[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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[176] | 18 | |
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[477] | 19 | namespace bdm { |
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[384] | 20 | using std::string; |
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[176] | 21 | |
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[384] | 22 | //!Merging methods |
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| 23 | enum MERGER_METHOD {ARITHMETIC = 1, GEOMETRIC = 2, LOGNORMAL = 3}; |
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[176] | 24 | |
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[384] | 25 | /*! |
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| 26 | @brief Base class for general combination of pdfs on discrete support |
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[176] | 27 | |
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[384] | 28 | Mixtures of Gaussian densities are used internally. Switching to other densities should be trivial. |
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[198] | 29 | |
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[384] | 30 | The merged pdfs are expected to be of the form: |
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| 31 | \f[ f(x_i|y_i), i=1..n \f] |
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| 32 | where the resulting merger is a density on \f$ \cup [x_i,y_i] \f$ . |
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| 33 | Note that all variables will be joined. |
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[205] | 34 | |
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[384] | 35 | As a result of this feature, each source must be extended to common support |
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| 36 | \f[ f(z_i|y_i,x_i) f(x_i|y_i) f(y_i) i=1..n \f] |
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| 37 | where \f$ z_i \f$ accumulate variables that were not in the original source. |
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| 38 | These extensions are calculated on-the-fly. |
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[299] | 39 | |
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[384] | 40 | 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$. |
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| 41 | For merging of more general cases, use offsprings merger_mix and merger_grid. |
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| 42 | */ |
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| 43 | |
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[507] | 44 | class merger_base : public epdf { |
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[477] | 45 | protected: |
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[507] | 46 | //! Elements of composition |
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| 47 | Array<shared_ptr<mpdf> > mpdfs; |
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| 48 | |
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[477] | 49 | //! Data link for each mpdf in mpdfs |
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| 50 | Array<datalink_m2e*> dls; |
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[507] | 51 | |
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[477] | 52 | //! Array of rvs that are not modelled by mpdfs at all, \f$ z_i \f$ |
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| 53 | Array<RV> rvzs; |
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[507] | 54 | |
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[477] | 55 | //! Data Links for extension \f$ f(z_i|x_i,y_i) \f$ |
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| 56 | Array<datalink_m2e*> zdls; |
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[507] | 57 | |
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[477] | 58 | //! number of support points |
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| 59 | int Npoints; |
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[507] | 60 | |
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[477] | 61 | //! number of sources |
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| 62 | int Nsources; |
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[384] | 63 | |
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[477] | 64 | //! switch of the methoh used for merging |
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| 65 | MERGER_METHOD METHOD; |
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| 66 | //! Default for METHOD |
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| 67 | static const MERGER_METHOD DFLT_METHOD; |
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[384] | 68 | |
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[477] | 69 | //!Prior on the log-normal merging model |
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| 70 | double beta; |
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| 71 | //! default for beta |
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| 72 | static const double DFLT_beta; |
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[384] | 73 | |
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[477] | 74 | //! Projection to empirical density (could also be piece-wise linear) |
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| 75 | eEmp eSmp; |
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[384] | 76 | |
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[477] | 77 | //! debug or not debug |
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| 78 | bool DBG; |
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[423] | 79 | |
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[477] | 80 | //! debugging file |
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| 81 | it_file* dbg_file; |
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| 82 | public: |
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| 83 | //! \name Constructors |
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| 84 | //! @{ |
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[423] | 85 | |
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[507] | 86 | //! Default constructor |
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| 87 | merger_base () : Npoints(0), Nsources(0), DBG(false), dbg_file(0) { |
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[477] | 88 | } |
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[384] | 89 | |
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[477] | 90 | //!Constructor from sources |
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[507] | 91 | merger_base ( const Array<shared_ptr<mpdf> > &S ); |
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[384] | 92 | |
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[477] | 93 | //! Function setting the main internal structures |
