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 = cube(-expm1(-temp1)); |
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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)/M_PI_2; |
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57 | |
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58 | return(integrand); |
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59 | } |
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60 | |
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61 | double Iq(double q, |
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62 | double dnn, |
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63 | double d_factor, |
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64 | double radius, |
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65 | double sphere_sld, |
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66 | double solvent_sld) |
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67 | { |
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68 | const double va = 0.0; |
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69 | const double vb = M_PI_2; //orientation average, outer integral |
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70 | |
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71 | double summ=0.0; |
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72 | double answer=0.0; |
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73 | |
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74 | for(int i=0;i<150;i++) { |
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75 | //setup inner integral over the ellipsoidal cross-section |
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76 | double summj=0.0; |
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77 | double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; |
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78 | for(int j=0;j<150;j++) { |
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79 | //150 gauss points for the inner integral |
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80 | double zij = ( Gauss150Z[j]*(vb-va) + va + vb )/2.0; |
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81 | double tmp = Gauss150Wt[j] * sc_integrand(dnn,d_factor,q,zi,zij); |
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82 | summj += tmp; |
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83 | } |
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84 | //now calculate the value of the inner integral |
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85 | answer = (vb-va)/2.0*summj; |
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86 | |
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87 | //now calculate outer integral |
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88 | double tmp = Gauss150Wt[i] * answer; |
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89 | summ += tmp; |
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90 | } //final scaling is done at the end of the function, after the NT_FP64 case |
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91 | |
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92 | answer = (vb-va)/2.0*summ; |
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93 | |
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94 | //Volume fraction calculated from lattice symmetry and sphere radius |
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95 | // NB: 4/3 pi r^3 / dnn^3 = 4/3 pi(r/dnn)^3 |
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96 | const double latticeScale = sphere_volume(radius/dnn); |
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97 | |
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98 | answer *= sphere_form(q, radius, sphere_sld, solvent_sld)*latticeScale; |
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99 | |
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100 | return answer; |
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101 | } |
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102 | |
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103 | double Iqxy(double qx, double qy, |
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104 | double dnn, |
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105 | double d_factor, |
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106 | double radius, |
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107 | double sphere_sld, |
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108 | double solvent_sld, |
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109 | double theta, |
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110 | double phi, |
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111 | double psi) |
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112 | { |
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113 | double q, cos_a1, cos_a2, cos_a3; |
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114 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_a3, cos_a2, cos_a1); |
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115 | |
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116 | const double qd = q*dnn; |
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117 | const double arg = 0.5*square(qd*d_factor); |
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118 | const double tanh_qd = tanh(arg); |
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119 | const double cosh_qd = cosh(arg); |
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120 | const double Zq = tanh_qd/(1. - cos(qd*cos_a1)/cosh_qd) |
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121 | * tanh_qd/(1. - cos(qd*cos_a2)/cosh_qd) |
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122 | * tanh_qd/(1. - cos(qd*cos_a3)/cosh_qd); |
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123 | |
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124 | const double Fq = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq; |
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125 | //the occupied volume of the lattice |
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126 | const double lattice_scale = sphere_volume(radius/dnn); |
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127 | return lattice_scale * Fq; |
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128 | } |
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