1 | double form_volume(double radius, |
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2 | double thickness); |
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3 | |
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4 | double Iq(double q, |
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5 | double radius, |
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6 | double thickness, |
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7 | double alpha, |
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8 | double beta, |
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9 | double sld_pringle, |
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10 | double sld_solvent); |
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11 | |
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12 | double Iqxy(double qx, double qy, |
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13 | double radius, |
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14 | double thickness, |
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15 | double alpha, |
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16 | double beta, |
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17 | double sld_pringle, |
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18 | double sld_solvent); |
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19 | |
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20 | static |
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21 | double pringleC(double radius, |
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22 | double alpha, |
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23 | double beta, |
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24 | double q, |
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25 | double phi, |
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26 | double n) { |
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27 | |
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28 | double va, vb; |
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29 | double bessargs, cosarg, bessargcb; |
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30 | double r, retval, yyy; |
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31 | |
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32 | |
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33 | va = 0; |
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34 | vb = radius; |
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35 | |
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36 | // evaluate at Gauss points |
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37 | // remember to index from 0,size-1 |
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38 | |
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39 | double summ = 0.0; // initialize integral |
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40 | int ii = 0; |
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41 | do { |
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42 | // Using 76 Gauss points |
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43 | r = (Gauss76Z[ii] * (vb - va) + vb + va) / 2.0; |
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44 | |
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45 | bessargs = q*r*sin(phi); |
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46 | cosarg = q*r*r*alpha*cos(phi); |
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47 | bessargcb = q*r*r*beta*cos(phi); |
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48 | |
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49 | yyy = Gauss76Wt[ii]*r*cos(cosarg) |
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50 | *sas_JN(n, bessargcb) |
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51 | *sas_JN(2*n, bessargs); |
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52 | summ += yyy; |
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53 | |
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54 | ii += 1; |
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55 | } while (ii < N_POINTS_76); // end of loop over quadrature points |
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56 | // |
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57 | // calculate value of integral to return |
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58 | |
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59 | retval = (vb - va) / 2.0 * summ; |
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60 | retval = retval / pow(r, 2.0); |
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61 | |
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62 | return retval; |
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63 | } |
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64 | |
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65 | static |
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66 | double pringleS(double radius, |
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67 | double alpha, |
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68 | double beta, |
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69 | double q, |
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70 | double phi, |
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71 | double n) { |
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72 | |
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73 | double va, vb, summ; |
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74 | double bessargs, sinarg, bessargcb; |
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75 | double r, retval, yyy; |
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76 | // set up the integration |
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77 | // end points and weights |
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78 | |
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79 | va = 0; |
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80 | vb = radius; |
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81 | |
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82 | // evaluate at Gauss points |
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83 | // remember to index from 0,size-1 |
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84 | |
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85 | summ = 0.0; // initialize integral |
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86 | int ii = 0; |
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87 | do { |
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88 | // Using 76 Gauss points |
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89 | r = (Gauss76Z[ii] * (vb - va) + vb + va) / 2.0; |
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90 | |
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91 | bessargs = q*r*sin(phi); |
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92 | sinarg = q*r*r*alpha*cos(phi); |
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93 | bessargcb = q*r*r*beta*cos(phi); |
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94 | |
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95 | yyy = Gauss76Wt[ii]*r*sin(sinarg) |
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96 | *sas_JN(n, bessargcb) |
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97 | *sas_JN(2*n, bessargs); |
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98 | summ += yyy; |
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99 | |
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100 | ii += 1; |
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101 | } while (ii < N_POINTS_76); |
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102 | |
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103 | // end of loop over quadrature points |
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104 | // |
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105 | // calculate value of integral to return |
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106 | |
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107 | retval = (vb-va)/2.0*summ; |
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108 | retval = retval/pow(r, 2.0); |
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109 | |
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110 | return retval; |
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111 | } |
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112 | |
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113 | static |
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114 | double _kernel(double thickness, |
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115 | double radius, |
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116 | double alpha, |
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117 | double beta, |
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118 | double q, |
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119 | double phi) { |
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120 | |
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121 | const double sincarg = q * thickness * cos(phi) / 2.0; |
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122 | const double sincterm = pow(sin(sincarg) / sincarg, 2.0); |
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123 | |
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124 | //calculate sum term from n = -3 to 3 |
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125 | double sumterm = 0.0; |
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126 | for (int nn = -3; nn <= 3; nn++) { |
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127 | double powc = pringleC(radius, alpha, beta, q, phi, nn); |
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128 | double pows = pringleS(radius, alpha, beta, q, phi, nn); |
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129 | sumterm += pow(powc, 2.0) + pow(pows, 2.0); |
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130 | } |
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131 | double retval = 4.0 * sin(phi) * sumterm * sincterm; |
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132 | |
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133 | return retval; |
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134 | |
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135 | } |
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136 | |
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137 | static double pringles_kernel(double q, |
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138 | double radius, |
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139 | double thickness, |
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140 | double alpha, |
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141 | double beta, |
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142 | double sld_pringle, |
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143 | double sld_solvent) |
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144 | { |
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145 | |
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146 | //upper and lower integration limits |
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147 | const double lolim = 0.0; |
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148 | const double uplim = M_PI / 2.0; |
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149 | |
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150 | double summ = 0.0; //initialize integral |
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151 | |
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152 | double delrho = sld_pringle - sld_solvent; //make contrast term |
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153 | |
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154 | for (int i = 0; i < N_POINTS_76; i++) { |
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155 | double phi = (Gauss76Z[i] * (uplim - lolim) + uplim + lolim) / 2.0; |
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156 | summ += Gauss76Wt[i] * _kernel(thickness, radius, alpha, beta, q, phi); |
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157 | } |
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158 | |
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159 | double answer = (uplim - lolim) / 2.0 * summ; |
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160 | answer *= delrho*delrho; |
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161 | |
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162 | return answer; |
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163 | } |
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164 | |
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165 | double form_volume(double radius, |
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166 | double thickness){ |
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167 | |
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168 | return 1.0; |
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169 | } |
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170 | |
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171 | double Iq(double q, |
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172 | double radius, |
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173 | double thickness, |
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174 | double alpha, |
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175 | double beta, |
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176 | double sld_pringle, |
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177 | double sld_solvent) |
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178 | { |
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179 | const double form = pringles_kernel(q, |
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180 | radius, |
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181 | thickness, |
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182 | alpha, |
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183 | beta, |
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184 | sld_pringle, |
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185 | sld_solvent); |
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186 | |
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187 | return 1.0e-4*form*M_PI*radius*radius*thickness; |
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188 | } |
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189 | |
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190 | double Iqxy(double qx, double qy, |
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191 | double radius, |
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192 | double thickness, |
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193 | double alpha, |
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194 | double beta, |
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195 | double sld_pringle, |
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196 | double sld_solvent) |
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197 | { |
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198 | double q = sqrt(qx*qx + qy*qy); |
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199 | return Iq(q, |
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200 | radius, |
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201 | thickness, |
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202 | alpha, |
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203 | beta, |
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204 | sld_pringle, |
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205 | sld_solvent); |
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206 | } |
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207 | |
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