main.cpp

// This example need EIGEN, if we do not have NOP the full example

#include "config.h"

#ifndef HAVE_EIGEN

int main(int argc, char* argv[])
{
    return 0;
}

#else


#define EIGEN_USE_LAPACKE
#include "Vector/vector_dist.hpp"
#include "DMatrix/EMatrix.hpp"
#include <Eigen/Eigenvalues>
#include <Eigen/Jacobi>
#include <limits>
#include "Vector/vector_dist.hpp"
#include <f15_cec_fun.hpp>
#include <boost/math/special_functions/sign.hpp>



// PARAMETERS
constexpr int dim = 10;
// when you set dim set also lambda to to 4+std::floor(3*log(dim))
constexpr int lambda = 7;
constexpr int mu = lambda/2;
double psoWeight = 0.7;
// number of cma-step before pso step
int N_pso = 200;
double stopTolX = 2e-11;
double stopTolUpX = 2000.0;
int restart_cma = 1;
size_t max_fun_eval = 30000000;
constexpr int hist_size = 21;

// Convenient global variables (Their value is set after)
double mu_eff = 1.0;
double cs = 1.0;
double cc = 1.0;
double ccov = 1.0;
double chiN;
double d_amps = 1.0;
double stop_fitness = 1.0;
int eigeneval = 0;
double t_c = 0.1;
double b = 0.1;




constexpr int sigma = 0;
constexpr int Cov_m = 1;
constexpr int B = 2;
constexpr int D = 3;
constexpr int Zeta = 4;
constexpr int path_s = 5;
constexpr int path_c = 6;
constexpr int ord = 7;
constexpr int stop = 8;
constexpr int fithist = 9;
constexpr int weight = 10;
constexpr int validfit = 11;
constexpr int xold = 12;
constexpr int last_restart = 13;
constexpr int iniphase = 14;
constexpr int xmean_st = 15;
constexpr int meanz_st = 16;

typedef vector_dist<dim,double, aggregate<double,
                                         EMatrixXd,
                                         EMatrixXd,
                                         Eigen::DiagonalMatrix<double,Eigen::Dynamic>,
                                         EVectorXd[lambda],
                                         EVectorXd,
                                         EVectorXd,
                                         int[lambda],
                                         int,
                                         double [hist_size],
                                         double [dim],
                                         double,
                                         EVectorXd,
                                         int,
                                         bool,
                                         EVectorXd,
                                         EVectorXd> > particle_type;



double generateGaussianNoise(double mu, double sigma)
{
    static const double epsilon = std::numeric_limits<double>::min();
    static const double two_pi = 2.0*3.14159265358979323846;

    thread_local double z1;
    thread_local double generate;
    generate = !generate;

    if (!generate)
    {return z1 * sigma + mu;}

    double u1, u2;
    do
    {
       u1 = rand() * (1.0 / RAND_MAX);
       u2 = rand() * (1.0 / RAND_MAX);
    }
    while ( u1 <= epsilon );

    double z0;
    z0 = sqrt(-2.0 * log(u2)) * cos(two_pi * u1);
    z1 = sqrt(-2.0 * log(u2)) * sin(two_pi * u1);
    return z0 * sigma + mu;
}

template<unsigned int dim>
EVectorXd generateGaussianVector()
{
    EVectorXd tmp;
    tmp.resize(dim);

    for (size_t i = 0 ; i < dim ; i++)
    {
        tmp(i) = generateGaussianNoise(0,1);
    }

    return tmp;
}


template<unsigned int dim>
void fill_vector(double (& f)[dim], EVectorXd & ev)
{
    for (size_t i = 0 ; i < dim ; i++)
    {ev(i) = f[i];}
}

void fill_vector(const double * f, EVectorXd & ev)
{
    for (size_t i = 0 ; i < ev.size() ; i++)
    {ev(i) = f[i];}
}

struct fun_index
{
    double f;
    int id;

    bool operator<(const fun_index & tmp) const
    {
        return f < tmp.f;
    }
};

double wm[mu];

void init_weight()
{
    for (size_t i = 0 ; i < mu ; i++)
    {wm[i] = log(double(mu)+1.0) - log(double(i)+1.0);}

    double tot = 0.0;

    for (size_t i = 0 ; i < mu ; i++)
    {tot += wm[i];}

    double sum = 0.0;
    double sum2 = 0.0;

    for (size_t i = 0 ; i < mu ; i++)
    {
        wm[i] /= tot;
        sum += wm[i];
        sum2 += wm[i]*wm[i];
    }

