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NAME

       dstevx.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dstevx (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
           IWORK, IFAIL, INFO)
            DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for OTHER matrices

Function/Subroutine Documentation

   subroutine dstevx (characterJOBZ, characterRANGE, integerN, double precision, dimension( * )D,
       double precision, dimension( * )E, double precisionVL, double precisionVU, integerIL,
       integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, double
       precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK,
       integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)
        DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       OTHER matrices

       Purpose:

            DSTEVX 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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.

                     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)
                     The first M elements contain the selected eigenvalues in
                     ascending order.

           Z

                     Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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.

       Date:
           November 2011

       Definition at line 220 of file dstevx.f.

Author

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