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.

Definition at line 96 of file dsvdch.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
      DOUBLE PRECISION   TOL
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   E( * ), S( * ), SVD( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      parameter( one = 1.0d0 )
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            BPNT, COUNT, NUML, NUMU, TPNT
      DOUBLE PRECISION   EPS, LOWER, OVFL, TUPPR, UNFL, UNFLEP, UPPER
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           dlamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           dsvdct
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, sqrt
*     ..
*     .. Executable Statements ..
*
*     Get machine constants
*
      info = 0
      IF( n.LE.0 )
     $   RETURN
      unfl = dlamch( 'Safe minimum' )
      ovfl = dlamch( 'Overflow' )
      eps = dlamch( 'Epsilon' )*dlamch( 'Base' )
*
*     UNFLEP is chosen so that when an eigenvalue is multiplied by the
*     scale factor sqrt(OVFL)*sqrt(sqrt(UNFL))/MX in DSVDCT, it exceeds
*     sqrt(UNFL), which is the lower limit for DSVDCT.
*
      unflep = ( sqrt( sqrt( unfl ) ) / sqrt( ovfl ) )*svd( 1 ) +
     $         unfl / eps
*
*     The value of EPS works best when TOL .GE. 10.
*
      eps = tol*max( n / 10, 1 )*eps
*
*     TPNT points to singular value at right endpoint of interval
*     BPNT points to singular value at left  endpoint of interval
*
      tpnt = 1
      bpnt = 1
*
*     Begin loop over all intervals
*
   10 CONTINUE
      upper = ( one+eps )*svd( tpnt ) + unflep
      lower = ( one-eps )*svd( bpnt ) - unflep
      IF( lower.LE.unflep )
     $   lower = -upper
*
*     Begin loop merging overlapping intervals
*
   20 CONTINUE
      IF( bpnt.EQ.n )
     $   GO TO 30
      tuppr = ( one+eps )*svd( bpnt+1 ) + unflep
      IF( tuppr.LT.lower )
     $   GO TO 30
*
*     Merge
*
      bpnt = bpnt + 1
      lower = ( one-eps )*svd( bpnt ) - unflep
      IF( lower.LE.unflep )
     $   lower = -upper
      GO TO 20
   30 CONTINUE
*
*     Count singular values in interval [ LOWER, UPPER ]
*
      CALL dsvdct( n, s, e, lower, numl )
      CALL dsvdct( n, s, e, upper, numu )
      count = numu - numl
      IF( lower.LT.zero )
     $   count = count / 2
      IF( count.NE.bpnt-tpnt+1 ) THEN
*
*        Wrong number of singular values in interval
*
         info = tpnt
         GO TO 40
      END IF
      tpnt = bpnt + 1
      bpnt = tpnt
      IF( tpnt.LE.n )
     $   GO TO 10
   40 CONTINUE
      RETURN
*
*     End of DSVDCH
*

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