stat.cpp

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#include <stdlib.h>

//#include <gsl/gsl_rng.h>
//#include <gsl/gsl_randist.h>
//#include <gsl/gsl_eigen.h>
//#include <gsl/gsl_blas.h>
#include <math.h>
#include <gmapping/utils/stat.h>

namespace GMapping {

#if 0

int sampleUniformInt(int max)
{
  return (int)(max*(rand()/(RAND_MAX+1.0)));
}

double sampleUniformDouble(double min, double max)
{
  return min + (rand() / (double)RAND_MAX) * (max - min);
}


#endif

// Draw randomly from a zero-mean Gaussian distribution, with standard
// deviation sigma.
// We use the polar form of the Box-Muller transformation, explained here:
//   http://www.taygeta.com/random/gaussian.html
double pf_ran_gaussian(double sigma)
{
  double x1, x2, w;
  double r;

  do
  {
    do { r = drand48(); } while (r == 0.0);
    x1 = 2.0 * r - 1.0;
    do { r = drand48(); } while (r == 0.0);
    x2 = 2.0 * drand48() - 1.0;
    w = x1*x1 + x2*x2;
  } while(w > 1.0 || w==0.0);

  return(sigma * x2 * sqrt(-2.0*log(w)/w));
}

double sampleGaussian(double sigma, unsigned int S) {
  /*
        static gsl_rng * r = NULL;
        if(r==NULL) {
                gsl_rng_env_setup();
                r = gsl_rng_alloc (gsl_rng_default);
        }
        */
        if (S!=0)
        {
                //gsl_rng_set(r, S);
                srand(S);
        }
        if (sigma==0)
                return 0;
        //return gsl_ran_gaussian (r,sigma);
        return pf_ran_gaussian (sigma);
}
#if 0

double evalGaussian(double sigmaSquare, double delta){
        if (sigmaSquare<=0)
                sigmaSquare=1e-4;
        return exp(-.5*delta*delta/sigmaSquare)/sqrt(2*M_PI*sigmaSquare);
}

#endif
double evalLogGaussian(double sigmaSquare, double delta){
        if (sigmaSquare<=0)
                sigmaSquare=1e-4;
        return -.5*delta*delta/sigmaSquare-.5*log(2*M_PI*sigmaSquare);
}
#if 0


Covariance3 Covariance3::zero={0.,0.,0.,0.,0.,0.};

Covariance3 Covariance3::operator + (const Covariance3 & cov) const{
        Covariance3 r(*this);
        r.xx+=cov.xx;
        r.yy+=cov.yy;
        r.tt+=cov.tt;
        r.xy+=cov.xy;
        r.yt+=cov.yt;
        r.xt+=cov.xt;
        return r;
}

EigenCovariance3::EigenCovariance3(){}

EigenCovariance3::EigenCovariance3(const Covariance3& cov){
        static gsl_eigen_symmv_workspace * m_eigenspace=NULL;
        static gsl_matrix * m_cmat=NULL;
        static gsl_matrix * m_evec=NULL;
        static gsl_vector * m_eval=NULL;
        static gsl_vector * m_noise=NULL;
        static gsl_vector * m_pnoise=NULL;
        
        if (m_eigenspace==NULL){
                m_eigenspace=gsl_eigen_symmv_alloc(3);
                m_cmat=gsl_matrix_alloc(3,3);
                m_evec=gsl_matrix_alloc(3,3);
                m_eval=gsl_vector_alloc(3);
                m_noise=gsl_vector_alloc(3);
                m_pnoise=gsl_vector_alloc(3);
        }

        gsl_matrix_set(m_cmat,0,0,cov.xx); gsl_matrix_set(m_cmat,0,1,cov.xy); gsl_matrix_set(m_cmat,0,2,cov.xt);
        gsl_matrix_set(m_cmat,1,0,cov.xy); gsl_matrix_set(m_cmat,1,1,cov.yy); gsl_matrix_set(m_cmat,1,2,cov.yt);
        gsl_matrix_set(m_cmat,2,0,cov.xt); gsl_matrix_set(m_cmat,2,1,cov.yt); gsl_matrix_set(m_cmat,2,2,cov.tt);
        gsl_eigen_symmv (m_cmat, m_eval,  m_evec, m_eigenspace);
        for (int i=0; i<3; i++){
                eval[i]=gsl_vector_get(m_eval,i);
                for (int j=0; j<3; j++)
                        evec[i][j]=gsl_matrix_get(m_evec,i,j);
        }
}

EigenCovariance3 EigenCovariance3::rotate(double angle) const{
        static gsl_matrix * m_rmat=NULL;
        static gsl_matrix * m_vmat=NULL;
        static gsl_matrix * m_result=NULL;
        if (m_rmat==NULL){
                m_rmat=gsl_matrix_alloc(3,3);
                m_vmat=gsl_matrix_alloc(3,3);
                m_result=gsl_matrix_alloc(3,3);
        }
        
        double c=cos(angle);
        double s=sin(angle);
        gsl_matrix_set(m_rmat,0,0, c ); gsl_matrix_set(m_rmat,0,1, -s); gsl_matrix_set(m_rmat,0,2, 0.);
        gsl_matrix_set(m_rmat,1,0, s ); gsl_matrix_set(m_rmat,1,1,  c); gsl_matrix_set(m_rmat,1,2, 0.);
        gsl_matrix_set(m_rmat,2,0, 0.); gsl_matrix_set(m_rmat,2,1, 0.); gsl_matrix_set(m_rmat,2,2, 1.);
        
        for (unsigned int i=0; i<3; i++)
                for (unsigned int j=0; j<3; j++)
                        gsl_matrix_set(m_vmat,i,j,evec[i][j]);
        gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1., m_rmat, m_vmat, 0., m_result);
        EigenCovariance3 ecov(*this);
        for (int i=0; i<3; i++){
                for (int j=0; j<3; j++)
                        ecov.evec[i][j]=gsl_matrix_get(m_result,i,j);
        }
        return ecov;
}

