[2a0b2b1] | 1 | static double |
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[251f54b] | 2 | form_volume(double radius_minor, double r_ratio, double length) |
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[a8b3cdb] | 3 | { |
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[a807206] | 4 | return M_PI * radius_minor * radius_minor * r_ratio * length; |
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[a8b3cdb] | 5 | } |
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| 6 | |
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[d277229] | 7 | static double |
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| 8 | radius_from_volume(double radius_minor, double r_ratio, double length) |
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| 9 | { |
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| 10 | const double volume_ellcyl = form_volume(radius_minor,r_ratio,length); |
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| 11 | return cbrt(0.75*volume_ellcyl/M_PI); |
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| 12 | } |
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| 13 | |
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| 14 | static double |
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[a94046f] | 15 | radius_from_min_dimension(double radius_minor, double r_ratio, double hlength) |
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[d277229] | 16 | { |
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| 17 | const double rad_min = (r_ratio > 1.0 ? radius_minor : r_ratio*radius_minor); |
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[a94046f] | 18 | return (rad_min < length ? rad_min : hlength); |
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[d277229] | 19 | } |
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| 20 | |
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| 21 | static double |
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[a94046f] | 22 | radius_from_max_dimension(double radius_minor, double r_ratio, double hlength) |
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[d277229] | 23 | { |
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| 24 | const double rad_max = (r_ratio < 1.0 ? radius_minor : r_ratio*radius_minor); |
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[a94046f] | 25 | return (rad_max > length ? rad_max : hlength); |
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[d277229] | 26 | } |
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| 27 | |
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| 28 | static double |
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| 29 | radius_from_diagonal(double radius_minor, double r_ratio, double length) |
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| 30 | { |
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| 31 | const double radius_max = (r_ratio > 1.0 ? radius_minor*r_ratio : radius_minor); |
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| 32 | return sqrt(radius_max*radius_max + 0.25*length*length); |
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| 33 | } |
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| 34 | |
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| 35 | static double |
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| 36 | effective_radius(int mode, double radius_minor, double r_ratio, double length) |
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[a94046f] | 37 | //effective_radius_type = ["equivalent sphere","average radius","min radius","max radius", |
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| 38 | // "equivalent circular cross-section","half length","half min dimension","half max dimension","half diagonal"] |
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[d277229] | 39 | { |
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| 40 | if (mode == 1) { |
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| 41 | return radius_from_volume(radius_minor, r_ratio, length); |
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| 42 | } else if (mode == 2) { |
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| 43 | return 0.5*radius_minor*(1.0 + r_ratio); |
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| 44 | } else if (mode == 3) { |
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| 45 | return (r_ratio > 1.0 ? radius_minor : r_ratio*radius_minor); |
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| 46 | } else if (mode == 4) { |
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| 47 | return (r_ratio < 1.0 ? radius_minor : r_ratio*radius_minor); |
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| 48 | } else if (mode == 5) { |
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| 49 | return sqrt(radius_minor*radius_minor*r_ratio); |
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| 50 | } else if (mode == 6) { |
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| 51 | return 0.5*length; |
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| 52 | } else if (mode == 7) { |
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[a94046f] | 53 | return radius_from_min_dimension(radius_minor,r_ratio,0.5*length); |
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[d277229] | 54 | } else if (mode == 8) { |
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[a94046f] | 55 | return radius_from_max_dimension(radius_minor,r_ratio,0.5*length); |
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[d277229] | 56 | } else { |
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| 57 | return radius_from_diagonal(radius_minor,r_ratio,length); |
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| 58 | } |
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| 59 | } |
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| 60 | |
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[71b751d] | 61 | static void |
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| 62 | Fq(double q, double *F1, double *F2, double radius_minor, double r_ratio, double length, |
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[68425bf] | 63 | double sld, double solvent_sld) |
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| 64 | { |
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[a8b3cdb] | 65 | // orientational average limits |
