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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/LeastSquares>
template<typename VectorType,
typename HyperplaneType>
void makeNoisyCohyperplanarPoints(int numPoints,
VectorType **points,
HyperplaneType *hyperplane,
typename VectorType::Scalar noiseAmplitude)
{
typedef typename VectorType::Scalar Scalar;
const int size = points[0]->size();
// pick a random hyperplane, store the coefficients of its equation
hyperplane->coeffs().resize(size + 1);
for(int j = 0; j < size + 1; j++)
{
do {
hyperplane->coeffs().coeffRef(j) = ei_random<Scalar>();
} while(ei_abs(hyperplane->coeffs().coeff(j)) < 0.5);
}
// now pick numPoints random points on this hyperplane
for(int i = 0; i < numPoints; i++)
{
VectorType& cur_point = *(points[i]);
do
{
cur_point = VectorType::Random(size)/*.normalized()*/;
// project cur_point onto the hyperplane
Scalar x = - (hyperplane->coeffs().start(size).cwise()*cur_point).sum();
cur_point *= hyperplane->coeffs().coeff(size) / x;
} while( cur_point.norm() < 0.5
|| cur_point.norm() > 2.0 );
}
// add some noise to these points
for(int i = 0; i < numPoints; i++ )
*(points[i]) += noiseAmplitude * VectorType::Random(size);
}
template<typename VectorType>
void check_linearRegression(int numPoints,
VectorType **points,
const VectorType& original,
typename VectorType::Scalar tolerance)
{
int size = points[0]->size();
assert(size==2);
VectorType result(size);
linearRegression(numPoints, points, &result, 1);
typename VectorType::Scalar error = (result - original).norm() / original.norm();
VERIFY(ei_abs(error) < ei_abs(tolerance));
}
template<typename VectorType,
typename HyperplaneType>
void check_fitHyperplane(int numPoints,
VectorType **points,
const HyperplaneType& original,
typename VectorType::Scalar tolerance)
{
int size = points[0]->size();
HyperplaneType result(size);
fitHyperplane(numPoints, points, &result);
result.coeffs() *= original.coeffs().coeff(size)/result.coeffs().coeff(size);
typename VectorType::Scalar error = (result.coeffs() - original.coeffs()).norm() / original.coeffs().norm();
std::cout << ei_abs(error) << " xxx " << ei_abs(tolerance) << std::endl;
VERIFY(ei_abs(error) < ei_abs(tolerance));
}
void test_eigen2_regression()
{
for(int i = 0; i < g_repeat; i++)
{
#ifdef EIGEN_TEST_PART_1
{
Vector2f points2f [1000];
Vector2f *points2f_ptrs [1000];
for(int i = 0; i < 1000; i++) points2f_ptrs[i] = &(points2f[i]);
Vector2f coeffs2f;
Hyperplane<float,2> coeffs3f;
makeNoisyCohyperplanarPoints(1000, points2f_ptrs, &coeffs3f, 0.01f);
coeffs2f[0] = -coeffs3f.coeffs()[0]/coeffs3f.coeffs()[1];
coeffs2f[1] = -coeffs3f.coeffs()[2]/coeffs3f.coeffs()[1];
CALL_SUBTEST(check_linearRegression(10, points2f_ptrs, coeffs2f, 0.05f));
CALL_SUBTEST(check_linearRegression(100, points2f_ptrs, coeffs2f, 0.01f));
CALL_SUBTEST(check_linearRegression(1000, points2f_ptrs, coeffs2f, 0.002f));
}
#endif
#ifdef EIGEN_TEST_PART_2
{
Vector2f points2f [1000];
Vector2f *points2f_ptrs [1000];
for(int i = 0; i < 1000; i++) points2f_ptrs[i] = &(points2f[i]);
Hyperplane<float,2> coeffs3f;
makeNoisyCohyperplanarPoints(1000, points2f_ptrs, &coeffs3f, 0.01f);
CALL_SUBTEST(check_fitHyperplane(10, points2f_ptrs, coeffs3f, 0.05f));
CALL_SUBTEST(check_fitHyperplane(100, points2f_ptrs, coeffs3f, 0.01f));
CALL_SUBTEST(check_fitHyperplane(1000, points2f_ptrs, coeffs3f, 0.002f));
}
#endif
#ifdef EIGEN_TEST_PART_3
{
Vector4d points4d [1000];
Vector4d *points4d_ptrs [1000];
for(int i = 0; i < 1000; i++) points4d_ptrs[i] = &(points4d[i]);
Hyperplane<double,4> coeffs5d;
makeNoisyCohyperplanarPoints(1000, points4d_ptrs, &coeffs5d, 0.01);
CALL_SUBTEST(check_fitHyperplane(10, points4d_ptrs, coeffs5d, 0.05));
CALL_SUBTEST(check_fitHyperplane(100, points4d_ptrs, coeffs5d, 0.01));
CALL_SUBTEST(check_fitHyperplane(1000, points4d_ptrs, coeffs5d, 0.002));
}
#endif
#ifdef EIGEN_TEST_PART_4
{
VectorXcd *points11cd_ptrs[1000];
for(int i = 0; i < 1000; i++) points11cd_ptrs[i] = new VectorXcd(11);
Hyperplane<std::complex<double>,Dynamic> *coeffs12cd = new Hyperplane<std::complex<double>,Dynamic>(11);
makeNoisyCohyperplanarPoints(1000, points11cd_ptrs, coeffs12cd, 0.01);
CALL_SUBTEST(check_fitHyperplane(100, points11cd_ptrs, *coeffs12cd, 0.025));
CALL_SUBTEST(check_fitHyperplane(1000, points11cd_ptrs, *coeffs12cd, 0.006));
delete coeffs12cd;
for(int i = 0; i < 1000; i++) delete points11cd_ptrs[i];
}
#endif
}
}
|
