1 | Double_t Log10(Double_t lg)
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2 | {
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3 | // Avoid numerical limits
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4 | return lg<=1e-6 ? -6 : log10(lg);
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5 | }
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6 |
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7 | // The mass overburden in each layer is given by
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8 | // T = AATM + BATM * exp(-h/CATM)
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9 | // Note that the AATM are correlated with the layer border
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10 | Double_t fcn(Double_t *xx, Double_t *par)
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11 | {
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12 | Double_t *A = par;
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13 | Double_t *B = par+5;
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14 | Double_t *C = par+10;
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15 | Double_t *H = par+15;
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16 |
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17 | Double_t x = xx[0]*1e5;
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18 |
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19 | double Ai = A[0];
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20 |
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21 | for (int i=0; i<4; i++)
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22 | {
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23 | if (x>=H[i] && x<H[i+1])
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24 | return Log10(Ai + B[i]*exp(-x/C[i]));
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25 |
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26 | Ai += B[i] *exp(-H[i+1]/C[i]); // y-value of current bin function [i] at transition border H[i+1] to next layer
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27 | Ai -= B[i+1]*exp(-H[i+1]/C[i+1]); // y-value of next bin function [i+1] at transition border H[i+1] to next layer
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28 | }
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29 |
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30 | return Log10(Ai + B[4]*exp(-x/C[4]));
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31 | }
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32 |
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33 | void atmprof()
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34 | {
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35 | // As in CORSIKA the atmosphere for atmabs.dat is required up to 50 km
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36 | // the best is to do a fit which is bext up to at least 50 km
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37 | double MAX = 50.5;
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38 |
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39 | // MAGIC Winter (MAGIC Summer: atmprof9)
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40 | TGraph atmprof("/home/tbretz/SW/corsika-76900/bernlohr/atmprof8.dat", "%lg %*lg %lg, %*lg");
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41 |
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42 | // The last point has a thickness of 0 (log!)
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43 | atmprof.RemovePoint(atmprof.GetN()-1);
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44 |
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45 | // Calculate the logarithm (better fit)
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46 | double miny = log10(atmprof.GetY()[0]);
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47 | for (int i=0; i<atmprof.GetN(); i++)
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48 | {
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49 | atmprof.GetY()[i] = log10(atmprof.GetY()[i]);
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50 | if (atmprof.GetX()[i]<MAX)
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51 | miny = TMath::Min(miny, atmprof.GetY()[i]);
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52 | }
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53 |
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54 | // =============================================================================
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55 |
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56 | TCanvas *c = new TCanvas;
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57 | c->Divide(1, 2);
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58 | c->cd(1);
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59 |
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60 | atmprof.SetMarkerStyle(kFullDotMedium);
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61 | atmprof.GetHistogram()->GetXaxis()->SetRangeUser(0, MAX);
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62 | atmprof.GetHistogram()->GetYaxis()->SetRangeUser(miny, atmprof.GetY()[0]*1.05);
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63 | atmprof.DrawClone("ALP");
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64 |
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65 | TMarker m;
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66 | m.SetMarkerStyle(kFullDotLarge);
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67 |
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68 | // =============================================================================
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69 |
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70 | // Define the fit function betwene 0 and 50km with 15 free parameters
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71 | TF1 f("thickness", fcn, 0, MAX, 4*5);
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72 | f.SetNpx(10000);
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73 |
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74 | // This is the Keilhauer U.S. Standard Atmosphere (as starting values)
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75 | Double_t params[] =
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76 | {
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77 | -149.801663, -57.932486, 0.63631894, 4.35453690e-4, 0.01128292, // A
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78 | 1183.6071, 1143.0425, 1322.9748, 655.67307, 1, // B
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79 | 954248.34, 800005.34, 629568.93, 737521.77, 1e9, // C
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80 | 0, 7.0e5, 11.4e5, 37.0e5, 100e5, // H
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81 |
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82 | };
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83 | f.SetParameters(params);
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84 |
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85 | // =============================================================================
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86 | // Calc residuals
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87 |
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88 | TGraph g1;
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89 | for (int i=0; i<atmprof.GetN(); i++)
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90 | {
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91 | double x = atmprof.GetX()[i];
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92 | if (x>MAX)
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93 | break;
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94 |
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95 | double y = atmprof.GetY()[i];
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96 | g1.SetPoint(g1.GetN(), x, 1-pow(10, f.Eval(x))/pow(10, y));
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97 | }
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98 |
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99 |
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100 | // =============================================================================
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101 | // Plot and print
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102 |
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103 | m.SetMarkerColor(kRed);
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104 | f.SetLineColor(kRed);
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105 |
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106 | f.DrawCopy("same");
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107 |
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108 | cout << endl;
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109 | for (int i=0; i<5; i++)
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110 | {
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111 | double A[5] = { f.GetParameters()[0], 0, 0, 0, 0 };
