1 | static double |
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2 | form_volume(double radius_minor, double r_ratio, double length) |
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3 | { |
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4 | return M_PI * radius_minor * radius_minor * r_ratio * length; |
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5 | } |
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6 | |
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7 | static double |
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8 | radius_from_volume(double radius_minor, double r_ratio, double length) |
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9 | { |
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10 | const double volume_ellcyl = form_volume(radius_minor,r_ratio,length); |
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11 | return cbrt(0.75*volume_ellcyl/M_PI); |
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12 | } |
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13 | |
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14 | static double |
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15 | radius_from_min_dimension(double radius_minor, double r_ratio, double length) |
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16 | { |
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17 | const double rad_min = (r_ratio > 1.0 ? radius_minor : r_ratio*radius_minor); |
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18 | return (rad_min < length ? rad_min : length); |
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19 | } |
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20 | |
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21 | static double |
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22 | radius_from_max_dimension(double radius_minor, double r_ratio, double length) |
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23 | { |
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24 | const double rad_max = (r_ratio < 1.0 ? radius_minor : r_ratio*radius_minor); |
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25 | return (rad_max > length ? rad_max : length); |
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26 | } |
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27 | |
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28 | static double |
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29 | radius_from_diagonal(double radius_minor, double r_ratio, double length) |
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30 | { |
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31 | const double radius_max = (r_ratio > 1.0 ? radius_minor*r_ratio : radius_minor); |
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32 | return sqrt(radius_max*radius_max + 0.25*length*length); |
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33 | } |
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34 | |
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35 | static double |
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36 | effective_radius(int mode, double radius_minor, double r_ratio, double length) |
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37 | { |
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38 | if (mode == 1) { |
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39 | return radius_from_volume(radius_minor, r_ratio, length); |
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40 | } else if (mode == 2) { |
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41 | return 0.5*radius_minor*(1.0 + r_ratio); |
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42 | } else if (mode == 3) { |
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43 | return (r_ratio > 1.0 ? radius_minor : r_ratio*radius_minor); |
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44 | } else if (mode == 4) { |
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45 | return (r_ratio < 1.0 ? radius_minor : r_ratio*radius_minor); |
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46 | } else if (mode == 5) { |
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47 | return sqrt(radius_minor*radius_minor*r_ratio); |
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48 | } else if (mode == 6) { |
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49 | return 0.5*length; |
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50 | } else if (mode == 7) { |
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51 | return radius_from_min_dimension(radius_minor,r_ratio,length); |
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52 | } else if (mode == 8) { |
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53 | return radius_from_max_dimension(radius_minor,r_ratio,length); |
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54 | } else { |
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55 | return radius_from_diagonal(radius_minor,r_ratio,length); |
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56 | } |
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57 | } |
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58 | |
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59 | static void |
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60 | Fq(double q, double *F1, double *F2, double radius_minor, double r_ratio, double length, |
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61 | double sld, double solvent_sld) |
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62 | { |
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63 | // orientational average limits |
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64 | const double va = 0.0; |
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65 | const double vb = 1.0; |
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66 | // inner integral limits |
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67 | const double vaj=0.0; |
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68 | const double vbj=M_PI; |
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69 | |
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70 | const double radius_major = r_ratio * radius_minor; |
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71 | const double rA = 0.5*(square(radius_major) + square(radius_minor)); |
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72 | const double rB = 0.5*(square(radius_major) - square(radius_minor)); |
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73 | |
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74 | //initialize integral |
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75 | double outer_sum_F1 = 0.0; |
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76 | double outer_sum_F2 = 0.0; |
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77 | for(int i=0;i<GAUSS_N;i++) { |
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78 | //setup inner integral over the ellipsoidal cross-section |
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79 | const double cos_val = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0; |
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80 | const double sin_val = sqrt(1.0 - cos_val*cos_val); |
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81 | //const double arg = radius_minor*sin_val; |
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82 | double inner_sum_F1 = 0.0; |
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83 | double inner_sum_F2 = 0.0; |
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84 | for(int j=0;j<GAUSS_N;j++) { |
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85 | const double theta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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86 | const double r = sin_val*sqrt(rA - rB*cos(theta)); |
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87 | const double be = sas_2J1x_x(q*r); |
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88 | inner_sum_F1 += GAUSS_W[j] * be; |
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89 | inner_sum_F2 += GAUSS_W[j] * be * be; |
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90 | } |
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91 | //now calculate the value of the inner integral |
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92 | inner_sum_F1 *= 0.5*(vbj-vaj); |
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93 | inner_sum_F2 *= 0.5*(vbj-vaj); |
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94 | |
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95 | //now calculate outer integral |
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96 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
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97 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * si; |
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98 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * si * si; |
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99 | } |
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100 | // correct limits and divide integral by pi |
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101 | outer_sum_F1 *= 0.5*(vb-va)/M_PI; |
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102 | outer_sum_F2 *= 0.5*(vb-va)/M_PI; |
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103 | |
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104 | // scale by contrast and volume, and convert to to 1/cm units |
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105 | const double volume = form_volume(radius_minor, r_ratio, length); |
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106 | const double contrast = sld - solvent_sld; |
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107 | const double s = contrast*volume; |
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108 | *F1 = 1.0e-2*s*outer_sum_F1; |
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109 | *F2 = 1.0e-4*s*s*outer_sum_F2; |
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110 | } |
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111 | |
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112 | |
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113 | static double |
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114 | Iqabc(double qa, double qb, double qc, |
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115 | double radius_minor, double r_ratio, double length, |
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116 | double sld, double solvent_sld) |
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117 | { |
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118 | // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) |
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119 | // Given: radius_major = r_ratio * radius_minor |
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120 | const double qr = radius_minor*sqrt(square(r_ratio*qb) + square(qa)); |
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121 | const double be = sas_2J1x_x(qr); |
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122 | const double si = sas_sinx_x(qc*0.5*length); |
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123 | const double fq = be * si; |
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124 | const double contrast = sld - solvent_sld; |
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125 | const double volume = form_volume(radius_minor, r_ratio, length); |
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126 | return 1.0e-4 * square(contrast * volume * fq); |
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127 | } |
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