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