[176] | 1 | /*! |
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| 2 | \file |
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| 3 | \brief Mergers for combination of pdfs |
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| 4 | \author Vaclav Smidl. |
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| 5 | |
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| 6 | ----------------------------------- |
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| 7 | BDM++ - C++ library for Bayesian Decision Making under Uncertainty |
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| 8 | |
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| 9 | Using IT++ for numerical operations |
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| 10 | ----------------------------------- |
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| 11 | */ |
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| 12 | |
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[384] | 13 | #ifndef MERGER_H |
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| 14 | #define MERGER_H |
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[176] | 15 | |
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[262] | 16 | |
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[384] | 17 | #include "../estim/mixtures.h" |
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[556] | 18 | #include "discrete.h" |
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[176] | 19 | |
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[477] | 20 | namespace bdm { |
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[384] | 21 | using std::string; |
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[176] | 22 | |
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[384] | 23 | //!Merging methods |
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| 24 | enum MERGER_METHOD {ARITHMETIC = 1, GEOMETRIC = 2, LOGNORMAL = 3}; |
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[176] | 25 | |
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[384] | 26 | /*! |
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| 27 | @brief Base class for general combination of pdfs on discrete support |
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[176] | 28 | |
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[384] | 29 | Mixtures of Gaussian densities are used internally. Switching to other densities should be trivial. |
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[198] | 30 | |
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[384] | 31 | The merged pdfs are expected to be of the form: |
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| 32 | \f[ f(x_i|y_i), i=1..n \f] |
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| 33 | where the resulting merger is a density on \f$ \cup [x_i,y_i] \f$ . |
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| 34 | Note that all variables will be joined. |
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[205] | 35 | |
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[384] | 36 | As a result of this feature, each source must be extended to common support |
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| 37 | \f[ f(z_i|y_i,x_i) f(x_i|y_i) f(y_i) i=1..n \f] |
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| 38 | where \f$ z_i \f$ accumulate variables that were not in the original source. |
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| 39 | These extensions are calculated on-the-fly. |
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[299] | 40 | |
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[384] | 41 | However, these operations can not be performed in general. Hence, this class merges only sources on common support, \f$ y_i={}, z_i={}, \forall i \f$. |
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| 42 | For merging of more general cases, use offsprings merger_mix and merger_grid. |
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| 43 | */ |
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| 44 | |
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[507] | 45 | class merger_base : public epdf { |
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[477] | 46 | protected: |
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[507] | 47 | //! Elements of composition |
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| 48 | Array<shared_ptr<mpdf> > mpdfs; |
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| 49 | |
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[477] | 50 | //! Data link for each mpdf in mpdfs |
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| 51 | Array<datalink_m2e*> dls; |
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[507] | 52 | |
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[477] | 53 | //! Array of rvs that are not modelled by mpdfs at all, \f$ z_i \f$ |
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| 54 | Array<RV> rvzs; |
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[507] | 55 | |
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[477] | 56 | //! Data Links for extension \f$ f(z_i|x_i,y_i) \f$ |
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| 57 | Array<datalink_m2e*> zdls; |
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[507] | 58 | |
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[477] | 59 | //! number of support points |
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| 60 | int Npoints; |
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[507] | 61 | |
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[477] | 62 | //! number of sources |
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| 63 | int Nsources; |
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[384] | 64 | |
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[477] | 65 | //! switch of the methoh used for merging |
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| 66 | MERGER_METHOD METHOD; |
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| 67 | //! Default for METHOD |
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| 68 | static const MERGER_METHOD DFLT_METHOD; |
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[384] | 69 | |
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[477] | 70 | //!Prior on the log-normal merging model |
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| 71 | double beta; |
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| 72 | //! default for beta |
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| 73 | static const double DFLT_beta; |
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[384] | 74 | |
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[477] | 75 | //! Projection to empirical density (could also be piece-wise linear) |
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| 76 | eEmp eSmp; |
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[384] | 77 | |
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[477] | 78 | //! debug or not debug |
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| 79 | bool DBG; |
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[423] | 80 | |
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[477] | 81 | //! debugging file |
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| 82 | it_file* dbg_file; |
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| 83 | public: |
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| 84 | //! \name Constructors |
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| 85 | //! @{ |
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[423] | 86 | |
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[507] | 87 | //! Default constructor |
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| 88 | merger_base () : Npoints(0), Nsources(0), DBG(false), dbg_file(0) { |
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[477] | 89 | } |
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[384] | 90 | |
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[477] | 91 | //!Constructor from sources |
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[507] | 92 | merger_base ( const Array<shared_ptr<mpdf> > &S ); |
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[384] | 93 | |
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[477] | 94 | //! Function setting the main internal structures |
