Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  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
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.

LAPACK routine (version 3.2)               April 2011                            DDISNA(3lapack)