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_volume(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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11 | { |
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12 | return cbrt(radius_equat_minor*radius_equat_major*radius_polar); |
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13 | } |
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14 | |
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15 | static double |
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16 | radius_from_min_dimension(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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17 | { |
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18 | const double rad_equat_min = (radius_equat_minor < radius_equat_major ? radius_equat_minor : radius_equat_major); |
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19 | return (rad_equat_min < radius_polar ? rad_equat_min : radius_polar); |
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20 | } |
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21 | |
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22 | static double |
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23 | radius_from_max_dimension(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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24 | { |
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25 | const double rad_equat_max = (radius_equat_minor < radius_equat_major ? radius_equat_major : radius_equat_minor); |
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26 | return (rad_equat_max > radius_polar ? rad_equat_max : radius_polar); |
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27 | } |
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28 | |
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29 | static double |
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30 | effective_radius(int mode, double radius_equat_minor, double radius_equat_major, double radius_polar) |
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31 | { |
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32 | if (mode == 1) { |
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33 | return radius_from_volume(radius_equat_minor,radius_equat_major, radius_polar); |
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34 | } else if (mode == 2) { |
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35 | return radius_from_min_dimension(radius_equat_minor,radius_equat_major, radius_polar); |
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36 | } else { |
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37 | return radius_from_max_dimension(radius_equat_minor,radius_equat_major, radius_polar); |
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38 | } |
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39 | } |
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40 | |
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41 | static void |
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42 | Fq(double q, |
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43 | double *F1, |
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44 | double *F2, |
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45 | double sld, |
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46 | double sld_solvent, |
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47 | double radius_equat_minor, |
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48 | double radius_equat_major, |
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49 | double radius_polar) |
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50 | { |
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51 | const double pa = square(radius_equat_minor/radius_equat_major) - 1.0; |
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52 | const double pc = square(radius_polar/radius_equat_major) - 1.0; |
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53 | // translate a point in [-1,1] to a point in [0, pi/2] |
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54 | const double zm = M_PI_4; |
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55 | const double zb = M_PI_4; |
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56 | double outer_sum_F1 = 0.0; |
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57 | double outer_sum_F2 = 0.0; |
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58 | for (int i=0;i<GAUSS_N;i++) { |
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59 | //const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper + lower)/2; |
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60 | const double phi = GAUSS_Z[i]*zm + zb; |
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61 | const double pa_sinsq_phi = pa*square(sin(phi)); |
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62 | |
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63 | double inner_sum_F1 = 0.0; |
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64 | double inner_sum_F2 = 0.0; |
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65 | const double um = 0.5; |
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66 | const double ub = 0.5; |
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67 | for (int j=0;j<GAUSS_N;j++) { |
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68 | // translate a point in [-1,1] to a point in [0, 1] |
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69 | const double usq = square(GAUSS_Z[j]*um + ub); |
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70 | const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq); |
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71 | const double fq = sas_3j1x_x(q*r); |
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72 | inner_sum_F1 += GAUSS_W[j] * fq; |
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73 | inner_sum_F2 += GAUSS_W[j] * fq * fq; |
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74 | } |
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75 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1; // correcting for dx later |
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76 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2; // correcting for dx later |
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77 | } |
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78 | // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi |
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79 | outer_sum_F1 *= 0.25; // = outer*um*zm*8.0/(4.0*M_PI); |
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80 | outer_sum_F2 *= 0.25; // = outer*um*zm*8.0/(4.0*M_PI); |
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81 | |
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82 | const double volume = form_volume(radius_equat_minor, radius_equat_major, radius_polar); |
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83 | const double contrast = (sld - sld_solvent); |
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84 | *F1 = 1.0e-2 * contrast * volume * outer_sum_F1; |
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85 | *F2 = 1.0e-4 * square(contrast * volume) * outer_sum_F2; |
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86 | } |
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87 | |
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88 | |
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89 | static double |
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90 | Iqabc(double qa, double qb, double qc, |
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91 | double sld, |
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92 | double sld_solvent, |
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93 | double radius_equat_minor, |
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94 | double radius_equat_major, |
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95 | double radius_polar) |
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96 | { |
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97 | const double qr = sqrt(square(radius_equat_minor*qa) |
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98 | + square(radius_equat_major*qb) |
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99 | + square(radius_polar*qc)); |
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100 | const double fq = sas_3j1x_x(qr); |
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101 | const double vol = form_volume(radius_equat_minor, radius_equat_major, radius_polar); |
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102 | const double drho = (sld - sld_solvent); |
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103 | |
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104 | return 1.0e-4 * square(vol * drho * fq); |
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105 | } |
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