-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathORTHRDS2.SIF
263 lines (192 loc) · 6.09 KB
/
ORTHRDS2.SIF
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
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
***************************
* SET UP THE INITIAL DATA *
***************************
NAME ORTHRDS2
* Problem :
* *********
* An orthogonal regression problem.
* The problem is to fit (orthogonally) a planar curve to a set of points
* in the plane. This set of points is generated by perturbing a
* first set lying exactly on the predefined curve.
* The curve is referred to as a cardioid in the original paper,
* but is in fact a circle.
* This problem is a modification of ORTHREGD.SIF.
* The start coordinates of certain data points were moved to
* force convergence to the center of the circle, where
* the Jacobian of the constraints is singular.
* Source: adapted from:
* M. Gulliksson,
* "Algorithms for nonlinear Least-squares with Applications to
* Orthogonal Regression",
* UMINF-178.90, University of Umea, Sweden, 1990.
* SIF input: Ph. Toint, Mar 1991.
* modified by T Plantagena, May 1994.
* classification QOR2-AY-V-V
* Number of data points
* (number of variables = 2 NPTS + 3 )
*IE NPTS 10 $-PARAMETER n = 23
*IE NPTS 50 $-PARAMETER n = 103
*IE NPTS 76 $-PARAMETER n = 155
*IE NPTS 100 $-PARAMETER n = 203 original value
*IE NPTS 250 $-PARAMETER n = 503
*IE NPTS 500 $-PARAMETER n = 1003
IE NPTS 2500 $-PARAMETER n = 5003
*IE NPTS 5000 $-PARAMETER n = 10003
* True curve parameters (centered at the origin)
RE TZ3 1.7
* Perturbation parameters
RE PSEED 237.1531
RE PSIZE 0.2
* Constants
IE 1 1
IE 0 0
* Of the NPTS data points, TDP_lo, TDP_lo + 1, ..., TDP_hi
* will be modified. Change TDP_hi for different numbers of
* singular solution points.
IE TDP_lo 5
IE TDP_hi 5
RE PI 3.1415926535
* Computed parameters
RM 2PI PI 2.0
RI RNPTS NPTS
RD ICR0 RNPTS 1.0
R* INCR ICR0 2PI
R* Z3SQ TZ3 TZ3
RA 1+TZ3SQ Z3SQ 1.0
* Construct the data points
DO I 1 NPTS
IA I-1 I -1
RI RI-1 I-1
R* THETA RI-1 INCR
R( ST SIN THETA
R( CT COS THETA
R+ FACT 1+TZ3SQ CT
R* R1 FACT CT
R* R2 FACT ST
R* XSEED THETA PSEED
R( SSEED COS XSEED
R* PER-1 PSIZE SSEED
RA PERT PER-1 1.0
A* XD(I) R1 PERT
A* YD(I) R2 PERT
ND
DO I TDP_lo TDP_hi
AE XD(I) 1.1
AE YD(I) 0.1
ND
VARIABLES
* Parameters of the curve
Z1
Z2
Z3
DO I 1 NPTS
* Projections of the data points onto the curve
X X(I)
X Y(I)
ND
GROUPS
DO I 1 NPTS
XN OX(I) X(I) 1.0
XN OY(I) Y(I) 1.0
XE E(I)
ND
CONSTANTS
DO I 1 NPTS
ZN ORTHRDS2 OX(I) XD(I)
ZN ORTHRDS2 OY(I) YD(I)
ND
BOUNDS
FR ORTHRDS2 'DEFAULT'
START POINT
ORTHRDS2 Z1 1.0
ORTHRDS2 Z2 0.0
ORTHRDS2 Z3 1.0
DO I 1 NPTS
Z ORTHRDS2 X(I) XD(I)
Z ORTHRDS2 Y(I) YD(I)
ND
ELEMENT TYPE
EV TA X Y
EV TA ZA ZB
IV TA DX DY
EV TB X Y
EV TB ZA ZB
EV TB ZC
IV TB DX DY
IV TB ZZ
ELEMENT USES
DO I 1 NPTS
XT EA(I) TA
ZV EA(I) X X(I)
ZV EA(I) Y Y(I)
ZV EA(I) ZA Z1
ZV EA(I) ZB Z2
XT EB(I) TB
ZV EB(I) X X(I)
ZV EB(I) Y Y(I)
ZV EB(I) ZA Z1
ZV EB(I) ZB Z2
ZV EB(I) ZC Z3
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 NPTS
XT OX(I) L2
XT OY(I) L2
XE E(I) EA(I) EB(I) -1.0
ND
OBJECT BOUND
LO ORTHRDS2 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ORTHRDS2
TEMPORARIES
R T
R T1
R T1SQ
R ZZSQ
INDIVIDUALS
T TA
R DX X 1.0 ZA -1.0
R DY Y 1.0 ZB -1.0
A T DX * DX + DY * DY
F T * T
G DX 4.0 * T * DX
G DY 4.0 * T * DY
H DX DX 4.0 * ( T + 2.0 * DX * DX )
H DX DY 8.0 * DX * DY
H DY DY 4.0 * ( T + 2.0 * DY * DY )
T TB
R DX X 1.0 ZA -1.0
R DY Y 1.0 ZB -1.0
R ZZ ZC 1.0
A T DX * DX + DY * DY
A ZZSQ ZZ * ZZ
A T1 1.0 + ZZSQ
A T1SQ T1 * T1
F T * T1SQ
G DX 2.0 * DX * T1SQ
G DY 2.0 * DY * T1SQ
G ZZ 4.0 * T * T1 * ZZ
H DX DX 2.0 * T1SQ
H DX ZZ 8.0 * DX * T1 * ZZ
H DY DY 2.0 * T1SQ
H DY ZZ 8.0 * DY * T1 * ZZ
H ZZ ZZ 4.0 * T * ( 2.0 * ZZSQ + T1)
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS ORTHRDS2
* Least-square groups
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA