1 | #include <math.h> |
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2 | |
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3 | #include <itpp/base/bessel.h> |
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4 | #include "exp_family.h" |
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5 | |
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6 | namespace bdm { |
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7 | |
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8 | Uniform_RNG UniRNG; |
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9 | Normal_RNG NorRNG; |
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10 | Gamma_RNG GamRNG; |
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11 | |
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12 | using std::cout; |
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13 | |
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14 | /////////// |
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15 | |
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16 | void BMEF::bayes ( const vec &yt, const vec &cond ) { |
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17 | this->bayes_weighted ( yt, cond, 1.0 ); |
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18 | }; |
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19 | |
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20 | void egiw::set_parameters ( int dimx0, ldmat V0, double nu0 ) { |
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21 | dimx = dimx0; |
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22 | nPsi = V0.rows() - dimx; |
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23 | dim = dimx * ( dimx + nPsi ); // size(R) + size(Theta) |
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24 | |
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25 | V = V0; |
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26 | if ( nu0 < 0 ) { |
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27 | nu = 0.1 + nPsi + 2 * dimx + 2; // +2 assures finite expected value of R |
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28 | // terms before that are sufficient for finite normalization |
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29 | } else { |
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30 | nu = nu0; |
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31 | } |
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32 | } |
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33 | |
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34 | vec egiw::sample() const { |
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35 | mat M; |
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36 | chmat R; |
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37 | sample_mat ( M, R ); |
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38 | |
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39 | return concat ( cvectorize ( M ), cvectorize ( R.to_mat() ) ); |
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40 | } |
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41 | |
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42 | mat egiw::sample_mat ( int n ) const { |
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43 | // TODO - correct approach - convert to product of norm * Wishart |
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44 | mat M; |
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45 | ldmat Vz; |
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46 | ldmat Lam; |
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47 | factorize ( M, Vz, Lam ); |
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48 | |
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49 | chmat ChLam ( Lam.to_mat() ); |
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50 | chmat iChLam; |
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51 | ChLam.inv ( iChLam ); |
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52 | |
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53 | eWishartCh Omega; //inverse Wishart, result is R, |
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54 | Omega.set_parameters ( iChLam, nu - 2*nPsi - dimx ); // 2*nPsi is there to match numercial simulations - check if analytically correct |
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55 | |
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56 | mat OmChi; |
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57 | mat Z ( M.rows(), M.cols() ); |
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58 | |
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59 | mat Mi; |
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60 | mat RChiT; |
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61 | mat tmp ( dimension(), n ); |
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62 | for ( int i = 0; i < n; i++ ) { |
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63 | OmChi = Omega.sample_mat(); |
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64 | RChiT = inv ( OmChi ); |
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65 | Z = randn ( M.rows(), M.cols() ); |
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66 | Mi = M + RChiT * Z * inv ( Vz._L().T() * diag ( sqrt ( Vz._D() ) ) ); |
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67 | |
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68 | tmp.set_col ( i, concat ( cvectorize ( Mi ), cvectorize ( RChiT*RChiT.T() ) ) ); |
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69 | } |
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70 | return tmp; |
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71 | } |
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72 | |
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73 | void egiw::sample_mat ( mat &Mi, chmat &Ri ) const { |
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74 | |
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75 | // TODO - correct approach - convert to product of norm * Wishart |
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76 | mat M; |
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77 | ldmat Vz; |
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78 | ldmat Lam; |
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79 | factorize ( M, Vz, Lam ); |
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80 | |
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81 | chmat Ch; |
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82 | Ch.setCh ( Lam._L() *diag ( sqrt ( Lam._D() ) ) ); |
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83 | chmat iCh; |
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84 | Ch.inv ( iCh ); |
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85 | |
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86 | eWishartCh Omega; //inverse Wishart, result is R, |
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87 | Omega.set_parameters ( iCh, nu - 2*nPsi - dimx ); // 2*nPsi is there to match numercial simulations - check if analytically correct |
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88 | |
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89 | chmat Omi; |
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90 | Omi.setCh ( Omega.sample_mat() ); |
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91 | |
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92 | mat Z = randn ( M.rows(), M.cols() ); |
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93 | Mi = M + Omi._Ch() * Z * inv ( Vz._L() * diag ( sqrt ( Vz._D() ) ) ); |
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94 | Omi.inv ( Ri ); |
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95 | } |
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96 | |
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97 | double egiw::evallog_nn ( const vec &val ) const { |
