paradiseo/edo/src/edoSamplerNormalMulti.h

/*
The Evolving Distribution Objects framework (EDO) is a template-based,
ANSI-C++ evolutionary computation library which helps you to write your
own estimation of distribution algorithms.

This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.

This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

Copyright (C) 2010 Thales group
*/
/*
Authors:
    Johann Dréo <johann.dreo@thalesgroup.com>
    Caner Candan <caner.candan@thalesgroup.com>
*/

#ifndef _edoSamplerNormalMulti_h
#define _edoSamplerNormalMulti_h

#include <cmath>
#include <limits>

#include <edoSampler.h>


#ifdef WITH_BOOST
#include <utils/edoCholesky.h>
#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/symmetric.hpp>
namespace ublas = boost::numeric::ublas;
#else
#ifdef WITH_EIGEN
#include <Eigen/Dense>
#endif // WITH_EIGEN
#endif // WITH_BOOST


/** Sample points in a multi-normal law defined by a mean vector and a covariance matrix.
 *
 * Given M the mean vector and V the covariance matrix, of order n:
 *   - draw a vector T in N(0,I) (i.e. each value is drawn in a normal law with mean=0 an stddev=1)
 *   - compute the Cholesky decomposition L of V (i.e. such as V=LL*)
 *   - return X = M + LT
 *
 * Exists in two implementations, using either
 * <a href="http://www.boost.org/doc/libs/1_50_0/libs/numeric/ublas/doc/index.htm">Boost::uBLAS</a> (if compiled WITH_BOOST)
 * or <a href="http://eigen.tuxfamily.org">Eigen3</a> (WITH_EIGEN).
 *
 * @ingroup Samplers
 * @ingroup EMNA
 * @ingroup Multinormal
 */
template< typename EOT, typename D = edoNormalMulti< EOT > >
class edoSamplerNormalMulti : public edoSampler< D >
{

#ifdef WITH_BOOST

public:
    typedef typename EOT::AtomType AtomType;

    edoSamplerNormalMulti( edoRepairer<EOT> & repairer ) 
        : edoSampler< D >( repairer)
    {}


    EOT sample( D& distrib )
    {
        unsigned int size = distrib.size();
        assert(size > 0);

        // L = cholesky decomposition of varcovar
        const typename cholesky::CholeskyBase<AtomType>::FactorMat& L = _cholesky( distrib.varcovar() );

        // T = vector of size elements drawn in N(0,1)
        ublas::vector< AtomType > T( size );
        for ( unsigned int i = 0; i < size; ++i ) {
            T( i ) = rng.normal();
        }

        // LT = L * T
        ublas::vector< AtomType > LT = ublas::prod( L, T );

        // solution = means + LT
        ublas::vector< AtomType > mean = distrib.mean();
        ublas::vector< AtomType > ublas_solution = mean + LT;
        EOT solution( size );
        std::copy( ublas_solution.begin(), ublas_solution.end(), solution.begin() );

        return solution;
    }

protected:
    cholesky::CholeskyLLT<AtomType> _cholesky;

#else
#ifdef WITH_EIGEN

public:
    typedef typename EOT::AtomType AtomType;

    typedef typename D::Vector Vector;
    typedef typename D::Matrix Matrix;

    edoSamplerNormalMulti( edoRepairer<EOT> & repairer ) 
        : edoSampler< D >( repairer)
    {}


    EOT sample( D& distrib )
    {
        unsigned int size = distrib.size();
        assert(size > 0);

        // LsD = cholesky decomposition of varcovar

        // Computes L and mD such as V = L mD L^T
        Eigen::LDLT<Matrix> cholesky( distrib.varcovar() );
        Matrix L = cholesky.matrixL();
        assert(L.innerSize() == size);
        assert(L.outerSize() == size);

        Matrix mD = cholesky.vectorD().asDiagonal();
        assert(mD.innerSize() == size);
        assert(mD.outerSize() == size);

        // now compute the final symetric matrix: LsD = L mD^1/2
        // remember that V = ( L mD^1/2) ( L mD^1/2)^T
        // fortunately, the square root of a diagonal matrix is the square 
        // root of all its elements
        Matrix sqrtD = mD.cwiseSqrt();
        assert(sqrtD.innerSize() == size);
        assert(sqrtD.outerSize() == size);

        Matrix LsD = L * sqrtD;
        assert(LsD.innerSize() == size);
        assert(LsD.outerSize() == size);

        // T = vector of size elements drawn in N(0,1)
        Vector T( size );
        for ( unsigned int i = 0; i < size; ++i ) {
            T( i ) = rng.normal();
        }
        assert(T.innerSize() == size);
        assert(T.outerSize() == 1);

        // LDT = (L mD^1/2) * T
        Vector LDT = LsD * T;
        assert(LDT.innerSize() == size);
        assert(LDT.outerSize() == 1);

        // solution = means + LDT
        Vector mean = distrib.mean();
        assert(mean.innerSize() == size);
        assert(mean.outerSize() == 1);

        Vector typed_solution = mean + LDT;
        assert(typed_solution.innerSize() == size);
        assert(typed_solution.outerSize() == 1);

        // copy in the EOT structure (more probably a vector)
        EOT solution( size );
        for( unsigned int i = 0; i < mean.innerSize(); i++ ) {
            solution[i]= typed_solution(i);
        }
        assert( solution.size() == size );

        return solution;
    }
#endif // WITH_EIGEN
#endif // WITH_BOOST
}; // class edoNormalMulti


#endif // !_edoSamplerNormalMulti_h