LAPACK

NAME¶

disna - disna: eig condition numbers

SYNOPSIS¶

Functions¶

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

Detailed Description¶

Function Documentation¶

subroutine ddisna (character job, integer m, integer n, double precision, dimension( * ) d, double precision, dimension( * ) sep, integer info)¶

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 is INTEGER


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



          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 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.

subroutine sdisna (character job, integer m, integer n, real, dimension( * ) d, real, dimension( * ) sep, integer info)¶

SDISNA