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[507] | 94 | void set_sources ( const Array<shared_ptr<mpdf> > &Sources ) { |
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| 95 | mpdfs = Sources; |
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[477] | 96 | Nsources = mpdfs.length(); |
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| 97 | //set sizes |
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| 98 | dls.set_size ( Sources.length() ); |
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| 99 | rvzs.set_size ( Sources.length() ); |
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| 100 | zdls.set_size ( Sources.length() ); |
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[384] | 101 | |
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[507] | 102 | rv = get_composite_rv ( mpdfs, /* checkoverlap = */ false ); |
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| 103 | |
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[477] | 104 | RV rvc; |
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[507] | 105 | // Extend rv by rvc! |
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| 106 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 107 | RV rvx = mpdfs ( i )->_rvc().subt ( rv ); |
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| 108 | rvc.add ( rvx ); // add rv to common rvc |
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| 109 | } |
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| 110 | |
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[477] | 111 | // join rv and rvc - see descriprion |
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| 112 | rv.add ( rvc ); |
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| 113 | // get dimension |
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| 114 | dim = rv._dsize(); |
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| 115 | |
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| 116 | // create links between sources and common rv |
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| 117 | RV xytmp; |
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| 118 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 119 | //Establich connection between mpdfs and merger |
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| 120 | dls ( i ) = new datalink_m2e; |
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| 121 | dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), rv ); |
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| 122 | |
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| 123 | // find out what is missing in each mpdf |
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| 124 | xytmp = mpdfs ( i )->_rv(); |
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| 125 | xytmp.add ( mpdfs ( i )->_rvc() ); |
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| 126 | // z_i = common_rv-xy |
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| 127 | rvzs ( i ) = rv.subt ( xytmp ); |
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| 128 | //establish connection between extension (z_i|x,y)s and common rv |
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| 129 | zdls ( i ) = new datalink_m2e; |
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| 130 | zdls ( i )->set_connection ( rvzs ( i ), xytmp, rv ) ; |
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| 131 | }; |
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| 132 | } |
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| 133 | //! Rectangular support each vector of XYZ specifies (begining-end) interval for each dimension. Same number of points, \c dimsize, in each dimension. |
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| 134 | void set_support ( const Array<vec> &XYZ, const int dimsize ) { |
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| 135 | set_support ( XYZ, dimsize*ones_i ( XYZ.length() ) ); |
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| 136 | } |
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| 137 | //! Rectangular support each vector of XYZ specifies (begining-end) interval for each dimension. \c gridsize specifies number of points is each dimension. |
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| 138 | void set_support ( const Array<vec> &XYZ, const ivec &gridsize ) { |
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| 139 | int dim = XYZ.length(); //check with internal dim!! |
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| 140 | Npoints = prod ( gridsize ); |
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| 141 | eSmp.set_parameters ( Npoints, false ); |
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| 142 | Array<vec> &samples = eSmp._samples(); |
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| 143 | eSmp._w() = ones ( Npoints ) / Npoints; //unifrom size of bins |
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| 144 | //set samples |
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| 145 | ivec ind = zeros_i ( dim ); //indeces of dimensions in for cycle; |
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| 146 | vec smpi ( dim ); // ith sample |
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| 147 | vec steps = zeros ( dim ); // ith sample |
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| 148 | // first corner |
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| 149 | for ( int j = 0; j < dim; j++ ) { |
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| 150 | smpi ( j ) = XYZ ( j ) ( 0 ); /* beginning of the interval*/ |
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| 151 | it_assert ( gridsize ( j ) != 0.0, "Zeros in gridsize!" ); |
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| 152 | steps ( j ) = ( XYZ ( j ) ( 1 ) - smpi ( j ) ) / gridsize ( j ); |
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[384] | 153 | } |
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[477] | 154 | // fill samples |
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| 155 | for ( int i = 0; i < Npoints; i++ ) { |
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| 156 | // copy |
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| 157 | samples ( i ) = smpi; |
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| 158 | // go through all dimensions |
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| 159 | for ( int j = 0; j < dim; j++ ) { |
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| 160 | if ( ind ( j ) == gridsize ( j ) - 1 ) { //j-th index is full |
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| 161 | ind ( j ) = 0; //shift back |
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| 162 | smpi ( j ) = XYZ ( j ) ( 0 ); |
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| 163 | |
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| 164 | if ( i < Npoints - 1 ) { |