OrientedPoint EigenCovariance3::sample() const{
        static gsl_matrix * m_evec=NULL;
        static gsl_vector * m_noise=NULL;
        static gsl_vector * m_pnoise=NULL;
        if (m_evec==NULL){
                m_evec=gsl_matrix_alloc(3,3);
                m_noise=gsl_vector_alloc(3);
                m_pnoise=gsl_vector_alloc(3);
        }
        for (int i=0; i<3; i++){
                for (int j=0; j<3; j++)
                        gsl_matrix_set(m_evec,i,j, evec[i][j]);
        }
        for (int i=0; i<3; i++){
                double v=sampleGaussian(sqrt(eval[i]));
                if(isnan(v))
                        v=0;
                gsl_vector_set(m_pnoise,i, v);
        }
        gsl_blas_dgemv (CblasNoTrans, 1., m_evec, m_pnoise, 0, m_noise);
        OrientedPoint ret(gsl_vector_get(m_noise,0),gsl_vector_get(m_noise,1),gsl_vector_get(m_noise,2));
        ret.theta=atan2(sin(ret.theta), cos(ret.theta));
        return ret;
}

#endif

double Gaussian3::eval(const OrientedPoint& p) const{
        OrientedPoint q=p-mean;
        q.theta=atan2(sin(p.theta-mean.theta),cos(p.theta-mean.theta));
        double v1,v2,v3;
        v1 = covariance.evec[0][0]*q.x+covariance.evec[1][0]*q.y+covariance.evec[2][0]*q.theta;
        v2 = covariance.evec[0][1]*q.x+covariance.evec[1][1]*q.y+covariance.evec[2][1]*q.theta;
        v3 = covariance.evec[0][2]*q.x+covariance.evec[1][2]*q.y+covariance.evec[2][2]*q.theta;
        return evalLogGaussian(covariance.eval[0], v1)+evalLogGaussian(covariance.eval[1], v2)+evalLogGaussian(covariance.eval[2], v3);
}

#if 0
void Gaussian3::computeFromSamples(const std::vector<OrientedPoint> & poses, const std::vector<double>& weights ){
        OrientedPoint mean=OrientedPoint(0,0,0);
        double wcum=0;
        double s=0, c=0;
        std::vector<double>::const_iterator w=weights.begin();
        for (std::vector<OrientedPoint>::const_iterator p=poses.begin(); p!=poses.end(); p++){
                s+=*w*sin(p->theta);
                c+=*w*cos(p->theta);
                mean.x+=*w*p->x;
                mean.y+=*w*p->y;
                wcum+=*w;
                w++;
        }
        mean.x/=wcum;
        mean.y/=wcum;
        s/=wcum;
        c/=wcum;
        mean.theta=atan2(s,c);

        Covariance3 cov=Covariance3::zero;
        w=weights.begin();
        for (std::vector<OrientedPoint>::const_iterator p=poses.begin(); p!=poses.end(); p++){
                OrientedPoint delta=(*p)-mean;
                delta.theta=atan2(sin(delta.theta),cos(delta.theta));
                cov.xx+=*w*delta.x*delta.x;
                cov.yy+=*w*delta.y*delta.y;
                cov.tt+=*w*delta.theta*delta.theta;
                cov.xy+=*w*delta.x*delta.y;
                cov.yt+=*w*delta.y*delta.theta;
                cov.xt+=*w*delta.x*delta.theta;
                w++;
        }
        cov.xx/=wcum;
        cov.yy/=wcum;
        cov.tt/=wcum;
        cov.xy/=wcum;
        cov.yt/=wcum;
        cov.xt/=wcum;
        EigenCovariance3 ecov(cov);
        this->mean=mean;
        this->covariance=ecov;
        this->cov=cov;
}

void Gaussian3::computeFromSamples(const std::vector<OrientedPoint> & poses){
        OrientedPoint mean=OrientedPoint(0,0,0);
        double wcum=1;
        double s=0, c=0;
        for (std::vector<OrientedPoint>::const_iterator p=poses.begin(); p!=poses.end(); p++){
                s+=sin(p->theta);
                c+=cos(p->theta);
                mean.x+=p->x;
                mean.y+=p->y;
                wcum+=1.;
        }
        mean.x/=wcum;
        mean.y/=wcum;
        s/=wcum;
        c/=wcum;
        mean.theta=atan2(s,c);

        Covariance3 cov=Covariance3::zero;
        for (std::vector<OrientedPoint>::const_iterator p=poses.begin(); p!=poses.end(); p++){
                OrientedPoint delta=(*p)-mean;
                delta.theta=atan2(sin(delta.theta),cos(delta.theta));
                cov.xx+=delta.x*delta.x;
                cov.yy+=delta.y*delta.y;
                cov.tt+=delta.theta*delta.theta;
                cov.xy+=delta.x*delta.y;
                cov.yt+=delta.y*delta.theta;
                cov.xt+=delta.x*delta.theta;
        }
        cov.xx/=wcum;
        cov.yy/=wcum;
        cov.tt/=wcum;
        cov.xy/=wcum;
        cov.yt/=wcum;
        cov.xt/=wcum;
        EigenCovariance3 ecov(cov);
        this->mean=mean;
        this->covariance=ecov;
        this->cov=cov;
}
#endif

}// end namespace