root/library/tests/mixtures_test.cpp @ 550

#include "estim/mixtures.h"
#include "estim/arx.h"
#include "stat/exp_family.h"
using namespace bdm;

//These lines are needed for use of cout and endl
using std::cout;
using std::endl;

void disp_mix2D ( const MixEF &Mi ) {
        const eprod &ep = ( ( const eprod& ) ( Mi.posterior() ) );
        int i;
        mat Var ( 2, 2 ), M ( 1, 2 );
        for ( i = 0; i < ep._rv().length() - 1; i++ ) { // -1 => last one is the weight
                ( ( egiw* ) ep ( i ) )->mean_mat ( M, Var );
                cout << "Mean: " << M << endl << "Variance: " << endl << Var << endl;
        }
        cout << "Weights: " << ep ( i )->mean() << endl;
}

mat grid2D ( const MixEF &M, const vec &xb, const vec &yb, int Ngr = 100 ) {
        mat PPdf ( Ngr + 1, Ngr + 1 );
        vec rgr ( 3 );

        rgr ( 2 ) = 1;
        int i = 0, j = 0;
        double xstep = ( xb ( 1 ) - xb ( 0 ) ) / Ngr;
        double ystep = ( yb ( 1 ) - yb ( 0 ) ) / Ngr;

        for ( double x = xb ( 0 ); x <= xb ( 1 ); x += xstep, i++ ) {
                rgr ( 0 ) = x;
                j = 0;
                for ( double y = yb ( 0 ); y <= yb ( 1 ); y += ystep, j++ ) {
                        rgr ( 1 ) = y;
                        PPdf ( i, j ) = exp ( M.logpred ( rgr ) );
                }
        }
        return PPdf;
}

int main() {
        RV x ( "{x }", "2" );


        cout << "Test for estimation of a 2D Gaussian mixture" << endl;
        ///////////////////////////////////
        // Setup model

        vec m1 ( "-2 -2" );
        vec m2 ( "2 2" );

        fsqmat V1 ( mat ( "1 0.5; 0.5 1" ) );
        fsqmat V2 ( mat ( "2 -0.1; -0.1 2" ) );

        enorm_fsqmat_ptr C1;
        C1->set_rv ( x );
        C1->set_parameters ( m1, V1 );
        enorm_fsqmat_ptr C2;
        C2->set_rv ( x );
        C2->set_parameters ( m2, V2 );

        epdf_array Sim ( 2 );
        Sim ( 0 ) = C1;
        Sim ( 1 ) = C2;
        emix Simul;
        Simul.set_rv ( x );
        Simul.set_parameters ( "0.5 0.6", Sim );

        // Sample parameters
        int ndat = 100;
        mat Smp = Simul.sample_m ( ndat );

        cout << "Simulated means: " << m1 << " and " << m2 << endl;
        cout << "Simulated covariances: " << endl << V1 << " and " << endl << V2 << endl;

        //////////////////////////////
        // Prepare estimator manually

        // Initial values of components
        mat V0 = 1e-4 * eye ( 3 );
        V0 ( 0, 0 ) *= 100;
        V0 ( 1, 1 ) *= 100;
        mat Vp = "0 0 1; 0 0 1; 1 1 0";
        Vp *= 5 * 1e-5;

        ARX M1;
        M1.set_statistics ( 2, V0 - Vp, 8 );
        ARX M2;
        M2.set_statistics ( 2, V0 + Vp, 8 );

        // Build mixture model
        Array<BMEF*> A ( 2 );
        A ( 0 ) = &M1;
        A ( 1 ) = &M2;
        MixEF Post ( A, "0.5 0.5" );
        cout << "Initial mixture:" << endl;
        disp_mix2D ( Post );

        // Add ones for constant coefficients
        mat Data = concat_vertical ( Smp, ones ( 1, Smp.cols() ) );
        Post.bayes ( Data );

        cout << "Posterior mixture:" << endl;
        disp_mix2D ( Post );

        //TEST random initialization
        RNG_randomize();
        ARX Aflat;
        Aflat.set_statistics ( 2, V0, 7 );
        MixEF RND;
        RND.init ( &Aflat, Data, 10 ); // already initialized!
        cout << endl << "== Randomly initialized mixture ==" << endl;
        cout << endl << "== INIT ==" << endl;
        disp_mix2D ( RND );
        mat PPdf_I = grid2D ( RND, vec_2 ( -5.0, 5.0 ), vec_2 ( -5.0, 5.0 ) );;

        RND.bayes ( Data );
        cout << endl << "== BAYES ==" << endl;
        disp_mix2D ( RND );


        it_file of ( "mixef_test.it", true );
        of << Name ( "Smp" ) << Smp;
        of << Name ( "PPdf" ) << grid2D ( Post, vec_2 ( -5.0, 5.0 ), vec_2 ( -5.0, 5.0 ) );
        of << Name ( "PPdf_I" ) << PPdf_I;
        of << Name ( "PPdf_RND" ) << grid2D ( RND, vec_2 ( -5.0, 5.0 ), vec_2 ( -5.0, 5.0 ) );

        cout << endl << "Variables written to file mixef_test.it:" << endl;
        cout << "Smp  : data sampled from the simulator " << endl;
        cout << "PPdf : posterior density on a grid <-5,5><-5,5>" << endl;
        cout << "PPdf_RND : posterior density of randomly initilaized mixture on a grid <-5,5><-5,5>" << endl;
}