[2222134] | 1 | double form_volume(double radius_bell, double radius, double length); |
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[3c97ff0] | 2 | double Iq(double q, double sld, double solvent_sld, |
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[2222134] | 3 | double radius_bell, double radius, double length); |
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[58f41fe] | 4 | double Iqxy(double qx, double qy, double sld, double solvent_sld, |
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[2222134] | 5 | double radius_bell, double radius, double length, |
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[3c97ff0] | 6 | double theta, double phi); |
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[58f41fe] | 7 | |
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[2222134] | 8 | #define INVALID(v) (v.radius_bell < v.radius) |
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[2f5c6d4] | 9 | |
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[58f41fe] | 10 | //barbell kernel - same as dumbell |
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[50e1e40] | 11 | static double |
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[2222134] | 12 | _bell_kernel(double q, double h, double radius_bell, |
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[50e1e40] | 13 | double half_length, double sin_alpha, double cos_alpha) |
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[58f41fe] | 14 | { |
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[50e1e40] | 15 | // translate a point in [-1,1] to a point in [lower,upper] |
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[58f41fe] | 16 | const double upper = 1.0; |
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[2222134] | 17 | const double lower = h/radius_bell; |
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[50e1e40] | 18 | const double zm = 0.5*(upper-lower); |
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| 19 | const double zb = 0.5*(upper+lower); |
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| 20 | |
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| 21 | // cos term in integral is: |
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| 22 | // cos (q (R t - h + L/2) cos(alpha)) |
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| 23 | // so turn it into: |
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| 24 | // cos (m t + b) |
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| 25 | // where: |
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| 26 | // m = q R cos(alpha) |
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| 27 | // b = q(L/2-h) cos(alpha) |
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[2222134] | 28 | const double m = q*radius_bell*cos_alpha; // cos argument slope |
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[50e1e40] | 29 | const double b = q*(half_length-h)*cos_alpha; // cos argument intercept |
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[2222134] | 30 | const double qrst = q*radius_bell*sin_alpha; // Q*R*sin(theta) |
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[58f41fe] | 31 | double total = 0.0; |
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| 32 | for (int i = 0; i < 76; i++){ |
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[50e1e40] | 33 | const double t = Gauss76Z[i]*zm + zb; |
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| 34 | const double radical = 1.0 - t*t; |
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[26141cb] | 35 | const double bj = sas_J1c(qrst*sqrt(radical)); |
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[50e1e40] | 36 | const double Fq = cos(m*t + b) * radical * bj; |
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[3c97ff0] | 37 | total += Gauss76Wt[i] * Fq; |
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[58f41fe] | 38 | } |
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[50e1e40] | 39 | // translate dx in [-1,1] to dx in [lower,upper] |
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| 40 | const double integral = total*zm; |
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[3a48772] | 41 | const double bell_fq = 2.0*M_PI*cube(radius_bell)*integral; |
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[11ca2ab] | 42 | return bell_fq; |
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[58f41fe] | 43 | } |
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| 44 | |
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[11ca2ab] | 45 | static double |
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| 46 | _fq(double q, double h, |
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| 47 | double radius_bell, double radius, double half_length, |
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| 48 | double sin_alpha, double cos_alpha) |
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| 49 | { |
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| 50 | const double bell_fq = _bell_kernel(q, h, radius_bell, half_length, sin_alpha, cos_alpha); |
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| 51 | const double bj = sas_J1c(q*radius*sin_alpha); |
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[1e7b0db0] | 52 | const double si = sas_sinx_x(q*half_length*cos_alpha); |
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[11ca2ab] | 53 | const double cyl_fq = 2.0*M_PI*radius*radius*half_length*bj*si; |
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| 54 | const double Aq = bell_fq + cyl_fq; |
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| 55 | return Aq; |
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| 56 | } |
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| 57 | |
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| 58 | |
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[2222134] | 59 | double form_volume(double radius_bell, |
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[58f41fe] | 60 | double radius, |
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| 61 | double length) |
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| 62 | { |
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| 63 | // bell radius should never be less than radius when this is called |
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[2222134] | 64 | const double hdist = sqrt(square(radius_bell) - square(radius)); |
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| 65 | const double p1 = 2.0/3.0*cube(radius_bell); |
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| 66 | const double p2 = square(radius_bell)*hdist; |
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[50e1e40] | 67 | const double p3 = cube(hdist)/3.0; |
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[58f41fe] | 68 | |
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[50e1e40] | 69 | return M_PI*square(radius)*length + 2.0*M_PI*(p1+p2-p3); |
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[58f41fe] | 70 | } |
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| 71 | |
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[50e1e40] | 72 | double Iq(double q, double sld, double solvent_sld, |
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[2222134] | 73 | double radius_bell, double radius, double length) |
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[58f41fe] | 74 | { |
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[2222134] | 75 | const double h = -sqrt(radius_bell*radius_bell - radius*radius); |
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[50e1e40] | 76 | const double half_length = 0.5*length; |
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[58f41fe] | 77 | |
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[50e1e40] | 78 | // translate a point in [-1,1] to a point in [0, pi/2] |
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| 79 | const double zm = M_PI_4; |
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| 80 | const double zb = M_PI_4; |
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[58f41fe] | 81 | double total = 0.0; |
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| 82 | for (int i = 0; i < 76; i++){ |
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[50e1e40] | 83 | const double alpha= Gauss76Z[i]*zm + zb; |
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| 84 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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| 85 | SINCOS(alpha, sin_alpha, cos_alpha); |
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[11ca2ab] | 86 | const double Aq = _fq(q, h, radius_bell, radius, half_length, sin_alpha, cos_alpha); |
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[50e1e40] | 87 | total += Gauss76Wt[i] * Aq * Aq * sin_alpha; |
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[58f41fe] | 88 | } |
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[50e1e40] | 89 | // translate dx in [-1,1] to dx in [lower,upper] |
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| 90 | const double form = total*zm; |
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[58f41fe] | 91 | |
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[50e1e40] | 92 | //Contrast |
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[58f41fe] | 93 | const double s = (sld - solvent_sld); |
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[50e1e40] | 94 | return 1.0e-4 * s * s * form; |
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[58f41fe] | 95 | } |
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| 96 | |
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| 97 | |
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| 98 | double Iqxy(double qx, double qy, |
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[50e1e40] | 99 | double sld, double solvent_sld, |
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[2222134] | 100 | double radius_bell, double radius, double length, |
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[50e1e40] | 101 | double theta, double phi) |
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[58f41fe] | 102 | { |
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[11ca2ab] | 103 | double q, sin_alpha, cos_alpha; |
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| 104 | ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); |
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[58f41fe] | 105 | |
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[2222134] | 106 | const double h = -sqrt(square(radius_bell) - square(radius)); |
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[11ca2ab] | 107 | const double Aq = _fq(q, h, radius_bell, radius, 0.5*length, sin_alpha, cos_alpha); |
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[58f41fe] | 108 | |
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[50e1e40] | 109 | // Multiply by contrast^2 and convert to cm-1 |
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[58f41fe] | 110 | const double s = (sld - solvent_sld); |
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[50e1e40] | 111 | return 1.0e-4 * square(s * Aq); |
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[58f41fe] | 112 | } |
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