| 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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| 13 | #ifndef MERGER_H |
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| 14 | #define MERGER_H |
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| 15 | |
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| 16 | |
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| 17 | #include "../estim/mixtures.h" |
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| 18 | |
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| 19 | namespace bdm |
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| 20 | { |
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| 21 | using std::string; |
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| 22 | |
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| 23 | //!Merging methods |
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| 24 | enum MERGER_METHOD {ARITHMETIC = 1, GEOMETRIC = 2, LOGNORMAL = 3}; |
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| 25 | |
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| 26 | /*! |
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| 27 | @brief Base class for general combination of pdfs on discrete support |
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| 28 | |
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| 29 | Mixtures of Gaussian densities are used internally. Switching to other densities should be trivial. |
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| 30 | |
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| 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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| 35 | |
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| 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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| 40 | |
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| 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$. |
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| 42 | For merging of more general cases, use offsprings merger_mix and merger_grid. |
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| 43 | */ |
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| 44 | |
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| 45 | class merger_base : public compositepdf, public epdf |
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| 46 | { |
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| 47 | protected: |
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| 48 | //! Data link for each mpdf in mpdfs |
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| 49 | Array<datalink_m2e*> dls; |
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| 50 | //! Array of rvs that are not modelled by mpdfs at all, \f$ z_i \f$ |
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| 51 | Array<RV> rvzs; |
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| 52 | //! Data Links for extension \f$ f(z_i|x_i,y_i) \f$ |
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| 53 | Array<datalink_m2e*> zdls; |
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| 54 | //! number of support points |
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| 55 | int Npoints; |
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| 56 | //! number of sources |
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| 57 | int Nsources; |
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| 58 | |
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| 59 | //! switch of the methoh used for merging |
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| 60 | MERGER_METHOD METHOD; |
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| 61 | //!Prior on the log-normal merging model |
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| 62 | double beta; |
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| 63 | |
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| 64 | //! Projection to empirical density (could also be piece-wise linear) |
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| 65 | eEmp eSmp; |
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| 66 | |
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| 67 | //! debug or not debug |
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| 68 | bool DBG; |
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| 69 | |
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| 70 | //! debugging file |
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| 71 | it_file* dbg_file; |
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| 72 | public: |
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| 73 | //! \name Constructors |
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| 74 | //! @{ |
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| 75 | |
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| 76 | //!Empty constructor |
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| 77 | merger_base () : compositepdf() {DBG = false;dbg_file = NULL;}; |
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| 78 | //!Constructor from sources |
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| 79 | merger_base (const Array<mpdf*> &S, bool own=false) {set_sources (S,own);}; |
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| 80 | //! Function setting the main internal structures |
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| 81 | void set_sources (const Array<mpdf*> &Sources, bool own) { |
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| 82 | compositepdf::set_elements (Sources,own); |
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| 83 | //set sizes |
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| 84 | dls.set_size (Sources.length()); |
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| 85 | rvzs.set_size (Sources.length()); |
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| 86 | zdls.set_size (Sources.length()); |
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| 87 | |
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| 88 | rv = getrv (/* checkoverlap = */ false); |
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| 89 | RV rvc; setrvc (rv, rvc); // Extend rv by rvc! |
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| 90 | // join rv and rvc - see descriprion |
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| 91 | rv.add (rvc); |
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| 92 | // get dimension |
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| 93 | dim = rv._dsize(); |
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| 94 | |
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| 95 | // create links between sources and common rv |
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| 96 | RV xytmp; |
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| 97 | for (int i = 0;i < mpdfs.length();i++) { |
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| 98 | //Establich connection between mpdfs and merger |
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| 99 | dls (i) = new datalink_m2e; |
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| 100 | dls (i)->set_connection (mpdfs (i)->_rv(), mpdfs (i)->_rvc(), rv); |
