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 = 'L' or 'R') of the matrix, in either increasing or decreasing 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.