1 | //#define INVALID(v) (v.radius_equat_minor > v.radius_equat_major || v.radius_equat_major > v.radius_polar) |
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2 | |
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3 | static double |
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4 | form_volume(double radius_equat_minor, double radius_equat_major, double radius_polar) |
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5 | { |
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6 | return M_4PI_3*radius_equat_minor*radius_equat_major*radius_polar; |
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7 | } |
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8 | |
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9 | |
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10 | static void |
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11 | Fq(double q, |
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12 | double *F1, |
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13 | double *F2, |
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14 | double sld, |
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15 | double sld_solvent, |
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16 | double radius_equat_minor, |
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17 | double radius_equat_major, |
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18 | double radius_polar) |
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19 | { |
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20 | const double pa = square(radius_equat_minor/radius_equat_major) - 1.0; |
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21 | const double pc = square(radius_polar/radius_equat_major) - 1.0; |
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22 | // translate a point in [-1,1] to a point in [0, pi/2] |
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23 | const double zm = M_PI_4; |
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24 | const double zb = M_PI_4; |
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25 | double outer_sum_F1 = 0.0; |
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26 | double outer_sum_F2 = 0.0; |
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27 | for (int i=0;i<GAUSS_N;i++) { |
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28 | //const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper + lower)/2; |
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29 | const double phi = GAUSS_Z[i]*zm + zb; |
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30 | const double pa_sinsq_phi = pa*square(sin(phi)); |
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31 | |
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32 | double inner_sum_F1 = 0.0; |
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33 | double inner_sum_F2 = 0.0; |
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34 | const double um = 0.5; |
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35 | const double ub = 0.5; |
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36 | for (int j=0;j<GAUSS_N;j++) { |
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37 | // translate a point in [-1,1] to a point in [0, 1] |
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38 | const double usq = square(GAUSS_Z[j]*um + ub); |
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39 | const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq); |
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40 | const double fq = sas_3j1x_x(q*r); |
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41 | inner_sum_F1 += GAUSS_W[j] * fq; |
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42 | inner_sum_F2 += GAUSS_W[j] * fq * fq; |
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43 | } |
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44 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1; // correcting for dx later |
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45 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2; // correcting for dx later |
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46 | } |
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47 | // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi |
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48 | outer_sum_F1 *= 0.25; // = outer*um*zm*8.0/(4.0*M_PI); |
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49 | outer_sum_F2 *= 0.25; // = outer*um*zm*8.0/(4.0*M_PI); |
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50 | |
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51 | const double volume = form_volume(radius_equat_minor, radius_equat_major, radius_polar); |
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52 | const double contrast = (sld - sld_solvent); |
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53 | *F1 = 1.0e-2 * contrast * volume * outer_sum_F1; |
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54 | *F2 = 1.0e-4 * square(contrast * volume) * outer_sum_F2; |
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55 | } |
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56 | |
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57 | |
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58 | static double |
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59 | Iqabc(double qa, double qb, double qc, |
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60 | double sld, |
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61 | double sld_solvent, |
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62 | double radius_equat_minor, |
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63 | double radius_equat_major, |
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64 | double radius_polar) |
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65 | { |
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66 | const double qr = sqrt(square(radius_equat_minor*qa) |
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67 | + square(radius_equat_major*qb) |
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68 | + square(radius_polar*qc)); |
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69 | const double fq = sas_3j1x_x(qr); |
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70 | const double vol = form_volume(radius_equat_minor, radius_equat_major, radius_polar); |
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71 | const double drho = (sld - sld_solvent); |
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72 | |
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73 | return 1.0e-4 * square(vol * drho * fq); |
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74 | } |
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