dsvdch()

subroutine dsvdch	(	integer	N,
		double precision, dimension( * )	S,
		double precision, dimension( * )	E,
		double precision, dimension( * )	SVD,
		double precision	TOL,
		integer	INFO
	)

DSVDCH

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.

Parameters

[in]	N	N is INTEGER The dimension of the bidiagonal matrix B.
[in]	S	S is DOUBLE PRECISION array, dimension (N) The diagonal entries of the bidiagonal matrix B.
[in]	E	E is DOUBLE PRECISION array, dimension (N-1) The superdiagonal entries of the bidiagonal matrix B.
[in]	SVD	SVD is DOUBLE PRECISION array, dimension (N) The computed singular values to be checked.
[in]	TOL	TOL is DOUBLE PRECISION Error tolerance for checking, a multiplier of the machine precision.
[out]	INFO	INFO is 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.