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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 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 = order. If singular val‐
	       ues, 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 version 3.0		 15 June 2000			     DDISNA(l)
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