
DDISNA(l) ) DDISNA(l)
NAME
DDISNA  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 mbyn
matrix
SYNOPSIS
SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO )
CHARACTER JOB
INTEGER INFO, M, N
DOUBLE PRECISION D( * ), SEP( * )
PURPOSE
DDISNA 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 mbyn
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 Ith computed vector is given
by
DLAMCH( 'E' ) * ( ANORM / SEP( I ) )
where ANORM = 2norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed to be smaller than
DLAMCH( 'E' )*ANORM in order to limit the size of the error bound.
DDISNA may also be used to compute error bounds for eigenvectors of the generalized sym
metric 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) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
dimension (min(M,N)) if JOB = 'L' or 'R' The eigenvalues (if JOB = 'E') or singu
lar values (if JOB = order. If singular values, they must be nonnegative.
SEP (output) DOUBLE PRECISION 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 ith argument had an illegal value.
LAPACK version 3.0 15 June 2000 DDISNA(l) 
