CRNPolynomialRegression.cpp

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/* Copyright 2011-2016 CoReNum, INSA-Lyon, ENS-Lyon
 * 
 * This file is part of libcrn.
 * 
 * libcrn is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * libcrn is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with libcrn.  If not, see <http://www.gnu.org/licenses/>.
 * 
 * file: CRNPolynomialRegression.cpp
 * \author Yann LEYDIER
 */

#include <CRNMath/CRNPolynomialRegression.h>
#include <CRNMath/CRNSquareMatrixDouble.h>
#include <CRNProtocols.h>

using namespace crn;

void PolynomialRegression::TranslateY(int increment)
{
    coefficients[0] += increment;
    for (Point2DDouble &p : data)
    {
        p.Y += increment;
    }
}

void PolynomialRegression::computeCoeffs()
{
    std::sort(data.begin(), data.end(), Point2DDouble::Comparer(Direction::LEFT));
    // create matrices
    MatrixDouble X(data.size(), dimension + 1);
    MatrixDouble Y(data.size(), size_t(1));
    for (size_t tmp = 0; tmp < data.size(); ++tmp)
    {
        X[tmp][0] = 1;
        for (size_t d = 1; d <= dimension; ++d)
        {
            X[tmp][d] = X[tmp][d - 1] * data[tmp].X;
        }
        Y[tmp][0] = data[tmp].Y;
    }
    // Y = X ⋅ A + ε ⇒ Â = (tX ⋅ X)^-1 ⋅ tX ⋅ Y
    SquareMatrixDouble tmpMat(X.MakeCovariance());
    tmpMat *= (double)data.size(); // covariance is normalized, we don't want this
    tmpMat = tmpMat.MakeGaussJordanInverse();
    X.Transpose();
    MatrixDouble res(tmpMat);
    res *= X;
    res *= Y;
    for (size_t d = 0; d <= dimension; ++d)
    {
        coefficients[d] = res[d][0];
    }
}

double PolynomialRegression::operator[](double x) const
{
    if (extrapolation == Extrapolation::LINEAR)
    {
        if (x < data.front().X)
        {
            double x0 = data[0].X;
            double x1 = x0 + (data[1].X - x0) / 5;
            double y0 = (*this)[x0];
            double y1 = (*this)[x1];
            double slope = (y1 - y0) / (x1 - x0);
            return y0 + slope * (x - x0);
        }
        if (x > data.back().X)
        {
            double xn = data.back().X;
            double xn1 = xn - (xn - data[data.size() - 2].X) / 5;
            double yn = (*this)[xn];
            double yn1 = (*this)[xn1];
            double slope = (yn - yn1) / (xn - xn1);
            return yn + slope * (x - xn);
        }
    }
    double y = coefficients[0];
    double xx = 1;
    for (size_t d = 1; d <= dimension; ++d)
    {
        xx *= x;
        y += coefficients[d] * xx;
    }
    return y;
}

CRN_BEGIN_CLASS_CONSTRUCTOR(PolynomialRegression)
    Cloner::Register<PolynomialRegression>();
CRN_END_CLASS_CONSTRUCTOR(PolynomialRegression)