SSTEVX(3)      LAPACK routine of NEC Numeric Library Collection      SSTEVX(3)



NAME
       SSTEVX

SYNOPSIS
       SUBROUTINE SSTEVX (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W,
           Z, LDZ, WORK, IWORK, IFAIL, INFO)



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.




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

           RANGE     (input)
                     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         (input)
                     N is INTEGER
                     The order of the matrix.  N >= 0.

           D         (input/output)
                     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         (input/output)
                     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        (input)
                     VL is REAL

           VU        (input)
                     VU is REAL
                     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        (input)
                     IL is INTEGER

           IU        (input)
                     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    (input)
                     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 "Computing Small Singular Values of Bidiagonal Matrices
                     with Guaranteed High Relative Accuracy," by Demmel and
                     Kahan, LAPACK Working Note #3.

           M         (output)
                     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         (output)
                     W is REAL array, dimension (N)
                     The first M elements contain the selected eigenvalues in
                     ascending order.

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

           WORK      (output)
                     WORK is REAL array, dimension (5*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (5*N)

           IFAIL     (output)
                     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      (output)
                     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.



LAPACK routine                  31 October 2017                      SSTEVX(3)