1 | double form_volume(double radius_polar, double radius_equatorial); |
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2 | double Iq(double q, double sld, double sld_solvent, double radius_polar, double radius_equatorial); |
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3 | double Iqxy(double qx, double qy, double sld, double sld_solvent, |
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4 | double radius_polar, double radius_equatorial, double theta, double phi); |
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5 | |
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6 | static double |
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7 | _ellipsoid_kernel(double q, double radius_polar, double radius_equatorial, double cos_alpha) |
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8 | { |
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9 | double ratio = radius_polar/radius_equatorial; |
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10 | // Using ratio v = Rp/Re, we can expand the following to match the |
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11 | // form given in Guinier (1955) |
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12 | // r = Re * sqrt(1 + cos^2(T) (v^2 - 1)) |
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13 | // = Re * sqrt( (1 - cos^2(T)) + v^2 cos^2(T) ) |
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14 | // = Re * sqrt( sin^2(T) + v^2 cos^2(T) ) |
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15 | // = sqrt( Re^2 sin^2(T) + Rp^2 cos^2(T) ) |
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16 | // |
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17 | // Instead of using pythagoras we could pass in sin and cos; this may be |
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18 | // slightly better for 2D which has already computed it, but it introduces |
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19 | // an extra sqrt and square for 1-D not required by the current form, so |
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20 | // leave it as is. |
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21 | const double r = radius_equatorial |
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22 | * sqrt(1.0 + cos_alpha*cos_alpha*(ratio*ratio - 1.0)); |
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23 | const double f = sas_3j1x_x(q*r); |
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24 | |
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25 | return f*f; |
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26 | } |
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27 | |
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28 | double form_volume(double radius_polar, double radius_equatorial) |
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29 | { |
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30 | return M_4PI_3*radius_polar*radius_equatorial*radius_equatorial; |
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31 | } |
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32 | |
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33 | double Iq(double q, |
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34 | double sld, |
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35 | double sld_solvent, |
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36 | double radius_polar, |
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37 | double radius_equatorial) |
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38 | { |
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39 | // translate a point in [-1,1] to a point in [0, 1] |
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40 | const double zm = 0.5; |
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41 | const double zb = 0.5; |
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42 | double total = 0.0; |
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43 | for (int i=0;i<76;i++) { |
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44 | //const double cos_alpha = (Gauss76Z[i]*(upper-lower) + upper + lower)/2; |
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45 | const double cos_alpha = Gauss76Z[i]*zm + zb; |
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46 | total += Gauss76Wt[i] * _ellipsoid_kernel(q, radius_polar, radius_equatorial, cos_alpha); |
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47 | } |
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48 | // translate dx in [-1,1] to dx in [lower,upper] |
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49 | const double form = total*zm; |
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50 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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51 | return 1.0e-4 * s * s * form; |
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52 | } |
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53 | |
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54 | double Iqxy(double qx, double qy, |
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55 | double sld, |
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56 | double sld_solvent, |
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57 | double radius_polar, |
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58 | double radius_equatorial, |
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59 | double theta, |
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60 | double phi) |
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61 | { |
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62 | double q, sin_alpha, cos_alpha; |
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63 | ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); |
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64 | const double form = _ellipsoid_kernel(q, radius_polar, radius_equatorial, cos_alpha); |
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65 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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66 | |
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67 | return 1.0e-4 * form * s * s; |
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68 | } |
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69 | |
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