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98 | bdm_assert_debug(val.length()==nPsi+dimx,"Incorrect cond in egiw::evallog_nn" ); |
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99 | |
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100 | int vend = val.length() - 1; |
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101 | |
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102 | if ( dimx == 1 ) { //same as the following, just quicker. |
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103 | double r = val ( vend ); //last entry! |
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104 | if ( r < 0 ) return -inf; |
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105 | vec Psi ( nPsi + dimx ); |
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106 | Psi ( 0 ) = -1.0; |
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107 | Psi.set_subvector ( 1, val ( 0, vend - 1 ) ); // fill the rest |
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108 | |
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109 | double Vq = V.qform ( Psi ); |
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110 | return -0.5* ( nu*log ( r ) + Vq / r ); |
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111 | } else { |
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112 | mat Th = reshape ( val ( 0, nPsi * dimx - 1 ), nPsi, dimx ); |
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113 | fsqmat R ( reshape ( val ( nPsi*dimx, vend ), dimx, dimx ) ); |
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114 | double ldetR = R.logdet(); |
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115 | if ( ldetR ) return -inf; |
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116 | mat Tmp = concat_vertical ( -eye ( dimx ), Th ); |
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117 | fsqmat iR ( dimx ); |
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118 | R.inv ( iR ); |
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119 | |
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120 | return -0.5* ( nu*ldetR + trace ( iR.to_mat() *Tmp.T() *V.to_mat() *Tmp ) ); |
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121 | } |
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122 | } |
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123 | |
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124 | double egiw::lognc() const { |
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125 | const vec& D = V._D(); |
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126 | |
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127 | double m = nu - nPsi - dimx - 1; |
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128 | #define log2 0.693147180559945286226763983 |
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129 | #define logpi 1.144729885849400163877476189 |
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130 | #define log2pi 1.83787706640935 |
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131 | #define Inf std::numeric_limits<double>::infinity() |
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132 | |
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133 | double nkG = 0.5 * dimx * ( -nPsi * log2pi + sum ( log ( D ( dimx, D.length() - 1 ) ) ) ); |
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134 | // temporary for lgamma in Wishart |
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135 | double lg = 0; |
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136 | for ( int i = 0; i < dimx; i++ ) { |
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137 | lg += lgamma ( 0.5 * ( m - i ) ); |
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138 | } |
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139 | |
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140 | double nkW = 0.5 * ( m * sum ( log ( D ( 0, dimx - 1 ) ) ) ) \ |
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141 | - 0.5 * dimx * ( m * log2 + 0.5 * ( dimx - 1 ) * log2pi ) - lg; |
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142 | |
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143 | // bdm_assert_debug ( ( ( -nkG - nkW ) > -Inf ) && ( ( -nkG - nkW ) < Inf ), "ARX improper" ); |
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144 | if ( -nkG - nkW == Inf ) { |
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145 | cout << "??" << endl; |
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146 | } |
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147 | return -nkG - nkW; |
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148 | } |
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149 | |
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150 | vec egiw::est_theta() const { |
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151 | if ( dimx == 1 ) { |
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152 | const mat &L = V._L(); |
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153 | int end = L.rows() - 1; |
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154 | |
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155 | mat iLsub = ltuinv ( L ( dimx, end, dimx, end ) ); |
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156 | |
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157 | vec L0 = L.get_col ( 0 ); |
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158 | |
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159 | return iLsub * L0 ( 1, end ); |
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160 | } else { |
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161 | bdm_error ( "ERROR: est_theta() not implemented for dimx>1" ); |
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162 | return vec(); |
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163 | } |
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164 | } |
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165 | |
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166 | void egiw::factorize ( mat &M, ldmat &Vz, ldmat &Lam ) const { |
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167 | const mat &L = V._L(); |
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168 | const vec &D = V._D(); |
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169 | int end = L.rows() - 1; |
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170 | |
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171 | Vz = ldmat ( L ( dimx, end, dimx, end ), D ( dimx, end ) ); |
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172 | mat iLsub = ltuinv ( Vz._L() ); |
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173 | // set mean value |
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174 | mat Lpsi = L ( dimx, end, 0, dimx - 1 ); |
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175 | M = iLsub * Lpsi; |
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176 | |
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177 | Lam = ldmat ( L ( 0, dimx - 1, 0, dimx - 1 ), D ( 0, dimx - 1 ) ); //exp val of R |
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178 | if ( 1 ) { // test with Peterka |
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179 | mat VF = V.to_mat(); |
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180 | mat Vf = VF ( 0, dimx - 1, 0, dimx - 1 ); |
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181 | mat Vzf = VF ( dimx, end, 0, dimx - 1 ); |
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182 | mat VZ = VF ( dimx, end, dimx, end ); |
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183 | |
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184 | mat Lam2 = Vf - Vzf.T() * inv ( VZ ) * Vzf; |
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185 | } |
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186 | } |
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187 | |
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188 | ldmat egiw::est_theta_cov() const { |
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189 | if ( dimx == 1 ) { |
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190 | const mat &L = V._L(); |
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191 | const vec &D = V._D(); |
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192 | int end = D.length() - 1; |
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193 | |
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194 | mat Lsub = L ( 1, end, 1, end ); |
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195 | // mat Dsub = diag ( D ( 1, end ) ); |
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196 | |
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197 | ldmat LD ( inv ( Lsub ).T(), 1.0 / D ( 1, end ) ); |
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198 | return LD; |
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199 | |
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200 | } else { |
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201 | bdm_error ( "ERROR: est_theta_cov() not implemented for dimx>1" ); |
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202 | return ldmat(); |
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203 | } |
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204 | |
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205 | } |
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206 | |
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207 | vec egiw::mean() const { |
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208 | |
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209 | if ( dimx == 1 ) { |
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210 | const vec &D = V._D(); |
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211 | int end = D.length() - 1; |
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212 | |
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213 | vec m ( dim ); |
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214 | m.set_subvector ( 0, est_theta() ); |
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215 | m ( end ) = D ( 0 ) / ( nu - nPsi - 2 * dimx - 2 ); |
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216 | return m; |
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217 | } else { |
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218 | mat M; |
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219 | mat R; |
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220 | mean_mat ( M, R ); |
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221 | return concat ( cvectorize ( M ), cvectorize ( R ) ); |
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222 | } |
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223 | |
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224 | } |
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225 | |
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226 | vec egiw::variance() const { |
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227 | int l = V.rows(); |
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228 | // cut out rest of lower-right part of V |
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229 | const ldmat tmp ( V, linspace ( dimx, l - 1 ) ); |
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230 | // invert it |
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231 | ldmat itmp ( l ); |
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232 | tmp.inv ( itmp ); |
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233 | |
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234 | // following Wikipedia notation |
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235 | // m=nu-nPsi-dimx-1, p=dimx |
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236 | double mp1p = nu - nPsi - 2 * dimx; // m-p+1 |
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237 | double mp1m = mp1p - 2; // m-p-1 |
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238 | |
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239 | if ( dimx == 1 ) { |
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240 | double cove = V._D() ( 0 ) / mp1m ; |
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241 | |
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242 | vec var ( l ); |
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243 | var.set_subvector ( 0, diag ( itmp.to_mat() ) *cove ); |
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244 | var ( l - 1 ) = cove * cove / ( mp1m - 2 ); |
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245 | return var; |
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246 | } else { |
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247 | ldmat Vll ( V, linspace ( 0, dimx - 1 ) ); // top-left part of V |
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248 | mat Y = Vll.to_mat(); |
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249 | mat varY ( Y.rows(), Y.cols() ); |
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250 | |
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251 | double denom = ( mp1p - 1 ) * mp1m * mp1m * ( mp1m - 2 ); // (m-p)(m-p-1)^2(m-p-3) |
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252 | |
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253 | int i, j; |
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254 | for ( i = 0; i < Y.rows(); i++ ) { |
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255 | for ( j = 0; j < Y.cols(); j++ ) { |
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256 | varY ( i, j ) = ( mp1p * Y ( i, j ) * Y ( i, j ) + mp1m * Y ( i, i ) * Y ( j, j ) ) / denom; |
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257 | } |
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258 | } |
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259 | vec mean_dR = diag ( Y ) / mp1m; // corresponds to cove |
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260 | vec var_th = diag ( itmp.to_mat() ); |
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261 | vec var_Th ( mean_dR.length() *var_th.length() ); |
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262 | // diagonal of diag(mean_dR) \kron diag(var_th) |
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263 | for ( int i = 0; i < mean_dR.length(); i++ ) { |
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264 | var_Th.set_subvector ( i*var_th.length(), var_th*mean_dR ( i ) ); |
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265 | } |
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266 | |
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267 | return concat ( var_Th, cvectorize ( varY ) ); |
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268 | } |
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269 | } |
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270 | |
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271 | void egiw::mean_mat ( mat &M, mat&R ) const { |
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272 | const mat &L = V._L(); |
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273 | const vec &D = V._D(); |
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274 | int end = L.rows() - 1; |
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275 | |
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276 | ldmat ldR ( L ( 0, dimx - 1, 0, dimx - 1 ), D ( 0, dimx - 1 ) / ( nu - nPsi - 2*dimx - 2 ) ); //exp val of R |
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277 | mat iLsub = ltuinv ( L ( dimx, end, dimx, end ) ); |
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278 | |
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279 | // set mean value |
