auxiliary_pf.h

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#ifndef AUXILIARY_PF_H
#define AUXILIARY_PF_H
 
#include <array> //array
#include <vector> // vector
#include <functional> // function
 
#ifdef DROPPINGTHISINRPACKAGE
    #include <RcppEigen.h>
    // [[Rcpp::depends(RcppEigen)]]
#else
    #include <Eigen/Dense>
#endif
 
#include <cmath>
 
#include "pf_base.h"
#include "rv_samp.h" // for k_generator
 
 
namespace pf {
 
namespace filters {
 
 
template<size_t nparts, size_t dimx, size_t dimy, typename resamp_t, typename float_t, bool debug=false>
class APF : public bases::pf_base<float_t, dimy, dimx>
{
private:
 
    using ssv = Eigen::Matrix<float_t,dimx,1>;
    using osv = Eigen::Matrix<float_t,dimy,1>;
    using Mat = Eigen::Matrix<float_t,Eigen::Dynamic,Eigen::Dynamic>;
    using arrayfloat_t = std::array<float_t, nparts>;
    using arrayVec = std::array<ssv, nparts>;
    using arrayUInt = std::array<unsigned int, nparts>;
 
public:
 
    APF(const unsigned int &rs=1);
    
    
    virtual ~APF();
    
    float_t getLogCondLike () const; 
    
    
    std::vector<Mat> getExpectations () const;
    
 
    void filter(const osv &data, const std::vector<std::function<const Mat(const ssv&)> >& fs = std::vector<std::function<const Mat(const ssv&)> >());
    
 
    virtual float_t logMuEv (const ssv &x1 ) = 0;
    
    
    virtual ssv propMu (const ssv &xtm1 ) = 0;
    
    
    virtual ssv q1Samp (const osv &y1) = 0;
    
    
    virtual ssv fSamp (const ssv &xtm1) = 0;
    
    
    virtual float_t logQ1Ev (const ssv &x1, const osv &y1) = 0;
    
    
    virtual float_t logGEv (const osv &yt, const ssv &xt) = 0;
 
 
protected:
    std::array<ssv,nparts>  m_particles;
    
    std::array<float_t,nparts> m_logUnNormWeights;
    
    unsigned int m_now; 
    
    float_t m_logLastCondLike; 
    
    unsigned int m_rs;
    
    resamp_t m_resampler;
    
    rvsamp::k_gen<nparts,float_t> m_kGen;
    
    std::vector<Mat> m_expectations;
    
};
 
 
 
template<size_t nparts, size_t dimx, size_t dimy, typename resamp_t, typename float_t, bool debug>
APF<nparts, dimx, dimy, resamp_t, float_t, debug>::APF(const unsigned int &rs) 
    : m_now(0)
    , m_logLastCondLike(0.0)
    , m_rs(rs)
{
    std::fill(m_logUnNormWeights.begin(), m_logUnNormWeights.end(), 0.0);
}
 
 
template<size_t nparts, size_t dimx, size_t dimy, typename resamp_t, typename float_t, bool debug>
APF<nparts, dimx, dimy, resamp_t, float_t, debug>::~APF() { }
 
 
template<size_t nparts, size_t dimx, size_t dimy, typename resamp_t, typename float_t, bool debug>
void APF<nparts, dimx, dimy, resamp_t, float_t, debug>::filter(const osv &data, const std::vector<std::function<const Mat(const ssv&)> >& fs)
{
    
    if(m_now > 0)
    { 
        
        // set up "first stage weights" to make k index sampler 
        arrayfloat_t logFirstStageUnNormWeights = m_logUnNormWeights;
        arrayVec oldPartics = m_particles;
        float_t m3(-std::numeric_limits<float_t>::infinity());
        float_t m2(-std::numeric_limits<float_t>::infinity());
        for(size_t ii = 0; ii < nparts; ++ii)  
        {
            // update m3
            if(m_logUnNormWeights[ii] > m3)
                m3 = m_logUnNormWeights[ii];
            
            // sample
            ssv xtm1                        = oldPartics[ii];
            logFirstStageUnNormWeights[ii] += logGEv(data, propMu(xtm1)); 
            
            // accumulate things
            if(logFirstStageUnNormWeights[ii] > m2)
                m2 = logFirstStageUnNormWeights[ii];
            
            // print stuff if debug mode is on
            #ifndef DROPPINGTHISINRPACKAGE
            if constexpr(debug) {
                std::cout << "time: " << m_now 
                          << ", first stage log unnorm weight: " << logFirstStageUnNormWeights[ii] 
                          << "\n";
            }
            #endif
 
 
        }
               
        // draw ks (indexes) (handles underflow issues)
        arrayUInt myKs = m_kGen.sample(logFirstStageUnNormWeights); 
                
        // now draw xts
        float_t m1(-std::numeric_limits<float_t>::infinity());
        float_t first_cll_sum(0.0);
        float_t second_cll_sum(0.0);
        float_t third_cll_sum(0.0);
        ssv xtm1k;
        ssv muT;
        for(size_t ii = 0; ii < nparts; ++ii)   
        {
            // calclations for log p(y_t|y_{1:t-1}) (using log-sum-exp trick)
            second_cll_sum += std::exp( logFirstStageUnNormWeights[ii] - m2 );
            third_cll_sum  += std::exp( m_logUnNormWeights[ii] - m3 );            
            
