1 | /** |
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2 | This software was developed by the University of Tennessee as part of the |
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3 | Distributed Data Analysis of Neutron Scattering Experiments (DANSE) |
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4 | project funded by the US National Science Foundation. |
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5 | |
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6 | If you use DANSE applications to do scientific research that leads to |
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7 | publication, we ask that you acknowledge the use of the software with the |
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8 | following sentence: |
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9 | |
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10 | "This work benefited from DANSE software developed under NSF award DMR-0520547." |
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11 | |
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12 | copyright 2008, University of Tennessee |
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13 | */ |
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14 | |
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15 | /** |
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16 | * Scattering model classes |
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17 | * The classes use the IGOR library found in |
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18 | * sansmodels/src/libigor |
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19 | * |
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20 | */ |
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21 | |
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22 | #include <math.h> |
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23 | #include "parameters.hh" |
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24 | #include <stdio.h> |
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25 | using namespace std; |
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26 | #include "ellipsoid.h" |
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27 | |
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28 | extern "C" { |
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29 | #include "libCylinder.h" |
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30 | #include "libStructureFactor.h" |
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31 | } |
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32 | |
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33 | typedef struct { |
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34 | double scale; |
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35 | double radius_a; |
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36 | double radius_b; |
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37 | double sldEll; |
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38 | double sldSolv; |
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39 | double background; |
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40 | double axis_theta; |
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41 | double axis_phi; |
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42 | } EllipsoidParameters; |
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43 | |
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44 | /** |
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45 | * Function to evaluate 2D scattering function |
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46 | * @param pars: parameters of the ellipsoid |
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47 | * @param q: q-value |
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48 | * @param q_x: q_x / q |
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49 | * @param q_y: q_y / q |
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50 | * @return: function value |
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51 | */ |
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52 | static double ellipsoid_analytical_2D_scaled(EllipsoidParameters *pars, double q, double q_x, double q_y) { |
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53 | double cyl_x, cyl_y;//, cyl_z; |
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54 | //double q_z; |
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55 | double alpha, vol, cos_val; |
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56 | double answer; |
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57 | //convert angle degree to radian |
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58 | double pi = 4.0*atan(1.0); |
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59 | double theta = pars->axis_theta * pi/180.0; |
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60 | double phi = pars->axis_phi * pi/180.0; |
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61 | |
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62 | // Ellipsoid orientation |
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63 | cyl_x = cos(theta) * cos(phi); |
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64 | cyl_y = sin(theta); |
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65 | //cyl_z = -cos(theta) * sin(phi); |
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66 | |
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67 | // q vector |
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68 | //q_z = 0.0; |
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69 | |
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70 | // Compute the angle btw vector q and the |
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71 | // axis of the cylinder |
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72 | cos_val = cyl_x*q_x + cyl_y*q_y;// + cyl_z*q_z; |
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73 | |
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74 | // The following test should always pass |
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75 | if (fabs(cos_val)>1.0) { |
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76 | printf("ellipsoid_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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77 | return 0; |
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78 | } |
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79 | |
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80 | // Angle between rotation axis and q vector |
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81 | alpha = acos( cos_val ); |
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82 | |
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83 | // Call the IGOR library function to get the kernel |
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84 | answer = EllipsoidKernel(q, pars->radius_b, pars->radius_a, cos_val); |
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85 | |
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86 | // Multiply by contrast^2 |
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87 | answer *= (pars->sldEll - pars->sldSolv) * (pars->sldEll - pars->sldSolv); |
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88 | |
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89 | //normalize by cylinder volume |
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90 | vol = 4.0/3.0 * acos(-1.0) * pars->radius_b * pars->radius_b * pars->radius_a; |
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91 | answer *= vol; |
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92 | |
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93 | //convert to [cm-1] |
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94 | answer *= 1.0e8; |
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95 | |
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96 | //Scale |
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97 | answer *= pars->scale; |
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98 | |
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99 | // add in the background |
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100 | answer += pars->background; |
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101 | |
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102 | return answer; |
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103 | } |
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104 | |
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105 | /** |
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106 | * Function to evaluate 2D scattering function |
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107 | * @param pars: parameters of the ellipsoid |
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108 | * @param q: q-value |
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109 | * @return: function value |
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110 | */ |
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111 | static double ellipsoid_analytical_2DXY(EllipsoidParameters *pars, double qx, double qy) { |
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112 | double q; |
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113 | q = sqrt(qx*qx+qy*qy); |
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114 | return ellipsoid_analytical_2D_scaled(pars, q, qx/q, qy/q); |
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115 | } |
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116 | |
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117 | EllipsoidModel :: EllipsoidModel() { |
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118 | scale = Parameter(1.0); |
