DISNA - 5.2 English - 68552

DISNA computes the reciprocal condition numbers for the eigenvectors

of a real symmetric or complex Hermitian matrix.

Purpose:

  DISNA 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

         SLAMCH( 'E') * ( ANORM / SEP( I))

  where ANORM = 2-norm(A) = fla_max( abs( D(j))).  SEP(I) is not allowed
  to be smaller than SLAMCH( 'E')*ANORM in order to limit the size of
  the error bound.

  SDISNA may also be used to compute error bounds for eigenvectors of
  the generalized symmetric definite eigenproblem.

Parameters:

• JOB – [in]

  JOB is 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 – [in]

  M is INTEGER

  The number of rows of the matrix. M >= 0.

• N – [in]

  N is INTEGER

  If JOB = ‘L’ or ‘R’, the number of columns of the matrix, in which case N >= 0. Ignored if JOB = ‘E’.

• D – [in]

  D is REAL 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 – [out]

  SEP is REAL array, dimension (M) if JOB = ‘E’ dimension (min(M,N)) if JOB = ‘L’ or ‘R’

  The reciprocal condition numbers of the vectors.

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit.

  < 0: if INFO = -i, the i-th argument had an illegal value.