test/sparseLM.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <iostream>
#include <fstream>
#include <iomanip>

#include "main.h"
#include <Eigen/LevenbergMarquardt>

using namespace std;
using namespace Eigen;

template <typename Scalar>
struct sparseGaussianTest : SparseFunctor<Scalar, int> {
  typedef Matrix<Scalar, Dynamic, 1> VectorType;
  typedef SparseFunctor<Scalar, int> Base;
  typedef typename Base::JacobianType JacobianType;
  sparseGaussianTest(int inputs, int values) : SparseFunctor<Scalar, int>(inputs, values) {}

  VectorType model(const VectorType& uv, VectorType& x) {
    VectorType y;  // Change this to use expression template
    int m = Base::values();
    int n = Base::inputs();
    eigen_assert(uv.size() % 2 == 0);
    eigen_assert(uv.size() == n);
    eigen_assert(x.size() == m);
    y.setZero(m);
    int half = n / 2;
    VectorBlock<const VectorType> u(uv, 0, half);
    VectorBlock<const VectorType> v(uv, half, half);
    Scalar coeff;
    for (int j = 0; j < m; j++) {
      for (int i = 0; i < half; i++) {
        coeff = (x(j) - i) / v(i);
        coeff *= coeff;
        if (coeff < 1. && coeff > 0.) y(j) += u(i) * std::pow((1 - coeff), 2);
      }
    }
    return y;
  }
  void initPoints(VectorType& uv_ref, VectorType& x) {
    m_x = x;
    m_y = this->model(uv_ref, x);
  }
  int operator()(const VectorType& uv, VectorType& fvec) {
    int m = Base::values();
    int n = Base::inputs();
    eigen_assert(uv.size() % 2 == 0);
    eigen_assert(uv.size() == n);
    int half = n / 2;
    VectorBlock<const VectorType> u(uv, 0, half);
    VectorBlock<const VectorType> v(uv, half, half);
    fvec = m_y;
    Scalar coeff;
    for (int j = 0; j < m; j++) {
      for (int i = 0; i < half; i++) {
        coeff = (m_x(j) - i) / v(i);
        coeff *= coeff;
        if (coeff < 1. && coeff > 0.) fvec(j) -= u(i) * std::pow((1 - coeff), 2);
      }
    }
    return 0;
  }

  int df(const VectorType& uv, JacobianType& fjac) {
    int m = Base::values();
    int n = Base::inputs();
    eigen_assert(n == uv.size());
    eigen_assert(fjac.rows() == m);
    eigen_assert(fjac.cols() == n);
    int half = n / 2;
    VectorBlock<const VectorType> u(uv, 0, half);
    VectorBlock<const VectorType> v(uv, half, half);
    Scalar coeff;

    // Derivatives with respect to u
    for (int col = 0; col < half; col++) {
      for (int row = 0; row < m; row++) {
        coeff = (m_x(row) - col) / v(col);
        coeff = coeff * coeff;
        if (coeff < 1. && coeff > 0.) {
          fjac.coeffRef(row, col) = -(1 - coeff) * (1 - coeff);
        }
      }
    }
    // Derivatives with respect to v
    for (int col = 0; col < half; col++) {
      for (int row = 0; row < m; row++) {
        coeff = (m_x(row) - col) / v(col);
        coeff = coeff * coeff;
        if (coeff < 1. && coeff > 0.) {
          fjac.coeffRef(row, col + half) = -4 * (u(col) / v(col)) * coeff * (1 - coeff);
        }
      }
    }
    return 0;
  }

  VectorType m_x, m_y;  // Data points
};

template <typename T>
void test_sparseLM_T() {
  typedef Matrix<T, Dynamic, 1> VectorType;

  int inputs = 10;
  int values = 2000;
  sparseGaussianTest<T> sparse_gaussian(inputs, values);
  VectorType uv(inputs), uv_ref(inputs);
  VectorType x(values);
  // Generate the reference solution
  uv_ref << -2, 1, 4, 8, 6, 1.8, 1.2, 1.1, 1.9, 3;
  // Generate the reference data points
  x.setRandom();
  x = 10 * x;
  x.array() += 10;
  sparse_gaussian.initPoints(uv_ref, x);

  // Generate the initial parameters
  VectorBlock<VectorType> u(uv, 0, inputs / 2);
  VectorBlock<VectorType> v(uv, inputs / 2, inputs / 2);
  v.setOnes();
  // Generate u or Solve for u from v
  u.setOnes();

  // Solve the optimization problem
  LevenbergMarquardt<sparseGaussianTest<T> > lm(sparse_gaussian);
  int info;
  //   info = lm.minimize(uv);

  VERIFY_IS_EQUAL(info, 1);
  // Do a step by step solution and save the residual
  int maxiter = 200;
  int iter = 0;
  MatrixXd Err(values, maxiter);
  MatrixXd Mod(values, maxiter);
  LevenbergMarquardtSpace::Status status;
  status = lm.minimizeInit(uv);
  if (status == LevenbergMarquardtSpace::ImproperInputParameters) return;
}
EIGEN_DECLARE_TEST(sparseLM) {
  CALL_SUBTEST_1(test_sparseLM_T<double>());

  // CALL_SUBTEST_2(test_sparseLM_T<std::complex<double>());
}