1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
|
*> \brief \b DLARRA computes the splitting points with the specified threshold.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLARRA + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarra.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarra.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
* NSPLIT, ISPLIT, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, N, NSPLIT
* DOUBLE PRECISION SPLTOL, TNRM
* ..
* .. Array Arguments ..
* INTEGER ISPLIT( * )
* DOUBLE PRECISION D( * ), E( * ), E2( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Compute the splitting points with threshold SPLTOL.
*> DLARRA sets any "small" off-diagonal elements to zero.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix. N > 0.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> On entry, the N diagonal elements of the tridiagonal
*> matrix T.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (N)
*> On entry, the first (N-1) entries contain the subdiagonal
*> elements of the tridiagonal matrix T; E(N) need not be set.
*> On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
*> are set to zero, the other entries of E are untouched.
*> \endverbatim
*>
*> \param[in,out] E2
*> \verbatim
*> E2 is DOUBLE PRECISION array, dimension (N)
*> On entry, the first (N-1) entries contain the SQUARES of the
*> subdiagonal elements of the tridiagonal matrix T;
*> E2(N) need not be set.
*> On exit, the entries E2( ISPLIT( I ) ),
*> 1 <= I <= NSPLIT, have been set to zero
*> \endverbatim
*>
*> \param[in] SPLTOL
*> \verbatim
*> SPLTOL is DOUBLE PRECISION
*> The threshold for splitting. Two criteria can be used:
*> SPLTOL<0 : criterion based on absolute off-diagonal value
*> SPLTOL>0 : criterion that preserves relative accuracy
*> \endverbatim
*>
*> \param[in] TNRM
*> \verbatim
*> TNRM is DOUBLE PRECISION
*> The norm of the matrix.
*> \endverbatim
*>
*> \param[out] NSPLIT
*> \verbatim
*> NSPLIT is INTEGER
*> The number of blocks T splits into. 1 <= NSPLIT <= N.
*> \endverbatim
*>
*> \param[out] ISPLIT
*> \verbatim
*> ISPLIT is INTEGER array, dimension (N)
*> The splitting points, at which T breaks up into blocks.
*> The first block consists of rows/columns 1 to ISPLIT(1),
*> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
*> etc., and the NSPLIT-th consists of rows/columns
*> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup OTHERauxiliary
*
*> \par Contributors:
* ==================
*>
*> Beresford Parlett, University of California, Berkeley, USA \n
*> Jim Demmel, University of California, Berkeley, USA \n
*> Inderjit Dhillon, University of Texas, Austin, USA \n
*> Osni Marques, LBNL/NERSC, USA \n
*> Christof Voemel, University of California, Berkeley, USA
*
* =====================================================================
SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
$ NSPLIT, ISPLIT, INFO )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, N, NSPLIT
DOUBLE PRECISION SPLTOL, TNRM
* ..
* .. Array Arguments ..
INTEGER ISPLIT( * )
DOUBLE PRECISION D( * ), E( * ), E2( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION EABS, TMP1
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
INFO = 0
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
RETURN
END IF
*
* Compute splitting points
NSPLIT = 1
IF(SPLTOL.LT.ZERO) THEN
* Criterion based on absolute off-diagonal value
TMP1 = ABS(SPLTOL)* TNRM
DO 9 I = 1, N-1
EABS = ABS( E(I) )
IF( EABS .LE. TMP1) THEN
E(I) = ZERO
E2(I) = ZERO
ISPLIT( NSPLIT ) = I
NSPLIT = NSPLIT + 1
END IF
9 CONTINUE
ELSE
* Criterion that guarantees relative accuracy
DO 10 I = 1, N-1
EABS = ABS( E(I) )
IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
$ THEN
E(I) = ZERO
E2(I) = ZERO
ISPLIT( NSPLIT ) = I
NSPLIT = NSPLIT + 1
END IF
10 CONTINUE
ENDIF
ISPLIT( NSPLIT ) = N
RETURN
*
* End of DLARRA
*
END
|