    // also set mu_eff
    mu_eff=sum*sum/sum2;

}

double weight_sample(int i)
{
    return wm[i];
}


void create_rotmat(EVectorXd & S,EVectorXd & T, EMatrixXd & R)
{
    EVectorXd S_work(dim);
    EVectorXd T_work(dim);
    EVectorXd S_sup(dim);
    EVectorXd T_sup(dim);

    EMatrixXd R_tar(dim,dim);
    EMatrixXd R_tmp(dim,dim);
    EMatrixXd R_sup(dim,dim);
    double G_S,G_C;
    EMatrixXd S_tmp(2,2);
    EMatrixXd T_tmp(2,2);
    int p,q,i;

    S_work = S;
    T_work = T;

    R.setIdentity();
    R_tar = R;
    R_tmp = R;

    for (p = dim - 2; p >= 0 ; p -= 1)
    {

        for (q = dim - 1 ; q >= p+1 ; q-= 1)
        {
            T_tmp(0) = T_work(p);
            T_tmp(1) = T_work(q);
            S_tmp(0) = S_work(p);
            S_tmp(1) = S_work(q);

            // Perform Givens Rotation on start vector

            Eigen::JacobiRotation<double> G;
            double z;
            G.makeGivens(S_tmp(0), S_tmp(1),&z);

            // Check direction of rotation
            double sign = 1.0;
            if (z < 0.0)
            {sign = -1.0;}

            // Build a Rotation Matrix out of G_C and G_S
            R_tmp.setIdentity();
            R_tmp(p,p) = sign*G.c();
            R_tmp(q,q) = sign*G.c();
            R_tmp(p,q) = sign*-G.s();
            R_tmp(q,p) = sign*G.s();

            // Rotate start vector and update R
            // S_work = R_tmp*S_work

            S_work = R_tmp*S_work;
            // R = R_tmp*R
            R = R_tmp*R;

            // Perform Givens Rotation on target vector

            G.makeGivens(T_tmp(0), T_tmp(1),&z);

            sign = 1.0;
            if (z < 0.0)
            {sign = -1.0;}

            R_tmp.setIdentity();
            R_tmp(p,p) = sign*G.c();
            R_tmp(q,q) = sign*G.c();
            R_tmp(p,q) = sign*-G.s();
            R_tmp(q,p) = sign*G.s();

            // Rotate target vector and update R_tar

            T_work = R_tmp*T_work;
            R_tar = R_tmp*R_tar;
        }
    }

    R = R_tar.transpose()*R;

    // Check the rotation

    EVectorXd Check(dim);
    Check = R*S;
}



void updatePso(openfpm::vector<double> & best_sol,
               double sigma,
               EVectorXd & xmean,
               EVectorXd & xold,
               EMatrixXd & B,
               Eigen::DiagonalMatrix<double,Eigen::Dynamic> & D,
               EMatrixXd & C_pso)
{
    EVectorXd best_sol_ei(dim);

    double bias_weight = psoWeight;
    fill_vector(&best_sol.get(0),best_sol_ei);
    EVectorXd gb_vec = best_sol_ei-xmean;
    double gb_vec_length = sqrt(gb_vec.transpose() * gb_vec);
    EVectorXd b_main = B.col(dim-1);
    EVectorXd bias(dim);
    bias.setZero();

    // Rotation Matrix
    EMatrixXd R(dim,dim);

    if (gb_vec_length > 0.0)
    {
        if(sigma < gb_vec_length)
        {
            if(sigma/gb_vec_length <= t_c*gb_vec_length)
            {bias = 0.5*gb_vec;}
            else
            {bias = sigma*gb_vec/gb_vec_length;}
        }
        else
        {bias.setZero();}
    }

      xmean = xmean + bias;

      if (psoWeight < 1.0)
      {
          EMatrixXd B_rot(dim,dim);
          Eigen::DiagonalMatrix<double,Eigen::Dynamic> D_square(dim);

