radial_approx.cpp

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#include "dmp/radial_approx.h"
#include<stdio.h>
using namespace Eigen;
using namespace std;

namespace dmp{

RadialApprox::RadialApprox(int num_bases, double base_width, double alpha)
{
        n_bases = num_bases;
        features = new double[n_bases];
        centers = new double[n_bases];
        widths = new double[n_bases];
        weights.resize(n_bases);
        for(int i=0; i<n_bases; i++){
                features[i] = 0;
                centers[i] = exp((-alpha*i)/n_bases);
                widths[i] = base_width * (1/exp((-alpha*i)/n_bases));
        }
}


RadialApprox::RadialApprox(const vector<double> &w, double base_width, double alpha)
{
        weights = w;
        n_bases = w.size();
        features = new double[n_bases];
                centers = new double[n_bases];
                widths = new double[n_bases];
                for(int i=0; i<n_bases; i++){
                        features[i] = 0;
                        centers[i] = ((double)i)/((double)n_bases);  //exp((-alpha*i)/n_bases);
                        widths[i] = base_width; //base_width * exp((-alpha*i)/n_bases);
                }
}


RadialApprox::~RadialApprox()
{
        delete[] features;
        delete[] centers;
        delete[] widths;
}


double RadialApprox::evalAt(double x)
{
        calcFeatures(x);

        double wsum = 0;
        for(int i=0; i<n_bases; i++){
                wsum += features[i] * weights[i];
        }
        return wsum;
}


void RadialApprox::leastSquaresWeights(double *X, double *Y, int n_pts)
{
        MatrixXd D_mat = MatrixXd(n_pts,n_bases);
        MatrixXd Y_mat = MatrixXd(n_pts,1);

        //Calculate the design matrix
        for(int i=0; i<n_pts; i++){
                Y_mat(i,0) = Y[i];
                calcFeatures(X[i]);
                for(int j=0; j<n_bases; j++){
                        D_mat(i,j) = features[j];
                }
        }

        //Calculate the least squares weights via projection onto the basis functions
        MatrixXd w = pseudoinverse(D_mat.transpose() * D_mat) * D_mat.transpose() * Y_mat;
        for(int i=0; i<n_bases; i++){
                weights[i] = w(i,0);
        }
}


void RadialApprox::calcFeatures(double x)
{
        double sum = 0;
        for(int i=0; i<n_bases; i++){
                features[i] = exp(-widths[i]*(x-centers[i])*(x-centers[i]));
                sum += features[i];
        }
        for(int i=0; i<n_bases; i++){
                features[i] /= sum;
        }
}


MatrixXd RadialApprox::pseudoinverse(MatrixXd mat){
        //Numpy uses 1e-15 by default.  I use 1e-10 just to be safe.
        double precisionCutoff = 1e-10;

        //Compute the SVD of the matrix
        JacobiSVD<MatrixXd> svd(mat, ComputeThinU | ComputeThinV);
        MatrixXd U = svd.matrixU();
        MatrixXd V = svd.matrixV();
        MatrixXd S = svd.singularValues();

        //Psuedoinvert the diagonal matrix of singular values
        MatrixXd S_plus = MatrixXd::Zero(n_bases, n_bases);
        for(int i=0; i<n_bases; i++){
                if(S(i) > precisionCutoff){  //Cutoff to avoid huge inverted values for numerical stability
                        S_plus(i,i) = 1.0/S(i);
                }
        }

        //Compute psuedoinverse of orginal matrix
        return V * S_plus * U.transpose();
}

}