1 | static double |
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2 | form_volume(double length_a, double length_b, double length_c) |
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3 | { |
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4 | return length_a * length_b * length_c; |
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5 | } |
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6 | |
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7 | static double |
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8 | effective_radius(int mode, double length_a, double length_b, double length_c) |
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9 | { |
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10 | if (mode == 1) { |
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11 | return cbrt(0.75*length_a*length_b*length_c/M_PI); |
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12 | } else if (mode == 2) { |
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13 | return 0.5 * length_a; |
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14 | } else if (mode == 3) { |
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15 | return 0.5 * length_b; |
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16 | } else if (mode == 4) { |
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17 | return 0.5 * length_c; |
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18 | } else if (mode == 5) { |
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19 | return sqrt(length_a*length_b/M_PI); |
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20 | } else if (mode == 6) { |
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21 | return 0.5*sqrt(length_a*length_a + length_b*length_b); |
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22 | } else { |
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23 | return 0.5*sqrt(length_a*length_a + length_b*length_b + length_c*length_c); |
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24 | } |
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25 | } |
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26 | |
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27 | |
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28 | static void |
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29 | Fq(double q, |
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30 | double *F1, |
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31 | double *F2, |
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32 | double sld, |
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33 | double solvent_sld, |
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34 | double length_a, |
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35 | double length_b, |
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36 | double length_c) |
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37 | { |
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38 | const double mu = 0.5 * q * length_b; |
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39 | |
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40 | // Scale sides by B |
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41 | const double a_scaled = length_a / length_b; |
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42 | const double c_scaled = length_c / length_b; |
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43 | |
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44 | // outer integral (with gauss points), integration limits = 0, 1 |
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45 | double outer_total_F1 = 0.0; //initialize integral |
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46 | double outer_total_F2 = 0.0; //initialize integral |
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47 | for( int i=0; i<GAUSS_N; i++) { |
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48 | const double sigma = 0.5 * ( GAUSS_Z[i] + 1.0 ); |
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49 | const double mu_proj = mu * sqrt(1.0-sigma*sigma); |
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50 | |
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51 | // inner integral (with gauss points), integration limits = 0, 1 |
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52 | // corresponding to angles from 0 to pi/2. |
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53 | double inner_total_F1 = 0.0; |
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54 | double inner_total_F2 = 0.0; |
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55 | for(int j=0; j<GAUSS_N; j++) { |
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56 | const double uu = 0.5 * ( GAUSS_Z[j] + 1.0 ); |
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57 | double sin_uu, cos_uu; |
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58 | SINCOS(M_PI_2*uu, sin_uu, cos_uu); |
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59 | const double si1 = sas_sinx_x(mu_proj * sin_uu * a_scaled); |
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60 | const double si2 = sas_sinx_x(mu_proj * cos_uu); |
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61 | const double fq = si1 * si2; |
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62 | inner_total_F1 += GAUSS_W[j] * fq; |
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63 | inner_total_F2 += GAUSS_W[j] * fq * fq; |
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64 | } |
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65 | // now complete change of inner integration variable (1-0)/(1-(-1))= 0.5 |
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66 | inner_total_F1 *= 0.5; |
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67 | inner_total_F2 *= 0.5; |
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68 | |
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69 | const double si = sas_sinx_x(mu * c_scaled * sigma); |
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70 | outer_total_F1 += GAUSS_W[i] * inner_total_F1 * si; |
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71 | outer_total_F2 += GAUSS_W[i] * inner_total_F2 * si * si; |
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72 | } |
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73 | // now complete change of outer integration variable (1-0)/(1-(-1))= 0.5 |
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74 | outer_total_F1 *= 0.5; |
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75 | outer_total_F2 *= 0.5; |
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76 | |
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77 | // Multiply by contrast^2 and convert from [1e-12 A-1] to [cm-1] |
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78 | const double V = form_volume(length_a, length_b, length_c); |
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79 | const double contrast = (sld-solvent_sld); |
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80 | const double s = contrast * V; |
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81 | *F1 = 1.0e-2 * s * outer_total_F1; |
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82 | *F2 = 1.0e-4 * s * s * outer_total_F2; |
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83 | } |
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84 | |
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85 | static double |
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86 | Iqabc(double qa, double qb, double qc, |
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87 | double sld, |
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88 | double solvent_sld, |
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89 | double length_a, |
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90 | double length_b, |
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91 | double length_c) |
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92 | { |
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93 | const double siA = sas_sinx_x(0.5*length_a*qa); |
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94 | const double siB = sas_sinx_x(0.5*length_b*qb); |
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95 | const double siC = sas_sinx_x(0.5*length_c*qc); |
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96 | const double V = form_volume(length_a, length_b, length_c); |
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97 | const double drho = (sld - solvent_sld); |
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98 | const double form = V * drho * siA * siB * siC; |
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99 | // Square and convert from [1e-12 A-1] to [cm-1] |
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100 | return 1.0e-4 * form * form; |
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101 | } |
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