          EVectorXd gb_vec_old = best_sol_ei - xold;
          create_rotmat(b_main,gb_vec_old,R);
          for (size_t i = 0 ; i < dim ; i++)
          {B_rot.col(i) = R*B.col(i);}

          for (size_t i = 0 ; i < dim ; i++)
          {D_square.diagonal()[i] = D.diagonal()[i] * D.diagonal()[i];}
          C_pso = B_rot * D_square * B_rot.transpose();

          EMatrixXd trUp = C_pso.triangularView<Eigen::Upper>();
          EMatrixXd trDw = C_pso.triangularView<Eigen::StrictlyUpper>();
          C_pso = trUp + trDw.transpose();
      }
}



void broadcast_best_solution(particle_type & vd,
                             openfpm::vector<double> & best_sol,
                             double & best,
                             double best_sample,
                             openfpm::vector<double> & best_sample_sol)
{
    best_sol.resize(dim);
    auto & v_cl = create_vcluster();

    double best_old = best_sample;
    v_cl.min(best_sample);
    v_cl.execute();

    // The old solution remain the best
    if (best < best_sample)
    {return;}

    best = best_sample;

    size_t rank;
    if (best_old == best_sample)
    {
        rank = v_cl.getProcessUnitID();

        // we own the minimum and we decide who broad cast
        v_cl.min(rank);
        v_cl.execute();

        if (rank == v_cl.getProcessUnitID())
        {
            for (size_t i = 0 ; i < dim ; i++)
            {best_sol.get(i) = best_sample_sol.get(i);}
        }
    }
    else
    {
        rank = std::numeric_limits<size_t>::max();

        // we do not own  decide who broad cast
        v_cl.min(rank);
        v_cl.execute();
    }

    // now we broad cast the best solution across processors

    v_cl.Bcast(best_sol,rank);
    v_cl.execute();
}



void cmaes_myprctile(openfpm::vector<fun_index> & f_obj, double (& perc)[2], double (& res)[2])
{
    double sar[lambda];
    double availablepercentiles[lambda];
    int idx[hist_size];
    int i,k;

    for (size_t i = 0 ; i < lambda ; i++)
    {
        availablepercentiles[i] = 0.0;
        sar[i] = f_obj.get(i).f;
    }
    std::sort(&sar[0],&sar[lambda]);

    for (size_t i = 0 ; i < 2 ; i++)
    {
        if (perc[i] <= (100.0*0.5/lambda))
        {res[i] = sar[0];}
        else if (perc[i] >= (100.0*(lambda-0.5)/lambda) )
        {res[i] = sar[lambda-1];}
        else
        {
            for (size_t j = 0 ; j < lambda ; j++)
            {availablepercentiles[j] = 100.0 * ((double(j)+1.0)-0.5) / lambda;}

            for (k = 0 ; k < lambda ; k++)
            {if(availablepercentiles[k] >= perc[i]) {break;}}
            k-=1;

            res[i] = sar[k] + (sar[k+1]-sar[k]) * (perc[i]
                            -availablepercentiles[k]) / (availablepercentiles[k+1] - availablepercentiles[k]);
        }
    }
}


double maxval(double (& buf)[hist_size], bool (& mask)[hist_size])
{
    double max = 0.0;
    for (size_t i = 0 ; i < hist_size ; i++)
    {
        if (buf[i] > max && mask[i] == true)
        {max = buf[i];}
    }

    return max;
}

double minval(double (& buf)[hist_size], bool (& mask)[hist_size])
{
    double min = std::numeric_limits<double>::max();
    for (size_t i = 0 ; i < hist_size ; i++)
    {
        if (buf[i] < min && mask[i] == true)
        {min = buf[i];}
    }

    return min;
}


void cmaes_intobounds(EVectorXd & x, EVectorXd & xout,bool (& idx)[dim], bool & idx_any)
{
    idx_any = false;
    for (size_t i = 0; i < dim ; i++)
    {
        if(x(i) < -5.0)
        {
            xout(i) = -5.0;
            idx[i] = true;
            idx_any = true;
        }
        else if (x(i) > 5.0)
        {
            xout(i) = 5.0;
            idx[i] = true;
            idx_any = true;
        }
        else
        {
            xout(i) = x(i);
            idx[i] = false;
        }
    }
}



