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: *> \endverbatim
64: *>
65: *> \param[in] VU
66: *> \verbatim
67: *> VU is DOUBLE PRECISION
68: *> The lower and upper bounds for the eigenvalues.
69: *> \endverbatim
70: *>
71: *> \param[in] D
72: *> \verbatim
73: *> D is DOUBLE PRECISION array, dimension (N)
74: *> JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
75: *> JOBT = 'L': The N diagonal elements of the diagonal matrix D.
76: *> \endverbatim
77: *>
78: *> \param[in] E
79: *> \verbatim
80: *> E is DOUBLE PRECISION array, dimension (N)
81: *> JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
82: *> JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
83: *> \endverbatim
84: *>
85: *> \param[in] PIVMIN
86: *> \verbatim
87: *> PIVMIN is DOUBLE PRECISION
88: *> The minimum pivot in the Sturm sequence for T.
89: *> \endverbatim
90: *>
91: *> \param[out] EIGCNT
92: *> \verbatim
93: *> EIGCNT is INTEGER
94: *> The number of eigenvalues of the symmetric tridiagonal matrix T
95: *> that are in the interval (VL,VU]
96: *> \endverbatim
97: *>
98: *> \param[out] LCNT
99: *> \verbatim
100: *> LCNT is INTEGER
101: *> \endverbatim
102: *>
103: *> \param[out] RCNT
104: *> \verbatim
105: *> RCNT is INTEGER
106: *> The left and right negcounts of the interval.
107: *> \endverbatim
108: *>
109: *> \param[out] INFO
110: *> \verbatim
111: *> INFO is INTEGER
112: *> \endverbatim
113: *
114: * Authors:
115: * ========
116: *
117: *> \author Univ. of Tennessee
118: *> \author Univ. of California Berkeley
119: *> \author Univ. of Colorado Denver
120: *> \author NAG Ltd.
121: *
122: *> \date September 2012
123: *
124: *> \ingroup auxOTHERauxiliary
125: *
126: *> \par Contributors:
127: * ==================
128: *>
129: *> Beresford Parlett, University of California, Berkeley, USA \n
130: *> Jim Demmel, University of California, Berkeley, USA \n
131: *> Inderjit Dhillon, University of Texas, Austin, USA \n
132: *> Osni Marques, LBNL/NERSC, USA \n
133: *> Christof Voemel, University of California, Berkeley, USA
134: *
135: * =====================================================================
136: SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
137: $ EIGCNT, LCNT, RCNT, INFO )
138: *
139: * -- LAPACK auxiliary routine (version 3.4.2) --
140: * -- LAPACK is a software package provided by Univ. of Tennessee, --
141: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142: * September 2012
143: *
144: * .. Scalar Arguments ..
145: CHARACTER JOBT
146: INTEGER EIGCNT, INFO, LCNT, N, RCNT
147: DOUBLE PRECISION PIVMIN, VL, VU
148: * ..
149: * .. Array Arguments ..
150: DOUBLE PRECISION D( * ), E( * )
151: * ..
152: *
153: * =====================================================================
154: *
155: * .. Parameters ..
156: DOUBLE PRECISION ZERO
157: PARAMETER ( ZERO = 0.0D0 )
158: * ..
159: * .. Local Scalars ..
160: INTEGER I
161: LOGICAL MATT
162: DOUBLE PRECISION LPIVOT, RPIVOT, SL, SU, TMP, TMP2
163:
164: * ..
165: * .. External Functions ..
166: LOGICAL LSAME
167: EXTERNAL LSAME
168: * ..
169: * .. Executable Statements ..
170: *
171: INFO = 0
172: LCNT = 0
173: RCNT = 0
174: EIGCNT = 0
175: MATT = LSAME( JOBT, 'T' )
176:
177:
178: IF (MATT) THEN
179: * Sturm sequence count on T
180: LPIVOT = D( 1 ) - VL
181: RPIVOT = D( 1 ) - VU
182: IF( LPIVOT.LE.ZERO ) THEN
183: LCNT = LCNT + 1
184: ENDIF
185: IF( RPIVOT.LE.ZERO ) THEN
186: RCNT = RCNT + 1
187: ENDIF
188: DO 10 I = 1, N-1
189: TMP = E(I)**2
190: LPIVOT = ( D( I+1 )-VL ) - TMP/LPIVOT
191: RPIVOT = ( D( I+1 )-VU ) - TMP/RPIVOT
192: IF( LPIVOT.LE.ZERO ) THEN
193: LCNT = LCNT + 1
194: ENDIF
195: IF( RPIVOT.LE.ZERO ) THEN
196: RCNT = RCNT + 1
197: ENDIF
198: 10 CONTINUE
199: ELSE
200: * Sturm sequence count on L D L^T
201: SL = -VL
202: SU = -VU
203: DO 20 I = 1, N - 1
204: LPIVOT = D( I ) + SL
205: RPIVOT = D( I ) + SU
206: IF( LPIVOT.LE.ZERO ) THEN
207: LCNT = LCNT + 1
208: ENDIF
209: IF( RPIVOT.LE.ZERO ) THEN
210: RCNT = RCNT + 1
211: ENDIF
212: TMP = E(I) * D(I) * E(I)
213: *
214: TMP2 = TMP / LPIVOT
215: IF( TMP2.EQ.ZERO ) THEN
216: SL = TMP - VL
217: ELSE
218: SL = SL*TMP2 - VL
219: END IF
220: *
221: TMP2 = TMP / RPIVOT
222: IF( TMP2.EQ.ZERO ) THEN
223: SU = TMP - VU
224: ELSE
225: SU = SU*TMP2 - VU
226: END IF
227: 20 CONTINUE
228: LPIVOT = D( N ) + SL
229: RPIVOT = D( N ) + SU
230: IF( LPIVOT.LE.ZERO ) THEN
231: LCNT = LCNT + 1
232: ENDIF
233: IF( RPIVOT.LE.ZERO ) THEN
234: RCNT = RCNT + 1
235: ENDIF
236: ENDIF
237: EIGCNT = RCNT - LCNT
238:
239: RETURN
240: *
241: * end of DLARRC
242: *
243: END
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