1 | static double |
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2 | form_volume(double radius_minor, double r_ratio, double length) |
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3 | { |
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4 | return M_PI * radius_minor * radius_minor * r_ratio * length; |
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5 | } |
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6 | |
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7 | static void |
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8 | Fq(double q, double *F1, double *F2, double radius_minor, double r_ratio, double length, |
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9 | double sld, double solvent_sld) |
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10 | { |
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11 | // orientational average limits |
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12 | const double va = 0.0; |
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13 | const double vb = 1.0; |
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14 | // inner integral limits |
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15 | const double vaj=0.0; |
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16 | const double vbj=M_PI; |
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17 | |
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18 | const double radius_major = r_ratio * radius_minor; |
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19 | const double rA = 0.5*(square(radius_major) + square(radius_minor)); |
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20 | const double rB = 0.5*(square(radius_major) - square(radius_minor)); |
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21 | |
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22 | //initialize integral |
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23 | double outer_sum_F1 = 0.0; |
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24 | double outer_sum_F2 = 0.0; |
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25 | for(int i=0;i<GAUSS_N;i++) { |
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26 | //setup inner integral over the ellipsoidal cross-section |
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27 | const double cos_val = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0; |
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28 | const double sin_val = sqrt(1.0 - cos_val*cos_val); |
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29 | //const double arg = radius_minor*sin_val; |
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30 | double inner_sum_F1 = 0.0; |
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31 | double inner_sum_F2 = 0.0; |
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32 | for(int j=0;j<GAUSS_N;j++) { |
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33 | const double theta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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34 | const double r = sin_val*sqrt(rA - rB*cos(theta)); |
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35 | const double be = sas_2J1x_x(q*r); |
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36 | inner_sum_F1 += GAUSS_W[j] * be; |
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37 | inner_sum_F2 += GAUSS_W[j] * be * be; |
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38 | } |
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39 | //now calculate the value of the inner integral |
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40 | inner_sum_F1 *= 0.5*(vbj-vaj); |
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41 | inner_sum_F2 *= 0.5*(vbj-vaj); |
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42 | |
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43 | //now calculate outer integral |
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44 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
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45 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * si; |
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46 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * si * si; |
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47 | } |
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48 | // correct limits and divide integral by pi |
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49 | outer_sum_F1 *= 0.5*(vb-va)/M_PI; |
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50 | outer_sum_F2 *= 0.5*(vb-va)/M_PI; |
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51 | |
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52 | // scale by contrast and volume, and convert to to 1/cm units |
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53 | const double volume = form_volume(radius_minor, r_ratio, length); |
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54 | const double contrast = sld - solvent_sld; |
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55 | const double s = contrast*volume; |
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56 | *F1 = 1.0e-2*s*outer_sum_F1; |
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57 | *F2 = 1.0e-4*s*s*outer_sum_F2; |
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58 | } |
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59 | |
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60 | |
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61 | static double |
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62 | Iqabc(double qa, double qb, double qc, |
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63 | double radius_minor, double r_ratio, double length, |
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64 | double sld, double solvent_sld) |
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65 | { |
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66 | // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) |
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67 | // Given: radius_major = r_ratio * radius_minor |
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68 | const double qr = radius_minor*sqrt(square(r_ratio*qb) + square(qa)); |
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69 | const double be = sas_2J1x_x(qr); |
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70 | const double si = sas_sinx_x(qc*0.5*length); |
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71 | const double fq = be * si; |
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72 | const double contrast = sld - solvent_sld; |
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73 | const double volume = form_volume(radius_minor, r_ratio, length); |
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74 | return 1.0e-4 * square(contrast * volume * fq); |
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75 | } |
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