void cmaes_handlebounds(openfpm::vector<fun_index> & f_obj,
                        double sigma,
                        double & validfit,
                        EVectorXd (& arxvalid)[lambda],
                        EVectorXd (& arx)[lambda],
                        EMatrixXd & C,
                        EVectorXd & xmean,
                        EVectorXd & xold,
                        double (& weight)[dim],
                        double (& fithist)[hist_size],
                        bool & iniphase,
                        double & validfitval,
                        double mu_eff,
                        int step,
                        int last_restart)
{
    double val[2];
    double value;
    double diag[dim];
    double meandiag;
    int i,k,maxI;
    bool mask[hist_size];
    bool idx[dim];
    EVectorXd tx(dim);
    int dfitidx[hist_size];
    double dfitsort[hist_size];
    double prct[2] = {25.0,75.0};
    bool idx_any;

    for (size_t i = 0 ; i < hist_size ; i++)
    {
        dfitsort[i] = 0.0;
        dfitidx[i] = 0;

        if (fithist[i] > 0.0)
        {mask[i] = true;}
        else
        {mask[i] = false;}
    }

    for (size_t i = 0 ; i < dim ; i++)
    {diag[i] = C(i,i);}

    maxI = 0;

    meandiag = C.trace()/dim;

    cmaes_myprctile(f_obj, prct, val);
    value = (val[1] - val[0]) / dim / meandiag / (sigma*sigma);

    if (value >= std::numeric_limits<double>::max())
    {
        auto & v_cl = create_vcluster();
        std::cout << "Process " << v_cl.rank() << " warning: Non-finite fitness range" << std::endl;
        value = maxval(fithist,mask);
    }
    else if(value == 0.0)
    {
        value = minval(fithist,mask);
    }
    else if (validfit == 0.0)
    {
        for (size_t i = 0 ; i < hist_size ; i++)
        {fithist[i] = -1.0;}
        validfit = 1;
    }

    for (size_t i = 0; i < hist_size ; i++)
    {
        if(fithist[i] < 0.0)
        {
            fithist[i] = value;
            maxI = i;
            break;
        }
        else if(i == hist_size-1)
        {
            for (size_t k = 0 ; k < hist_size-1 ; k++)
            {fithist[k] = fithist[k+1];}
            fithist[i] = value;
            maxI = i;
        }
    }

    cmaes_intobounds(xmean,tx,idx,idx_any);

    if (iniphase)
    {
        if (idx_any)
        {
            if(maxI == 0)
            {value = fithist[0];}
            else
            {
                openfpm::vector<fun_index> fitsort(maxI+1);
                for (size_t i = 0 ; i <= maxI; i++)
                {
                    fitsort.get(i).f = fithist[i];
                    fitsort.get(i).id = i;
                }

                fitsort.sort();
                for (size_t k = 0; k <= maxI ; k++)
                {fitsort.get(k).f = fithist[fitsort.get(k).id];}

                if ((maxI+1) % 2 == 0)
                {value = (fitsort.get(maxI/2).f+fitsort.get(maxI/2+1).f)/2.0;}
                else
                {value = fitsort.get(maxI/2).f;}
            }
            for (size_t i = 0 ; i < dim ; i++)
            {
                diag[i] = diag[i]/meandiag;
                weight[i] = 2.0002 * value / diag[i];
            }
            if (validfitval == 1.0 && step-last_restart > 2)
            {
                iniphase = false;
            }
        }
    }

    if(idx_any)
    {
        tx = xmean - tx;
        for(size_t i = 0 ; i < dim ; i++)
        {
            idx[i] = (idx[i] && (fabs(tx(i)) > 3.0*std::max(1.0,sqrt(dim)/mu_eff) * sigma * sqrt(diag[i])));
            idx[i] = (idx[i] && (std::copysign(1.0,tx(i)) == std::copysign(1.0,(xmean(i)-xold(i)))) );
        }
        for (size_t i = 0 ; i < dim ; i++)
        {
            if (idx[i] == true)
            {
                weight[i] = pow(1.2,(std::max(1.0,mu_eff/10.0/dim)))*weight[i];
            }
        }
    }
    double arpenalty[lambda];
    for (size_t i = 0 ; i < lambda ; i++)
    {
        arpenalty[i] = 0.0;
        for (size_t j = 0 ; j < dim ; j++)
        {
            arpenalty[i] += weight[j] * (arxvalid[i](j) - arx[i](j))*(arxvalid[i](j) - arx[i](j));
        }
        f_obj.get(i).f += arpenalty[i];
    }
//  fitness%sel = fitness%raw + bnd%arpenalty;
}


