forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathdlaqge.f
233 lines (233 loc) · 6.12 KB
/
dlaqge.f
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
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
*> \brief \b DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAQGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqge.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqge.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqge.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
* EQUED )
*
* .. Scalar Arguments ..
* CHARACTER EQUED
* INTEGER LDA, M, N
* DOUBLE PRECISION AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAQGE equilibrates a general M by N matrix A using the row and
*> column scaling factors in the vectors R and C.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the M by N matrix A.
*> On exit, the equilibrated matrix. See EQUED for the form of
*> the equilibrated matrix.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(M,1).
*> \endverbatim
*>
*> \param[in] R
*> \verbatim
*> R is DOUBLE PRECISION array, dimension (M)
*> The row scale factors for A.
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (N)
*> The column scale factors for A.
*> \endverbatim
*>
*> \param[in] ROWCND
*> \verbatim
*> ROWCND is DOUBLE PRECISION
*> Ratio of the smallest R(i) to the largest R(i).
*> \endverbatim
*>
*> \param[in] COLCND
*> \verbatim
*> COLCND is DOUBLE PRECISION
*> Ratio of the smallest C(i) to the largest C(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 the form of equilibration that was done.
*> = 'N': No equilibration
*> = 'R': Row equilibration, i.e., A has been premultiplied by
*> diag(R).
*> = 'C': Column equilibration, i.e., A has been postmultiplied
*> by diag(C).
*> = 'B': Both row and column equilibration, i.e., A has been
*> replaced by diag(R) * A * diag(C).
*> \endverbatim
*
*> \par Internal Parameters:
* =========================
*>
*> \verbatim
*> THRESH is a threshold value used to decide if row or column scaling
*> should be done based on the ratio of the row or column scaling
*> factors. If ROWCND < THRESH, row scaling is done, and if
*> COLCND < THRESH, column scaling is done.
*>
*> LARGE and SMALL are threshold values used to decide if row scaling
*> should be done based on the absolute size of the largest matrix
*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleGEauxiliary
*
* =====================================================================
SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
$ EQUED )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER EQUED
INTEGER LDA, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
* ..
*
* =====================================================================
*
* .. 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 ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Initialize LARGE and SMALL.
*
SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
LARGE = ONE / SMALL
*
IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
$ THEN
*
* No row scaling
*
IF( COLCND.GE.THRESH ) THEN
*
* No column scaling
*
EQUED = 'N'
ELSE
*
* Column scaling
*
DO 20 J = 1, N
CJ = C( J )
DO 10 I = 1, M
A( I, J ) = CJ*A( I, J )
10 CONTINUE
20 CONTINUE
EQUED = 'C'
END IF
ELSE IF( COLCND.GE.THRESH ) THEN
*
* Row scaling, no column scaling
*
DO 40 J = 1, N
DO 30 I = 1, M
A( I, J ) = R( I )*A( I, J )
30 CONTINUE
40 CONTINUE
EQUED = 'R'
ELSE
*
* Row and column scaling
*
DO 60 J = 1, N
CJ = C( J )
DO 50 I = 1, M
A( I, J ) = CJ*R( I )*A( I, J )
50 CONTINUE
60 CONTINUE
EQUED = 'B'
END IF
*
RETURN
*
* End of DLAQGE
*
END