[a807206] | 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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[a8b3cdb] | 3 | double sld, double solvent_sld); |
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[a807206] | 4 | double Iqxy(double qx, double qy, double radius_minor, double r_ratio, double length, |
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[a8b3cdb] | 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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[251f54b] | 8 | double |
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| 9 | form_volume(double radius_minor, double r_ratio, double length) |
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[a8b3cdb] | 10 | { |
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[a807206] | 11 | return M_PI * radius_minor * radius_minor * r_ratio * length; |
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[a8b3cdb] | 12 | } |
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| 13 | |
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[68425bf] | 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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[a8b3cdb] | 18 | // orientational average limits |
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[68425bf] | 19 | const double va = 0.0; |
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| 20 | const double vb = 1.0; |
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[a8b3cdb] | 21 | // inner integral limits |
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[68425bf] | 22 | const double vaj=0.0; |
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| 23 | const double vbj=M_PI; |
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[a8b3cdb] | 24 | |
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[68425bf] | 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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[a8b3cdb] | 28 | |
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[68425bf] | 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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[a8b3cdb] | 32 | //setup inner integral over the ellipsoidal cross-section |
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[68425bf] | 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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[a8b3cdb] | 38 | //20 gauss points for the inner integral |
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[68425bf] | 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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[592343f] | 41 | const double be = sas_2J1x_x(q*r); |
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[68425bf] | 42 | inner_sum += Gauss20Wt[j] * be * be; |
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[a8b3cdb] | 43 | } |
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| 44 | //now calculate the value of the inner integral |
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[68425bf] | 45 | inner_sum *= 0.5*(vbj-vaj); |
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[a8b3cdb] | 46 | |
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| 47 | //now calculate outer integral |
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[1e7b0db0] | 48 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
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[68425bf] | 49 | outer_sum += Gauss76Wt[i] * inner_sum * si * si; |
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[a8b3cdb] | 50 | } |
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[68425bf] | 51 | outer_sum *= 0.5*(vb-va); |
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[a8b3cdb] | 52 | |
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[40a87fa] | 53 | //divide integral by Pi |
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[68425bf] | 54 | const double form = outer_sum/M_PI; |
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[a8b3cdb] | 55 | |
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[68425bf] | 56 | // scale by contrast and volume, and convert to to 1/cm units |
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[a807206] | 57 | const double vol = form_volume(radius_minor, r_ratio, length); |
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[68425bf] | 58 | const double delrho = sld - solvent_sld; |
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| 59 | return 1.0e-4*square(delrho*vol)*form; |
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[a8b3cdb] | 60 | } |
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| 61 | |
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| 62 | |
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[68425bf] | 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, cos_val, cos_mu, cos_nu; |
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| 70 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_val, cos_mu, cos_nu); |
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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*cos_nu) + cos_mu*cos_mu); |
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[592343f] | 75 | const double be = sas_2J1x_x(q*r); |
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[1e7b0db0] | 76 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
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[68425bf] | 77 | const double Aq = be * si; |
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| 78 | const double delrho = sld - solvent_sld; |
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[a807206] | 79 | const double vol = form_volume(radius_minor, r_ratio, length); |
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[68425bf] | 80 | return 1.0e-4 * square(delrho * vol * Aq); |
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[a8b3cdb] | 81 | } |
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