double adjust_sigma(double sigma, EMatrixXd & C)
{
    for (size_t i = 0 ; i < dim ; i++)
    {
        if (sigma*sqrt(C(i,i)) > 5.0)
        {sigma = 5.0/sqrt(C(i,i));}
    }

    return sigma;
}


void cma_step(particle_type & vd, int step,  double & best,
              int & best_i, openfpm::vector<double> & best_sol,
              size_t & fun_eval)
{
    size_t fe = 0;
    EVectorXd xmean(dim);
    EVectorXd mean_z(dim);
    EVectorXd arxvalid[lambda];
    EVectorXd arx[lambda];

    for (size_t i = 0 ; i < lambda ; i++)
    {
        arx[i].resize(dim);
        arxvalid[i].resize(dim);
    }

    double best_sample = std::numeric_limits<double>::max();
    openfpm::vector<double> best_sample_sol(dim);

    openfpm::vector<fun_index> f_obj(lambda);

    int counteval = step*lambda;

    auto it = vd.getDomainIterator();
    while (it.isNext())
    {
        auto p = it.get();

        if (vd.getProp<stop>(p) == true)
        {++it;continue;}

        EVectorXd (& arz)[lambda] = vd.getProp<Zeta>(p);

        // fill the mean vector;

        fill_vector(vd.getPos(p),xmean);

        for (size_t j = 0 ; j < lambda ; j++)
        {
            vd.getProp<Zeta>(p)[j] = generateGaussianVector<dim>();
            arx[j] = xmean + vd.getProp<sigma>(p)*vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<Zeta>(p)[j];

            // sample point has to be inside -5.0 and 5.0
            for (size_t i = 0 ; i < dim ; i++)
            {
                if (arx[j](i) < -5.0)
                {arxvalid[j](i) = -5.0;}
                else if (arx[j](i) > 5.0)
                {arxvalid[j](i) = 5.0;}
                else
                {arxvalid[j](i) = arx[j](i);}
            }

            f_obj.get(j).f = hybrid_composition<dim>(arxvalid[j]);
            f_obj.get(j).id = j;
            fe++;

            // Get the best ever
            if (f_obj.get(j).f < best_sample)
            {
                best_sample = f_obj.get(j).f;

                // Copy the new mean as position of the particle
                for (size_t i = 0 ; i < dim ; i++)
                {best_sample_sol.get(i) = arxvalid[j](i);}
            }
        }

        // Add penalities for out of bound points
        cmaes_handlebounds(f_obj,vd.getProp<sigma>(p),
                           vd.getProp<validfit>(p),arxvalid,
                           arx,vd.getProp<Cov_m>(p),
                           xmean,vd.getProp<xold>(p),vd.getProp<weight>(p),
                           vd.getProp<fithist>(p),vd.getProp<iniphase>(p),
                           vd.getProp<validfit>(p),mu_eff,
                           step,vd.getProp<last_restart>(p));

        f_obj.sort();

        for (size_t j = 0 ; j < lambda ; j++)
        {vd.getProp<ord>(p)[j] = f_obj.get(j).id;}

        vd.getProp<xold>(p) = xmean;

        // Calculate weighted mean

        xmean.setZero();
        mean_z.setZero();
        for (size_t j = 0 ; j < mu ; j++)
        {
            xmean += weight_sample(j)*arx[vd.getProp<ord>(p)[j]];
            mean_z += weight_sample(j)*vd.getProp<Zeta>(p)[vd.getProp<ord>(p)[j]];
        }

        vd.getProp<xmean_st>(p) = xmean;
        vd.getProp<meanz_st>(p) = mean_z;

        ++it;
    }

    // Find the best point across processors
    broadcast_best_solution(vd,best_sol,best,best_sample,best_sample_sol);