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| 101 | |
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| 102 | // find out what is missing in each mpdf |
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| 103 | xytmp = mpdfs (i)->_rv(); |
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| 104 | xytmp.add (mpdfs (i)->_rvc()); |
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| 105 | // z_i = common_rv-xy |
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| 106 | rvzs (i) = rv.subt (xytmp); |
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| 107 | //establish connection between extension (z_i|x,y)s and common rv |
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| 108 | zdls (i) = new datalink_m2e; zdls (i)->set_connection (rvzs (i), xytmp, rv) ; |
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| 109 | }; |
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| 110 | } |
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| 111 | //! 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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| 112 | void set_support (const Array<vec> &XYZ, const int dimsize) { |
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| 113 | set_support(XYZ,dimsize*ones_i(XYZ.length())); |
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| 114 | } |
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| 115 | //! 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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| 116 | void set_support (const Array<vec> &XYZ, const ivec &gridsize) { |
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| 117 | int dim = XYZ.length(); //check with internal dim!! |
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| 118 | Npoints = prod (gridsize); |
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| 119 | eSmp.set_parameters (Npoints, false); |
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| 120 | Array<vec> &samples = eSmp._samples(); |
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| 121 | eSmp._w() = ones (Npoints) / Npoints; //unifrom size of bins |
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| 122 | //set samples |
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| 123 | ivec ind = zeros_i (dim); //indeces of dimensions in for cycle; |
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| 124 | vec smpi (dim); // ith sample |
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| 125 | vec steps =zeros(dim); // ith sample |
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| 126 | // first corner |
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| 127 | for (int j = 0; j < dim; j++) { |
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| 128 | smpi (j) = XYZ (j) (0); /* beginning of the interval*/ |
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| 129 | it_assert(gridsize(j)!=0.0,"Zeros in gridsize!"); |
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| 130 | steps (j) = (smpi(j) - XYZ(j)(1))/gridsize(j); |
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| 131 | } |
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| 132 | // fill samples |
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| 133 | int act_dim=0; //active dimension |
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| 134 | for (int i = 0; i < Npoints; i++) { |
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| 135 | // copy |
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| 136 | samples(i) = smpi; |
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| 137 | // go through all dimensions |
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| 138 | for (int j = 0;j < dim;j++) { |
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| 139 | if (ind (j) == gridsize (j) - 1) { //j-th index is full |
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| 140 | ind (j) = 0; //shift back |
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| 141 | smpi(j) = XYZ(j)(0); |
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| 142 | |
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| 143 | ind (j + 1) ++; //increase the next dimension; |
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| 144 | smpi(j+1) += steps(j+1); |
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| 145 | |
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| 146 | if (ind (j + 1) < gridsize (j + 1) - 1) break; |
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| 147 | } else { |
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| 148 | ind (j) ++; |
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| 149 | smpi(j) +=steps(j); |
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| 150 | break; |
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| 151 | } |
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| 152 | } |
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| 153 | } |
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| 154 | } |
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| 155 | //! set debug file |
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| 156 | void set_debug_file (const string fname) { |
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| 157 | if (DBG) delete dbg_file; |
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| 158 | dbg_file = new it_file (fname); |
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| 159 | if (dbg_file) DBG = true; |
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| 160 | } |
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| 161 | //! Set internal parameters used in approximation |
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| 162 | void set_method (MERGER_METHOD MTH, double beta0 = 0.0) { |
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| 163 | METHOD = MTH; |
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| 164 | beta = beta0; |
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| 165 | } |
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| 166 | //! Set support points from a pdf by drawing N samples |
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| 167 | void set_support (const epdf &overall, int N) { |
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| 168 | eSmp.set_statistics (&overall, N); |
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| 169 | Npoints = N; |
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| 170 | } |
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| 171 | |
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| 172 | //! Destructor |
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| 173 | virtual ~merger_base() { |
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| 174 | for (int i = 0; i < Nsources; i++) { |
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| 175 | delete dls (i); |
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| 176 | delete zdls (i); |
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| 177 | } |
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| 178 | if (DBG) delete dbg_file; |
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| 179 | }; |
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| 180 | //!@} |
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| 181 | |
