1 | /*! |
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2 | \file |
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3 | \brief Probability distributions for Mixtures 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 MX_H |
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14 | #define MX_H |
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15 | |
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16 | #include "libBM.h" |
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17 | #include "libEF.h" |
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18 | //#include <std> |
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19 | |
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20 | using namespace itpp; |
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21 | |
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22 | /*! |
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23 | * \brief Mixture of epdfs |
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24 | |
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25 | Density function: |
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26 | \f[ |
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27 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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28 | \f] |
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29 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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30 | |
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31 | */ |
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32 | class emix : public epdf { |
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33 | protected: |
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34 | //! weights of the components |
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35 | vec w; |
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36 | //! Component (epdfs) |
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37 | Array<epdf*> Coms; |
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38 | public: |
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39 | //!Default constructor |
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40 | emix ( RV &rv ) : epdf ( rv ) {}; |
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41 | //! Set weights \c w and components \c R |
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42 | void set_parameters ( const vec &w, const Array<epdf*> &Coms ); |
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43 | |
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44 | vec sample() const; |
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45 | vec mean() const { |
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46 | int i; vec mu = zeros ( rv.count() ); |
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47 | for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); } |
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48 | return mu; |
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49 | } |
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50 | double evalpdflog ( const vec &val ) const { |
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51 | int i; |
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52 | double sum = 0.0; |
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53 | for ( i = 0;i < w.length();i++ ) {sum += w ( i ) * Coms ( i )->evalpdflog ( val );} |
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54 | return log ( sum ); |
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55 | }; |
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56 | |
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57 | //Access methods |
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58 | //! returns a pointer to the internal mean value. Use with Care! |
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59 | vec& _w() {return w;} |
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60 | }; |
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61 | |
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62 | /*! \brief Chain rule decomposition of epdf |
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63 | |
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64 | Probability density in the form of Chain-rule decomposition: |
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65 | \[ |
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66 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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67 | \] |
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68 | Note that |
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69 | */ |
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70 | class mprod: public compositepdf, public mpdf { |
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71 | protected: |
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72 | // pointers to epdfs |
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73 | Array<epdf*> epdfs; |
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74 | //! Indeces of rvc in common rvc |
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75 | Array<ivec> rvcinds; |
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76 | public: |
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77 | /*!\brief Constructor from list of mFacs, |
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78 | Additional parameter overlap is left for future use. Do not set to true for mprod. |
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79 | */ |
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80 | mprod ( Array<mpdf*> mFacs): compositepdf(mFacs), mpdf(getrv(true),RV()), epdfs(n), rvcinds(n) |
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81 | { setrvc(rv,rvc); |
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82 | setrvcinrv(rvc,rvcinds); |
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83 | setindices(rv); |
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84 | for(int i=0;i<n;i++){epdfs(i)=&(mpdfs(i)->_epdf());} |
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85 | }; |
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86 | |
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87 | double evalpdflog ( const vec &val ) const { |
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88 | int i; |
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89 | double res = 0.0; |
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90 | for ( i = n - 1;i > 0;i++ ) { |
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91 | if ( rvcinds ( i ).length() > 0 ) |
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92 | {mpdfs ( i )->condition ( val ( rvcinds ( i ) ) );} |
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93 | // add logarithms |
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94 | res += epdfs ( i )->evalpdflog ( val ( rvsinrv ( i ) ) ); |
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95 | } |
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96 | return res; |
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97 | } |
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98 | vec samplecond ( const vec &cond, double &ll ) { |
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99 | vec smp=zeros ( rv.count() ); |
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100 | vec condi; |
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101 | vec smpi; |
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102 | ll = 0; |
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103 | for ( int i = ( n - 1 );i >= 0;i-- ) { |
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104 | if ( rvcinds ( i ).length() > 0 ) { |
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105 | condi = zeros ( rvcsinrv.length() + rvcinds.length() ); |
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106 | // copy data in condition |
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107 | set_subvector ( condi,rvcinds ( i ), cond ); |