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280 | mat Lpsi = L ( dimx, end, 0, dimx - 1 ); |
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281 | M = iLsub * Lpsi; |
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282 | R = ldR.to_mat() ; |
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283 | } |
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284 | |
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285 | void egiw::log_register ( bdm::logger& L, const string& prefix ) { |
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286 | if ( log_level == 3 ) { |
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287 | root::log_register ( L, prefix ); |
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288 | logrec->ids.set_length ( 2 ); |
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289 | int th_dim = dimension() - dimx * ( dimx + 1 ) / 2; |
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290 | logrec->ids ( 0 ) = L.add_vector ( RV ( "", th_dim ), prefix + logrec->L.prefix_sep() + "mean" ); |
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291 | logrec->ids ( 1 ) = L.add_vector ( RV ( "", th_dim * th_dim ), prefix + logrec->L.prefix_sep() + "variance" ); |
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292 | } else { |
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293 | epdf::log_register ( L, prefix ); |
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294 | } |
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295 | } |
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296 | |
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297 | void egiw::log_write() const { |
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298 | if ( log_level == 3 ) { |
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299 | mat M; |
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300 | ldmat Lam; |
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301 | ldmat Vz; |
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302 | factorize ( M, Vz, Lam ); |
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303 | logrec->L.log_vector ( logrec->ids ( 0 ), est_theta() ); |
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304 | logrec->L.log_vector ( logrec->ids ( 1 ), cvectorize ( est_theta_cov().to_mat() ) ); |
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305 | } else { |
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306 | epdf::log_write(); |
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307 | } |
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308 | |
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309 | } |
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310 | |
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311 | void multiBM::bayes ( const vec &yt, const vec &cond ) { |
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312 | if ( frg < 1.0 ) { |
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313 | beta *= frg; |
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314 | last_lognc = est.lognc(); |
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315 | } |
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316 | beta += yt; |
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317 | if ( evalll ) { |
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318 | ll = est.lognc() - last_lognc; |
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319 | } |
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320 | } |
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321 | |
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322 | double multiBM::logpred ( const vec &yt ) const { |
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323 | eDirich pred ( est ); |
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324 | vec &beta = pred._beta(); |
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325 | |
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326 | double lll; |
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327 | if ( frg < 1.0 ) { |
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328 | beta *= frg; |
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329 | lll = pred.lognc(); |
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330 | } else if ( evalll ) { |
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331 | lll = last_lognc; |
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332 | } else { |
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333 | lll = pred.lognc(); |
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334 | } |
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335 | |
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336 | beta += yt; |
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337 | return pred.lognc() - lll; |
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338 | } |
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339 | void multiBM::flatten ( const BMEF* B ) { |
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340 | const multiBM* E = dynamic_cast<const multiBM*> ( B ); |
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341 | // sum(beta) should be equal to sum(B.beta) |
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342 | const vec &Eb = E->beta;//const_cast<multiBM*> ( E )->_beta(); |
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343 | beta *= ( sum ( Eb ) / sum ( beta ) ); |
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344 | if ( evalll ) { |
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345 | last_lognc = est.lognc(); |
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346 | } |
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347 | } |
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348 | |
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349 | vec egamma::sample() const { |
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350 | vec smp ( dim ); |
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351 | int i; |
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352 | |
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353 | for ( i = 0; i < dim; i++ ) { |
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354 | if ( beta ( i ) > std::numeric_limits<double>::epsilon() ) { |
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355 | GamRNG.setup ( alpha ( i ), beta ( i ) ); |
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356 | } else { |
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357 | GamRNG.setup ( alpha ( i ), std::numeric_limits<double>::epsilon() ); |
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358 | } |
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359 | #pragma omp critical |
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360 | smp ( i ) = GamRNG(); |
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361 | } |
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362 | |
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363 | return smp; |
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364 | } |
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365 | |
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366 | // mat egamma::sample ( int N ) const { |
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367 | // mat Smp ( rv.count(),N ); |
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368 | // int i,j; |
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369 | // |
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370 | // for ( i=0; i<rv.count(); i++ ) { |
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371 | // GamRNG.setup ( alpha ( i ),beta ( i ) ); |
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372 | // |
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373 | // for ( j=0; j<N; j++ ) { |
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374 | // Smp ( i,j ) = GamRNG(); |