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| 182 | //! \name Mathematical operations |
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| 183 | //!@{ |
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| 184 | |
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| 185 | //!Merge given sources in given points |
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| 186 | void merge () { |
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| 187 | validate(); |
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| 188 | |
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| 189 | //check if sources overlap: |
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| 190 | bool OK = true; |
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| 191 | for (int i = 0;i < mpdfs.length(); i++) { |
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| 192 | OK &= (rvzs (i)._dsize() == 0); // z_i is empty |
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| 193 | OK &= (mpdfs (i)->_rvc()._dsize() == 0); // y_i is empty |
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| 194 | } |
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| 195 | |
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| 196 | if (OK) { |
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| 197 | mat lW = zeros (mpdfs.length(), eSmp._w().length()); |
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| 198 | |
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| 199 | vec emptyvec (0); |
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| 200 | for (int i = 0; i < mpdfs.length(); i++) { |
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| 201 | for (int j = 0; j < eSmp._w().length(); j++) { |
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| 202 | lW (i, j) = mpdfs (i)->evallogcond (eSmp._samples() (j), emptyvec); |
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| 203 | } |
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| 204 | } |
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| 205 | |
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| 206 | vec wtmp = exp (merge_points (lW)); |
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| 207 | //renormalize |
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| 208 | eSmp._w() = wtmp / sum (wtmp); |
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| 209 | } else { |
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| 210 | it_error ("Sources are not compatible - use merger_mix"); |
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| 211 | } |
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| 212 | }; |
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| 213 | |
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| 214 | |
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| 215 | //! Merge log-likelihood values in points using method specified by parameter METHOD |
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| 216 | vec merge_points (mat &lW); |
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| 217 | |
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| 218 | |
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| 219 | //! sample from merged density |
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| 220 | //! weight w is a |
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| 221 | vec mean() const { |
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| 222 | const Vec<double> &w = eSmp._w(); |
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| 223 | const Array<vec> &S = eSmp._samples(); |
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| 224 | vec tmp = zeros (dim); |
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| 225 | for (int i = 0; i < Npoints; i++) { |
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| 226 | tmp += w (i) * S (i); |
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| 227 | } |
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| 228 | return tmp; |
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| 229 | } |
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| 230 | mat covariance() const { |
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| 231 | const vec &w = eSmp._w(); |
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| 232 | const Array<vec> &S = eSmp._samples(); |
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| 233 | |
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| 234 | vec mea = mean(); |
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| 235 | |
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| 236 | cout << sum (w) << "," << w*w << endl; |
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| 237 | |
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| 238 | mat Tmp = zeros (dim, dim); |
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| 239 | for (int i = 0; i < Npoints; i++) { |
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| 240 | Tmp += w (i) * outer_product (S (i), S (i)); |
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| 241 | } |
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| 242 | return Tmp -outer_product (mea, mea); |
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| 243 | } |
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| 244 | vec variance() const { |
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| 245 | const vec &w = eSmp._w(); |
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| 246 | const Array<vec> &S = eSmp._samples(); |
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| 247 | |
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| 248 | vec tmp = zeros (dim); |
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| 249 | for (int i = 0; i < Nsources; i++) { |
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| 250 | tmp += w (i) * pow (S (i), 2); |
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| 251 | } |
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| 252 | return tmp -pow (mean(), 2); |
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| 253 | } |
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| 254 | //!@} |
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| 255 | |
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| 256 | //! \name Access to attributes |
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| 257 | //! @{ |
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| 258 | |
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| 259 | //! Access function |
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| 260 | eEmp& _Smp() {return eSmp;} |
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| 261 | |
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| 262 | //! load from setting |
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| 263 | void from_setting (const Setting& set) { |
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| 264 | // get support |
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| 265 | // find which method to use |
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| 266 | string meth_str; |
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| 267 | UI::get<string> (meth_str, set, "method"); |
