DDISNA(3f)

NAME
DDISNA - 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 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
       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 condition numbers of the vectors.

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