GaussianKernelMatrix.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Efficient special case if the kernel is gaussian and the inputs are sparse vectors
 * 
 * 
 * \par
 * 
 * 
 *
 * \author      T. Glasmachers
 * \date        2007-2012
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <https://shark-ml.github.io/Shark/>
 * 
 * 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_LINALG_GAUSSIANKERNELMATRIX_H
#define SHARK_LINALG_GAUSSIANKERNELMATRIX_H
 
#include <shark/Data/Dataset.h>
#include <shark/LinAlg/Base.h>
 
#include <vector>
#include <cmath>
 
 
namespace shark {
 
 
///\brief Efficient special case if the kernel is Gaussian and the inputs are sparse vectors
template <class T, class CacheType>
class GaussianKernelMatrix
{
public:
 
    typedef CacheType QpFloatType;
    typedef T InputType;
 
    /// Constructor
    /// \param gamma   bandwidth parameter of Gaussian kernel
    /// \param data    data evaluated by the kernel function
    GaussianKernelMatrix(
        double gamma,
        Data<InputType> const& data
    )
    : m_squaredNorms(data.numberOfElements())
    , m_gamma(gamma)
    , m_accessCounter( 0 )
    {
        std::size_t elements = data.numberOfElements();
        x.resize(elements);
        PointerType iter=data.elements().begin();
        for(std::size_t i = 0; i != elements; ++i,++iter){
            x[i]=iter;
            m_squaredNorms(i) =inner_prod(*x[i],*x[i]);//precompute the norms
        }
    }
 
    /// return a single matrix entry
    QpFloatType operator () (std::size_t i, std::size_t j) const
    { return entry(i, j); }
 
    /// return a single matrix entry
    QpFloatType entry(std::size_t i, std::size_t j) const
    {
        ++m_accessCounter;
        double distance = m_squaredNorms(i)-2*inner_prod(*x[i], *x[j])+m_squaredNorms(j);
        return (QpFloatType)std::exp(- m_gamma * distance);
    }
    
    /// \brief Computes the i-th row of the kernel matrix.
    ///
    ///The entries start,...,end of the i-th row are computed and stored in storage.
    ///There must be enough room for this operation preallocated.
    void row(std::size_t i, std::size_t start,std::size_t end, QpFloatType* storage) const
    {
        typename ConstProxyReference<T>::type xi = *x[i];
        m_accessCounter +=end-start;
        SHARK_PARALLEL_FOR(int j = start; j < (int) end; j++)
        {
            double distance = m_squaredNorms(i)-2*inner_prod(xi, *x[j])+m_squaredNorms(j);
            storage[j-start] = std::exp(- m_gamma * distance);
        }
    }
    
    /// \brief Computes the kernel-matrix
    template<class M>
    void matrix(
        blas::matrix_expression<M, blas::cpu_tag> & storage
    ) const{
        for(std::size_t i = 0; i != size(); ++i){
            row(i,0,size(),&storage()(i,0));
        }
    }
 
    /// swap two variables
    void flipColumnsAndRows(std::size_t i, std::size_t j){
        using std::swap;
        swap(x[i],x[j]);
        swap(m_squaredNorms[i],m_squaredNorms[j]);
    }
 
    /// return the size of the quadratic matrix
    std::size_t size() const
    { return x.size(); }
 
    /// query the kernel access counter
    unsigned long long getAccessCount() const
    { return m_accessCounter; }
 
    /// reset the kernel access counter
    void resetAccessCount()
    { m_accessCounter = 0; }
 
protected:
 
    //~ typedef blas::sparse_vector_adaptor<typename T::value_type const,std::size_t> PointerType;
    typedef typename Data<InputType>::const_element_range::iterator PointerType;
    /// Array of data pointers for kernel evaluations
    std::vector<PointerType> x;
    
    RealVector m_squaredNorms;
 
    double m_gamma;
 
    /// counter for the kernel accesses
    mutable unsigned long long m_accessCounter;
};
 
}
#endif