sdisna(3)

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 ma

trix. 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 eigen

vectors of the generalized symmetric definite eigenproblem.

ARGUMENTS

JOB (input) CHARACTER*1

Specifies for which problem the reciprocal condi

tion numbers should be computed:
= 'E': the eigenvectors of a symmetric/Hermitian

matrix;
= 'L': the left singular vectors of a general ma

trix;
= '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 re

ciprocal condition numbers of the vectors.

INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille

gal value.

LAPACK version 3.0 15 June 2000

SDISNA(3)