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108 | // copy data in already generated sample |
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109 | set_subvector ( condi,rvcsinrv ( i ), smp ); |
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110 | |
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111 | mpdfs ( i )->condition ( condi ); |
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112 | } |
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113 | smpi = epdfs ( i )->sample(); |
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114 | // copy contribution of this pdf into smp |
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115 | set_subvector ( smp,rvsinrv ( i ), smpi ); |
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116 | // add ith likelihood contribution |
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117 | ll+=epdfs ( i )->evalpdflog ( smpi ); |
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118 | } |
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119 | return smp; |
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120 | } |
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121 | mat samplecond ( const vec &cond, vec &ll, int N ) { |
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122 | mat Smp ( rv.count(),N ); |
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123 | for ( int i=0;i<N;i++ ) {Smp.set_col ( i,samplecond ( cond,ll ( i ) ) );} |
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124 | return Smp; |
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125 | } |
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126 | |
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127 | ~mprod() {}; |
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128 | }; |
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129 | |
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130 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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131 | class eprod: public epdf { |
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132 | protected: |
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133 | //! Components (epdfs) |
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134 | Array<const epdf*> epdfs; |
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135 | //! Array of indeces |
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136 | Array<ivec> rvinds; |
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137 | public: |
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138 | eprod ( const Array<const epdf*> epdfs0 ) : epdf ( RV() ),epdfs ( epdfs0 ),rvinds ( epdfs.length() ) { |
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139 | bool independent=true; |
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140 | for ( int i=0;i<epdfs.length();i++ ) { |
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141 | independent=rv.add ( epdfs ( i )->_rv() ); |
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142 | it_assert_debug ( independent==true, "eprod:: given components are not independent ." ); |
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143 | rvinds ( i ) = ( epdfs ( i )->_rv() ).dataind ( rv ); |
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144 | } |
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145 | } |
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146 | |
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147 | vec mean() const { |
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148 | vec tmp ( rv.count() ); |
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149 | for ( int i=0;i<epdfs.length();i++ ) { |
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150 | vec pom = epdfs ( i )->mean(); |
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151 | set_subvector ( tmp,rvinds ( i ), pom ); |
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152 | } |
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153 | return tmp; |
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154 | } |
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155 | vec sample() const { |
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156 | vec tmp ( rv.count() ); |
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157 | for ( int i=0;i<epdfs.length();i++ ) { |
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158 | vec pom = epdfs ( i )->sample(); |
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159 | set_subvector ( tmp,rvinds ( i ), pom ); |
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160 | } |
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161 | return tmp; |
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162 | } |
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163 | double evalpdflog ( const vec &val ) const { |
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164 | double tmp=0; |
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165 | for ( int i=0;i<epdfs.length();i++ ) { |
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166 | tmp+=epdfs(i)->evalpdflog(val(rvinds(i))); |
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167 | } |
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168 | return tmp; |
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169 | } |
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170 | //!access function |
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171 | const epdf* operator () (int i) const {it_assert_debug(i<epdfs.length(),"wrong index");return epdfs(i);} |
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172 | }; |
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173 | |
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174 | |
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175 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type |
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176 | |
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177 | */ |
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178 | class mmix : public mpdf { |
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179 | protected: |
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180 | //! Component (epdfs) |
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181 | Array<mpdf*> Coms; |
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182 | //!Internal epdf |
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183 | emix Epdf; |
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184 | public: |
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185 | //!Default constructor |
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186 | mmix ( RV &rv, RV &rvc ) : mpdf ( rv, rvc ), Epdf ( rv ) {ep = &Epdf;}; |
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187 | //! Set weights \c w and components \c R |
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188 | void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) { |
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189 | Array<epdf*> Eps ( Coms.length() ); |
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190 | |
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191 | for ( int i = 0;i < Coms.length();i++ ) { |
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192 | Eps ( i ) = & ( Coms ( i )->_epdf() ); |
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193 | } |
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194 | Epdf.set_parameters ( w, Eps ); |
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195 | }; |
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196 | |
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197 | void condition ( const vec &cond ) { |
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198 | for ( int i = 0;i < Coms.length();i++ ) {Coms ( i )->condition ( cond );} |
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199 | }; |
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200 | }; |
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201 | #endif //MX_H |
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