    // bool calculate B and D
    bool calc_bd = counteval - eigeneval > lambda/(ccov)/dim/10;
    if (calc_bd == true)
    {eigeneval = counteval;}

    auto it2 = vd.getDomainIterator();
    while (it2.isNext())
    {
        auto p = it2.get();

        if (vd.getProp<stop>(p) == true)
        {++it2;continue;}

        xmean = vd.getProp<xmean_st>(p);
        mean_z = vd.getProp<meanz_st>(p);

        vd.getProp<path_s>(p) = vd.getProp<path_s>(p)*(1.0 - cs) + sqrt(cs*(2.0-cs)*mu_eff)*vd.getProp<B>(p)*mean_z;

        double hsig = vd.getProp<path_s>(p).norm()/sqrt(1.0-pow((1.0-cs),(2.0*double((step-vd.getProp<last_restart>(p))))))/chiN < 1.4 + 2.0/(dim+1);

        vd.getProp<path_c>(p) = (1-cc)*vd.getProp<path_c>(p) + hsig * sqrt(cc*(2-cc)*mu_eff)*(vd.getProp<B>(p)*vd.getProp<D>(p)*mean_z);

        if (step % N_pso == 0)
        {
            EMatrixXd C_pso(dim,dim);
            updatePso(best_sol,vd.getProp<sigma>(p),xmean,vd.getProp<xold>(p),vd.getProp<B>(p),vd.getProp<D>(p),C_pso);

            // Adapt covariance matrix C
            vd.getProp<Cov_m>(p) = (1.0-ccov+(1.0-hsig)*ccov*cc*(2.0-cc)/mu_eff)*vd.getProp<Cov_m>(p) +
                                    ccov*(1.0/mu_eff)*(vd.getProp<path_c>(p)*vd.getProp<path_c>(p).transpose());

            for (size_t i = 0 ; i < mu ; i++)
            {vd.getProp<Cov_m>(p) += ccov*(1.0-1.0/mu_eff)*(vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<Zeta>(p)[vd.getProp<ord>(p)[i]])*weight_sample(i)*
                                          (vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<Zeta>(p)[vd.getProp<ord>(p)[i]]).transpose();
            }

            vd.getProp<Cov_m>(p) = psoWeight*vd.getProp<Cov_m>(p) + (1.0 - psoWeight)*C_pso;
        }
        else
        {
            // Adapt covariance matrix C
            vd.getProp<Cov_m>(p) = (1.0-ccov+(1.0-hsig)*ccov*cc*(2.0-cc)/mu_eff)*vd.getProp<Cov_m>(p) +
                                    ccov*(1.0/mu_eff)*(vd.getProp<path_c>(p)*vd.getProp<path_c>(p).transpose());

            for (size_t i = 0 ; i < mu ; i++)
            {vd.getProp<Cov_m>(p) += ccov*(1.0-1.0/mu_eff)*(vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<Zeta>(p)[vd.getProp<ord>(p)[i]])*weight_sample(i)*
                                          (vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<Zeta>(p)[vd.getProp<ord>(p)[i]]).transpose();
            }
        }

        // Numeric error

        double smaller = std::numeric_limits<double>::max();
        for (size_t i = 0 ; i < dim ; i++)
        {
            if (vd.getProp<sigma>(p)*sqrt(vd.getProp<D>(p).diagonal()[i]) > 5.0)
            {
                if (smaller > 5.0/sqrt(vd.getProp<D>(p).diagonal()[i]))
                {smaller = 5.0/sqrt(vd.getProp<D>(p).diagonal()[i]);}
            }
        }
        if (smaller != std::numeric_limits<double>::max())
        {vd.getProp<sigma>(p) = smaller;}

        //Adapt step-size sigma
        vd.getProp<sigma>(p) = vd.getProp<sigma>(p)*exp((cs/d_amps)*(vd.getProp<path_s>(p).norm()/chiN - 1));

        // Update B and D from C

        if (calc_bd)
        {
            EMatrixXd trUp = vd.getProp<Cov_m>(p).triangularView<Eigen::Upper>();
            EMatrixXd trDw = vd.getProp<Cov_m>(p).triangularView<Eigen::StrictlyUpper>();
            vd.getProp<Cov_m>(p) = trUp + trDw.transpose();