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| 165 | ind ( j + 1 ) ++; //increase the next dimension; |
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| 166 | smpi ( j + 1 ) += steps ( j + 1 ); |
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[388] | 167 | break; |
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| 168 | } |
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[477] | 169 | |
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| 170 | } else { |
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| 171 | ind ( j ) ++; |
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| 172 | smpi ( j ) += steps ( j ); |
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| 173 | break; |
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[388] | 174 | } |
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| 175 | } |
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| 176 | } |
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[477] | 177 | } |
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| 178 | //! set debug file |
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| 179 | void set_debug_file ( const string fname ) { |
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| 180 | if ( DBG ) delete dbg_file; |
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| 181 | dbg_file = new it_file ( fname ); |
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| 182 | if ( dbg_file ) DBG = true; |
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| 183 | } |
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| 184 | //! Set internal parameters used in approximation |
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| 185 | void set_method ( MERGER_METHOD MTH = DFLT_METHOD, double beta0 = DFLT_beta ) { |
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| 186 | METHOD = MTH; |
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| 187 | beta = beta0; |
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| 188 | } |
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| 189 | //! Set support points from a pdf by drawing N samples |
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| 190 | void set_support ( const epdf &overall, int N ) { |
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[488] | 191 | eSmp.set_statistics ( overall, N ); |
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[477] | 192 | Npoints = N; |
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| 193 | } |
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| 194 | |
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| 195 | //! Destructor |
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| 196 | virtual ~merger_base() { |
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| 197 | for ( int i = 0; i < Nsources; i++ ) { |
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| 198 | delete dls ( i ); |
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| 199 | delete zdls ( i ); |
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[384] | 200 | } |
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[477] | 201 | if ( DBG ) delete dbg_file; |
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| 202 | }; |
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| 203 | //!@} |
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[388] | 204 | |
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[477] | 205 | //! \name Mathematical operations |
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| 206 | //!@{ |
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[388] | 207 | |
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[477] | 208 | //!Merge given sources in given points |
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| 209 | virtual void merge () { |
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| 210 | validate(); |
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[388] | 211 | |
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[477] | 212 | //check if sources overlap: |
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| 213 | bool OK = true; |
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| 214 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 215 | OK &= ( rvzs ( i )._dsize() == 0 ); // z_i is empty |
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| 216 | OK &= ( mpdfs ( i )->_rvc()._dsize() == 0 ); // y_i is empty |
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| 217 | } |
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[388] | 218 | |
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[477] | 219 | if ( OK ) { |
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| 220 | mat lW = zeros ( mpdfs.length(), eSmp._w().length() ); |
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[384] | 221 | |
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[477] | 222 | vec emptyvec ( 0 ); |
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| 223 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 224 | for ( int j = 0; j < eSmp._w().length(); j++ ) { |
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| 225 | lW ( i, j ) = mpdfs ( i )->evallogcond ( eSmp._samples() ( j ), emptyvec ); |
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[299] | 226 | } |
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| 227 | } |
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[176] | 228 | |
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[477] | 229 | vec w_nn = merge_points ( lW ); |
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| 230 | vec wtmp = exp ( w_nn - max ( w_nn ) ); |
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| 231 | //renormalize |
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| 232 | eSmp._w() = wtmp / sum ( wtmp ); |
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| 233 | } else { |
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| 234 | it_error ( "Sources are not compatible - use merger_mix" ); |
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| 235 | } |
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| 236 | }; |
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[384] | 237 | |
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[388] | 238 | |
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[477] | 239 | //! Merge log-likelihood values in points using method specified by parameter METHOD |
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| 240 | vec merge_points ( mat &lW ); |
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[388] | 241 | |
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[477] | 242 | |
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| 243 | //! sample from merged density |
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[192] | 244 | //! weight w is a |
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[477] | 245 | vec mean() const { |
