1 | double form_volume(double a_side, double b2a_ratio, double c2a_ratio); |
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2 | double Iq(double q, double sld, double solvent_sld, double a_side, |
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3 | double b2a_ratio, double c2a_ratio); |
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4 | double Iqxy(double qx, double qy, double sld, double solvent_sld, |
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5 | double a_side, double b2a_ratio, double c2a_ratio); |
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6 | |
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7 | double form_volume(double a_side, double b2a_ratio, double c2a_ratio) |
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8 | { |
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9 | return a_side * (a_side*b2a_ratio) * (a_side*c2a_ratio); |
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10 | } |
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11 | |
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12 | double Iq(double q, |
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13 | double sld, |
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14 | double solvent_sld, |
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15 | double a_side, |
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16 | double b2a_ratio, |
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17 | double c2a_ratio) |
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18 | { |
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19 | double termA, termB, termC; |
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20 | |
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21 | double b_side = a_side * b2a_ratio; |
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22 | double c_side = a_side * c2a_ratio; |
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23 | double volume = a_side * b_side * c_side; |
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24 | double a_half = 0.5 * a_side; |
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25 | double b_half = 0.5 * b_side; |
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26 | double c_half = 0.5 * c_side; |
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27 | |
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28 | //Integration limits to use in Gaussian quadrature |
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29 | double v1a = 0.0; |
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30 | double v1b = 0.5 * M_PI; //theta integration limits |
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31 | double v2a = 0.0; |
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32 | double v2b = 0.5 * M_PI; //phi integration limits |
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33 | |
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34 | //Order of integration |
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35 | int nordi=76; |
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36 | int nordj=76; |
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37 | |
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38 | double sumi = 0.0; |
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39 | |
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40 | for(int i=0; i<nordi; i++) { |
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41 | |
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42 | double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); |
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43 | |
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44 | double arg = q * c_half * cos(theta); |
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45 | if (fabs(arg) > 1.e-16) {termC = sin(arg)/arg;} else {termC = 1.0;} |
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46 | |
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47 | double sumj = 0.0; |
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48 | |
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49 | for(int j=0; j<nordj; j++) { |
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50 | |
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51 | double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); |
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52 | |
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53 | // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0 |
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54 | |
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55 | arg = q * a_half * sin(theta) * sin(phi); |
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56 | if (fabs(arg) > 1.e-16) {termA = sin(arg)/arg;} else {termA = 1.0;} |
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57 | |
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58 | arg = q * b_half * sin(theta) * cos(phi); |
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59 | if (fabs(arg) > 1.e-16) {termB = sin(arg)/arg;} else {termB = 1.0;} |
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60 | |
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61 | double AP = termA * termB * termC; |
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62 | |
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63 | sumj += Gauss76Wt[j] * (AP*AP); |
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64 | |
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65 | } |
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66 | |
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67 | sumj = 0.5 * (v2b-v2a) * sumj; |
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68 | sumi += Gauss76Wt[i] * sumj * sin(theta); |
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69 | |
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70 | } |
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71 | |
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72 | double answer = 0.5*(v1b-v1a)*sumi; |
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73 | |
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74 | // Normalize by Pi (Eqn. 16). |
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75 | // The term (ABC)^2 does not appear because it was introduced before on |
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76 | // the definitions of termA, termB, termC. |
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77 | // The factor 2 appears because the theta integral has been defined between |
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78 | // 0 and pi/2, instead of 0 to pi. |
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79 | answer *= (2.0/M_PI); //Form factor P(q) |
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80 | |
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81 | // Multiply by contrast^2 and volume^2 |
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82 | answer *= (sld-solvent_sld)*(sld-solvent_sld)*volume*volume; |
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83 | |
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84 | // Convert from [1e-12 A-1] to [cm-1] |
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85 | answer *= 1.0e-4; |
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86 | |
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87 | return answer; |
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88 | |
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89 | } |
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90 | |
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91 | double Iqxy(double qx, double qy, |
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92 | double sld, |
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93 | double solvent_sld, |
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94 | double a_side, |
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95 | double b2a_ratio, |
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96 | double c2a_ratio) |
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97 | { |
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98 | double q = sqrt(qx*qx + qy*qy); |
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99 | double intensity = Iq(q, sld, solvent_sld, a_side, b2a_ratio, c2a_ratio); |
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100 | return intensity; |
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101 | } |
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