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 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 = 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 version 3.0						   15 June 2000 							 DDISNA(l)