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: *> \date June 2016
124: *
125: *> \ingroup OTHERauxiliary
126: *
127: *> \par Contributors:
128: * ==================
129: *>
130: *> Beresford Parlett, University of California, Berkeley, USA \n
131: *> Jim Demmel, University of California, Berkeley, USA \n
132: *> Inderjit Dhillon, University of Texas, Austin, USA \n
133: *> Osni Marques, LBNL/NERSC, USA \n
134: *> Christof Voemel, University of California, Berkeley, USA
135: *
136: * =====================================================================
137: SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
138: $ EIGCNT, LCNT, RCNT, INFO )
139: *
140: * -- LAPACK auxiliary routine (version 3.7.0) --
141: * -- LAPACK is a software package provided by Univ. of Tennessee, --
142: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143: * June 2016
144: *
145: * .. Scalar Arguments ..
146: CHARACTER JOBT
147: INTEGER EIGCNT, INFO, LCNT, N, RCNT
148: DOUBLE PRECISION PIVMIN, VL, VU
149: * ..
150: * .. Array Arguments ..
151: DOUBLE PRECISION D( * ), E( * )
152: * ..
153: *
154: * =====================================================================
155: *
156: * .. Parameters ..
157: DOUBLE PRECISION ZERO
158: PARAMETER ( ZERO = 0.0D0 )
159: * ..
160: * .. Local Scalars ..
161: INTEGER I
162: LOGICAL MATT
163: DOUBLE PRECISION LPIVOT, RPIVOT, SL, SU, TMP, TMP2
164:
165: * ..
166: * .. External Functions ..
167: LOGICAL LSAME
168: EXTERNAL LSAME
169: * ..
170: * .. Executable Statements ..
171: *
172: INFO = 0
173: LCNT = 0
174: RCNT = 0
175: EIGCNT = 0
176: MATT = LSAME( JOBT, 'T' )
177:
178:
179: IF (MATT) THEN
180: * Sturm sequence count on T
181: LPIVOT = D( 1 ) - VL
182: RPIVOT = D( 1 ) - VU
183: IF( LPIVOT.LE.ZERO ) THEN
184: LCNT = LCNT + 1
185: ENDIF
186: IF( RPIVOT.LE.ZERO ) THEN
187: RCNT = RCNT + 1
188: ENDIF
189: DO 10 I = 1, N-1
190: TMP = E(I)**2
191: LPIVOT = ( D( I+1 )-VL ) - TMP/LPIVOT
192: RPIVOT = ( D( I+1 )-VU ) - TMP/RPIVOT
193: IF( LPIVOT.LE.ZERO ) THEN
194: LCNT = LCNT + 1
195: ENDIF
196: IF( RPIVOT.LE.ZERO ) THEN
197: RCNT = RCNT + 1
198: ENDIF
199: 10 CONTINUE
200: ELSE
201: * Sturm sequence count on L D L^T
202: SL = -VL
203: SU = -VU
204: DO 20 I = 1, N - 1
205: LPIVOT = D( I ) + SL
206: RPIVOT = D( I ) + SU
207: IF( LPIVOT.LE.ZERO ) THEN
208: LCNT = LCNT + 1
209: ENDIF
210: IF( RPIVOT.LE.ZERO ) THEN
211: RCNT = RCNT + 1
212: ENDIF
213: TMP = E(I) * D(I) * E(I)
214: *
215: TMP2 = TMP / LPIVOT
216: IF( TMP2.EQ.ZERO ) THEN
217: SL = TMP - VL
218: ELSE
219: SL = SL*TMP2 - VL
220: END IF
221: *
222: TMP2 = TMP / RPIVOT
223: IF( TMP2.EQ.ZERO ) THEN
224: SU = TMP - VU
225: ELSE
226: SU = SU*TMP2 - VU
227: END IF
228: 20 CONTINUE
229: LPIVOT = D( N ) + SL
230: RPIVOT = D( N ) + SU
231: IF( LPIVOT.LE.ZERO ) THEN
232: LCNT = LCNT + 1
233: ENDIF
234: IF( RPIVOT.LE.ZERO ) THEN
235: RCNT = RCNT + 1
236: ENDIF
237: ENDIF
238: EIGCNT = RCNT - LCNT
239:
240: RETURN
241: *
242: * end of DLARRC
243: *
244: END
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