1 | double form_volume(double radius); |
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2 | |
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3 | double Iq(double q, |
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4 | double dnn, |
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5 | double d_factor, |
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6 | double radius, |
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7 | double sphere_sld, |
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8 | double solvent_sld); |
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9 | |
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10 | double Iqxy(double qx, double qy, |
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11 | double dnn, |
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12 | double d_factor, |
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13 | double radius, |
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14 | double sphere_sld, |
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15 | double solvent_sld, |
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16 | double theta, |
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17 | double phi, |
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18 | double psi); |
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19 | |
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20 | double form_volume(double radius) |
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21 | { |
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22 | return sphere_volume(radius); |
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23 | } |
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24 | |
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25 | static double |
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26 | sc_eval(double theta, double phi, double temp3, double temp4, double temp5) |
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27 | { |
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28 | double cnt, snt; |
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29 | SINCOS(theta, cnt, snt); |
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30 | |
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31 | double cnp, snp; |
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32 | SINCOS(phi, cnp, snp); |
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33 | |
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34 | double temp6 = snt; |
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35 | double temp7 = -1.0*temp3*snt*cnp; |
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36 | double temp8 = temp3*snt*snp; |
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37 | double temp9 = temp3*cnt; |
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38 | double result = temp6/((1.0-temp4*cos((temp7))+temp5)* |
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39 | (1.0-temp4*cos((temp8))+temp5)* |
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40 | (1.0-temp4*cos((temp9))+temp5)); |
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41 | return (result); |
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42 | } |
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43 | |
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44 | static double |
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45 | sc_integrand(double dnn, double d_factor, double qq, double xx, double yy) |
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46 | { |
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47 | //Function to calculate integrand values for simple cubic structure |
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48 | |
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49 | double da = d_factor*dnn; |
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50 | double temp1 = qq*qq*da*da; |
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51 | double temp2 = pow( 1.0-exp(-1.0*temp1) ,3); |
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52 | double temp3 = qq*dnn; |
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53 | double temp4 = 2.0*exp(-0.5*temp1); |
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54 | double temp5 = exp(-1.0*temp1); |
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55 | |
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56 | double integrand = temp2*sc_eval(yy,xx,temp3,temp4,temp5); |
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57 | integrand *= 2.0/M_PI; |
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58 | |
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59 | return(integrand); |
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60 | } |
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61 | |
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62 | static |
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63 | double sc_crystal_kernel(double q, |
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64 | double dnn, |
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65 | double d_factor, |
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66 | double radius, |
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67 | double sphere_sld, |
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68 | double solvent_sld) |
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69 | { |
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70 | const double va = 0.0; |
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71 | const double vb = M_PI/2.0; //orientation average, outer integral |
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72 | |
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73 | double summ=0.0; |
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74 | double answer=0.0; |
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75 | |
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76 | for(int i=0;i<150;i++) { |
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77 | //setup inner integral over the ellipsoidal cross-section |
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78 | double summj=0.0; |
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79 | double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; |
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80 | for(int j=0;j<150;j++) { |
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81 | //150 gauss points for the inner integral |
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82 | double zij = ( Gauss150Z[j]*(vb-va) + va + vb )/2.0; |
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83 | double tmp = Gauss150Wt[j] * sc_integrand(dnn,d_factor,q,zi,zij); |
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84 | summj += tmp; |
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85 | } |
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86 | //now calculate the value of the inner integral |
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87 | answer = (vb-va)/2.0*summj; |
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88 | |
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89 | //now calculate outer integral |
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90 | double tmp = Gauss150Wt[i] * answer; |
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91 | summ += tmp; |
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92 | } //final scaling is done at the end of the function, after the NT_FP64 case |
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93 | |
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94 | answer = (vb-va)/2.0*summ; |
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95 | |
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96 | //Volume fraction calculated from lattice symmetry and sphere radius |
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97 | // NB: 4/3 pi r^3 / dnn^3 = 4/3 pi(r/dnn)^3 |
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98 | const double latticeScale = sphere_volume(radius/dnn); |
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99 | |
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100 | answer *= sphere_form(q, radius, sphere_sld, solvent_sld)*latticeScale; |
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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 | static |
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106 | double sc_crystal_kernel_2d(double q, double q_x, double q_y, |
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107 | double dnn, |
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108 | double d_factor, |
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109 | double radius, |
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110 | double sphere_sld, |
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111 | double solvent_sld, |
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112 | double theta, |
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113 | double phi, |
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114 | double psi) |
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115 | { |