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| 246 | const Vec<double> &w = eSmp._w(); |
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| 247 | const Array<vec> &S = eSmp._samples(); |
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| 248 | vec tmp = zeros ( dim ); |
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| 249 | for ( int i = 0; i < Npoints; i++ ) { |
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| 250 | tmp += w ( i ) * S ( i ); |
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[384] | 251 | } |
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[477] | 252 | return tmp; |
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| 253 | } |
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| 254 | mat covariance() const { |
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| 255 | const vec &w = eSmp._w(); |
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| 256 | const Array<vec> &S = eSmp._samples(); |
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[299] | 257 | |
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[477] | 258 | vec mea = mean(); |
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[299] | 259 | |
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[404] | 260 | // cout << sum (w) << "," << w*w << endl; |
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[299] | 261 | |
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[477] | 262 | mat Tmp = zeros ( dim, dim ); |
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| 263 | for ( int i = 0; i < Npoints; i++ ) { |
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| 264 | Tmp += w ( i ) * outer_product ( S ( i ), S ( i ) ); |
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[384] | 265 | } |
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[477] | 266 | return Tmp - outer_product ( mea, mea ); |
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| 267 | } |
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| 268 | vec variance() const { |
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| 269 | const vec &w = eSmp._w(); |
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| 270 | const Array<vec> &S = eSmp._samples(); |
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[299] | 271 | |
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[477] | 272 | vec tmp = zeros ( dim ); |
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| 273 | for ( int i = 0; i < Nsources; i++ ) { |
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| 274 | tmp += w ( i ) * pow ( S ( i ), 2 ); |
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[384] | 275 | } |
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[477] | 276 | return tmp - pow ( mean(), 2 ); |
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| 277 | } |
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| 278 | //!@} |
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[192] | 279 | |
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[477] | 280 | //! \name Access to attributes |
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| 281 | //! @{ |
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[384] | 282 | |
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[477] | 283 | //! Access function |
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| 284 | eEmp& _Smp() { |
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| 285 | return eSmp; |
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| 286 | } |
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[388] | 287 | |
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[477] | 288 | //! load from setting |
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| 289 | void from_setting ( const Setting& set ) { |
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| 290 | // get support |
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| 291 | // find which method to use |
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| 292 | string meth_str; |
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| 293 | UI::get<string> ( meth_str, set, "method", UI::compulsory ); |
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| 294 | if ( !strcmp ( meth_str.c_str(), "arithmetic" ) ) |
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| 295 | set_method ( ARITHMETIC ); |
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| 296 | else { |
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| 297 | if ( !strcmp ( meth_str.c_str(), "geometric" ) ) |
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| 298 | set_method ( GEOMETRIC ); |
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| 299 | else if ( !strcmp ( meth_str.c_str(), "lognormal" ) ) { |
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| 300 | set_method ( LOGNORMAL ); |
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| 301 | set.lookupValue ( "beta", beta ); |
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[388] | 302 | } |
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| 303 | } |
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[477] | 304 | string dbg_file; |
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| 305 | if ( UI::get ( dbg_file, set, "dbg_file" ) ) |
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| 306 | set_debug_file ( dbg_file ); |
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| 307 | //validate() - not used |
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| 308 | } |
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[388] | 309 | |
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[477] | 310 | void validate() { |
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| 311 | it_assert ( eSmp._w().length() > 0, "Empty support, use set_support()." ); |
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| 312 | it_assert ( dim == eSmp._samples() ( 0 ).length(), "Support points and rv are not compatible!" ); |
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| 313 | it_assert ( isnamed(), "mergers must be named" ); |
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| 314 | } |
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| 315 | //!@} |
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[384] | 316 | }; |
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[477] | 317 | UIREGISTER ( merger_base ); |
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[384] | 318 | |
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[477] | 319 | class merger_mix : public merger_base { |
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| 320 | protected: |
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| 321 | //!Internal mixture of EF models |
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| 322 | MixEF Mix; |
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| 323 | //!Number of components in a mixture |
