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// 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 DenseLM : DenseFunctor<Scalar>
{
typedef DenseFunctor<Scalar> Base;
typedef typename Base::JacobianType JacobianType;
typedef Matrix<Scalar,Dynamic,1> VectorType;
DenseLM(int n, int m) : DenseFunctor<Scalar>(n,m)
{ }
VectorType model(const VectorType& uv, VectorType& x)
{
VectorType y; // Should change 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);
for (int j = 0; j < m; j++)
{
for (int i = 0; i < half; i++)
y(j) += u(i)*std::exp(-(x(j)-i)*(x(j)-i)/(v(i)*v(i)));
}
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);
eigen_assert(fvec.size() == m);
int half = n/2;
VectorBlock<const VectorType> u(uv, 0, half);
VectorBlock<const VectorType> v(uv, half, half);
for (int j = 0; j < m; j++)
{
fvec(j) = m_y(j);
for (int i = 0; i < half; i++)
{
fvec(j) -= u(i) *std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));
}
}
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);
for (int j = 0; j < m; j++)
{
for (int i = 0; i < half; i++)
{
fjac.coeffRef(j,i) = -std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));
fjac.coeffRef(j,i+half) = -2.*u(i)*(m_x(j)-i)*(m_x(j)-i)/(std::pow(v(i),3)) * std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));
}
}
return 0;
}
VectorType m_x, m_y; //Data Points
};
template<typename FunctorType, typename VectorType>
int test_minimizeLM(FunctorType& functor, VectorType& uv)
{
LevenbergMarquardt<FunctorType> lm(functor);
LevenbergMarquardtSpace::Status info;
info = lm.minimize(uv);
VERIFY_IS_EQUAL(info, 1);
//FIXME Check other parameters
return info;
}
template<typename FunctorType, typename VectorType>
int test_lmder(FunctorType& functor, VectorType& uv)
{
typedef typename VectorType::Scalar Scalar;
LevenbergMarquardtSpace::Status info;
LevenbergMarquardt<FunctorType> lm(functor);
info = lm.lmder1(uv);
VERIFY_IS_EQUAL(info, 1);
//FIXME Check other parameters
return info;
}
template<typename FunctorType, typename VectorType>
int test_minimizeSteps(FunctorType& functor, VectorType& uv)
{
LevenbergMarquardtSpace::Status info;
LevenbergMarquardt<FunctorType> lm(functor);
info = lm.minimizeInit(uv);
if (info==LevenbergMarquardtSpace::ImproperInputParameters)
return info;
do
{
info = lm.minimizeOneStep(uv);
} while (info==LevenbergMarquardtSpace::Running);
VERIFY_IS_EQUAL(info, 1);
//FIXME Check other parameters
return info;
}
template<typename T>
void test_denseLM_T()
{
typedef Matrix<T,Dynamic,1> VectorType;
int inputs = 10;
int values = 1000;
DenseLM<T> dense_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;
dense_gaussian.initPoints(uv_ref, x);
// Generate the initial parameters
VectorBlock<VectorType> u(uv, 0, inputs/2);
VectorBlock<VectorType> v(uv, inputs/2, inputs/2);
// Solve the optimization problem
//Solve in one go
u.setOnes(); v.setOnes();
test_minimizeLM(dense_gaussian, uv);
//Solve until the machine precision
u.setOnes(); v.setOnes();
test_lmder(dense_gaussian, uv);
// Solve step by step
v.setOnes(); u.setOnes();
test_minimizeSteps(dense_gaussian, uv);
}
void test_denseLM()
{
CALL_SUBTEST_2(test_denseLM_T<double>());
// CALL_SUBTEST_2(test_sparseLM_T<std::complex<double>());
}
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