root/library/tests/stresssuite/mixtures_stress.cpp

#include "estim/mixtures.h"
#include "estim/arx.h"
#include "stat/exp_family.h"
#include "../mat_checks.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.factor ( i ) )->mean_mat ( M, Var );
        cout << "Mean: " << M << endl << "Variance: " << endl << Var << endl;
    }
    cout << "Weights: " << ep.factor ( 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, empty_vec ) );
        }
    }
    return PPdf;
}

TEST ( mixtures_stress ) {
    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._w() = "0.5 0.6";
    Simul._Coms() = Sim;
    Simul.validate();

    // Sample parameters
    int ndat = 100;
    mat Smp = Simul.sample_mat ( 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 );
    M1.validate();
    ARX M2;
    M2.set_statistics ( 2, V0 + Vp, 8 );
    M2.validate();

    // 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 , empty_vec );

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

    //TEST random initialization
    RNG_randomize();
    ARX Aflat;
    Aflat.set_statistics ( 2, V0, 7 );
    Aflat.validate();
    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, empty_vec );
    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;
}