ProductKernel.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Product of kernel functions.
 * 
 * 
 *
 * \author      T. Glasmachers, O.Krause
 * \date        2012
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark 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 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark 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 Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
//===========================================================================

#ifndef SHARK_MODELS_KERNELS_PRODUCTKERNEL_H
#define SHARK_MODELS_KERNELS_PRODUCTKERNEL_H


#include <shark/Models/Kernels/AbstractKernelFunction.h>

namespace shark{


///
/// \brief Product of kernel functions.
///
/// \par
/// The product of any number of kernels is again a valid kernel.
/// This class supports a kernel af the form
/// \f$ k(x, x') = k_1(x, x') \cdot k_2(x, x') \cdot \dots \cdot k_n(x, x') \f$
/// for any number of base kernels. All kernels need to be defined
/// on the same input space.
///
/// \par
/// Derivatives are currently not implemented. Only the plain
/// kernel value can be computed. Everyone is free to add this
/// functionality :)
///
template<class InputType>
class ProductKernel : public AbstractKernelFunction<InputType>
{
private:
    typedef AbstractKernelFunction<InputType> base_type;
public:
    typedef AbstractKernelFunction<InputType> SubKernel;
    typedef typename base_type::BatchInputType BatchInputType;
    typedef typename base_type::ConstInputReference ConstInputReference;
    typedef typename base_type::ConstBatchInputReference ConstBatchInputReference;
    /// \brief Default constructor.
    ProductKernel(){
        // this->m_features |= base_type::HAS_FIRST_PARAMETER_DERIVATIVE;
        // this->m_features |= base_type::HAS_SECOND_PARAMETER_DERIVATIVE;
        // this->m_features |= base_type::HAS_FIRST_INPUT_DERIVATIVE;
        // this->m_features |= base_type::HAS_SECOND_INPUT_DERIVATIVE;
        this->m_features |= base_type::IS_NORMALIZED;    // an "empty" product is a normalized kernel (k(x, x) = 1).
    }

    /// \brief Constructor for a product of two kernels.
    ProductKernel(SubKernel* k1, SubKernel* k2){
        // this->m_features |= base_type::HAS_FIRST_PARAMETER_DERIVATIVE;
        // this->m_features |= base_type::HAS_SECOND_PARAMETER_DERIVATIVE;
        // this->m_features |= base_type::HAS_FIRST_INPUT_DERIVATIVE;
        // this->m_features |= base_type::HAS_SECOND_INPUT_DERIVATIVE;
        this->m_features |= base_type::IS_NORMALIZED;    // an "empty" product is a normalized kernel (k(x, x) = 1).
        addKernel(k1);
        addKernel(k2);
    }
    ProductKernel(std::vector<SubKernel*> kernels){
        // this->m_features |= base_type::HAS_FIRST_PARAMETER_DERIVATIVE;
        // this->m_features |= base_type::HAS_SECOND_PARAMETER_DERIVATIVE;
        // this->m_features |= base_type::HAS_FIRST_INPUT_DERIVATIVE;
        // this->m_features |= base_type::HAS_SECOND_INPUT_DERIVATIVE;
        this->m_features |= base_type::IS_NORMALIZED;    // an "empty" product is a normalized kernel (k(x, x) = 1).
        for(std::size_t i = 0; i != kernels.size(); ++i)
            addKernel(kernels[i]);
    }

    /// \brief From INameable: return the class name.
    std::string name() const
    { return "ProductKernel"; }

    /// \brief Add one more kernel to the expansion.
    ///
    /// \param  k  The pointer is expected to remain valid during the lifetime of the ProductKernel object.
    ///
    void addKernel(SubKernel* k){
        SHARK_ASSERT(k != NULL);

        m_kernels.push_back(k);
        m_numberOfParameters += k->numberOfParameters();
        if (! k->isNormalized()) this->m_features.reset(base_type::IS_NORMALIZED);   // products of normalized kernels are normalized.
    }

    RealVector parameterVector() const{
        RealVector ret(m_numberOfParameters);
        std::size_t pos = 0;
        for(auto kernel: m_kernels){
            auto const& params = kernel->parameterVector();
            noalias(subrange(ret,pos, pos + params.size())) = params;
            pos += params.size();
        }
        return ret;
    }

    void setParameterVector(RealVector const& newParameters){
        SIZE_CHECK(newParameters.size() == m_numberOfParameters);
        
        std::size_t pos = 0;
        for(auto kernel: m_kernels){
            std::size_t numParams = kernel->numberOfParameters();
            kernel->setParameterVector(subrange(newParameters,pos, pos + numParams));
            pos += numParams;
        }
    }

    std::size_t numberOfParameters() const{
        return m_numberOfParameters;
    }

    /// \brief evaluates the kernel function
    ///
    /// This function returns the product of all sub-kernels.
    double eval(ConstInputReference x1, ConstInputReference x2) const{
        double prod = 1.0;
        for (std::size_t i=0; i<m_kernels.size(); i++) 
            prod *= m_kernels[i]->eval(x1, x2);
        return prod;
    }
    
    void eval(ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix& result) const{
        std::size_t sizeX1 = batchSize(batchX1);
        std::size_t sizeX2 = batchSize(batchX2);
        
        //evaluate first kernel to initialize the result
        m_kernels[0]->eval(batchX1,batchX2,result);
        
        RealMatrix kernelResult(sizeX1,sizeX2);
        for(std::size_t i = 1; i != m_kernels.size(); ++i){
            m_kernels[i]->eval(batchX1,batchX2,kernelResult);
            noalias(result) *= kernelResult;
        }
    }
    
    void eval(ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix& result, State& state) const{
        eval(batchX1,batchX2,result);
    }
        
    /// From ISerializable.
    void read(InArchive& ar){
        for(std::size_t i = 0;i != m_kernels.size(); ++i ){
            ar >> *m_kernels[i];
        }
        ar >> m_numberOfParameters;
    }

    /// From ISerializable.
    void write(OutArchive& ar) const{
        for(std::size_t i = 0;i != m_kernels.size(); ++i ){
            ar << const_cast<AbstractKernelFunction<InputType> const&>(*m_kernels[i]);//prevent serialization warning
        }
        ar << m_numberOfParameters;
    }

protected:
    std::vector<SubKernel*> m_kernels;           ///< vector of sub-kernels
    std::size_t m_numberOfParameters;        ///< total number of parameters in the product (this is redundant information)
};


}
#endif