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// 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>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#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
}
}
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