[2222134] | 1 | #define INVALID(v) (v.radius_bell < v.radius) |
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[2f5c6d4] | 2 | |
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[58f41fe] | 3 | //barbell kernel - same as dumbell |
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[50e1e40] | 4 | static double |
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[2a0b2b1] | 5 | _bell_kernel(double qab, double qc, double h, double radius_bell, |
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| 6 | double half_length) |
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[58f41fe] | 7 | { |
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[50e1e40] | 8 | // translate a point in [-1,1] to a point in [lower,upper] |
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[58f41fe] | 9 | const double upper = 1.0; |
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[2222134] | 10 | const double lower = h/radius_bell; |
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[50e1e40] | 11 | const double zm = 0.5*(upper-lower); |
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| 12 | const double zb = 0.5*(upper+lower); |
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| 13 | |
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| 14 | // cos term in integral is: |
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| 15 | // cos (q (R t - h + L/2) cos(alpha)) |
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| 16 | // so turn it into: |
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| 17 | // cos (m t + b) |
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| 18 | // where: |
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| 19 | // m = q R cos(alpha) |
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| 20 | // b = q(L/2-h) cos(alpha) |
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[2a0b2b1] | 21 | const double m = radius_bell*qc; // cos argument slope |
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| 22 | const double b = (half_length-h)*qc; // cos argument intercept |
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| 23 | const double qab_r = radius_bell*qab; // Q*R*sin(theta) |
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[58f41fe] | 24 | double total = 0.0; |
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[74768cb] | 25 | for (int i = 0; i < GAUSS_N; i++){ |
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| 26 | const double t = GAUSS_Z[i]*zm + zb; |
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[50e1e40] | 27 | const double radical = 1.0 - t*t; |
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[2a0b2b1] | 28 | const double bj = sas_2J1x_x(qab_r*sqrt(radical)); |
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[50e1e40] | 29 | const double Fq = cos(m*t + b) * radical * bj; |
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[74768cb] | 30 | total += GAUSS_W[i] * Fq; |
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[58f41fe] | 31 | } |
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[50e1e40] | 32 | // translate dx in [-1,1] to dx in [lower,upper] |
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| 33 | const double integral = total*zm; |
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[3a48772] | 34 | const double bell_fq = 2.0*M_PI*cube(radius_bell)*integral; |
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[11ca2ab] | 35 | return bell_fq; |
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[58f41fe] | 36 | } |
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| 37 | |
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[11ca2ab] | 38 | static double |
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[2a0b2b1] | 39 | _fq(double qab, double qc, double h, |
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| 40 | double radius_bell, double radius, double half_length) |
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[11ca2ab] | 41 | { |
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[2a0b2b1] | 42 | const double bell_fq = _bell_kernel(qab, qc, h, radius_bell, half_length); |
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| 43 | const double bj = sas_2J1x_x(radius*qab); |
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| 44 | const double si = sas_sinx_x(half_length*qc); |
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[11ca2ab] | 45 | const double cyl_fq = 2.0*M_PI*radius*radius*half_length*bj*si; |
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| 46 | const double Aq = bell_fq + cyl_fq; |
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| 47 | return Aq; |
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| 48 | } |
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| 49 | |
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[becded3] | 50 | static double |
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| 51 | form_volume(double radius_bell, |
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| 52 | double radius, |
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| 53 | double length) |
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[58f41fe] | 54 | { |
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| 55 | // bell radius should never be less than radius when this is called |
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[2222134] | 56 | const double hdist = sqrt(square(radius_bell) - square(radius)); |
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| 57 | const double p1 = 2.0/3.0*cube(radius_bell); |
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| 58 | const double p2 = square(radius_bell)*hdist; |
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[50e1e40] | 59 | const double p3 = cube(hdist)/3.0; |
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[58f41fe] | 60 | |
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[50e1e40] | 61 | return M_PI*square(radius)*length + 2.0*M_PI*(p1+p2-p3); |
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[58f41fe] | 62 | } |
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| 63 | |
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[d277229] | 64 | static double |
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[99658f6] | 65 | radius_from_excluded_volume(double radius_bell, double radius, double length) |
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| 66 | { |
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| 67 | const double hdist = sqrt(square(radius_bell) - square(radius)); |
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| 68 | const double length_tot = length + 2.0*(hdist+ radius); |
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| 69 | return 0.5*cbrt(0.75*radius_bell*(2.0*radius_bell*length_tot + (radius_bell + length_tot)*(M_PI*radius_bell + length_tot))); |
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| 70 | } |
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| 71 | |
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| 72 | static double |
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[d277229] | 73 | radius_from_volume(double radius_bell, double radius, double length) |
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| 74 | { |
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| 75 | const double vol_barbell = form_volume(radius_bell,radius,length); |
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[6d5601c] | 76 | return cbrt(vol_barbell/M_4PI_3); |
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[d277229] | 77 | } |
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| 78 | |
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| 79 | static double |
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| 80 | radius_from_totallength(double radius_bell, double radius, double length) |
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| 81 | { |
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| 82 | const double hdist = sqrt(square(radius_bell) - square(radius)); |
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| 83 | return 0.5*length + hdist + radius_bell; |
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| 84 | } |
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| 85 | |
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| 86 | static double |
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| 87 | effective_radius(int mode, double radius_bell, double radius, double length) |
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| 88 | { |
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[ee60aa7] | 89 | switch (mode) { |
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[d42dd4a] | 90 | default: |
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[99658f6] | 91 | case 1: // equivalent cylinder excluded volume |
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| 92 | return radius_from_excluded_volume(radius_bell, radius , length); |
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| 93 | case 2: // equivalent volume sphere |
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[d277229] | 94 | return radius_from_volume(radius_bell, radius , length); |
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[99658f6] | 95 | case 3: // radius |
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[d277229] | 96 | return radius; |
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[99658f6] | 97 | case 4: // half length |
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[d277229] | 98 | return 0.5*length; |
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[99658f6] | 99 | case 5: // half total length |
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[d277229] | 100 | return radius_from_totallength(radius_bell,radius,length); |
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| 101 | } |
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| 102 | } |
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| 103 | |
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[71b751d] | 104 | static void |
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| 105 | Fq(double q,double *F1, double *F2, double sld, double solvent_sld, |
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[becded3] | 106 | double radius_bell, double radius, double length) |
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[58f41fe] | 107 | { |
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[2222134] | 108 | const double h = -sqrt(radius_bell*radius_bell - radius*radius); |
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[50e1e40] | 109 | const double half_length = 0.5*length; |
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[58f41fe] | 110 | |
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[50e1e40] | 111 | // translate a point in [-1,1] to a point in [0, pi/2] |
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| 112 | const double zm = M_PI_4; |
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| 113 | const double zb = M_PI_4; |
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[71b751d] | 114 | double total_F1 = 0.0; |
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| 115 | double total_F2 = 0.0; |
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[74768cb] | 116 | for (int i = 0; i < GAUSS_N; i++){ |
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| 117 | const double alpha= GAUSS_Z[i]*zm + zb; |
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[50e1e40] | 118 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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| 119 | SINCOS(alpha, sin_alpha, cos_alpha); |
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[2a0b2b1] | 120 | const double Aq = _fq(q*sin_alpha, q*cos_alpha, h, radius_bell, radius, half_length); |
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[71b751d] | 121 | total_F1 += GAUSS_W[i] * Aq * sin_alpha; |
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| 122 | total_F2 += GAUSS_W[i] * Aq * Aq * sin_alpha; |
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[58f41fe] | 123 | } |
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[50e1e40] | 124 | // translate dx in [-1,1] to dx in [lower,upper] |
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[71b751d] | 125 | const double form_avg = total_F1*zm; |
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| 126 | const double form_squared_avg = total_F2*zm; |
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[58f41fe] | 127 | |
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[50e1e40] | 128 | //Contrast |
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[58f41fe] | 129 | const double s = (sld - solvent_sld); |
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[71b751d] | 130 | *F1 = 1.0e-2 * s * form_avg; |
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| 131 | *F2 = 1.0e-4 * s * s * form_squared_avg; |
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[58f41fe] | 132 | } |
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| 133 | |
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[becded3] | 134 | static double |
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[108e70e] | 135 | Iqac(double qab, double qc, |
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[becded3] | 136 | double sld, double solvent_sld, |
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| 137 | double radius_bell, double radius, double length) |
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[58f41fe] | 138 | { |
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[2222134] | 139 | const double h = -sqrt(square(radius_bell) - square(radius)); |
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[2a0b2b1] | 140 | const double Aq = _fq(qab, qc, h, radius_bell, radius, 0.5*length); |
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[58f41fe] | 141 | |
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[50e1e40] | 142 | // Multiply by contrast^2 and convert to cm-1 |
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[58f41fe] | 143 | const double s = (sld - solvent_sld); |
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[50e1e40] | 144 | return 1.0e-4 * square(s * Aq); |
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[58f41fe] | 145 | } |
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