NAME

       sdisna.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sdisna (JOB, M, N, D, SEP, INFO)
           SDISNA

Function/Subroutine Documentation

   subroutine sdisna (character JOB, integer M, integer N, real, dimension( * ) D, real,
       dimension( * ) SEP, integer INFO)
       SDISNA

       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.

       Parameters:
           JOB

                     JOB is 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

                     M is INTEGER
                     The number of rows of the matrix. M >= 0.

           N

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

           D

                     D is 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 =
                     'L' or 'R') of the matrix, in either increasing or decreasing
                     order. If singular values, they must be non-negative.

           SEP

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

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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