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119 | radius_a = Parameter(20.0, true); |
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120 | radius_a.set_min(0.0); |
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121 | radius_b = Parameter(400.0, true); |
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122 | radius_b.set_min(0.0); |
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123 | sldEll = Parameter(4.e-6); |
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124 | sldSolv = Parameter(1.e-6); |
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125 | background = Parameter(0.0); |
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126 | axis_theta = Parameter(57.325, true); |
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127 | axis_phi = Parameter(0.0, true); |
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128 | } |
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129 | |
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130 | /** |
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131 | * Function to evaluate 1D scattering function |
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132 | * The NIST IGOR library is used for the actual calculation. |
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133 | * @param q: q-value |
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134 | * @return: function value |
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135 | */ |
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136 | double EllipsoidModel :: operator()(double q) { |
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137 | double dp[6]; |
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138 | |
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139 | // Fill parameter array for IGOR library |
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140 | // Add the background after averaging |
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141 | dp[0] = scale(); |
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142 | dp[1] = radius_a(); |
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143 | dp[2] = radius_b(); |
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144 | dp[3] = sldEll(); |
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145 | dp[4] = sldSolv(); |
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146 | dp[5] = 0.0; |
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147 | |
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148 | // Get the dispersion points for the radius_a |
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149 | vector<WeightPoint> weights_rad_a; |
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150 | radius_a.get_weights(weights_rad_a); |
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151 | |
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152 | // Get the dispersion points for the radius_b |
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153 | vector<WeightPoint> weights_rad_b; |
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154 | radius_b.get_weights(weights_rad_b); |
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155 | |
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156 | // Perform the computation, with all weight points |
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157 | double sum = 0.0; |
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158 | double norm = 0.0; |
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159 | double vol = 0.0; |
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160 | |
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161 | // Loop over radius_a weight points |
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162 | for(size_t i=0; i<weights_rad_a.size(); i++) { |
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163 | dp[1] = weights_rad_a[i].value; |
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164 | |
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165 | // Loop over radius_b weight points |
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166 | for(size_t j=0; j<weights_rad_b.size(); j++) { |
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167 | dp[2] = weights_rad_b[j].value; |
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168 | //Un-normalize by volume |
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169 | sum += weights_rad_a[i].weight |
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170 | * weights_rad_b[j].weight * EllipsoidForm(dp, q) |
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171 | * pow(weights_rad_b[j].value,2) * weights_rad_a[i].value; |
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172 | |
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173 | //Find average volume |
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174 | vol += weights_rad_a[i].weight |
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175 | * weights_rad_b[j].weight |
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176 | * pow(weights_rad_b[j].value,2) |
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177 | * weights_rad_a[i].value; |
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178 | norm += weights_rad_a[i].weight |
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179 | * weights_rad_b[j].weight; |
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180 | } |
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181 | } |
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182 | |
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183 | if (vol != 0.0 && norm != 0.0) { |
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184 | //Re-normalize by avg volume |
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185 | sum = sum/(vol/norm);} |
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186 | |
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187 | return sum/norm + background(); |
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188 | } |
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189 | |
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190 | /** |
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191 | * Function to evaluate 2D scattering function |
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192 | * @param q_x: value of Q along x |
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193 | * @param q_y: value of Q along y |
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194 | * @return: function value |
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195 | */ |
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196 | double EllipsoidModel :: operator()(double qx, double qy) { |
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197 | EllipsoidParameters dp; |
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198 | // Fill parameter array |
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199 | dp.scale = scale(); |
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200 | dp.radius_a = radius_a(); |
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201 | dp.radius_b = radius_b(); |
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202 | dp.sldEll = sldEll(); |
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203 | dp.sldSolv = sldSolv(); |
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204 | dp.background = 0.0; |
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205 | dp.axis_theta = axis_theta(); |
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206 | dp.axis_phi = axis_phi(); |
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207 | |
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208 | // Get the dispersion points for the radius_a |
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209 | vector<WeightPoint> weights_rad_a; |
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210 | radius_a.get_weights(weights_rad_a); |
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211 | |
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212 | // Get the dispersion points for the radius_b |
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213 | vector<WeightPoint> weights_rad_b; |
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214 | radius_b.get_weights(weights_rad_b); |
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215 | |
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216 | // Get angular averaging for theta |
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217 | vector<WeightPoint> weights_theta; |
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218 | axis_theta.get_weights(weights_theta); |
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219 | |
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220 | // Get angular averaging for phi |
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221 | vector<WeightPoint> weights_phi; |
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222 | axis_phi.get_weights(weights_phi); |
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223 | |
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224 | // Perform the computation, with all weight points |
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225 | double sum = 0.0; |
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226 | double norm = 0.0; |
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227 | double norm_vol = 0.0; |
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228 | double vol = 0.0; |
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229 | double pi = 4.0*atan(1.0); |
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230 | // Loop over radius weight points |
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231 | for(size_t i=0; i<weights_rad_a.size(); i++) { |
