GaussianDistribution.cpp

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/*
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or
 * (at your option) any later version.
 *
 * Written (W) 2013 Heiko Strathmann
 */

#include <shogun/distributions/classical/GaussianDistribution.h>

#ifdef HAVE_EIGEN3

#include <shogun/base/Parameter.h>
#include <shogun/mathematics/eigen3.h>

using namespace shogun;
using namespace Eigen;

CGaussianDistribution::CGaussianDistribution() : CProbabilityDistribution()
{
    init();
}

CGaussianDistribution::CGaussianDistribution(SGVector<float64_t> mean,
        SGMatrix<float64_t> cov, bool cov_is_factor) :
                CProbabilityDistribution(mean.vlen)
{
    REQUIRE(cov.num_rows==cov.num_cols, "Covariance must be square but is "
            "%dx%d\n", cov.num_rows, cov.num_cols);
    REQUIRE(mean.vlen==cov.num_cols, "Mean must have same dimension as "
            "covariance, which is %dx%d, but is %d\n",
            cov.num_rows, cov.num_cols, mean.vlen);

    init();

    m_mean=mean;

    if (!cov_is_factor)
    {
        Map<MatrixXd> eigen_cov(cov.matrix, cov.num_rows, cov.num_cols);
        m_L=SGMatrix<float64_t>(cov.num_rows, cov.num_cols);
        Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);

        /* compute cholesky */
        LLT<MatrixXd> llt(eigen_cov);
        if (llt.info()==NumericalIssue)
        {
            /* try to compute smalles eigenvalue for information */
            SelfAdjointEigenSolver<MatrixXd> solver(eigen_cov);
            if (solver.info() == Success)
            {
                VectorXd ev=solver.eigenvalues();
                SG_ERROR("Error computing Cholesky of Gaussian's covariance. "
                        "Smallest Eigenvalue is %f.\n", ev[0]);
            }
        }

        eigen_L=llt.matrixL();
    }
    else
        m_L=cov;
}

CGaussianDistribution::~CGaussianDistribution()
{

}

SGMatrix<float64_t> CGaussianDistribution::sample(int32_t num_samples,
        SGMatrix<float64_t> pre_samples) const
{
    REQUIRE(num_samples>0, "Number of samples (%d) must be positive\n",
            num_samples);

    /* use pre-allocated samples? */
    SGMatrix<float64_t> samples;
    if (pre_samples.matrix)
    {
        REQUIRE(pre_samples.num_rows==m_dimension, "Dimension of pre-samples"
                " (%d) does not match dimension of Gaussian (%d)\n",
                pre_samples.num_rows, m_dimension);

        REQUIRE(pre_samples.num_cols==num_samples, "Number of pre-samples"
                " (%d) does not desired number of samples (%d)\n",
                pre_samples.num_cols, num_samples);

        samples=pre_samples;
    }
    else
    {
        /* allocate memory and sample from std normal */
        samples=SGMatrix<float64_t>(m_dimension, num_samples);
        for (index_t i=0; i<m_dimension*num_samples; ++i)
            samples.matrix[i]=sg_rand->std_normal_distrib();
    }

    /* map into desired Gaussian covariance */
    Map<MatrixXd> eigen_samples(samples.matrix, samples.num_rows,
            samples.num_cols);
    Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);
    eigen_samples=eigen_L*eigen_samples;

    /* add mean */
    Map<VectorXd> eigen_mean(m_mean.vector, m_mean.vlen);
    eigen_samples.colwise()+=eigen_mean;

    return samples;
}

SGVector<float64_t> CGaussianDistribution::log_pdf_multiple(SGMatrix<float64_t> samples) const
{
    REQUIRE(samples.num_cols>0, "Number of samples must be positive, but is %d\n",
            samples.num_cols);
    REQUIRE(samples.num_rows==m_dimension, "Sample dimension (%d) does not match"
            "Gaussian dimension (%d)\n", samples.num_rows, m_dimension);

    /* for easier to read code */
    index_t num_samples=samples.num_cols;

    float64_t const_part=-0.5 * m_dimension * CMath::log(2 * CMath::PI);

    /* determinant is product of diagonal elements of triangular matrix */
    float64_t log_det_part=0;
    Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);
    VectorXd diag=eigen_L.diagonal();
    log_det_part=-diag.array().log().sum();

    /* sample based part */
    Map<MatrixXd> eigen_samples(samples.matrix, samples.num_rows,
            samples.num_cols);
    Map<VectorXd> eigen_mean(m_mean.vector, m_mean.vlen);

    /* substract mean from samples (create copy) */
    SGMatrix<float64_t> centred(m_dimension, num_samples);
    Map<MatrixXd> eigen_centred(centred.matrix, centred.num_rows,
            centred.num_cols);
    for (index_t dim=0; dim<m_dimension; ++dim)
    {
        for (index_t sample_idx=0; sample_idx<num_samples; ++sample_idx)
            centred(dim,sample_idx)=samples(dim,sample_idx)-m_mean[dim];
    }

    /* solve the linear system based on factorization */
    MatrixXd solved=eigen_L.triangularView<Lower>().solve(eigen_centred);
    solved=eigen_L.transpose().triangularView<Upper>().solve(solved);

    /* one quadratic part x^T C^-1 x for each sample x */
    SGVector<float64_t> result(num_samples);
    Map<VectorXd> eigen_result(result.vector, result.vlen);
    for (index_t i=0; i<num_samples; ++i)
    {
        /* i-th centred sample */
        VectorXd left=eigen_centred.block(0, i, m_dimension, 1);

        /* inverted covariance times i-th centred sample */
        VectorXd right=solved.block(0,i,m_dimension,1);
        result[i]=-0.5*left.dot(right);
    }

    /* combine and return */
    eigen_result=eigen_result.array()+(log_det_part+const_part);

    /* contains everything */
    return result;

}

void CGaussianDistribution::init()
{
    SG_ADD(&m_mean, "mean", "Mean of the Gaussian.", MS_NOT_AVAILABLE);
    SG_ADD(&m_L, "L", "Lower factor of covariance matrix, "
            "depending on the factorization type.", MS_NOT_AVAILABLE);
}

#endif // HAVE_EIGEN3