1 | double form_volume(double radius_minor, double r_ratio, double length); |
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2 | double Iq(double q, double radius_minor, double r_ratio, double length, |
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3 | double sld, double solvent_sld); |
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4 | double Iqxy(double qx, double qy, double radius_minor, double r_ratio, double length, |
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5 | double sld, double solvent_sld, double theta, double phi, double psi); |
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6 | |
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7 | |
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8 | double |
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9 | form_volume(double radius_minor, double r_ratio, double length) |
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10 | { |
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11 | return M_PI * radius_minor * radius_minor * r_ratio * length; |
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12 | } |
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13 | |
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14 | double |
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15 | Iq(double q, double radius_minor, double r_ratio, double length, |
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16 | double sld, double solvent_sld) |
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17 | { |
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18 | // orientational average limits |
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19 | const double va = 0.0; |
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20 | const double vb = 1.0; |
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21 | // inner integral limits |
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22 | const double vaj=0.0; |
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23 | const double vbj=M_PI; |
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24 | |
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25 | const double radius_major = r_ratio * radius_minor; |
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26 | const double rA = 0.5*(square(radius_major) + square(radius_minor)); |
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27 | const double rB = 0.5*(square(radius_major) - square(radius_minor)); |
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28 | |
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29 | //initialize integral |
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30 | double outer_sum = 0.0; |
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31 | for(int i=0;i<76;i++) { |
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32 | //setup inner integral over the ellipsoidal cross-section |
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33 | const double cos_val = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; |
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34 | const double sin_val = sqrt(1.0 - cos_val*cos_val); |
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35 | //const double arg = radius_minor*sin_val; |
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36 | double inner_sum=0; |
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37 | for(int j=0;j<20;j++) { |
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38 | //20 gauss points for the inner integral |
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39 | const double theta = ( Gauss20Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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40 | const double r = sin_val*sqrt(rA - rB*cos(theta)); |
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41 | const double be = sas_2J1x_x(q*r); |
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42 | inner_sum += Gauss20Wt[j] * be * be; |
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43 | } |
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44 | //now calculate the value of the inner integral |
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45 | inner_sum *= 0.5*(vbj-vaj); |
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46 | |
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47 | //now calculate outer integral |
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48 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
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49 | outer_sum += Gauss76Wt[i] * inner_sum * si * si; |
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50 | } |
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51 | outer_sum *= 0.5*(vb-va); |
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52 | |
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53 | //divide integral by Pi |
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54 | const double form = outer_sum/M_PI; |
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55 | |
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56 | // scale by contrast and volume, and convert to to 1/cm units |
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57 | const double vol = form_volume(radius_minor, r_ratio, length); |
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58 | const double delrho = sld - solvent_sld; |
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59 | return 1.0e-4*square(delrho*vol)*form; |
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60 | } |
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61 | |
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62 | |
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63 | double |
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64 | Iqxy(double qx, double qy, |
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65 | double radius_minor, double r_ratio, double length, |
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66 | double sld, double solvent_sld, |
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67 | double theta, double phi, double psi) |
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68 | { |
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69 | double q, xhat, yhat, zhat; |
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70 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); |
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71 | |
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72 | // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) |
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73 | // Given: radius_major = r_ratio * radius_minor |
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74 | const double r = radius_minor*sqrt(square(r_ratio*xhat) + square(yhat)); |
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75 | const double be = sas_2J1x_x(q*r); |
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76 | const double si = sas_sinx_x(q*zhat*0.5*length); |
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77 | const double Aq = be * si; |
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78 | const double delrho = sld - solvent_sld; |
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79 | const double vol = form_volume(radius_minor, r_ratio, length); |
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80 | return 1.0e-4 * square(delrho * vol * Aq); |
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81 | } |
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