            // Eigen decomposition
            Eigen::SelfAdjointEigenSolver<EMatrixXd> eig_solver;

            eig_solver.compute(vd.getProp<Cov_m>(p));

            for (size_t i = 0 ; i < eig_solver.eigenvalues().size() ; i++)
            {vd.getProp<D>(p).diagonal()[i] = sqrt(eig_solver.eigenvalues()[i]);}
            vd.getProp<B>(p) = eig_solver.eigenvectors();

            // Make first component always positive
            for (size_t i = 0 ; i < dim ; i++)
            {
                if (vd.getProp<B>(p)(0,i) < 0)
                {vd.getProp<B>(p).col(i) = - vd.getProp<B>(p).col(i);}
            }

            EMatrixXd tmp = vd.getProp<B>(p).transpose();
        }

        // Copy the new mean as position of the particle
        for (size_t i = 0 ; i < dim ; i++)
        {vd.getPos(p)[i] = xmean(i);}

        vd.getProp<sigma>(p) = adjust_sigma(vd.getProp<sigma>(p),vd.getProp<Cov_m>(p));

        // Stop conditions
        bool stop_tol = true;
        bool stop_tolX = true;
        for (size_t i = 0 ; i < dim ; i++)
        {
            stop_tol &= (vd.getProp<sigma>(p)*std::max(fabs(vd.getProp<path_c>(p)(i)),sqrt(vd.getProp<Cov_m>(p)(i,i)))) < stopTolX;
            stop_tolX &= vd.getProp<sigma>(p)*sqrt(vd.getProp<D>(p).diagonal()[i]) > stopTolUpX;
        }

        vd.getProp<stop>(p) = stop_tol | stop_tolX;

        // Escape flat fitness, or better terminate?
        if (f_obj.get(0).f == f_obj.get(std::ceil(0.7*lambda)).f )
        {
            vd.getProp<sigma>(p) = vd.getProp<sigma>(p)*exp(0.2+cs/d_amps);
            std::cout << "warning: flat fitness, consider reformulating the objective";

            // Stop it
            vd.getProp<stop>(p) = true;
        }

        if (vd.getProp<stop>(p) == true)
        {std::cout << "Stopped" << std::endl;}

        if (restart_cma && vd.getProp<stop>(p) == true)
        {
            std::cout << "------- Restart #" << std::endl;

            std::cout << "---------------------------------" << std::endl;
            std::cout << "Best: " << best << "   " << fun_eval << std::endl;
            std::cout << "---------------------------------" << std::endl;

            vd.getProp<last_restart>(p) = step;
            vd.getProp<xold>(p).setZero();

            for (size_t i = 0 ; i < vd.getProp<D>(p).diagonal().size() ; i++)
            {vd.getProp<D>(p).diagonal()[i] = 1.0;}
            vd.getProp<B>(p).resize(dim,dim);
            vd.getProp<B>(p).setIdentity();
            vd.getProp<Cov_m>(p) = vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<D>(p)*vd.getProp<B>(p);
            vd.getProp<path_s>(p).resize(dim);
            vd.getProp<path_s>(p).setZero(dim);
            vd.getProp<path_c>(p).resize(dim);
            vd.getProp<path_c>(p).setZero(dim);
            vd.getProp<stop>(p) = false;
            vd.getProp<iniphase>(p) = true;
            vd.getProp<last_restart>(p) = 0;
            vd.getProp<sigma>(p) = 2.0;

            // a different point in space
            for (size_t i = 0 ; i < dim ; i++)
            {
                // we define x, assign a random position between 0.0 and 1.0
                vd.getPos(p)[i] = 10.0*(double)rand() / RAND_MAX - 5.0;
            }

            // Initialize the bound history

            for (size_t i = 0 ; i < hist_size ; i++)
            {vd.getProp<fithist>(p)[i] = -1.0;}
            vd.getProp<fithist>(p)[0] = 1.0;
            vd.getProp<validfit>(p) = 0.0;
        }

        ++it2;
    }

    auto & v_cl = create_vcluster();
    v_cl.sum(fe);
    v_cl.execute();

    fun_eval += fe;
}


int main(int argc, char* argv[])
{
    // initialize the library
    openfpm_init(&argc,&argv);

    auto & v_cl = create_vcluster();