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[507] | 95 | void set_sources ( const Array<shared_ptr<mpdf> > &Sources ) { |
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| 96 | mpdfs = Sources; |
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[477] | 97 | Nsources = mpdfs.length(); |
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| 98 | //set sizes |
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| 99 | dls.set_size ( Sources.length() ); |
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| 100 | rvzs.set_size ( Sources.length() ); |
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| 101 | zdls.set_size ( Sources.length() ); |
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[384] | 102 | |
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[507] | 103 | rv = get_composite_rv ( mpdfs, /* checkoverlap = */ false ); |
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| 104 | |
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[477] | 105 | RV rvc; |
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[507] | 106 | // Extend rv by rvc! |
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| 107 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 108 | RV rvx = mpdfs ( i )->_rvc().subt ( rv ); |
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| 109 | rvc.add ( rvx ); // add rv to common rvc |
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| 110 | } |
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| 111 | |
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[477] | 112 | // join rv and rvc - see descriprion |
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| 113 | rv.add ( rvc ); |
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| 114 | // get dimension |
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| 115 | dim = rv._dsize(); |
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| 116 | |
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| 117 | // create links between sources and common rv |
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| 118 | RV xytmp; |
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| 119 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 120 | //Establich connection between mpdfs and merger |
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| 121 | dls ( i ) = new datalink_m2e; |
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| 122 | dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), rv ); |
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| 123 | |
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| 124 | // find out what is missing in each mpdf |
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| 125 | xytmp = mpdfs ( i )->_rv(); |
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| 126 | xytmp.add ( mpdfs ( i )->_rvc() ); |
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| 127 | // z_i = common_rv-xy |
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| 128 | rvzs ( i ) = rv.subt ( xytmp ); |
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| 129 | //establish connection between extension (z_i|x,y)s and common rv |
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| 130 | zdls ( i ) = new datalink_m2e; |
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| 131 | zdls ( i )->set_connection ( rvzs ( i ), xytmp, rv ) ; |
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| 132 | }; |
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| 133 | } |
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[556] | 134 | //! Set support points from rectangular grid |
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| 135 | void set_support ( rectangular_support &Sup) { |
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| 136 | Npoints = Sup.points(); |
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[477] | 137 | eSmp.set_parameters ( Npoints, false ); |
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| 138 | Array<vec> &samples = eSmp._samples(); |
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| 139 | eSmp._w() = ones ( Npoints ) / Npoints; //unifrom size of bins |
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| 140 | //set samples |
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[556] | 141 | samples(0)=Sup.first_vec(); |
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| 142 | for (int j=1; j < Npoints; j++ ) { |
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| 143 | samples ( j ) = Sup.next_vec(); |
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[384] | 144 | } |
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[477] | 145 | } |
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[569] | 146 | //! Set support points from dicrete grid |
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| 147 | void set_support ( discrete_support &Sup) { |
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| 148 | Npoints = Sup.points(); |
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| 149 | eSmp.set_parameters(Sup._Spoints()); |
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| 150 | } |
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[477] | 151 | //! set debug file |
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| 152 | void set_debug_file ( const string fname ) { |
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| 153 | if ( DBG ) delete dbg_file; |
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| 154 | dbg_file = new it_file ( fname ); |
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| 155 | if ( dbg_file ) DBG = true; |
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| 156 | } |
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| 157 | //! Set internal parameters used in approximation |
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| 158 | void set_method ( MERGER_METHOD MTH = DFLT_METHOD, double beta0 = DFLT_beta ) { |
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| 159 | METHOD = MTH; |
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| 160 | beta = beta0; |
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| 161 | } |
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| 162 | //! Set support points from a pdf by drawing N samples |
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| 163 | void set_support ( const epdf &overall, int N ) { |
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[488] | 164 | eSmp.set_statistics ( overall, N ); |
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[477] | 165 | Npoints = N; |
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| 166 | } |
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| 167 | |
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| 168 | //! Destructor |
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| 169 | virtual ~merger_base() { |
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| 170 | for ( int i = 0; i < Nsources; i++ ) { |
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| 171 | delete dls ( i ); |
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| 172 | delete zdls ( i ); |
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[384] | 173 | } |
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[477] | 174 | if ( DBG ) delete dbg_file; |
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| 175 | }; |
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| 176 | //!@} |
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[388] | 177 | |
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[477] | 178 | //! \name Mathematical operations |
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| 179 | //!@{ |
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[388] | 180 | |
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[477] | 181 | //!Merge given sources in given points |
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| 182 | virtual void merge () { |
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| 183 | validate(); |
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[388] | 184 | |
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[477] | 185 | //check if sources overlap: |
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| 186 | bool OK = true; |
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| 187 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 188 | OK &= ( rvzs ( i )._dsize() == 0 ); // z_i is empty |