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| 324 | int Ncoms; |
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| 325 | //! coefficient of resampling [0,1] |
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| 326 | double effss_coef; |
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| 327 | //! stop after niter iterations |
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| 328 | int stop_niter; |
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[384] | 329 | |
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[477] | 330 | //! default value for Ncoms |
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| 331 | static const int DFLT_Ncoms; |
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| 332 | //! default value for efss_coef; |
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| 333 | static const double DFLT_effss_coef; |
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[388] | 334 | |
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[477] | 335 | public: |
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| 336 | //!\name Constructors |
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| 337 | //!@{ |
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[507] | 338 | merger_mix ():Ncoms(0), effss_coef(0), stop_niter(0) { } |
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| 339 | |
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| 340 | merger_mix ( const Array<shared_ptr<mpdf> > &S ): |
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| 341 | Ncoms(0), effss_coef(0), stop_niter(0) { |
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| 342 | set_sources ( S ); |
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| 343 | } |
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| 344 | |
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[477] | 345 | //! Set sources and prepare all internal structures |
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[507] | 346 | void set_sources ( const Array<shared_ptr<mpdf> > &S ) { |
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| 347 | merger_base::set_sources ( S ); |
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[477] | 348 | Nsources = S.length(); |
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| 349 | } |
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[507] | 350 | |
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[477] | 351 | //! Set internal parameters used in approximation |
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| 352 | void set_parameters ( int Ncoms0 = DFLT_Ncoms, double effss_coef0 = DFLT_effss_coef ) { |
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| 353 | Ncoms = Ncoms0; |
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| 354 | effss_coef = effss_coef0; |
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| 355 | } |
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| 356 | //!@} |
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[388] | 357 | |
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[477] | 358 | //! \name Mathematical operations |
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| 359 | //!@{ |
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[384] | 360 | |
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[477] | 361 | //!Merge values using mixture approximation |
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| 362 | void merge (); |
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[384] | 363 | |
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[477] | 364 | //! sample from the approximating mixture |
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| 365 | vec sample () const { |
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| 366 | return Mix.posterior().sample(); |
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| 367 | } |
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| 368 | //! loglikelihood computed on mixture models |
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| 369 | double evallog ( const vec &dt ) const { |
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| 370 | vec dtf = ones ( dt.length() + 1 ); |
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| 371 | dtf.set_subvector ( 0, dt ); |
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| 372 | return Mix.logpred ( dtf ); |
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| 373 | } |
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| 374 | //!@} |
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| 375 | |
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| 376 | //!\name Access functions |
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| 377 | //!@{ |
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[192] | 378 | //! Access function |
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[477] | 379 | MixEF& _Mix() { |
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| 380 | return Mix; |
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| 381 | } |
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| 382 | //! Access function |
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| 383 | emix* proposal() { |
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| 384 | emix* tmp = Mix.epredictor(); |
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| 385 | tmp->set_rv ( rv ); |
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| 386 | return tmp; |
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| 387 | } |
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| 388 | //! from_settings |
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| 389 | void from_setting ( const Setting& set ) { |
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| 390 | merger_base::from_setting ( set ); |
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| 391 | set.lookupValue ( "ncoms", Ncoms ); |
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| 392 | set.lookupValue ( "effss_coef", effss_coef ); |
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| 393 | set.lookupValue ( "stop_niter", stop_niter ); |
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| 394 | } |
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[388] | 395 | |
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[477] | 396 | //! @} |
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| 397 | |
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[384] | 398 | }; |
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[477] | 399 | UIREGISTER ( merger_mix ); |
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[176] | 400 | |
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[254] | 401 | } |
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[176] | 402 | |
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| 403 | #endif // MER_H |
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