    // Here we define our domain a 2D box with internals from 0 to 1.0 for x and y
    Box<dim,double> domain;

    for (size_t i = 0 ; i < dim ; i++)
    {
        domain.setLow(i,0.0);
        domain.setHigh(i,1.0);
    }

    // Here we define the boundary conditions of our problem
    size_t bc[dim];
    for (size_t i = 0 ; i < dim ; i++)
    {bc[i] = NON_PERIODIC;};

    prepare_f15<dim>();

    // extended boundary around the domain, and the processor domain
    Ghost<dim,double> g(0.0);

    particle_type vd(16,domain,bc,g);

    // Initialize constants

    stop_fitness = 1e-10;
    size_t stopeval = 1e3*dim*dim;

    // Strategy parameter setting: Selection
    init_weight();

    // Strategy parameter setting: Adaptation
    cc = 4.0 / (dim+4.0);
    cs = (mu_eff+2.0) / (double(dim)+mu_eff+3.0);
    ccov = (1.0/mu_eff) * 2.0/((dim+1.41)*(dim+1.41)) +
           (1.0 - 1.0/mu_eff)* std::min(1.0,(2.0*mu_eff-1.0)/((dim+2.0)*(dim+2.0) + mu_eff));
    d_amps = 1 + 2*std::max(0.0, sqrt((mu_eff-1.0)/(dim+1))-1) + cs;

    chiN = sqrt(dim)*(1.0-1.0/(4.0*dim)+1.0/(21.0*dim*dim));



    // initialize the srand
    int seed = 24756*v_cl.rank()*v_cl.rank() + time(NULL);
    srand(seed);

    auto it = vd.getDomainIterator();

    while (it.isNext())
    {
        auto p = it.get();

        for (size_t i = 0 ; i < dim ; i++)
        {
            // we define x, assign a random position between 0.0 and 1.0
            vd.getPos(p)[i] = 10.0*(double)rand() / RAND_MAX - 5.0;
        }

        vd.getProp<sigma>(p) = 2.0;

        // Initialize the covariant Matrix,B and D to identity

        vd.getProp<D>(p).resize(dim);
        for (size_t i = 0 ; i < vd.getProp<D>(p).diagonal().size() ; i++)
        {vd.getProp<D>(p).diagonal()[i] = 1.0;}
        vd.getProp<B>(p).resize(dim,dim);
        vd.getProp<B>(p).setIdentity();
        vd.getProp<Cov_m>(p) = vd.getProp<B>(p)*vd.getProp<D>(p)*vd.getProp<D>(p)*vd.getProp<B>(p);
        vd.getProp<path_s>(p).resize(dim);
        vd.getProp<path_s>(p).setZero(dim);
        vd.getProp<path_c>(p).resize(dim);
        vd.getProp<path_c>(p).setZero(dim);
        vd.getProp<stop>(p) = false;
        vd.getProp<iniphase>(p) = true;
        vd.getProp<last_restart>(p) = 0;

        // Initialize the bound history

        for (size_t i = 0 ; i < hist_size ; i++)
        {vd.getProp<fithist>(p)[i] = -1.0;}
        vd.getProp<fithist>(p)[0] = 1.0;
        vd.getProp<validfit>(p) = 0.0;

        // next particle
        ++it;
    }

    if (v_cl.rank() == 0)
    {std::cout << "Starting PS-CMA-ES" << std::endl;}

    double best = 0.0;
    int best_i = 0;

    best = std::numeric_limits<double>::max();
    openfpm::vector<double> best_sol(dim);
    // now do several iteration

    int stop_cond = 0;
    size_t fun_eval = 0;
    int i = 0;
    while (fun_eval < max_fun_eval && best > 120.000001)
    {
        // sample offspring
        cma_step(vd,i+1,best,best_i,best_sol,fun_eval);

        i++;
    }

    if (v_cl.rank() == 0)
    {
        std::cout << "Best solution: " << best << " with " << fun_eval << std::endl;
        std::cout << "at: " << std::endl;

        for (size_t i = 0 ; i < best_sol.size() ; i++)
        {
            std::cout << best_sol.get(i) << " ";
        }
    }

    openfpm_finalize();


}

#endif