Annotation of rpl/lapack/lapack/dlarrc.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLARRC
! 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 November 2011
! 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: * =====================================================================
1.1 bertrand 136: SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
137: $ EIGCNT, LCNT, RCNT, INFO )
138: *
1.8 ! bertrand 139: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 140: * -- LAPACK is a software package provided by Univ. of Tennessee, --
141: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 142: * November 2011
1.1 bertrand 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
CVSweb interface <joel.bertrand@systella.fr>