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| 268 | if (!strcmp (meth_str.c_str(), "arithmetic")) |
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| 269 | set_method (ARITHMETIC); |
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| 270 | else { |
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| 271 | if (!strcmp (meth_str.c_str(), "geometric")) |
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| 272 | set_method (GEOMETRIC); |
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| 273 | else if (!strcmp (meth_str.c_str(), "lognormal")) { |
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| 274 | set_method (GEOMETRIC); |
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| 275 | set.lookupValue( "beta",beta); |
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| 276 | } |
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| 277 | } |
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| 278 | validate(); |
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| 279 | } |
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| 280 | |
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| 281 | void validate() { |
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| 282 | it_assert (eSmp._w().length() > 0, "Empty support, use set_support()."); |
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| 283 | it_assert (dim == eSmp._samples() (0).length(), "Support points and rv are not compatible!"); |
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| 284 | it_assert (isnamed(),"mergers must be named"); |
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| 285 | } |
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| 286 | //!@} |
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| 287 | }; |
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| 288 | UIREGISTER(merger_base); |
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| 289 | |
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| 290 | class merger_mix : public merger_base |
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| 291 | { |
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| 292 | protected: |
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| 293 | //!Internal mixture of EF models |
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| 294 | MixEF Mix; |
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| 295 | //!Number of components in a mixture |
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| 296 | int Ncoms; |
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| 297 | //! coefficient of resampling |
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| 298 | double effss_coef; |
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| 299 | |
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| 300 | public: |
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| 301 | //!\name Constructors |
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| 302 | //!@{ |
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| 303 | merger_mix () {}; |
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| 304 | merger_mix (const Array<mpdf*> &S,bool own=false) {set_sources (S,own);}; |
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| 305 | //! Set sources and prepare all internal structures |
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| 306 | void set_sources (const Array<mpdf*> &S, bool own) { |
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| 307 | merger_base::set_sources (S,own); |
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| 308 | Nsources = S.length(); |
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| 309 | } |
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| 310 | //! Set internal parameters used in approximation |
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| 311 | void set_parameters (int Ncoms0 = 10, double effss_coef0 = 0.5) { |
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| 312 | Ncoms = Ncoms0; |
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| 313 | effss_coef = effss_coef0; |
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| 314 | } |
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| 315 | //!@} |
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| 316 | |
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| 317 | //! \name Mathematical operations |
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| 318 | //!@{ |
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| 319 | |
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| 320 | //!Merge values using mixture approximation |
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| 321 | void merge (); |
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| 322 | |
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| 323 | //! sample from the approximating mixture |
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| 324 | vec sample () const { return Mix.posterior().sample();} |
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| 325 | //! loglikelihood computed on mixture models |
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| 326 | double evallog (const vec &dt) const { |
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| 327 | vec dtf = ones (dt.length() + 1); |
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| 328 | dtf.set_subvector (0, dt); |
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| 329 | return Mix.logpred (dtf); |
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| 330 | } |
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| 331 | //!@} |
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| 332 | |
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| 333 | //!\name Access functions |
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| 334 | //!@{ |
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| 335 | //! Access function |
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| 336 | MixEF& _Mix() {return Mix;} |
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| 337 | //! Access function |
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| 338 | emix* proposal() {emix* tmp = Mix.epredictor(); tmp->set_rv (rv); return tmp;} |
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| 339 | //! from_settings |
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| 340 | void from_settings(const Setting& set){ |
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| 341 | merger_base::from_setting(set); |
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| 342 | set.lookupValue("ncoms",Ncoms); |
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| 343 | } |
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| 344 | |
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| 345 | //! @} |
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| 346 | |
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| 347 | }; |
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| 348 | UIREGISTER(merger_mix); |
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| 349 | |
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| 350 | } |
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| 351 | |
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| 352 | #endif // MER_H |
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