1 | /** |
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2 | * Scattering model for a cylinder |
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3 | * @author: Mathieu Doucet / UTK |
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4 | */ |
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5 | |
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6 | #include "cylinder.h" |
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7 | #include "smeared_cylinder.h" |
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8 | #include <math.h> |
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9 | #include "libCylinder.h" |
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10 | |
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11 | |
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12 | /** |
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13 | * Function to evaluate 1D scattering function |
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14 | * @param pars: parameters of the cylinder |
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15 | * @param q: q-value |
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16 | * @return: function value |
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17 | */ |
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18 | double smeared_cylinder_analytical_1D(SmearCylinderParameters *pars, double q) { |
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19 | double dp[5]; |
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20 | int i_r; |
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21 | double r_0, r, step_r, min_r; |
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22 | int npts; |
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23 | double weight, func, norm; |
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24 | |
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25 | // Fill paramater array |
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26 | dp[0] = pars->scale; |
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27 | dp[1] = pars->radius; |
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28 | dp[2] = pars->length; |
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29 | dp[3] = pars->contrast; |
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30 | dp[4] = pars->background; |
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31 | |
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32 | if(pars->sigma_radius==0) { |
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33 | return CylinderForm(dp, q); |
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34 | } |
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35 | |
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36 | // Central value is the current value |
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37 | r_0 = pars->radius; |
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38 | |
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39 | npts = 100; |
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40 | step_r = 4.0*pars->sigma_radius/npts; |
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41 | min_r = r_0 - 2.0*pars->sigma_radius; |
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42 | |
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43 | |
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44 | norm = 0.0; |
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45 | func = 0.0; |
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46 | |
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47 | for (i_r=0; i_r<100; i_r++) { |
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48 | r = min_r + step_r*i_r; |
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49 | dp[1] = r; |
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50 | |
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51 | // Weigth for that position |
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52 | weight = smeared_cylinder_dist( r, r_0, pars->sigma_radius ); |
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53 | norm += weight; |
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54 | |
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55 | // Evaluate I(q) at that r-value |
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56 | func += weight * CylinderForm(dp, q); |
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57 | } |
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58 | |
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59 | return func/norm; |
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60 | } |
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61 | |
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62 | |
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63 | /** |
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64 | * Function to evaluate 2D scattering function |
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65 | * @param pars: parameters of the cylinder |
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66 | * @param q: q-value |
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67 | * @return: function value |
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68 | */ |
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69 | double smeared_cylinder_analytical_2D(SmearCylinderParameters *pars, double q, double phi) { |
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70 | CylinderParameters cyl_pars; |
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71 | int i_theta, i_phi, i_r; |
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72 | int n_theta, n_phi, n_r; |
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73 | double theta_0, phi_0, r_0; |
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74 | int npts; |
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75 | double weight_theta, weight_phi, weight_r; |
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76 | double min_theta, min_phi, min_r; |
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77 | double step_theta, step_phi, step_r; |
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78 | double func, norm; |
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79 | double n_width = 3.0; |
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80 | |
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81 | // Fill paramater struct |
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82 | cyl_pars.scale = pars->scale; |
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83 | cyl_pars.radius = pars->radius; |
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84 | cyl_pars.length = pars->length; |
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85 | cyl_pars.contrast = pars->contrast; |
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86 | cyl_pars.background = pars->background; |
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87 | cyl_pars.cyl_phi = pars->cyl_phi; |
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88 | cyl_pars.cyl_theta = pars->cyl_theta; |
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89 | |
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90 | theta_0 = pars->cyl_theta; |
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91 | phi_0 = pars->cyl_phi; |
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92 | r_0 = pars->radius; |
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93 | |
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94 | npts = 25; |
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95 | step_theta = 2.0*n_width*pars->sigma_theta/npts; |
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96 | step_phi = 2.0*n_width*pars->sigma_phi/npts; |
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97 | step_r = 2.0*n_width*pars->sigma_radius/npts; |
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98 | |
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99 | if (step_theta>0) { |
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100 | n_theta = npts; |
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101 | } else { |
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102 | n_theta = 1; |
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103 | } |
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104 | |
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105 | if (step_phi>0) { |
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106 | n_phi = npts; |
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107 | } else { |
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108 | n_phi = 1; |
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109 | } |
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110 | |
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111 | if (step_r>0) { |
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112 | n_r = npts; |
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113 | } else { |
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114 | n_r = 1; |
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115 | } |
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116 | |
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117 | |
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118 | |
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119 | min_theta = theta_0 - n_width*pars->sigma_theta; |
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120 | min_phi = phi_0 - n_width*pars->sigma_phi; |
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121 | min_r = r_0 - n_width*pars->sigma_radius; |
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122 | |
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123 | func = 0.0; |
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124 | norm = 0.0; |
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125 | |
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126 | for (i_theta=0; i_theta<n_theta; i_theta++) { |
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127 | |
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128 | // Weight for that position |
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129 | if(pars->sigma_theta>0) { |
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130 | cyl_pars.cyl_theta = min_theta + step_theta*i_theta; |
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131 | weight_theta = smeared_cylinder_dist( cyl_pars.cyl_theta, theta_0, pars->sigma_theta ); |
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132 | } else { |
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133 | weight_theta = 1.0; |
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134 | } |
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135 | |
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136 | for (i_phi=0; i_phi<n_phi; i_phi++) { |
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137 | |
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138 | // Weight for that position |
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139 | if(pars->sigma_phi>0) { |
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140 | cyl_pars.cyl_phi = min_phi + step_phi*i_phi; |
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141 | weight_phi = smeared_cylinder_dist( cyl_pars.cyl_phi, phi_0, pars->sigma_phi ); |
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142 | } else { |
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143 | weight_phi = 1.0; |
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144 | } |
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145 | |
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146 | for (i_r=0; i_r<n_r; i_r++) { |
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147 | |
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148 | if(pars->sigma_radius>0) { |
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149 | cyl_pars.radius = min_r + step_r*i_r; |
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150 | |
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151 | // Weight for that position |
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152 | weight_r = smeared_cylinder_dist( cyl_pars.radius, r_0, pars->sigma_radius ); |
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153 | } else { |
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154 | weight_r = 1.0; |
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155 | } |
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156 | |
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157 | // Evaluate I(q) at that r-value |
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158 | func += weight_theta * weight_r * weight_phi * cylinder_analytical_2D(&cyl_pars, q, phi); |
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159 | norm += weight_theta * weight_r * weight_phi; |
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160 | } |
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161 | } |
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162 | } |
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163 | |
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164 | |
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165 | return func/norm; |
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166 | } |
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167 | |
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168 | double smeared_cylinder_dist( double x, double mean, double sigma ) { |
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169 | double vary; |
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170 | double expo; |
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171 | |
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172 | //return 1.0; |
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173 | |
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174 | vary = x-mean; |
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175 | expo = -vary*vary/(2.0*sigma*sigma); |
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176 | return exp(expo); |
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177 | |
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178 | } |
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