[c047acf] | 1 | double form_volume(double radius, double thickness, double alpha, double beta); |
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[9da407c] | 2 | |
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| 3 | double Iq(double q, |
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| 4 | double radius, |
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| 5 | double thickness, |
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| 6 | double alpha, |
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| 7 | double beta, |
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[30fbe2e] | 8 | double sld, |
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[9da407c] | 9 | double sld_solvent); |
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| 10 | |
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| 11 | |
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| 12 | static |
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[c047acf] | 13 | void _integrate_bessel( |
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| 14 | double radius, |
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| 15 | double alpha, |
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| 16 | double beta, |
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| 17 | double q_sin_psi, |
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| 18 | double q_cos_psi, |
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| 19 | double n, |
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| 20 | double *Sn, |
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| 21 | double *Cn) |
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| 22 | { |
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| 23 | // translate gauss point z in [-1,1] to a point in [0, radius] |
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| 24 | const double zm = 0.5*radius; |
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| 25 | const double zb = 0.5*radius; |
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[9da407c] | 26 | |
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| 27 | // evaluate at Gauss points |
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[c047acf] | 28 | double sumS = 0.0; // initialize integral |
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| 29 | double sumC = 0.0; // initialize integral |
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| 30 | double r; |
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| 31 | for (int i=0; i < 76; i++) { |
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| 32 | r = Gauss76Z[i]*zm + zb; |
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| 33 | |
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| 34 | const double qrs = r*q_sin_psi; |
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| 35 | const double qrrc = r*r*q_cos_psi; |
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| 36 | |
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| 37 | double y = Gauss76Wt[i] * r * sas_JN(n, beta*qrrc) * sas_JN(2*n, qrs); |
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| 38 | double S, C; |
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| 39 | SINCOS(alpha*qrrc, S, C); |
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| 40 | sumS += y*S; |
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| 41 | sumC += y*C; |
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| 42 | } |
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[9da407c] | 43 | |
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[c047acf] | 44 | *Sn = zm*sumS / (radius*radius); |
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| 45 | *Cn = zm*sumC / (radius*radius); |
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[9da407c] | 46 | } |
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| 47 | |
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| 48 | static |
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[c047acf] | 49 | double _sum_bessel_orders( |
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| 50 | double radius, |
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| 51 | double alpha, |
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| 52 | double beta, |
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| 53 | double q_sin_psi, |
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| 54 | double q_cos_psi) |
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| 55 | { |
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[9da407c] | 56 | //calculate sum term from n = -3 to 3 |
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[c047acf] | 57 | //Note 1: |
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| 58 | // S_n(-x) = (-1)^S_n(x) |
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| 59 | // => S_n^2(-x) = S_n^2(x), |
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| 60 | // => sum_-k^k Sk = S_0^2 + 2*sum_1^kSk^2 |
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| 61 | //Note 2: |
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| 62 | // better precision to sum terms from smaller to larger |
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| 63 | // though it doesn't seem to make a difference in this case. |
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| 64 | double Sn, Cn, sum; |
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| 65 | sum = 0.0; |
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| 66 | for (int n=3; n>0; n--) { |
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| 67 | _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, n, &Sn, &Cn); |
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| 68 | sum += 2.0*(Sn*Sn + Cn*Cn); |
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[9da407c] | 69 | } |
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[c047acf] | 70 | _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, 0, &Sn, &Cn); |
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| 71 | sum += Sn*Sn+ Cn*Cn; |
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| 72 | return sum; |
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[9da407c] | 73 | } |
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| 74 | |
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[c047acf] | 75 | static |
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| 76 | double _integrate_psi( |
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| 77 | double q, |
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| 78 | double radius, |
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| 79 | double thickness, |
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| 80 | double alpha, |
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| 81 | double beta) |
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[9da407c] | 82 | { |
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[c047acf] | 83 | // translate gauss point z in [-1,1] to a point in [0, pi/2] |
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| 84 | const double zm = M_PI_4; |
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| 85 | const double zb = M_PI_4; |
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| 86 | |
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| 87 | double sum = 0.0; |
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| 88 | for (int i = 0; i < 76; i++) { |
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| 89 | double psi = Gauss76Z[i]*zm + zb; |
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| 90 | double sin_psi, cos_psi; |
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| 91 | SINCOS(psi, sin_psi, cos_psi); |
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| 92 | double bessel_term = _sum_bessel_orders(radius, alpha, beta, q*sin_psi, q*cos_psi); |
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[1e7b0db0] | 93 | double sinc_term = square(sas_sinx_x(q * thickness * cos_psi / 2.0)); |
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[c047acf] | 94 | double pringle_kernel = 4.0 * sin_psi * bessel_term * sinc_term; |
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| 95 | sum += Gauss76Wt[i] * pringle_kernel; |
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[9da407c] | 96 | } |
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| 97 | |
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[c047acf] | 98 | return zm * sum; |
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[9da407c] | 99 | } |
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| 100 | |
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[c047acf] | 101 | double form_volume(double radius, double thickness, double alpha, double beta) |
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| 102 | { |
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[58c3367] | 103 | return M_PI*radius*radius*thickness; |
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[9da407c] | 104 | } |
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| 105 | |
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[c047acf] | 106 | double Iq( |
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| 107 | double q, |
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| 108 | double radius, |
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| 109 | double thickness, |
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| 110 | double alpha, |
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| 111 | double beta, |
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[30fbe2e] | 112 | double sld, |
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[c047acf] | 113 | double sld_solvent) |
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[9da407c] | 114 | { |
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[c047acf] | 115 | double form = _integrate_psi(q, radius, thickness, alpha, beta); |
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[30fbe2e] | 116 | double contrast = sld - sld_solvent; |
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[c047acf] | 117 | double volume = M_PI*radius*radius*thickness; |
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[58c3367] | 118 | return 1.0e-4*form * square(contrast * volume); |
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[9da407c] | 119 | } |
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