LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dlarrc.f
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1*> \brief \b DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLARRC + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrc.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrc.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrc.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
22* EIGCNT, LCNT, RCNT, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBT
26* INTEGER EIGCNT, INFO, LCNT, N, RCNT
27* DOUBLE PRECISION PIVMIN, VL, VU
28* ..
29* .. Array Arguments ..
30* DOUBLE PRECISION D( * ), E( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> Find the number of eigenvalues of the symmetric tridiagonal matrix T
40*> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
41*> if JOBT = 'L'.
42*> \endverbatim
43*
44* Arguments:
45* ==========
46*
47*> \param[in] JOBT
48*> \verbatim
49*> JOBT is CHARACTER*1
50*> = 'T': Compute Sturm count for matrix T.
51*> = 'L': Compute Sturm count for matrix L D L^T.
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*> N is INTEGER
57*> The order of the matrix. N > 0.
58*> \endverbatim
59*>
60*> \param[in] VL
61*> \verbatim
62*> VL is DOUBLE PRECISION
63*> The lower bound for the eigenvalues.
64*> \endverbatim
65*>
66*> \param[in] VU
67*> \verbatim
68*> VU is DOUBLE PRECISION
69*> The upper bound for the eigenvalues.
70*> \endverbatim
71*>
72*> \param[in] D
73*> \verbatim
74*> D is DOUBLE PRECISION array, dimension (N)
75*> JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
76*> JOBT = 'L': The N diagonal elements of the diagonal matrix D.
77*> \endverbatim
78*>
79*> \param[in] E
80*> \verbatim
81*> E is DOUBLE PRECISION array, dimension (N)
82*> JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
83*> JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
84*> \endverbatim
85*>
86*> \param[in] PIVMIN
87*> \verbatim
88*> PIVMIN is DOUBLE PRECISION
89*> The minimum pivot in the Sturm sequence for T.
90*> \endverbatim
91*>
92*> \param[out] EIGCNT
93*> \verbatim
94*> EIGCNT is INTEGER
95*> The number of eigenvalues of the symmetric tridiagonal matrix T
96*> that are in the interval (VL,VU]
97*> \endverbatim
98*>
99*> \param[out] LCNT
100*> \verbatim
101*> LCNT is INTEGER
102*> \endverbatim
103*>
104*> \param[out] RCNT
105*> \verbatim
106*> RCNT is INTEGER
107*> The left and right negcounts of the interval.
108*> \endverbatim
109*>
110*> \param[out] INFO
111*> \verbatim
112*> INFO is INTEGER
113*> \endverbatim
114*
115* Authors:
116* ========
117*
118*> \author Univ. of Tennessee
119*> \author Univ. of California Berkeley
120*> \author Univ. of Colorado Denver
121*> \author NAG Ltd.
122*
123*> \ingroup OTHERauxiliary
124*
125*> \par Contributors:
126* ==================
127*>
128*> Beresford Parlett, University of California, Berkeley, USA \n
129*> Jim Demmel, University of California, Berkeley, USA \n
130*> Inderjit Dhillon, University of Texas, Austin, USA \n
131*> Osni Marques, LBNL/NERSC, USA \n
132*> Christof Voemel, University of California, Berkeley, USA
133*
134* =====================================================================
135 SUBROUTINE dlarrc( JOBT, N, VL, VU, D, E, PIVMIN,
136 $ EIGCNT, LCNT, RCNT, INFO )
137*
138* -- LAPACK auxiliary routine --
139* -- LAPACK is a software package provided by Univ. of Tennessee, --
140* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141*
142* .. Scalar Arguments ..
143 CHARACTER JOBT
144 INTEGER EIGCNT, INFO, LCNT, N, RCNT
145 DOUBLE PRECISION PIVMIN, VL, VU
146* ..
147* .. Array Arguments ..
148 DOUBLE PRECISION D( * ), E( * )
149* ..
150*
151* =====================================================================
152*
153* .. Parameters ..
154 DOUBLE PRECISION ZERO
155 parameter( zero = 0.0d0 )
156* ..
157* .. Local Scalars ..
158 INTEGER I
159 LOGICAL MATT
160 DOUBLE PRECISION LPIVOT, RPIVOT, SL, SU, TMP, TMP2
161
162* ..
163* .. External Functions ..
164 LOGICAL LSAME
165 EXTERNAL lsame
166* ..
167* .. Executable Statements ..
168*
169 info = 0
170*
171* Quick return if possible
172*
173 IF( n.LE.0 ) THEN
174 RETURN
175 END IF
176*
177 lcnt = 0
178 rcnt = 0
179 eigcnt = 0
180 matt = lsame( jobt, 'T' )
181
182
183 IF (matt) THEN
184* Sturm sequence count on T
185 lpivot = d( 1 ) - vl
186 rpivot = d( 1 ) - vu
187 IF( lpivot.LE.zero ) THEN
188 lcnt = lcnt + 1
189 ENDIF
190 IF( rpivot.LE.zero ) THEN
191 rcnt = rcnt + 1
192 ENDIF
193 DO 10 i = 1, n-1
194 tmp = e(i)**2
195 lpivot = ( d( i+1 )-vl ) - tmp/lpivot
196 rpivot = ( d( i+1 )-vu ) - tmp/rpivot
197 IF( lpivot.LE.zero ) THEN
198 lcnt = lcnt + 1
199 ENDIF
200 IF( rpivot.LE.zero ) THEN
201 rcnt = rcnt + 1
202 ENDIF
203 10 CONTINUE
204 ELSE
205* Sturm sequence count on L D L^T
206 sl = -vl
207 su = -vu
208 DO 20 i = 1, n - 1
209 lpivot = d( i ) + sl
210 rpivot = d( i ) + su
211 IF( lpivot.LE.zero ) THEN
212 lcnt = lcnt + 1
213 ENDIF
214 IF( rpivot.LE.zero ) THEN
215 rcnt = rcnt + 1
216 ENDIF
217 tmp = e(i) * d(i) * e(i)
218*
219 tmp2 = tmp / lpivot
220 IF( tmp2.EQ.zero ) THEN
221 sl = tmp - vl
222 ELSE
223 sl = sl*tmp2 - vl
224 END IF
225*
226 tmp2 = tmp / rpivot
227 IF( tmp2.EQ.zero ) THEN
228 su = tmp - vu
229 ELSE
230 su = su*tmp2 - vu
231 END IF
232 20 CONTINUE
233 lpivot = d( n ) + sl
234 rpivot = d( n ) + su
235 IF( lpivot.LE.zero ) THEN
236 lcnt = lcnt + 1
237 ENDIF
238 IF( rpivot.LE.zero ) THEN
239 rcnt = rcnt + 1
240 ENDIF
241 ENDIF
242 eigcnt = rcnt - lcnt
243
244 RETURN
245*
246* End of DLARRC
247*
248 END
subroutine dlarrc(JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO)
DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
Definition: dlarrc.f:137