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116 | //convert angle degree to radian |
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117 | theta = theta * M_PI_180; |
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118 | phi = phi * M_PI_180; |
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119 | psi = psi * M_PI_180; |
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120 | |
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121 | const double qda_2 = pow(q*d_factor*dnn,2.0); |
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122 | |
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123 | double snt, cnt; |
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124 | SINCOS(theta, snt, cnt); |
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125 | |
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126 | double snp, cnp; |
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127 | SINCOS(phi, snp, cnp); |
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128 | |
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129 | double sns, cns; |
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130 | SINCOS(psi, sns, cns); |
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131 | |
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132 | /// Angles here are respect to detector coordinate instead of against |
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133 | // q coordinate(PRB 36, 3, 1754) |
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134 | // a3 axis orientation |
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135 | |
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136 | const double a3_x = cnt * cnp; |
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137 | const double a3_y = snt; |
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138 | |
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139 | // Compute the angle btw vector q and the a3 axis |
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140 | double cos_val_a3 = a3_x*q_x + a3_y*q_y; |
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141 | |
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142 | // a1 axis orientation |
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143 | const double a1_x = -cnp*sns * snt+snp*cns; |
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144 | const double a1_y = sns*cnt; |
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145 | |
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146 | double cos_val_a1 = a1_x*q_x + a1_y*q_y; |
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147 | |
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148 | // a2 axis orientation |
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149 | const double a2_x = -snt*cns*cnp-sns*snp; |
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150 | const double a2_y = cnt*cns; |
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151 | |
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152 | // a2 axis |
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153 | const double cos_val_a2 = a2_x*q_x + a2_y*q_y; |
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154 | |
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155 | // The following test should always pass |
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156 | if (fabs(cos_val_a3)>1.0) { |
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157 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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158 | cos_val_a3 = 1.0; |
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159 | } |
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160 | if (fabs(cos_val_a1)>1.0) { |
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161 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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162 | cos_val_a1 = 1.0; |
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163 | } |
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164 | if (fabs(cos_val_a2)>1.0) { |
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165 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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166 | cos_val_a3 = 1.0; |
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167 | } |
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168 | |
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169 | const double a3_dot_q = dnn*q*cos_val_a3; |
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170 | const double a1_dot_q = dnn*q*cos_val_a1; |
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171 | const double a2_dot_q = dnn*q*cos_val_a2; |
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172 | |
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173 | // Call Zq=Z1*Z2*Z3 |
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174 | double Zq = (1.0-exp(-qda_2))/(1.0-2.0*exp(-0.5*qda_2)*cos(a1_dot_q)+exp(-qda_2)); |
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175 | Zq *= (1.0-exp(-qda_2))/(1.0-2.0*exp(-0.5*qda_2)*cos(a2_dot_q)+exp(-qda_2)); |
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176 | Zq *= (1.0-exp(-qda_2))/(1.0-2.0*exp(-0.5*qda_2)*cos(a3_dot_q)+exp(-qda_2)); |
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177 | |
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178 | // Use SphereForm directly from libigor |
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179 | double answer = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq; |
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180 | |
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181 | //consider scales |
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182 | const double latticeScale = sphere_volume(radius/dnn); |
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183 | answer *= latticeScale; |
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184 | |
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185 | return answer; |
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186 | } |
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187 | |
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188 | double Iq(double q, |
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189 | double dnn, |
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190 | double d_factor, |
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191 | double radius, |
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192 | double sphere_sld, |
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193 | double solvent_sld) |
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194 | { |
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195 | return sc_crystal_kernel(q, |
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196 | dnn, |
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197 | d_factor, |
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198 | radius, |
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199 | sphere_sld, |
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200 | solvent_sld); |
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201 | } |
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202 | |
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203 | // Iqxy is never called since no orientation or magnetic parameters. |
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204 | double Iqxy(double qx, double qy, |
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205 | double dnn, |
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206 | double d_factor, |
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207 | double radius, |
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208 | double sphere_sld, |
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209 | double solvent_sld, |
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210 | double theta, |
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211 | double phi, |
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212 | double psi) |
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213 | { |
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214 | double q = sqrt(qx*qx + qy*qy); |
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215 | |
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216 | |
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217 | return sc_crystal_kernel_2d(q, qx/q, qy/q, |
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218 | dnn, |
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219 | d_factor, |
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220 | radius, |
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221 | sphere_sld, |
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222 | solvent_sld, |
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223 | theta, |
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224 | phi, |
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225 | psi); |
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226 | |
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227 | } |
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228 | |
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