DDISNA(1) LAPACK routine (version 3.2) DDISNA(1)NAME
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 m-by-n 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 m-by-n matrix. The reciprocal con‐
dition number is the 'gap' between the corresponding eigenvalue or sin‐
gular value and the nearest other one.
The bound on the error, measured by angle in radians, in the I-th com‐
puted vector is given by
DLAMCH( 'E' ) * ( ANORM / SEP( I ) )
where ANORM = 2-norm(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 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (M) if JOB = 'E'
dimension (min(M,N)) if JOB = 'L' or 'R' The reciprocal condi‐
tion numbers of the vectors.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
LAPACK routine (version 3.2) November 2008 DDISNA(1)
