1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra. Eigen itself is part of the KDE project.
3 //
4 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #include "main.h"
11 #include <Eigen/LeastSquares>
12
13 template<typename VectorType,
14 typename HyperplaneType>
makeNoisyCohyperplanarPoints(int numPoints,VectorType ** points,HyperplaneType * hyperplane,typename VectorType::Scalar noiseAmplitude)15 void makeNoisyCohyperplanarPoints(int numPoints,
16 VectorType **points,
17 HyperplaneType *hyperplane,
18 typename VectorType::Scalar noiseAmplitude)
19 {
20 typedef typename VectorType::Scalar Scalar;
21 const int size = points[0]->size();
22 // pick a random hyperplane, store the coefficients of its equation
23 hyperplane->coeffs().resize(size + 1);
24 for(int j = 0; j < size + 1; j++)
25 {
26 do {
27 hyperplane->coeffs().coeffRef(j) = ei_random<Scalar>();
28 } while(ei_abs(hyperplane->coeffs().coeff(j)) < 0.5);
29 }
30
31 // now pick numPoints random points on this hyperplane
32 for(int i = 0; i < numPoints; i++)
33 {
34 VectorType& cur_point = *(points[i]);
35 do
36 {
37 cur_point = VectorType::Random(size)/*.normalized()*/;
38 // project cur_point onto the hyperplane
39 Scalar x = - (hyperplane->coeffs().start(size).cwise()*cur_point).sum();
40 cur_point *= hyperplane->coeffs().coeff(size) / x;
41 } while( cur_point.norm() < 0.5
42 || cur_point.norm() > 2.0 );
43 }
44
45 // add some noise to these points
46 for(int i = 0; i < numPoints; i++ )
47 *(points[i]) += noiseAmplitude * VectorType::Random(size);
48 }
49
50 template<typename VectorType>
check_linearRegression(int numPoints,VectorType ** points,const VectorType & original,typename VectorType::Scalar tolerance)51 void check_linearRegression(int numPoints,
52 VectorType **points,
53 const VectorType& original,
54 typename VectorType::Scalar tolerance)
55 {
56 int size = points[0]->size();
57 assert(size==2);
58 VectorType result(size);
59 linearRegression(numPoints, points, &result, 1);
60 typename VectorType::Scalar error = (result - original).norm() / original.norm();
61 VERIFY(ei_abs(error) < ei_abs(tolerance));
62 }
63
64 template<typename VectorType,
65 typename HyperplaneType>
check_fitHyperplane(int numPoints,VectorType ** points,const HyperplaneType & original,typename VectorType::Scalar tolerance)66 void check_fitHyperplane(int numPoints,
67 VectorType **points,
68 const HyperplaneType& original,
69 typename VectorType::Scalar tolerance)
70 {
71 int size = points[0]->size();
72 HyperplaneType result(size);
73 fitHyperplane(numPoints, points, &result);
74 result.coeffs() *= original.coeffs().coeff(size)/result.coeffs().coeff(size);
75 typename VectorType::Scalar error = (result.coeffs() - original.coeffs()).norm() / original.coeffs().norm();
76 std::cout << ei_abs(error) << " xxx " << ei_abs(tolerance) << std::endl;
77 VERIFY(ei_abs(error) < ei_abs(tolerance));
78 }
79
test_eigen2_regression()80 void test_eigen2_regression()
81 {
82 for(int i = 0; i < g_repeat; i++)
83 {
84 #ifdef EIGEN_TEST_PART_1
85 {
86 Vector2f points2f [1000];
87 Vector2f *points2f_ptrs [1000];
88 for(int i = 0; i < 1000; i++) points2f_ptrs[i] = &(points2f[i]);
89 Vector2f coeffs2f;
90 Hyperplane<float,2> coeffs3f;
91 makeNoisyCohyperplanarPoints(1000, points2f_ptrs, &coeffs3f, 0.01f);
92 coeffs2f[0] = -coeffs3f.coeffs()[0]/coeffs3f.coeffs()[1];
93 coeffs2f[1] = -coeffs3f.coeffs()[2]/coeffs3f.coeffs()[1];
94 CALL_SUBTEST(check_linearRegression(10, points2f_ptrs, coeffs2f, 0.05f));
95 CALL_SUBTEST(check_linearRegression(100, points2f_ptrs, coeffs2f, 0.01f));
96 CALL_SUBTEST(check_linearRegression(1000, points2f_ptrs, coeffs2f, 0.002f));
97 }
98 #endif
99 #ifdef EIGEN_TEST_PART_2
100 {
101 Vector2f points2f [1000];
102 Vector2f *points2f_ptrs [1000];
103 for(int i = 0; i < 1000; i++) points2f_ptrs[i] = &(points2f[i]);
104 Hyperplane<float,2> coeffs3f;
105 makeNoisyCohyperplanarPoints(1000, points2f_ptrs, &coeffs3f, 0.01f);
106 CALL_SUBTEST(check_fitHyperplane(10, points2f_ptrs, coeffs3f, 0.05f));
107 CALL_SUBTEST(check_fitHyperplane(100, points2f_ptrs, coeffs3f, 0.01f));
108 CALL_SUBTEST(check_fitHyperplane(1000, points2f_ptrs, coeffs3f, 0.002f));
109 }
110 #endif
111 #ifdef EIGEN_TEST_PART_3
112 {
113 Vector4d points4d [1000];
114 Vector4d *points4d_ptrs [1000];
115 for(int i = 0; i < 1000; i++) points4d_ptrs[i] = &(points4d[i]);
116 Hyperplane<double,4> coeffs5d;
117 makeNoisyCohyperplanarPoints(1000, points4d_ptrs, &coeffs5d, 0.01);
118 CALL_SUBTEST(check_fitHyperplane(10, points4d_ptrs, coeffs5d, 0.05));
119 CALL_SUBTEST(check_fitHyperplane(100, points4d_ptrs, coeffs5d, 0.01));
120 CALL_SUBTEST(check_fitHyperplane(1000, points4d_ptrs, coeffs5d, 0.002));
121 }
122 #endif
123 #ifdef EIGEN_TEST_PART_4
124 {
125 VectorXcd *points11cd_ptrs[1000];
126 for(int i = 0; i < 1000; i++) points11cd_ptrs[i] = new VectorXcd(11);
127 Hyperplane<std::complex<double>,Dynamic> *coeffs12cd = new Hyperplane<std::complex<double>,Dynamic>(11);
128 makeNoisyCohyperplanarPoints(1000, points11cd_ptrs, coeffs12cd, 0.01);
129 CALL_SUBTEST(check_fitHyperplane(100, points11cd_ptrs, *coeffs12cd, 0.025));
130 CALL_SUBTEST(check_fitHyperplane(1000, points11cd_ptrs, *coeffs12cd, 0.006));
131 delete coeffs12cd;
132 for(int i = 0; i < 1000; i++) delete points11cd_ptrs[i];
133 }
134 #endif
135 }
136 }
137