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
211
212
213
214
215
216
|
*> \brief \b DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAQSY + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsy.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsy.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsy.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* .. Scalar Arguments ..
* CHARACTER EQUED, UPLO
* INTEGER LDA, N
* DOUBLE PRECISION AMAX, SCOND
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), S( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAQSY equilibrates a symmetric matrix A using the scaling factors
*> in the vector S.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric matrix A is stored.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
*> n by n upper triangular part of A contains the upper
*> triangular part of the matrix A, and the strictly lower
*> triangular part of A is not referenced. If UPLO = 'L', the
*> leading n by n lower triangular part of A contains the lower
*> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced.
*>
*> On exit, if EQUED = 'Y', the equilibrated matrix:
*> diag(S) * A * diag(S).
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(N,1).
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is DOUBLE PRECISION array, dimension (N)
*> The scale factors for A.
*> \endverbatim
*>
*> \param[in] SCOND
*> \verbatim
*> SCOND is DOUBLE PRECISION
*> Ratio of the smallest S(i) to the largest S(i).
*> \endverbatim
*>
*> \param[in] AMAX
*> \verbatim
*> AMAX is DOUBLE PRECISION
*> Absolute value of largest matrix entry.
*> \endverbatim
*>
*> \param[out] EQUED
*> \verbatim
*> EQUED is CHARACTER*1
*> Specifies whether or not equilibration was done.
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
*> \endverbatim
*
*> \par Internal Parameters:
* =========================
*>
*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*>
*> LARGE and SMALL are threshold values used to decide if scaling should
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleSYauxiliary
*
* =====================================================================
SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* -- 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 ..
CHARACTER EQUED, UPLO
INTEGER LDA, N
DOUBLE PRECISION AMAX, SCOND
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), S( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, THRESH
PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION CJ, LARGE, SMALL
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, DLAMCH
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Initialize LARGE and SMALL.
*
SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
LARGE = ONE / SMALL
*
IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
*
* No equilibration
*
EQUED = 'N'
ELSE
*
* Replace A by diag(S) * A * diag(S).
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangle of A is stored.
*
DO 20 J = 1, N
CJ = S( J )
DO 10 I = 1, J
A( I, J ) = CJ*S( I )*A( I, J )
10 CONTINUE
20 CONTINUE
ELSE
*
* Lower triangle of A is stored.
*
DO 40 J = 1, N
CJ = S( J )
DO 30 I = J, N
A( I, J ) = CJ*S( I )*A( I, J )
30 CONTINUE
40 CONTINUE
END IF
EQUED = 'Y'
END IF
*
RETURN
*
* End of DLAQSY
*
END
|