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232 | dp.radius_a = weights_rad_a[i].value; |
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233 | |
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234 | |
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235 | // Loop over length weight points |
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236 | for(size_t j=0; j<weights_rad_b.size(); j++) { |
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237 | dp.radius_b = weights_rad_b[j].value; |
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238 | |
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239 | // Average over theta distribution |
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240 | for(size_t k=0; k<weights_theta.size(); k++) { |
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241 | dp.axis_theta = weights_theta[k].value; |
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242 | |
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243 | // Average over phi distribution |
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244 | for(size_t l=0; l<weights_phi.size(); l++) { |
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245 | dp.axis_phi = weights_phi[l].value; |
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246 | //Un-normalize by volume |
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247 | double _ptvalue = weights_rad_a[i].weight |
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248 | * weights_rad_b[j].weight |
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249 | * weights_theta[k].weight |
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250 | * weights_phi[l].weight |
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251 | * ellipsoid_analytical_2DXY(&dp, qx, qy) |
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252 | * pow(weights_rad_b[j].value,2) * weights_rad_a[i].value; |
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253 | if (weights_theta.size()>1) { |
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254 | _ptvalue *= fabs(cos(weights_theta[k].value*pi/180.0)); |
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255 | } |
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256 | sum += _ptvalue; |
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257 | //Find average volume |
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258 | vol += weights_rad_a[i].weight |
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259 | * weights_rad_b[j].weight |
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260 | * pow(weights_rad_b[j].value,2) * weights_rad_a[i].value; |
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261 | //Find norm for volume |
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262 | norm_vol += weights_rad_a[i].weight |
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263 | * weights_rad_b[j].weight; |
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264 | |
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265 | norm += weights_rad_a[i].weight |
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266 | * weights_rad_b[j].weight |
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267 | * weights_theta[k].weight |
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268 | * weights_phi[l].weight; |
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269 | |
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270 | } |
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271 | } |
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272 | } |
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273 | } |
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274 | // Averaging in theta needs an extra normalization |
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275 | // factor to account for the sin(theta) term in the |
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276 | // integration (see documentation). |
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277 | if (weights_theta.size()>1) norm = norm / asin(1.0); |
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278 | |
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279 | if (vol != 0.0 && norm_vol != 0.0) { |
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280 | //Re-normalize by avg volume |
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281 | sum = sum/(vol/norm_vol);} |
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282 | |
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283 | return sum/norm + background(); |
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284 | } |
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285 | |
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286 | /** |
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287 | * Function to evaluate 2D scattering function |
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288 | * @param pars: parameters of the cylinder |
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289 | * @param q: q-value |
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290 | * @param phi: angle phi |
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291 | * @return: function value |
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292 | */ |
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293 | double EllipsoidModel :: evaluate_rphi(double q, double phi) { |
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294 | double qx = q*cos(phi); |
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295 | double qy = q*sin(phi); |
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296 | return (*this).operator()(qx, qy); |
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297 | } |
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298 | |
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299 | /** |
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300 | * Function to calculate effective radius |
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301 | * @return: effective radius value |
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302 | */ |
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303 | double EllipsoidModel :: calculate_ER() { |
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304 | EllipsoidParameters dp; |
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305 | |
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306 | dp.radius_a = radius_a(); |
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307 | dp.radius_b = radius_b(); |
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308 | |
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309 | double rad_out = 0.0; |
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310 | |
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311 | // Perform the computation, with all weight points |
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312 | double sum = 0.0; |
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313 | double norm = 0.0; |
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314 | |
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315 | // Get the dispersion points for the major shell |
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316 | vector<WeightPoint> weights_radius_a; |
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317 | radius_a.get_weights(weights_radius_a); |
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318 | |
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319 | // Get the dispersion points for the minor shell |
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320 | vector<WeightPoint> weights_radius_b; |
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321 | radius_b.get_weights(weights_radius_b); |
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322 | |
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323 | // Loop over major shell weight points |
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324 | for(int i=0; i< (int)weights_radius_b.size(); i++) { |
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325 | dp.radius_b = weights_radius_b[i].value; |
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326 | for(int k=0; k< (int)weights_radius_a.size(); k++) { |
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327 | dp.radius_a = weights_radius_a[k].value; |
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328 | sum +=weights_radius_b[i].weight |
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329 | * weights_radius_a[k].weight*DiamEllip(dp.radius_a,dp.radius_b)/2.0; |
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330 | norm += weights_radius_b[i].weight* weights_radius_a[k].weight; |
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331 | } |
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332 | } |
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333 | if (norm != 0){ |
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334 | //return the averaged value |
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335 | rad_out = sum/norm;} |
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336 | else{ |
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337 | //return normal value |
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338 | rad_out = DiamEllip(dp.radius_a,dp.radius_b)/2.0;} |
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339 | |
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340 | return rad_out; |
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341 | } |
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342 | double EllipsoidModel :: calculate_VR() { |
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343 | return 1.0; |
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344 | } |
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