagonal
              and first superdiagonal of the tridiagonal matrix T overwrite
              the corresponding elements of A, and if UPLO = 'L', the
              diagonal and first subdiagonal of T overwrite the
              corresponding elements of A.

    VL

              VL is DOUBLE PRECISION

    VU

              VU is DOUBLE PRECISION
              If RANGE='V', the lower and upper bounds of the interval to
              be searched for eigenvalues. VL < VU.
              Not referenced if RANGE = 'A' or 'I'.

    IL

              IL is INTEGER

    IU

              IU is INTEGER
              If RANGE='I', the indices (in ascending order) of the
              smallest and largest eigenvalues to be returned.
              1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
              Not referenced if RANGE = 'A' or 'V'.

    ABSTOL

              ABSTOL is DOUBLE PRECISION
              The absolute error tolerance for the eigenvalues.
              An approximate eigenvalue is accepted as converged
              when it is determined to lie in an interval [a,b]
              of width less than or equal to
                      ABSTOL + EPS *   max( |a|,|b| ) ,
              where EPS is the machine precision.  If ABSTOL is less than
              or equal to zero, then  EPS*|T|  will be used in its place,
              where |T| is the 1-norm of the tridiagonal matrix obtained
              by reducing AP to tridiagonal form.
              Eigenvalues will be computed most accurately when ABSTOL is
              set to twice the underflow threshold 2*DLAMCH('S'), not zero.
              If this routine returns with INFO>0, indicating that some
              eigenvectors did not converge, try setting ABSTOL to
              2*DLAMCH('S').
              See "Computing Small Singular Values of Bidiagonal Matrices
              with Guaranteed High Relative Accuracy," by Demmel and
              Kahan, LAPACK Working Note #3.

    M

              M is INTEGER
              The total number of eigenvalues found.  0 <= M <= N.
              If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

    W

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

    Z

              Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
              If JOBZ = 'V', then if INFO = 0, the first M columns of Z
              contain the orthonormal eigenvectors of the matrix A
              corresponding to the selected eigenvalues, with the i-th
              column of Z holding the eigenvector associated with W(i).
              If an eigenvector fails to converge, then that column of Z
              contains the latest approximation to the eigenvector, and
              the index of the eigenvector is returned in IFAIL.
              If JOBZ = 'N', then Z is not referenced.
              Note: the user must ensure that at least max(1,M) columns are
              supplied in the array Z; if RANGE = 'V', the exact value of M
              is not known in advance and an upper bound must be used.

    LDZ

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

    WORK

              WORK is COMPLEX*16 array, dimension (2*N)

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (7*N)

    IWORK

              IWORK is INTEGER array, dimension (5*N)

    IFAIL

              IFAIL is INTEGER array, dimension (N)
              If JOBZ = 'V', then if INFO = 0, the first M elements of
              IFAIL are zero.  If INFO > 0, then IFAIL contains the
              indices of the eigenvectors that failed to converge.
              If JOBZ = 'N', then IFAIL is not referenced.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, then i eigenvectors failed to converge.
                    Their indices are stored in array IFAIL.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 232 of file zhpevx.f.

Author

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