            // sampling and unnormalized weight update
            xtm1k                   = oldPartics[myKs[ii]];
            m_particles[ii]         = fSamp(xtm1k); 
            muT                     = propMu(xtm1k); 
            m_logUnNormWeights[ii] += logGEv(data, m_particles[ii]) - logGEv(data, muT);
            
            
            #ifndef DROPPINGTHISINRPACKAGE
            if constexpr(debug){ 
                std::cout << "time: " << m_now 
                          << ", transposed sample: " << m_particles[ii].transpose() 
                          << ", log unnorm weight: " << m_logUnNormWeights[ii] << "\n";
            }
            #endif
 
            // update m1
            if(m_logUnNormWeights[ii] > m1)
                m1 = m_logUnNormWeights[ii];
        }
 
        // calculate estimate for log of last conditonal likelihood
        for(size_t p = 0; p < nparts; ++p)
             first_cll_sum += std::exp( m_logUnNormWeights[p] - m1 );
        m_logLastCondLike = m1 + std::log(first_cll_sum) + m2 + std::log(second_cll_sum) - 2*m3 - 2*std::log(third_cll_sum);
 
        #ifndef DROPPINGTHISINRPACKAGE
        if constexpr(debug) 
            std::cout << "time: " << m_now << ", log cond like: " << m_logLastCondLike << "\n";
        #endif
 
        // calculate expectations before you resample
        unsigned int fId(0);
        for(auto & h : fs){
    
            Mat testOutput = h(m_particles[0]);
            unsigned int rows = testOutput.rows();
            unsigned int cols = testOutput.cols();
            Mat numer = Mat::Zero(rows,cols);
            float_t denom(0.0);
            
            for(size_t prtcl = 0; prtcl < nparts; ++prtcl){ 
                numer += h(m_particles[prtcl]) * std::exp(m_logUnNormWeights[prtcl] - m1);
                denom += std::exp(m_logUnNormWeights[prtcl] - m1);
            }
            m_expectations[fId] = numer/denom;
 
            #ifndef DROPPINGTHISINRPACKAGE
            if constexpr(debug)
                std::cout << "transposed expectation " << fId << "; " << m_expectations[fId] << "\n";
            #endif
 
            fId++;
        }
 
        // if you have to resample
        if( (m_now+1)%m_rs == 0)
            m_resampler.resampLogWts(m_particles, m_logUnNormWeights);
            
        // advance time
        m_now += 1; 
    
    } else { // (m_now == 0) 
 
        float_t max(-std::numeric_limits<float_t>::infinity());
        for(size_t ii = 0; ii < nparts; ++ii)
        {
            // sample particles
            m_particles[ii]  = q1Samp(data);
            m_logUnNormWeights[ii]  = logMuEv(m_particles[ii]);
            m_logUnNormWeights[ii] += logGEv(data, m_particles[ii]);
            m_logUnNormWeights[ii] -= logQ1Ev(m_particles[ii], data);
 
            // print stuff if debug mode is on
            #ifndef DROPPINGTHISINRPACKAGE
            if constexpr(debug) {
                std::cout << "time: " << m_now 
                          << ", log unnorm weight: " << m_logUnNormWeights[ii] 
                          << ", transposed sample: " << m_particles[ii].transpose()
                          << "\n";
            }
            #endif
 
            // update maximum
            if( m_logUnNormWeights[ii] > max)
                max = m_logUnNormWeights[ii];
        }
        
        // calculate log-likelihood with log-exp-sum trick
        float_t sumExp(0.0);
        for( size_t i = 0; i < nparts; ++i){
            sumExp += std::exp( m_logUnNormWeights[i] - max );
        }
        m_logLastCondLike = - std::log( static_cast<float_t>(nparts) ) + max + std::log(sumExp);
        
        // calculate expectations before you resample
        m_expectations.resize(fs.size());
        unsigned int fId(0);
        for(auto & h : fs){
            
            Mat testOutput = h(m_particles[0]);
            unsigned int rows = testOutput.rows();
            unsigned int cols = testOutput.cols();
            Mat numer = Mat::Zero(rows,cols);
            float_t denom(0.0);
            for(size_t prtcl = 0; prtcl < nparts; ++prtcl){ 
                numer += h(m_particles[prtcl]) * std::exp(m_logUnNormWeights[prtcl] - max);
                denom += std::exp(m_logUnNormWeights[prtcl] - max);
            }
            m_expectations[fId] = numer/denom;
 
            #ifndef DROPPINGTHISINRPACKAGE
            if constexpr(debug)
                std::cout << "transposed expectation " << fId << "; " << m_expectations[fId] << "\n";
            #endif
 
            fId++;
        }
        
        // resample if you should (automatically normalizes)
        if( (m_now+1) % m_rs == 0)
            m_resampler.resampLogWts(m_particles, m_logUnNormWeights);
 
        // advance time step
        m_now += 1;    
    }
 
}
 
 
template<size_t nparts, size_t dimx, size_t dimy, typename resamp_t, typename float_t, bool debug>
float_t APF<nparts, dimx, dimy, resamp_t, float_t, debug>::getLogCondLike() const
{
    return m_logLastCondLike;
}
 
 
template<size_t nparts, size_t dimx, size_t dimy, typename resamp_t, typename float_t, bool debug>
auto APF<nparts, dimx, dimy, resamp_t, float_t, debug>::getExpectations() const -> std::vector<Mat>
{
    return m_expectations;
}
 
} // namespace filters 
} // namespace pf
#endif //APF_H