disna - Man Page

subroutine ddisna (job, m, n, d, sep, info)
DDISNA
subroutine sdisna (job, m, n, d, sep, info)
SDISNA

DDISNA  

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.

Parameters

JOB

          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

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

N

          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

          D is 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

          SEP is 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

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 116 of file ddisna.f.

SDISNA  

Purpose:

 SDISNA 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) = 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

          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

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

N

          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

          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

          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

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 116 of file sdisna.f.