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| 189 | OK &= ( mpdfs ( i )->_rvc()._dsize() == 0 ); // y_i is empty |
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| 190 | } |
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[388] | 191 | |
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[477] | 192 | if ( OK ) { |
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| 193 | mat lW = zeros ( mpdfs.length(), eSmp._w().length() ); |
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[384] | 194 | |
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[477] | 195 | vec emptyvec ( 0 ); |
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| 196 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 197 | for ( int j = 0; j < eSmp._w().length(); j++ ) { |
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| 198 | lW ( i, j ) = mpdfs ( i )->evallogcond ( eSmp._samples() ( j ), emptyvec ); |
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[299] | 199 | } |
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| 200 | } |
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[176] | 201 | |
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[477] | 202 | vec w_nn = merge_points ( lW ); |
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| 203 | vec wtmp = exp ( w_nn - max ( w_nn ) ); |
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| 204 | //renormalize |
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| 205 | eSmp._w() = wtmp / sum ( wtmp ); |
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| 206 | } else { |
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[565] | 207 | bdm_error ( "Sources are not compatible - use merger_mix" ); |
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[477] | 208 | } |
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| 209 | }; |
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[384] | 210 | |
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[388] | 211 | |
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[477] | 212 | //! Merge log-likelihood values in points using method specified by parameter METHOD |
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| 213 | vec merge_points ( mat &lW ); |
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[388] | 214 | |
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[477] | 215 | |
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| 216 | //! sample from merged density |
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[192] | 217 | //! weight w is a |
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[477] | 218 | vec mean() const { |
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| 219 | const Vec<double> &w = eSmp._w(); |
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| 220 | const Array<vec> &S = eSmp._samples(); |
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| 221 | vec tmp = zeros ( dim ); |
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| 222 | for ( int i = 0; i < Npoints; i++ ) { |
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| 223 | tmp += w ( i ) * S ( i ); |
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[384] | 224 | } |
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[477] | 225 | return tmp; |
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| 226 | } |
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| 227 | mat covariance() const { |
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| 228 | const vec &w = eSmp._w(); |
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| 229 | const Array<vec> &S = eSmp._samples(); |
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[299] | 230 | |
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[477] | 231 | vec mea = mean(); |
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[299] | 232 | |
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[404] | 233 | // cout << sum (w) << "," << w*w << endl; |
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[299] | 234 | |
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[477] | 235 | mat Tmp = zeros ( dim, dim ); |
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| 236 | for ( int i = 0; i < Npoints; i++ ) { |
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| 237 | Tmp += w ( i ) * outer_product ( S ( i ), S ( i ) ); |
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[384] | 238 | } |
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[477] | 239 | return Tmp - outer_product ( mea, mea ); |
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| 240 | } |
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| 241 | vec variance() const { |
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| 242 | const vec &w = eSmp._w(); |
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| 243 | const Array<vec> &S = eSmp._samples(); |
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[299] | 244 | |
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[477] | 245 | vec tmp = zeros ( dim ); |
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| 246 | for ( int i = 0; i < Nsources; i++ ) { |
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| 247 | tmp += w ( i ) * pow ( S ( i ), 2 ); |
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[384] | 248 | } |
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[477] | 249 | return tmp - pow ( mean(), 2 ); |
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| 250 | } |
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| 251 | //!@} |
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[192] | 252 | |
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[477] | 253 | //! \name Access to attributes |
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| 254 | //! @{ |
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[384] | 255 | |
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[477] | 256 | //! Access function |
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| 257 | eEmp& _Smp() { |
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| 258 | return eSmp; |
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| 259 | } |
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[388] | 260 | |
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[477] | 261 | //! load from setting |
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| 262 | void from_setting ( const Setting& set ) { |
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| 263 | // get support |
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| 264 | // find which method to use |
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| 265 | string meth_str; |
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| 266 | UI::get<string> ( meth_str, set, "method", UI::compulsory ); |
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| 267 | if ( !strcmp ( meth_str.c_str(), "arithmetic" ) ) |
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| 268 | set_method ( ARITHMETIC ); |
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| 269 | else { |
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| 270 | if ( !strcmp ( meth_str.c_str(), "geometric" ) ) |
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| 271 | set_method ( GEOMETRIC ); |
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| 272 | else if ( !strcmp ( meth_str.c_str(), "lognormal" ) ) { |
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| 273 | set_method ( LOGNORMAL ); |
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| 274 | set.lookupValue ( "beta", beta ); |
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[388] | 275 | } |
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| 276 | } |
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[477] | 277 | string dbg_file; |
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| 278 | if ( UI::get ( dbg_file, set, "dbg_file" ) ) |
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| 279 | set_debug_file ( dbg_file ); |
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| 280 | //validate() - not used |
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| 281 | } |
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[388] | 282 | |
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[477] | 283 | void validate() { |
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[565] | 284 | bdm_assert ( eSmp._w().length() > 0, "Empty support, use set_support()." ); |
