 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ssvdch()

 subroutine ssvdch ( integer N, real, dimension( * ) S, real, dimension( * ) E, real, dimension( * ) SVD, real TOL, integer INFO )

SSVDCH

Purpose:
``` SSVDCH 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
SSVDCT). Here EPS=TOL*MAX(N/10,1)*MACHEP, 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
Parameters
 [in] N ``` N is INTEGER The dimension of the bidiagonal matrix B.``` [in] S ``` S is REAL array, dimension (N) The diagonal entries of the bidiagonal matrix B.``` [in] E ``` E is REAL array, dimension (N-1) The superdiagonal entries of the bidiagonal matrix B.``` [in] SVD ``` SVD is REAL array, dimension (N) The computed singular values to be checked.``` [in] TOL ``` TOL is REAL 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*MACHEPS) >0 if the interval containing the INFO-th singular value contains the incorrect number of singular values.```

Definition at line 96 of file ssvdch.f.

97*
98* -- LAPACK test routine --
99* -- LAPACK is a software package provided by Univ. of Tennessee, --
100* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
101*
102* .. Scalar Arguments ..
103 INTEGER INFO, N
104 REAL TOL
105* ..
106* .. Array Arguments ..
107 REAL E( * ), S( * ), SVD( * )
108* ..
109*
110* =====================================================================
111*
112* .. Parameters ..
113 REAL ONE
114 parameter( one = 1.0e0 )
115 REAL ZERO
116 parameter( zero = 0.0e0 )
117* ..
118* .. Local Scalars ..
119 INTEGER BPNT, COUNT, NUML, NUMU, TPNT
120 REAL EPS, LOWER, OVFL, TUPPR, UNFL, UNFLEP, UPPER
121* ..
122* .. External Functions ..
123 REAL SLAMCH
124 EXTERNAL slamch
125* ..
126* .. External Subroutines ..
127 EXTERNAL ssvdct
128* ..
129* .. Intrinsic Functions ..
130 INTRINSIC max, sqrt
131* ..
132* .. Executable Statements ..
133*
134* Get machine constants
135*
136 info = 0
137 IF( n.LE.0 )
138 \$ RETURN
139 unfl = slamch( 'Safe minimum' )
140 ovfl = slamch( 'Overflow' )
141 eps = slamch( 'Epsilon' )*slamch( 'Base' )
142*
143* UNFLEP is chosen so that when an eigenvalue is multiplied by the
144* scale factor sqrt(OVFL)*sqrt(sqrt(UNFL))/MX in SSVDCT, it exceeds
145* sqrt(UNFL), which is the lower limit for SSVDCT.
146*
147 unflep = ( sqrt( sqrt( unfl ) ) / sqrt( ovfl ) )*svd( 1 ) +
148 \$ unfl / eps
149*
150* The value of EPS works best when TOL .GE. 10.
151*
152 eps = tol*max( n / 10, 1 )*eps
153*
154* TPNT points to singular value at right endpoint of interval
155* BPNT points to singular value at left endpoint of interval
156*
157 tpnt = 1
158 bpnt = 1
159*
160* Begin loop over all intervals
161*
162 10 CONTINUE
163 upper = ( one+eps )*svd( tpnt ) + unflep
164 lower = ( one-eps )*svd( bpnt ) - unflep
165 IF( lower.LE.unflep )
166 \$ lower = -upper
167*
168* Begin loop merging overlapping intervals
169*
170 20 CONTINUE
171 IF( bpnt.EQ.n )
172 \$ GO TO 30
173 tuppr = ( one+eps )*svd( bpnt+1 ) + unflep
174 IF( tuppr.LT.lower )
175 \$ GO TO 30
176*
177* Merge
178*
179 bpnt = bpnt + 1
180 lower = ( one-eps )*svd( bpnt ) - unflep
181 IF( lower.LE.unflep )
182 \$ lower = -upper
183 GO TO 20
184 30 CONTINUE
185*
186* Count singular values in interval [ LOWER, UPPER ]
187*
188 CALL ssvdct( n, s, e, lower, numl )
189 CALL ssvdct( n, s, e, upper, numu )
190 count = numu - numl
191 IF( lower.LT.zero )
192 \$ count = count / 2
193 IF( count.NE.bpnt-tpnt+1 ) THEN
194*
195* Wrong number of singular values in interval
196*
197 info = tpnt
198 GO TO 40
199 END IF
200 tpnt = bpnt + 1
201 bpnt = tpnt
202 IF( tpnt.LE.n )
203 \$ GO TO 10
204 40 CONTINUE
205 RETURN
206*
207* End of SSVDCH
208*
subroutine ssvdct(N, S, E, SHIFT, NUM)
SSVDCT
Definition: ssvdct.f:87
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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