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
|
// $Id$
//
// Copyright (C) 2004-2006 Rational Discovery LLC
//
// @@ All Rights Reserved @@
// This file is part of the RDKit.
// The contents are covered by the terms of the BSD license
// which is included in the file license.txt, found at the root
// of the RDKit source tree.
//
#include <RDGeneral/test.h>
#include <iostream>
#include <math.h>
#include <RDGeneral/Invariant.h>
#include "BFGSOpt.h"
double circ_0_0(double *v) {
double dx = v[0];
double dy = v[1];
return dx * dx + dy * dy;
}
double circ_0_0_grad(double *v, double *grad) {
double dx = v[0];
double dy = v[1];
grad[0] = 2 * dx;
grad[1] = 2 * dy;
return 1.0;
}
double circ_1_0(double *v) {
double dx = v[0] - 1;
double dy = v[1];
return dx * dx + dy * dy;
}
double circ_1_0_grad(double *v, double *grad) {
double dx = v[0] - 1;
double dy = v[1];
grad[0] = 2 * dx;
grad[1] = 2 * dy;
return 1.0;
}
double func2(double *v) {
double weight = .5;
double dx = v[0] - 1;
double dy = v[1];
double term1 = dx * dx - dy * dy;
double term2 = dx * dx + dy * dy;
return term1 * term1 + weight * term2;
}
double grad2(double *v, double *grad) {
double weight = .5;
double dx = v[0] - 1;
double dy = v[1];
double term1 = dx * dx - dy * dy;
grad[0] = 4 * dx * term1 + 2 * weight * dx;
grad[1] = -4 * dy * term1 + 2 * weight * dy;
return 1.0;
}
void test1() {
std::cerr << "-------------------------------------" << std::endl;
std::cerr << "Testing linear search." << std::endl;
int dim = 2;
double oLoc[2], oVal;
double grad[2], dir[2];
double nLoc[2], nVal;
int resCode;
double (*func)(double *);
double (*gradFunc)(double *, double *);
func = circ_0_0;
gradFunc = circ_0_0_grad;
oLoc[0] = 0;
oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal - 1.0) < 1e-4);
gradFunc(oLoc, grad);
dir[0] = 0;
dir[1] = -.5;
BFGSOpt::linearSearch(dim, oLoc, oVal, grad, dir, nLoc, nVal, func, 0.5,
resCode);
TEST_ASSERT(resCode == 0);
TEST_ASSERT(fabs(nVal - 0.25) < 1e-4);
TEST_ASSERT(fabs(nLoc[0]) < 1e-4);
TEST_ASSERT(fabs(nLoc[1] - 0.5) < 1e-4);
oLoc[0] = 1.0;
oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal - 2.0) < 1e-4);
gradFunc(oLoc, grad);
dir[0] = -.5;
dir[1] = -.5;
BFGSOpt::linearSearch(dim, oLoc, oVal, grad, dir, nLoc, nVal, func, 1.0,
resCode);
TEST_ASSERT(resCode == 0);
TEST_ASSERT(fabs(nVal - 0.5) < 1e-4);
TEST_ASSERT(fabs(nLoc[0] - 0.5) < 1e-4);
TEST_ASSERT(fabs(nLoc[1] - 0.5) < 1e-4);
// we go hugely too far, but the dir gets cut in half, so we
// immediately hit the minimum
func = circ_0_0;
oLoc[0] = 0;
oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal - 1.0) < 1e-4);
gradFunc(oLoc, grad);
dir[0] = 0;
dir[1] = -2;
BFGSOpt::linearSearch(dim, oLoc, oVal, grad, dir, nLoc, nVal, func, 2.0,
resCode);
TEST_ASSERT(resCode == 0);
TEST_ASSERT(fabs(nVal) < 1e-4);
TEST_ASSERT(fabs(nLoc[0]) < 1e-4);
TEST_ASSERT(fabs(nLoc[1]) < 1e-4);
std::cerr << " done" << std::endl;
}
void test2() {
std::cerr << "-------------------------------------" << std::endl;
std::cerr << "Testing BFGS optimization." << std::endl;
unsigned int dim = 2;
double oLoc[2], oVal;
double nVal;
unsigned int nIters;
double (*func)(double *);
double (*gradFunc)(double *, double *);
func = circ_0_0;
gradFunc = circ_0_0_grad;
oLoc[0] = 0;
oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal - 1.0) < 1e-4);
BFGSOpt::minimize(dim, oLoc, 1e-4, nIters, nVal, func, gradFunc);
TEST_ASSERT(nIters = 1);
TEST_ASSERT(fabs(nVal) < 1e-4);
TEST_ASSERT(fabs(oLoc[0]) < 1e-4);
TEST_ASSERT(fabs(oLoc[1]) < 1e-4);
func = func2;
gradFunc = grad2;
oLoc[0] = 2.0;
oLoc[1] = 0.5;
BFGSOpt::minimize(dim, oLoc, 1e-4, nIters, nVal, func, gradFunc);
// TEST_ASSERT(nIters=1);
TEST_ASSERT(fabs(nVal) < 1e-4);
TEST_ASSERT(fabs(oLoc[0] - 1) < 1e-3);
TEST_ASSERT(fabs(oLoc[1]) < 1e-3);
// up the tolerance:
oLoc[0] = 2.0;
oLoc[1] = 0.5;
BFGSOpt::minimize(dim, oLoc, 1e-4, nIters, nVal, func, gradFunc, 1e-8);
// TEST_ASSERT(nIters=1);
TEST_ASSERT(fabs(nVal) < 1e-4);
TEST_ASSERT(fabs(oLoc[0] - 1) < 1e-4);
TEST_ASSERT(fabs(oLoc[1]) < 1e-4);
std::cerr << " done" << std::endl;
}
int main() {
test1();
test2();
}
|
