[2a0b2b1] | 1 | static double |
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| 2 | form_volume(double radius_polar, double radius_equatorial) |
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[ce27e21] | 3 | { |
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[a807206] | 4 | return M_4PI_3*radius_polar*radius_equatorial*radius_equatorial; |
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[ce27e21] | 5 | } |
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| 6 | |
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[2a0b2b1] | 7 | static double |
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| 8 | Iq(double q, |
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[994d77f] | 9 | double sld, |
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[a807206] | 10 | double sld_solvent, |
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| 11 | double radius_polar, |
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| 12 | double radius_equatorial) |
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[ce27e21] | 13 | { |
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[3b571ae] | 14 | // Using ratio v = Rp/Re, we can implement the form given in Guinier (1955) |
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| 15 | // i(h) = int_0^pi/2 Phi^2(h a sqrt(cos^2 + v^2 sin^2) cos dT |
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| 16 | // = int_0^pi/2 Phi^2(h a sqrt((1-sin^2) + v^2 sin^2) cos dT |
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| 17 | // = int_0^pi/2 Phi^2(h a sqrt(1 + sin^2(v^2-1)) cos dT |
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| 18 | // u-substitution of |
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| 19 | // u = sin, du = cos dT |
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| 20 | // i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du |
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| 21 | const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0; |
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[01c8d9e] | 22 | |
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[50e1e40] | 23 | // translate a point in [-1,1] to a point in [0, 1] |
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[74768cb] | 24 | // const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper+lower)/2; |
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[50e1e40] | 25 | const double zm = 0.5; |
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| 26 | const double zb = 0.5; |
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[994d77f] | 27 | double total = 0.0; |
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[74768cb] | 28 | for (int i=0;i<GAUSS_N;i++) { |
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| 29 | const double u = GAUSS_Z[i]*zm + zb; |
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[3b571ae] | 30 | const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one); |
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| 31 | const double f = sas_3j1x_x(q*r); |
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[74768cb] | 32 | total += GAUSS_W[i] * f * f; |
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[ce27e21] | 33 | } |
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[50e1e40] | 34 | // translate dx in [-1,1] to dx in [lower,upper] |
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| 35 | const double form = total*zm; |
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[a807206] | 36 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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[50e1e40] | 37 | return 1.0e-4 * s * s * form; |
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[01c8d9e] | 38 | } |
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| 39 | |
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| 40 | static void |
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| 41 | Fq(double q, |
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| 42 | double *F1, |
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| 43 | double *F2, |
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| 44 | double sld, |
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| 45 | double sld_solvent, |
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| 46 | double radius_polar, |
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| 47 | double radius_equatorial) |
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| 48 | { |
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| 49 | // Using ratio v = Rp/Re, we can implement the form given in Guinier (1955) |
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| 50 | // i(h) = int_0^pi/2 Phi^2(h a sqrt(cos^2 + v^2 sin^2) cos dT |
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| 51 | // = int_0^pi/2 Phi^2(h a sqrt((1-sin^2) + v^2 sin^2) cos dT |
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| 52 | // = int_0^pi/2 Phi^2(h a sqrt(1 + sin^2(v^2-1)) cos dT |
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| 53 | // u-substitution of |
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| 54 | // u = sin, du = cos dT |
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| 55 | // i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du |
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| 56 | const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0; |
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| 57 | // translate a point in [-1,1] to a point in [0, 1] |
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| 58 | // const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper+lower)/2; |
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| 59 | const double zm = 0.5; |
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| 60 | const double zb = 0.5; |
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| 61 | double total_F2 = 0.0; |
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| 62 | double total_F1 = 0.0; |
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| 63 | for (int i=0;i<GAUSS_N;i++) { |
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| 64 | const double u = GAUSS_Z[i]*zm + zb; |
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| 65 | const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one); |
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| 66 | const double f = sas_3j1x_x(q*r); |
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| 67 | total_F2 += GAUSS_W[i] * f * f; |
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| 68 | total_F1 += GAUSS_W[i] * f; |
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| 69 | } |
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| 70 | // translate dx in [-1,1] to dx in [lower,upper] |
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| 71 | const double form_squared_avg = total_F2*zm; |
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| 72 | const double form_avg = total_F1*zm; |
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| 73 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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| 74 | *F2 = 1e-4 * s * s * form_squared_avg; |
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| 75 | *F1 = 1e-2 * s * form_avg; |
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[ce27e21] | 76 | } |
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| 77 | |
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[01c8d9e] | 78 | |
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| 79 | |
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| 80 | |
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| 81 | |
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| 82 | |
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[2a0b2b1] | 83 | static double |
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[108e70e] | 84 | Iqac(double qab, double qc, |
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[994d77f] | 85 | double sld, |
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[a807206] | 86 | double sld_solvent, |
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| 87 | double radius_polar, |
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[becded3] | 88 | double radius_equatorial) |
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[ce27e21] | 89 | { |
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[2a0b2b1] | 90 | const double qr = sqrt(square(radius_equatorial*qab) + square(radius_polar*qc)); |
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| 91 | const double f = sas_3j1x_x(qr); |
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[a807206] | 92 | const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); |
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[ce27e21] | 93 | |
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[3b571ae] | 94 | return 1.0e-4 * square(f * s); |
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[ce27e21] | 95 | } |
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