text: // 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
    }
  }
  