DSVDCH
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
DSVDCH checks to see if SVD(1) ,..., SVD(N) are accurate singular
values of the bidiagonal matrix B with diagonal entries
S(1) ,..., S(N) and superdiagonal entries E(1) ,..., E(N-1)).
It does this by expanding each SVD(I) into an interval
[SVD(I) * (1-EPS) , SVD(I) * (1+EPS)], merging overlapping intervals
if any, and using Sturm sequences to count and verify whether each
resulting interval has the correct number of singular values (using
DSVDCT). Here EPS=TOL*MAX(N/10,1)*MAZHEP, where MACHEP is the
machine precision. The routine assumes the singular values are sorted
with SVD(1) the largest and SVD(N) smallest. If each interval
contains the correct number of singular values, INFO = 0 is returned,
otherwise INFO is the index of the first singular value in the first
bad interval.
values of the bidiagonal matrix B with diagonal entries
S(1) ,..., S(N) and superdiagonal entries E(1) ,..., E(N-1)).
It does this by expanding each SVD(I) into an interval
[SVD(I) * (1-EPS) , SVD(I) * (1+EPS)], merging overlapping intervals
if any, and using Sturm sequences to count and verify whether each
resulting interval has the correct number of singular values (using
DSVDCT). Here EPS=TOL*MAX(N/10,1)*MAZHEP, where MACHEP is the
machine precision. The routine assumes the singular values are sorted
with SVD(1) the largest and SVD(N) smallest. If each interval
contains the correct number of singular values, INFO = 0 is returned,
otherwise INFO is the index of the first singular value in the first
bad interval.
Arguments
| N |
(input) INTEGER
The dimension of the bidiagonal matrix B.
|
| S |
(input) DOUBLE PRECISION array, dimension (N)
The diagonal entries of the bidiagonal matrix B.
|
| E |
(input) DOUBLE PRECISION array, dimension (N-1)
The superdiagonal entries of the bidiagonal matrix B.
|
| SVD |
(input) DOUBLE PRECISION array, dimension (N)
The computed singular values to be checked.
|
| TOL |
(input) DOUBLE PRECISION
Error tolerance for checking, a multiplier of the
machine precision. |
| INFO |
(output) INTEGER
=0 if the singular values are all correct (to within
1 +- TOL*MAZHEPS) >0 if the interval containing the INFO-th singular value contains the incorrect number of singular values. |