SRC/sstevx.f(3)

NAME
SRC/sstevx.f

SYNOPSIS

  Functions/Subroutines
subroutine sstevx (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)
SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

  subroutine sstevx (character jobz, character range, integer n, real, dimension( * ) d, real, dimension( * ) e, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

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

Purpose:

    !>
    !> SSTEVX computes selected eigenvalues and, optionally, eigenvectors
    !> of a real symmetric tridiagonal matrix A.  Eigenvalues and
    !> eigenvectors 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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix.  N >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          On entry, the n diagonal elements of the tridiagonal matrix
    !>          A.
    !>          On exit, D may be multiplied by a constant factor chosen
    !>          to avoid over/underflow in computing the eigenvalues.
    !>

    E

    !>          E is REAL array, dimension (max(1,N-1))
    !>          On entry, the (n-1) subdiagonal elements of the tridiagonal
    !>          matrix A in elements 1 to N-1 of E.
    !>          On exit, E may be multiplied by a constant factor chosen
    !>          to avoid over/underflow in computing the eigenvalues.
    !>

    VL

    !>          VL is REAL
    !>          If RANGE='V', the lower bound of the interval to
    !>          be searched for eigenvalues. VL < VU.
    !>          Not referenced if RANGE = 'A' or 'I'.
    !>

    VU

    !>          VU is REAL
    !>          If RANGE='V', the upper bound of the interval to
    !>          be searched for eigenvalues. VL < VU.
    !>          Not referenced if RANGE = 'A' or 'I'.
    !>

    IL

    !>          IL is INTEGER
    !>          If RANGE='I', the index of the
    !>          smallest eigenvalue 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'.
    !>

    IU

    !>          IU is INTEGER
    !>          If RANGE='I', the index of the
    !>          largest eigenvalue 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 REAL
    !>          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.
    !>
    !>          Eigenvalues will be computed most accurately when ABSTOL is
    !>          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
    !>          If this routine returns with INFO>0, indicating that some
    !>          eigenvectors did not converge, try setting ABSTOL to
    !>          2*SLAMCH('S').
    !>
    !>          See  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 REAL array, dimension (N)
    !>          The first M elements contain the selected eigenvalues in
    !>          ascending order.
    !>

    Z

    !>          Z is REAL 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 (INFO > 0), 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 REAL array, dimension (5*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.

Definition at line 225 of file sstevx.f.

Author

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