DDISNA (3lapack)

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.