Annotation of rpl/lapack/lapack/dlarra.f, revision 1.19
1.12 bertrand 1: *> \brief \b DLARRA computes the splitting points with the specified threshold.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download DLARRA + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarra.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarra.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
22: * NSPLIT, ISPLIT, INFO )
1.16 bertrand 23: *
1.9 bertrand 24: * .. Scalar Arguments ..
25: * INTEGER INFO, N, NSPLIT
26: * DOUBLE PRECISION SPLTOL, TNRM
27: * ..
28: * .. Array Arguments ..
29: * INTEGER ISPLIT( * )
30: * DOUBLE PRECISION D( * ), E( * ), E2( * )
31: * ..
1.16 bertrand 32: *
1.9 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> Compute the splitting points with threshold SPLTOL.
40: *> DLARRA sets any "small" off-diagonal elements to zero.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] N
47: *> \verbatim
48: *> N is INTEGER
49: *> The order of the matrix. N > 0.
50: *> \endverbatim
51: *>
52: *> \param[in] D
53: *> \verbatim
54: *> D is DOUBLE PRECISION array, dimension (N)
55: *> On entry, the N diagonal elements of the tridiagonal
56: *> matrix T.
57: *> \endverbatim
58: *>
59: *> \param[in,out] E
60: *> \verbatim
61: *> E is DOUBLE PRECISION array, dimension (N)
62: *> On entry, the first (N-1) entries contain the subdiagonal
63: *> elements of the tridiagonal matrix T; E(N) need not be set.
64: *> On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
65: *> are set to zero, the other entries of E are untouched.
66: *> \endverbatim
67: *>
68: *> \param[in,out] E2
69: *> \verbatim
70: *> E2 is DOUBLE PRECISION array, dimension (N)
71: *> On entry, the first (N-1) entries contain the SQUARES of the
72: *> subdiagonal elements of the tridiagonal matrix T;
73: *> E2(N) need not be set.
74: *> On exit, the entries E2( ISPLIT( I ) ),
75: *> 1 <= I <= NSPLIT, have been set to zero
76: *> \endverbatim
77: *>
78: *> \param[in] SPLTOL
79: *> \verbatim
80: *> SPLTOL is DOUBLE PRECISION
81: *> The threshold for splitting. Two criteria can be used:
82: *> SPLTOL<0 : criterion based on absolute off-diagonal value
83: *> SPLTOL>0 : criterion that preserves relative accuracy
84: *> \endverbatim
85: *>
86: *> \param[in] TNRM
87: *> \verbatim
88: *> TNRM is DOUBLE PRECISION
89: *> The norm of the matrix.
90: *> \endverbatim
91: *>
92: *> \param[out] NSPLIT
93: *> \verbatim
94: *> NSPLIT is INTEGER
95: *> The number of blocks T splits into. 1 <= NSPLIT <= N.
96: *> \endverbatim
97: *>
98: *> \param[out] ISPLIT
99: *> \verbatim
100: *> ISPLIT is INTEGER array, dimension (N)
101: *> The splitting points, at which T breaks up into blocks.
102: *> The first block consists of rows/columns 1 to ISPLIT(1),
103: *> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
104: *> etc., and the NSPLIT-th consists of rows/columns
105: *> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
106: *> \endverbatim
107: *>
108: *> \param[out] INFO
109: *> \verbatim
110: *> INFO is INTEGER
111: *> = 0: successful exit
112: *> \endverbatim
113: *
114: * Authors:
115: * ========
116: *
1.16 bertrand 117: *> \author Univ. of Tennessee
118: *> \author Univ. of California Berkeley
119: *> \author Univ. of Colorado Denver
120: *> \author NAG Ltd.
1.9 bertrand 121: *
1.18 bertrand 122: *> \date June 2017
1.9 bertrand 123: *
1.16 bertrand 124: *> \ingroup OTHERauxiliary
1.9 bertrand 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 DLARRA( N, D, E, E2, SPLTOL, TNRM,
137: $ NSPLIT, ISPLIT, INFO )
138: *
1.18 bertrand 139: * -- LAPACK auxiliary routine (version 3.7.1) --
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..--
1.18 bertrand 142: * June 2017
1.1 bertrand 143: *
144: * .. Scalar Arguments ..
145: INTEGER INFO, N, NSPLIT
146: DOUBLE PRECISION SPLTOL, TNRM
147: * ..
148: * .. Array Arguments ..
149: INTEGER ISPLIT( * )
150: DOUBLE PRECISION D( * ), E( * ), E2( * )
151: * ..
152: *
153: * =====================================================================
154: *
155: * .. Parameters ..
156: DOUBLE PRECISION ZERO
157: PARAMETER ( ZERO = 0.0D0 )
158: * ..
159: * .. Local Scalars ..
160: INTEGER I
161: DOUBLE PRECISION EABS, TMP1
162:
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC ABS
166: * ..
167: * .. Executable Statements ..
168: *
169: INFO = 0
1.18 bertrand 170: *
171: * Quick return if possible
172: *
173: IF( N.LE.0 ) THEN
174: RETURN
175: END IF
176: *
1.1 bertrand 177: * Compute splitting points
178: NSPLIT = 1
179: IF(SPLTOL.LT.ZERO) THEN
180: * Criterion based on absolute off-diagonal value
181: TMP1 = ABS(SPLTOL)* TNRM
182: DO 9 I = 1, N-1
183: EABS = ABS( E(I) )
184: IF( EABS .LE. TMP1) THEN
185: E(I) = ZERO
186: E2(I) = ZERO
187: ISPLIT( NSPLIT ) = I
188: NSPLIT = NSPLIT + 1
189: END IF
190: 9 CONTINUE
191: ELSE
192: * Criterion that guarantees relative accuracy
193: DO 10 I = 1, N-1
194: EABS = ABS( E(I) )
195: IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
196: $ THEN
197: E(I) = ZERO
198: E2(I) = ZERO
199: ISPLIT( NSPLIT ) = I
200: NSPLIT = NSPLIT + 1
201: END IF
202: 10 CONTINUE
203: ENDIF
204: ISPLIT( NSPLIT ) = N
205:
206: RETURN
207: *
208: * End of DLARRA
209: *
210: END
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