1 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio); |
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2 | double Iq(double q, double sld, double solvent_sld, double length_a, |
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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 length_a, double b2a_ratio, double c2a_ratio); |
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6 | |
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7 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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8 | { |
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9 | double b_side = length_a * b2a_ratio; |
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10 | double c_side = length_a * c2a_ratio; |
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11 | double vol_shell = 2.0 * (length_a*b_side + length_a*c_side + b_side*c_side); |
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12 | return vol_shell; |
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13 | } |
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14 | |
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15 | double Iq(double q, |
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16 | double sld, |
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17 | double solvent_sld, |
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18 | double length_a, |
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19 | double b2a_ratio, |
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20 | double c2a_ratio) |
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21 | { |
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22 | double b_side = length_a * b2a_ratio; |
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23 | double c_side = length_a * c2a_ratio; |
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24 | double a_half = 0.5 * length_a; |
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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 | // To check potential problems if denominator goes to zero here !!! |
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45 | double termAL_theta = 8.0*cos(q*c_half*cos(theta)) / (q*q*sin(theta)*sin(theta)); |
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46 | double termAT_theta = 8.0*sin(q*c_half*cos(theta)) / (q*q*sin(theta)*cos(theta)); |
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47 | |
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48 | double sumj = 0.0; |
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49 | |
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50 | for(int j=0; j<nordj; j++) { |
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51 | |
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52 | double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); |
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53 | |
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54 | // Amplitude AL from eqn. (7c) |
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55 | double AL = termAL_theta * sin(q*a_half*sin(theta)*sin(phi)) * |
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56 | sin(q*b_half*sin(theta)*cos(phi)) / (sin(phi)*cos(phi)); |
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57 | |
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58 | // Amplitude AT from eqn. (9) |
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59 | double AT = termAT_theta * ( (cos(q*a_half*sin(theta)*sin(phi))*sin(q*b_half*sin(theta)*cos(phi))/cos(phi)) |
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60 | + (cos(q*b_half*sin(theta)*cos(phi))*sin(q*a_half*sin(theta)*sin(phi))/sin(phi)) ); |
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61 | |
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62 | sumj += Gauss76Wt[j] * (AL+AT)*(AL+AT); |
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63 | |
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64 | } |
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65 | |
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66 | sumj = 0.5 * (v2b-v2a) * sumj; |
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67 | sumi += Gauss76Wt[i] * sumj * sin(theta); |
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68 | |
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69 | } |
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70 | |
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71 | double answer = 0.5*(v1b-v1a)*sumi; |
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72 | |
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73 | // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) |
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74 | // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) |
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75 | answer *= (2.0/M_PI); |
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76 | |
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77 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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78 | answer *= (sld-solvent_sld)*(sld-solvent_sld); |
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79 | |
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80 | // Convert from [1e-12 A-1] to [cm-1] |
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81 | answer *= 1.0e-4; |
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82 | |
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83 | return answer; |
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84 | |
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85 | } |
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86 | |
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87 | double Iqxy(double qx, double qy, |
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88 | double sld, |
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89 | double solvent_sld, |
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90 | double length_a, |
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91 | double b2a_ratio, |
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92 | double c2a_ratio) |
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93 | { |
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94 | double q = sqrt(qx*qx + qy*qy); |
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95 | double intensity = Iq(q, sld, solvent_sld, length_a, b2a_ratio, c2a_ratio); |
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96 | return intensity; |
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97 | } |
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