1 | static double |
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2 | shell_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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3 | { |
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4 | const double length_b = length_a * b2a_ratio; |
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5 | const double length_c = length_a * c2a_ratio; |
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6 | const double shell_volume = 2.0 * (length_a*length_b + length_a*length_c + length_b*length_c); |
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7 | return shell_volume; |
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8 | } |
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9 | |
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10 | static double |
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11 | form_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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12 | { |
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13 | const double length_b = length_a * b2a_ratio; |
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14 | const double length_c = length_a * c2a_ratio; |
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15 | const double form_volume = length_a * length_b * length_c; |
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16 | return form_volume; |
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17 | } |
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18 | |
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19 | static double |
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20 | radius_from_excluded_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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21 | { |
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22 | const double r_equiv = sqrt(length_a*length_a*b2a_ratio/M_PI); |
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23 | const double length_c = length_a*c2a_ratio; |
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24 | return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length_c + (r_equiv + length_c)*(M_PI*r_equiv + length_c))); |
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25 | } |
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26 | |
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27 | static double |
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28 | effective_radius(int mode, double length_a, double b2a_ratio, double c2a_ratio) |
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29 | { |
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30 | switch (mode) { |
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31 | default: |
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32 | case 1: // equivalent cylinder excluded volume |
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33 | return radius_from_excluded_volume(length_a, b2a_ratio, c2a_ratio); |
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34 | case 2: // equivalent outer volume sphere |
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35 | return cbrt(cube(length_a)*b2a_ratio*c2a_ratio/M_4PI_3); |
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36 | case 3: // half length_a |
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37 | return 0.5 * length_a; |
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38 | case 4: // half length_b |
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39 | return 0.5 * length_a*b2a_ratio; |
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40 | case 5: // half length_c |
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41 | return 0.5 * length_a*c2a_ratio; |
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42 | case 6: // equivalent outer circular cross-section |
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43 | return length_a*sqrt(b2a_ratio/M_PI); |
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44 | case 7: // half ab diagonal |
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45 | return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio))); |
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46 | case 8: // half diagonal |
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47 | return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio) + square(c2a_ratio))); |
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48 | } |
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49 | } |
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50 | |
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51 | static void |
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52 | Fq(double q, |
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53 | double *F1, |
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54 | double *F2, |
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55 | double sld, |
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56 | double solvent_sld, |
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57 | double length_a, |
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58 | double b2a_ratio, |
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59 | double c2a_ratio) |
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60 | { |
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61 | const double length_b = length_a * b2a_ratio; |
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62 | const double length_c = length_a * c2a_ratio; |
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63 | const double a_half = 0.5 * length_a; |
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64 | const double b_half = 0.5 * length_b; |
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65 | const double c_half = 0.5 * length_c; |
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66 | |
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67 | //Integration limits to use in Gaussian quadrature |
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68 | const double v1a = 0.0; |
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69 | const double v1b = M_PI_2; //theta integration limits |
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70 | const double v2a = 0.0; |
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71 | const double v2b = M_PI_2; //phi integration limits |
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72 | |
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73 | double outer_sum_F1 = 0.0; |
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74 | double outer_sum_F2 = 0.0; |
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75 | for(int i=0; i<GAUSS_N; i++) { |
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76 | const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b ); |
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77 | |
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78 | double sin_theta, cos_theta; |
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79 | double sin_c, cos_c; |
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80 | SINCOS(theta, sin_theta, cos_theta); |
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81 | SINCOS(q*c_half*cos_theta, sin_c, cos_c); |
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82 | |
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83 | // To check potential problems if denominator goes to zero here !!! |
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84 | const double termAL_theta = 8.0 * cos_c / (q*q*sin_theta*sin_theta); |
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85 | const double termAT_theta = 8.0 * sin_c / (q*q*sin_theta*cos_theta); |
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86 | |
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87 | double inner_sum_F1 = 0.0; |
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88 | double inner_sum_F2 = 0.0; |
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89 | for(int j=0; j<GAUSS_N; j++) { |
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90 | const double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b ); |
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91 | |
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92 | double sin_phi, cos_phi; |
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93 | double sin_a, cos_a; |
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94 | double sin_b, cos_b; |
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95 | SINCOS(phi, sin_phi, cos_phi); |
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96 | SINCOS(q*a_half*sin_theta*sin_phi, sin_a, cos_a); |
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97 | SINCOS(q*b_half*sin_theta*cos_phi, sin_b, cos_b); |
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98 | |
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99 | // Amplitude AL from eqn. (7c) |
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100 | const double AL = termAL_theta |
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101 | * sin_a*sin_b / (sin_phi*cos_phi); |
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102 | |
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103 | // Amplitude AT from eqn. (9) |
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104 | const double AT = termAT_theta |
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105 | * ( cos_a*sin_b/cos_phi + cos_b*sin_a/sin_phi ); |
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106 | |
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107 | inner_sum_F1 += GAUSS_W[j] * (AL+AT); |
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108 | inner_sum_F2 += GAUSS_W[j] * square(AL+AT); |
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109 | } |
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110 | |
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111 | inner_sum_F1 *= 0.5 * (v2b-v2a); |
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112 | inner_sum_F2 *= 0.5 * (v2b-v2a); |
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113 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta; |
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114 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta; |
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115 | } |
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116 | |
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117 | outer_sum_F1 *= 0.5*(v1b-v1a); |
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118 | outer_sum_F2 *= 0.5*(v1b-v1a); |
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119 | |
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120 | // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) |
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121 | // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) |
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122 | const double form_avg = outer_sum_F1/M_PI_2; |
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123 | const double form_squared_avg = outer_sum_F2/M_PI_2; |
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124 | |
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125 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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126 | const double contrast = sld - solvent_sld; |
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127 | |
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128 | // Convert from [1e-12 A-1] to [cm-1] |
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129 | *F1 = 1e-2 * contrast * form_avg; |
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130 | *F2 = 1e-4 * contrast * contrast * form_squared_avg; |
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131 | } |
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