1 | //#define INVALID(v) (v.radius_equat_minor > v.radius_equat_major || v.radius_equat_major > v.radius_polar) |
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2 | |
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3 | static double |
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4 | form_volume(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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5 | { |
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6 | return M_4PI_3*radius_equat_minor*radius_equat_major*radius_polar; |
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7 | } |
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8 | |
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9 | static double |
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10 | radius_from_curvature(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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11 | { |
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12 | // Trivial cases |
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13 | if (radius_equat_minor == radius_equat_major == radius_polar) return radius_polar; |
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14 | if (radius_equat_minor * radius_equat_major * radius_polar == 0.) return 0.; |
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15 | |
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16 | |
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17 | double r_equat_equiv, r_polar_equiv; |
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18 | double radii[3] = {radius_equat_minor, radius_equat_major, radius_polar}; |
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19 | double radmax = fmax(radii[0],fmax(radii[1],radii[2])); |
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20 | |
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21 | double radius_1 = radmax; |
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22 | double radius_2 = radmax; |
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23 | double radius_3 = radmax; |
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24 | |
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25 | for(int irad=0; irad<3; irad++) { |
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26 | if (radii[irad] < radius_1) { |
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27 | radius_3 = radius_2; |
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28 | radius_2 = radius_1; |
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29 | radius_1 = radii[irad]; |
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30 | } else { |
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31 | if (radii[irad] < radius_2) { |
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32 | radius_2 = radii[irad]; |
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33 | } |
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34 | } |
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35 | } |
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36 | if(radius_2-radius_1 > radius_3-radius_2) { |
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37 | r_equat_equiv = sqrt(radius_2*radius_3); |
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38 | r_polar_equiv = radius_1; |
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39 | } else { |
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40 | r_equat_equiv = sqrt(radius_1*radius_2); |
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41 | r_polar_equiv = radius_3; |
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42 | } |
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43 | |
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44 | // see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449 |
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45 | const double ratio = (r_polar_equiv < r_equat_equiv |
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46 | ? r_polar_equiv / r_equat_equiv |
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47 | : r_equat_equiv / r_polar_equiv); |
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48 | const double e1 = sqrt(1.0 - ratio*ratio); |
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49 | const double b1 = 1.0 + asin(e1) / (e1 * ratio); |
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50 | const double bL = (1.0 + e1) / (1.0 - e1); |
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51 | const double b2 = 1.0 + 0.5 * ratio * ratio / e1 * log(bL); |
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52 | const double delta = 0.75 * b1 * b2; |
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53 | const double ddd = 2.0 * (delta + 1.0) * r_polar_equiv * r_equat_equiv * r_equat_equiv; |
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54 | return 0.5 * cbrt(ddd); |
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55 | } |
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56 | |
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57 | static double |
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58 | radius_from_volume(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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59 | { |
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60 | return cbrt(radius_equat_minor*radius_equat_major*radius_polar); |
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61 | } |
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62 | |
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63 | static double |
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64 | radius_from_min_dimension(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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65 | { |
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66 | const double rad_equat_min = (radius_equat_minor < radius_equat_major ? radius_equat_minor : radius_equat_major); |
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67 | return (rad_equat_min < radius_polar ? rad_equat_min : radius_polar); |
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68 | } |
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69 | |
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70 | static double |
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71 | radius_from_max_dimension(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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72 | { |
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73 | const double rad_equat_max = (radius_equat_minor < radius_equat_major ? radius_equat_major : radius_equat_minor); |
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74 | return (rad_equat_max > radius_polar ? rad_equat_max : radius_polar); |
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75 | } |
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76 | |
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77 | static double |
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78 | effective_radius(int mode, double radius_equat_minor, double radius_equat_major, double radius_polar) |
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79 | { |
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80 | switch (mode) { |
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81 | default: |
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82 | case 1: // equivalent biaxial ellipsoid average curvature |
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83 | return radius_from_curvature(radius_equat_minor,radius_equat_major, radius_polar); |
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84 | case 2: // equivalent volume sphere |
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85 | return radius_from_volume(radius_equat_minor,radius_equat_major, radius_polar); |
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86 | case 3: // min radius |
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87 | return radius_from_min_dimension(radius_equat_minor,radius_equat_major, radius_polar); |
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88 | case 4: // max radius |
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89 | return radius_from_max_dimension(radius_equat_minor,radius_equat_major, radius_polar); |
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90 | } |
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91 | } |
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92 | |
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93 | static void |
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94 | Fq(double q, |
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95 | double *F1, |
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96 | double *F2, |
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97 | double sld, |
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98 | double sld_solvent, |
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99 | double radius_equat_minor, |
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100 | double radius_equat_major, |
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101 | double radius_polar) |
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102 | { |
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103 | const double pa = square(radius_equat_minor/radius_equat_major) - 1.0; |
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104 | const double pc = square(radius_polar/radius_equat_major) - 1.0; |
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105 | // translate a point in [-1,1] to a point in [0, pi/2] |
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106 | const double zm = M_PI_4; |
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107 | const double zb = M_PI_4; |
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108 | double outer_sum_F1 = 0.0; |
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109 | double outer_sum_F2 = 0.0; |
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110 | for (int i=0;i<GAUSS_N;i++) { |
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111 | //const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper + lower)/2; |
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112 | const double phi = GAUSS_Z[i]*zm + zb; |
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113 | const double pa_sinsq_phi = pa*square(sin(phi)); |
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114 | |
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115 | double inner_sum_F1 = 0.0; |
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116 | double inner_sum_F2 = 0.0; |
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117 | const double um = 0.5; |
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118 | const double ub = 0.5; |
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119 | for (int j=0;j<GAUSS_N;j++) { |
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120 | // translate a point in [-1,1] to a point in [0, 1] |
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121 | const double usq = square(GAUSS_Z[j]*um + ub); |
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122 | const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq); |
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123 | const double fq = sas_3j1x_x(q*r); |
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124 | inner_sum_F1 += GAUSS_W[j] * fq; |
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125 | inner_sum_F2 += GAUSS_W[j] * fq * fq; |
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126 | } |
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127 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1; // correcting for dx later |
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128 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2; // correcting for dx later |
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129 | } |
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130 | // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi |
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131 | outer_sum_F1 *= 0.25; // = outer*um*zm*8.0/(4.0*M_PI); |
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132 | outer_sum_F2 *= 0.25; // = outer*um*zm*8.0/(4.0*M_PI); |
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133 | |
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134 | const double volume = form_volume(radius_equat_minor, radius_equat_major, radius_polar); |
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135 | const double contrast = (sld - sld_solvent); |
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136 | *F1 = 1.0e-2 * contrast * volume * outer_sum_F1; |
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137 | *F2 = 1.0e-4 * square(contrast * volume) * outer_sum_F2; |
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138 | } |
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139 | |
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140 | |
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141 | static double |
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142 | Iqabc(double qa, double qb, double qc, |
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143 | double sld, |
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144 | double sld_solvent, |
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145 | double radius_equat_minor, |
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146 | double radius_equat_major, |
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147 | double radius_polar) |
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148 | { |
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149 | const double qr = sqrt(square(radius_equat_minor*qa) |
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150 | + square(radius_equat_major*qb) |
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151 | + square(radius_polar*qc)); |
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152 | const double fq = sas_3j1x_x(qr); |
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153 | const double vol = form_volume(radius_equat_minor, radius_equat_major, radius_polar); |
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154 | const double drho = (sld - sld_solvent); |
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155 | |
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156 | return 1.0e-4 * square(vol * drho * fq); |
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157 | } |
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