SDISNA - 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 gen
eral m-by-n matrix
SYNOPSIS
SUBROUTINE SDISNA( JOB, M, N, D, SEP, INFO )
CHARACTER JOB
INTEGER INFO, M, N
REAL D( * ), SEP( * )
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 gen
eral 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 eigen
vectors of the generalized symmetric definite eigenprob
lem.
ARGUMENTS
JOB (input) CHARACTER*1
Specifies for which problem the reciprocal condi
tion 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 =
D (input) 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 = order. If singular values, they must be non-
negative.
SEP (output) REAL 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 ille
gal value.
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