sdisna(3F)

NAME
     SDISNA - compute the reciprocal condition numbers for the eigenvectors of
     a real symmetric or complex Hermitian matrix or for the left or right
     singular vectors of a general m-by-n matrix

SYNOPSIS
     SUBROUTINE SDISNA( JOB, M, N, D, SEP, INFO )

         CHARACTER      JOB

         INTEGER        INFO, M, N

         REAL           D( * ), SEP( * )

PURPOSE
     SDISNA computes the reciprocal condition numbers for the eigenvectors of
     a real symmetric or complex Hermitian matrix or for the left or right
     singular vectors of a general m-by-n matrix. The reciprocal condition
     number is the 'gap' between the corresponding eigenvalue or singular
     value and the nearest other one.

     The bound on the error, measured by angle in radians, in the I-th
     computed vector is given by

            SLAMCH( 'E' ) * ( ANORM / SEP( I ) )

     where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed to
     be smaller than SLAMCH( 'E' )*ANORM in order to limit the size of the
     error bound.

     SDISNA may also be used to compute error bounds for eigenvectors of the
     generalized symmetric definite eigenproblem.


ARGUMENTS
     JOB     (input) CHARACTER*1
             Specifies for which problem the reciprocal condition numbers
             should be computed:
             = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
             = 'L':  the left singular vectors of a general matrix;
             = 'R':  the right singular vectors of a general matrix.

     M       (input) INTEGER
             The number of rows of the matrix. M >= 0.

     N       (input) INTEGER
             If JOB = 'L' or 'R', the number of columns of the matrix, in
             which case N >= 0. Ignored if JOB = 'E'.

     D       (input) REAL array, dimension (M) if JOB = 'E'
             dimension (min(M,N)) if JOB = 'L' or 'R' The eigenvalues (if JOB
             = 'E') or singular values (if JOB = order. If singular values,
             they must be non-negative.

     SEP     (output) REAL array, dimension (M) if JOB = 'E'
             dimension (min(M,N)) if JOB = 'L' or 'R' The reciprocal condition
             numbers of the vectors.

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.