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112 | double *B = f.GetParameters()+5;
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113 | double *C = f.GetParameters()+10;
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114 | double *H = f.GetParameters()+15;
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115 |
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116 | A[1] = A[0] + B[0]*exp(-H[1]/C[0]) - B[1]*exp(-H[1]/C[1]);
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117 | A[2] = A[1] + B[1]*exp(-H[2]/C[1]) - B[2]*exp(-H[2]/C[2]);
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118 | A[3] = A[2] + B[2]*exp(-H[3]/C[2]) - B[3]*exp(-H[3]/C[3]);
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119 | A[4] = A[3] + B[3]*exp(-H[4]/C[3]) - B[4]*exp(-H[4]/C[4]);
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120 |
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121 | cout << Form("A[%d]=%13f B[%d]=%13f C[%d]=%13f", i, A[i], i, B[i], i, C[i]);
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122 | if (i<4)
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123 | {
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124 | cout << Form(" H=%13f", H[i+1]/1e5);
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125 | m.DrawMarker(H[i+1]/1e5, f.Eval(H[i+1]/1e5));
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126 | }
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127 | cout << endl;
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128 | }
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129 |
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130 | // =============================================================================
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131 |
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132 | // The parameters above 50km should not be left free
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133 | f.FixParameter( 1, params[1]);
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134 | f.FixParameter( 2, params[2]);
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135 | f.FixParameter( 3, params[3]);
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136 | f.FixParameter( 4, params[4]);
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137 | f.FixParameter( 9, params[9]);
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138 | f.FixParameter(14, params[14]);
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139 | f.FixParameter(15, 0);
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140 |
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141 | // Fit
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142 | float max = 5;
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143 | while (max<MAX)
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144 | {
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145 | atmprof.Fit(&f, "", "", 0, max);
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146 | max += 5;
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147 | }
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148 |
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149 | // =============================================================================
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150 | // Plot and print
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151 |
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152 | m.SetMarkerColor(kBlue);
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153 | f.SetLineColor(kBlue);
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154 |
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155 | f.DrawCopy("same");
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156 |
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157 | cout << endl;
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158 | for (int i=0; i<5; i++)
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159 | {
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160 | double A[5] = { f.GetParameters()[0], 0, 0, 0, 0 };
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161 | double *B = f.GetParameters()+5;
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162 | double *C = f.GetParameters()+10;
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163 | double *H = f.GetParameters()+15;
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164 |
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165 | A[1] = A[0] + B[0]*exp(-H[1]/C[0]) - B[1]*exp(-H[1]/C[1]);
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166 | A[2] = A[1] + B[1]*exp(-H[2]/C[1]) - B[2]*exp(-H[2]/C[2]);
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167 | A[3] = A[2] + B[2]*exp(-H[3]/C[2]) - B[3]*exp(-H[3]/C[3]);
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168 | A[4] = A[3] + B[3]*exp(-H[4]/C[3]) - B[4]*exp(-H[4]/C[4]);
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169 |
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170 | cout << Form("A[%d]=%13f B[%d]=%13f C[%d]=%13f", i, A[i], i, B[i], i, C[i]);
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171 | if (i<4)
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172 | {
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173 | cout << Form(" H=%13f", H[i+1]/1e5);
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174 | m.DrawMarker(H[i+1]/1e5, f.Eval(H[i+1]/1e5));
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175 | }
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176 | cout << endl;
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177 | }
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178 |
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179 | // =============================================================================
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180 | // Plot residuals
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181 |
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182 | c->cd(2);
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183 |
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184 | TGraph g2;
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185 | for (int i=0; i<atmprof.GetN(); i++)
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186 | {
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187 | double x = atmprof.GetX()[i];
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188 | if (x>MAX)
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189 | break;
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190 |
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191 | double y = atmprof.GetY()[i];
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192 | g2.SetPoint(g2.GetN(), x, 1-pow(10, f.Eval(x))/pow(10, y));
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193 | }
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194 |
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195 | g1.SetLineColor(kRed);
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196 | g1.SetMarkerColor(kRed);
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197 | g1.SetMarkerStyle(kFullDotMedium);
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198 |
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199 | g2.SetLineColor(kBlue);
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200 | g2.SetMarkerColor(kBlue);
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201 | g2.SetMarkerStyle(kFullDotMedium);
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202 |
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203 | TH1C h("", "Residuals", 100, 0, MAX);
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204 | Double_t xmin, ymin, xmax, ymax;
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205 | g1.ComputeRange(xmin, ymin, xmax, ymax);
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206 | Double_t maxy = TMath::Max(fabs(ymin)*1.05, fabs(ymax)*1.05);
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207 | h.SetMinimum(-maxy);
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208 | h.SetMaximum( maxy);
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209 | h.SetStats(kFALSE);
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210 | h.DrawCopy();
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211 |
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212 | g1.GetHistogram()->GetXaxis()->SetRangeUser(0, MAX);
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213 | g1.DrawClone("LP");
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214 | g2.DrawClone("LP");
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215 |
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216 | g2.ComputeRange(xmin, ymin, xmax, ymax);
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217 | maxy = TMath::Max(fabs(ymin)*1.05, fabs(ymax)*1.05);
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218 |
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219 | cout << "\nMax residual after fit: " << maxy*100 << " %\n" << endl;
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220 | }
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