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375 | // } |
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376 | // } |
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377 | // |
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378 | // return Smp; |
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379 | // } |
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380 | |
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381 | double egamma::evallog ( const vec &val ) const { |
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382 | double res = 0.0; //the rest will be added |
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383 | int i; |
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384 | |
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385 | if ( any ( val <= 0. ) ) return -inf; |
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386 | if ( any ( beta <= 0. ) ) return -inf; |
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387 | for ( i = 0; i < dim; i++ ) { |
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388 | res += ( alpha ( i ) - 1 ) * std::log ( val ( i ) ) - beta ( i ) * val ( i ); |
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389 | } |
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390 | double tmp = res - lognc();; |
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391 | bdm_assert_debug ( std::isfinite ( tmp ), "Infinite value" ); |
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392 | return tmp; |
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393 | } |
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394 | |
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395 | double egamma::lognc() const { |
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396 | double res = 0.0; //will be added |
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397 | int i; |
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398 | |
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399 | for ( i = 0; i < dim; i++ ) { |
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400 | res += lgamma ( alpha ( i ) ) - alpha ( i ) * std::log ( beta ( i ) ) ; |
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401 | } |
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402 | |
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403 | return res; |
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404 | } |
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405 | |
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406 | void mgamma::set_parameters ( double k0, const vec &beta0 ) { |
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407 | k = k0; |
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408 | iepdf.set_parameters ( k * ones ( beta0.length() ), beta0 ); |
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409 | dimc = iepdf.dimension(); |
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410 | dim = iepdf.dimension(); |
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411 | } |
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412 | |
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413 | void eEmp::resample ( ivec &ind, RESAMPLING_METHOD method ) { |
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414 | ind = zeros_i ( n ); |
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415 | ivec N_babies = zeros_i ( n ); |
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416 | vec cumDist = cumsum ( w ); |
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417 | vec u ( n ); |
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418 | int i, j, parent; |
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419 | double u0; |
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420 | |
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421 | switch ( method ) { |
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422 | case MULTINOMIAL: |
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423 | u ( n - 1 ) = pow ( UniRNG.sample(), 1.0 / n ); |
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424 | |
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425 | for ( i = n - 2; i >= 0; i-- ) { |
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426 | u ( i ) = u ( i + 1 ) * pow ( UniRNG.sample(), 1.0 / ( i + 1 ) ); |
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427 | } |
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428 | |
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429 | break; |
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430 | |
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431 | case STRATIFIED: |
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432 | |
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433 | for ( i = 0; i < n; i++ ) { |
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434 | u ( i ) = ( i + UniRNG.sample() ) / n; |
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435 | } |
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436 | |
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437 | break; |
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438 | |
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439 | case SYSTEMATIC: |
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440 | u0 = UniRNG.sample(); |
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441 | |
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442 | for ( i = 0; i < n; i++ ) { |
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443 | u ( i ) = ( i + u0 ) / n; |
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444 | } |
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445 | |
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446 | break; |
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447 | |
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448 | default: |
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449 | bdm_error ( "PF::resample(): Unknown resampling method" ); |
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450 | } |
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451 | |
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452 | // U is now full |
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453 | j = 0; |
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454 | |
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455 | for ( i = 0; i < n; i++ ) { |
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456 | while ( u ( i ) > cumDist ( j ) ) j++; |
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457 | |
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458 | N_babies ( j ) ++; |
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459 | } |
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460 | // We have assigned new babies for each Particle |
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461 | // Now, we fill the resulting index such that: |
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462 | // * particles with at least one baby should not move * |
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463 | // This assures that reassignment can be done inplace; |
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464 | |
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465 | // find the first parent; |
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466 | parent = 0; |
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467 | while ( N_babies ( parent ) == 0 ) parent++; |
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468 | |
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469 | // Build index |
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470 | for ( i = 0; i < n; i++ ) { |
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471 | if ( N_babies ( i ) > 0 ) { |
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472 | ind ( i ) = i; |