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| 285 | bdm_assert ( dim == eSmp._samples() ( 0 ).length(), "Support points and rv are not compatible!" ); |
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| 286 | bdm_assert ( isnamed(), "mergers must be named" ); |
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[477] | 287 | } |
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| 288 | //!@} |
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[384] | 289 | }; |
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[477] | 290 | UIREGISTER ( merger_base ); |
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[529] | 291 | SHAREDPTR ( merger_base ); |
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[384] | 292 | |
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[536] | 293 | //! Merger using importance sampling with mixture proposal density |
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[477] | 294 | class merger_mix : public merger_base { |
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| 295 | protected: |
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| 296 | //!Internal mixture of EF models |
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| 297 | MixEF Mix; |
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| 298 | //!Number of components in a mixture |
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| 299 | int Ncoms; |
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| 300 | //! coefficient of resampling [0,1] |
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| 301 | double effss_coef; |
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| 302 | //! stop after niter iterations |
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| 303 | int stop_niter; |
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[384] | 304 | |
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[477] | 305 | //! default value for Ncoms |
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| 306 | static const int DFLT_Ncoms; |
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| 307 | //! default value for efss_coef; |
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| 308 | static const double DFLT_effss_coef; |
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[388] | 309 | |
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[477] | 310 | public: |
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| 311 | //!\name Constructors |
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| 312 | //!@{ |
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[507] | 313 | merger_mix ():Ncoms(0), effss_coef(0), stop_niter(0) { } |
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| 314 | |
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| 315 | merger_mix ( const Array<shared_ptr<mpdf> > &S ): |
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| 316 | Ncoms(0), effss_coef(0), stop_niter(0) { |
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| 317 | set_sources ( S ); |
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| 318 | } |
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| 319 | |
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[477] | 320 | //! Set sources and prepare all internal structures |
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[507] | 321 | void set_sources ( const Array<shared_ptr<mpdf> > &S ) { |
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| 322 | merger_base::set_sources ( S ); |
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[477] | 323 | Nsources = S.length(); |
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| 324 | } |
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[507] | 325 | |
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[477] | 326 | //! Set internal parameters used in approximation |
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| 327 | void set_parameters ( int Ncoms0 = DFLT_Ncoms, double effss_coef0 = DFLT_effss_coef ) { |
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| 328 | Ncoms = Ncoms0; |
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| 329 | effss_coef = effss_coef0; |
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| 330 | } |
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| 331 | //!@} |
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[388] | 332 | |
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[477] | 333 | //! \name Mathematical operations |
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| 334 | //!@{ |
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[384] | 335 | |
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[477] | 336 | //!Merge values using mixture approximation |
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| 337 | void merge (); |
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[384] | 338 | |
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[477] | 339 | //! sample from the approximating mixture |
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| 340 | vec sample () const { |
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| 341 | return Mix.posterior().sample(); |
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| 342 | } |
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| 343 | //! loglikelihood computed on mixture models |
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| 344 | double evallog ( const vec &dt ) const { |
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| 345 | vec dtf = ones ( dt.length() + 1 ); |
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| 346 | dtf.set_subvector ( 0, dt ); |
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| 347 | return Mix.logpred ( dtf ); |
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| 348 | } |
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| 349 | //!@} |
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| 350 | |
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| 351 | //!\name Access functions |
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| 352 | //!@{ |
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[192] | 353 | //! Access function |
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[477] | 354 | MixEF& _Mix() { |
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| 355 | return Mix; |
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| 356 | } |
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| 357 | //! Access function |
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| 358 | emix* proposal() { |
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| 359 | emix* tmp = Mix.epredictor(); |
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| 360 | tmp->set_rv ( rv ); |
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| 361 | return tmp; |
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| 362 | } |
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| 363 | //! from_settings |
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| 364 | void from_setting ( const Setting& set ) { |
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| 365 | merger_base::from_setting ( set ); |
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| 366 | set.lookupValue ( "ncoms", Ncoms ); |
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| 367 | set.lookupValue ( "effss_coef", effss_coef ); |
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| 368 | set.lookupValue ( "stop_niter", stop_niter ); |
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| 369 | } |
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[388] | 370 | |
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[477] | 371 | //! @} |
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| 372 | |
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[384] | 373 | }; |
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[477] | 374 | UIREGISTER ( merger_mix ); |
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[529] | 375 | SHAREDPTR ( merger_mix ); |
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[176] | 376 | |
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[254] | 377 | } |
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[176] | 378 | |
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| 379 | #endif // MER_H |
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