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473 | N_babies ( i ) --; //this index was now replicated; |
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474 | } else { |
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475 | // test if the parent has been fully replicated |
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476 | // if yes, find the next one |
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477 | while ( ( N_babies ( parent ) == 0 ) || ( N_babies ( parent ) == 1 && parent > i ) ) parent++; |
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478 | |
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479 | // Replicate parent |
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480 | ind ( i ) = parent; |
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481 | |
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482 | N_babies ( parent ) --; //this index was now replicated; |
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483 | } |
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484 | |
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485 | } |
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486 | |
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487 | // copy the internals according to ind |
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488 | for ( i = 0; i < n; i++ ) { |
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489 | if ( ind ( i ) != i ) { |
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490 | samples ( i ) = samples ( ind ( i ) ); |
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491 | } |
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492 | w ( i ) = 1.0 / n; |
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493 | } |
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494 | } |
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495 | |
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496 | void eEmp::set_statistics ( const vec &w0, const epdf &epdf0 ) { |
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497 | dim = epdf0.dimension(); |
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498 | w = w0; |
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499 | w /= sum ( w0 );//renormalize |
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500 | n = w.length(); |
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501 | samples.set_size ( n ); |
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502 | |
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503 | for ( int i = 0; i < n; i++ ) { |
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504 | samples ( i ) = epdf0.sample(); |
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505 | } |
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506 | } |
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507 | |
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508 | void eEmp::set_samples ( const epdf* epdf0 ) { |
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509 | w = 1; |
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510 | w /= sum ( w );//renormalize |
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511 | |
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512 | for ( int i = 0; i < n; i++ ) { |
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513 | samples ( i ) = epdf0->sample(); |
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514 | } |
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515 | } |
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516 | |
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517 | void migamma_ref::from_setting ( const Setting &set ) { |
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518 | vec ref; |
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519 | UI::get ( ref, set, "ref" , UI::compulsory ); |
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520 | set_parameters ( set["k"], ref, set["l"] ); |
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521 | } |
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522 | |
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523 | void mlognorm::from_setting ( const Setting &set ) { |
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524 | vec mu0; |
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525 | UI::get ( mu0, set, "mu0", UI::compulsory ); |
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526 | set_parameters ( mu0.length(), set["k"] ); |
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527 | condition ( mu0 ); |
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528 | } |
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529 | |
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530 | void mlstudent::condition ( const vec &cond ) { |
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531 | if ( cond.length() > 0 ) { |
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532 | iepdf._mu() = A * cond + mu_const; |
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533 | } else { |
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534 | iepdf._mu() = mu_const; |
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535 | } |
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536 | double zeta; |
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537 | //ugly hack! |
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538 | if ( ( cond.length() + 1 ) == Lambda.rows() ) { |
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539 | zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) ); |
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540 | } else { |
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541 | zeta = Lambda.invqform ( cond ); |
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542 | } |
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543 | _R = Re; |
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544 | _R *= ( 1 + zeta );// / ( nu ); << nu is in Re!!!!!! |
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545 | } |
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546 | |
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547 | void eEmp::qbounds ( vec &lb, vec &ub, double perc ) const { |
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548 | // lb in inf so than it will be pushed below; |
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549 | lb.set_size ( dim ); |
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550 | ub.set_size ( dim ); |
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551 | lb = std::numeric_limits<double>::infinity(); |
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552 | ub = -std::numeric_limits<double>::infinity(); |
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553 | int j; |
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554 | for ( int i = 0; i < n; i++ ) { |
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555 | for ( j = 0; j < dim; j++ ) { |
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556 | if ( samples ( i ) ( j ) < lb ( j ) ) { |
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557 | lb ( j ) = samples ( i ) ( j ); |
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558 | } |
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559 | if ( samples ( i ) ( j ) > ub ( j ) ) { |
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560 | ub ( j ) = samples ( i ) ( j ); |
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561 | } |
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562 | } |
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563 | } |
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564 | } |
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565 | |
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566 | |
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567 | }; |
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