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[68425bf] | 66 | const double va = 0.0; |
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| 67 | const double vb = 1.0; |
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[a8b3cdb] | 68 | // inner integral limits |
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[68425bf] | 69 | const double vaj=0.0; |
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| 70 | const double vbj=M_PI; |
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[a8b3cdb] | 71 | |
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[68425bf] | 72 | const double radius_major = r_ratio * radius_minor; |
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| 73 | const double rA = 0.5*(square(radius_major) + square(radius_minor)); |
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| 74 | const double rB = 0.5*(square(radius_major) - square(radius_minor)); |
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[a8b3cdb] | 75 | |
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[68425bf] | 76 | //initialize integral |
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[71b751d] | 77 | double outer_sum_F1 = 0.0; |
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| 78 | double outer_sum_F2 = 0.0; |
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[74768cb] | 79 | for(int i=0;i<GAUSS_N;i++) { |
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[a8b3cdb] | 80 | //setup inner integral over the ellipsoidal cross-section |
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[74768cb] | 81 | const double cos_val = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0; |
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[68425bf] | 82 | const double sin_val = sqrt(1.0 - cos_val*cos_val); |
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| 83 | //const double arg = radius_minor*sin_val; |
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[71b751d] | 84 | double inner_sum_F1 = 0.0; |
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| 85 | double inner_sum_F2 = 0.0; |
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[74768cb] | 86 | for(int j=0;j<GAUSS_N;j++) { |
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| 87 | const double theta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
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[68425bf] | 88 | const double r = sin_val*sqrt(rA - rB*cos(theta)); |
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[592343f] | 89 | const double be = sas_2J1x_x(q*r); |
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[71b751d] | 90 | inner_sum_F1 += GAUSS_W[j] * be; |
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| 91 | inner_sum_F2 += GAUSS_W[j] * be * be; |
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[a8b3cdb] | 92 | } |
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| 93 | //now calculate the value of the inner integral |
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[71b751d] | 94 | inner_sum_F1 *= 0.5*(vbj-vaj); |
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| 95 | inner_sum_F2 *= 0.5*(vbj-vaj); |
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[a8b3cdb] | 96 | |
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| 97 | //now calculate outer integral |
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[1e7b0db0] | 98 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
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[71b751d] | 99 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * si; |
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| 100 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * si * si; |
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[a8b3cdb] | 101 | } |
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[71b751d] | 102 | // correct limits and divide integral by pi |
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| 103 | outer_sum_F1 *= 0.5*(vb-va)/M_PI; |
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| 104 | outer_sum_F2 *= 0.5*(vb-va)/M_PI; |
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[a8b3cdb] | 105 | |
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[68425bf] | 106 | // scale by contrast and volume, and convert to to 1/cm units |
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[71b751d] | 107 | const double volume = form_volume(radius_minor, r_ratio, length); |
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| 108 | const double contrast = sld - solvent_sld; |
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| 109 | const double s = contrast*volume; |
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| 110 | *F1 = 1.0e-2*s*outer_sum_F1; |
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| 111 | *F2 = 1.0e-4*s*s*outer_sum_F2; |
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[a8b3cdb] | 112 | } |
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| 113 | |
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| 114 | |
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[2a0b2b1] | 115 | static double |
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[108e70e] | 116 | Iqabc(double qa, double qb, double qc, |
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[68425bf] | 117 | double radius_minor, double r_ratio, double length, |
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[becded3] | 118 | double sld, double solvent_sld) |
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[68425bf] | 119 | { |
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| 120 | // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) |
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| 121 | // Given: radius_major = r_ratio * radius_minor |
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[82592da] | 122 | const double qr = radius_minor*sqrt(square(r_ratio*qb) + square(qa)); |
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[2a0b2b1] | 123 | const double be = sas_2J1x_x(qr); |
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| 124 | const double si = sas_sinx_x(qc*0.5*length); |
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[71b751d] | 125 | const double fq = be * si; |
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| 126 | const double contrast = sld - solvent_sld; |
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| 127 | const double volume = form_volume(radius_minor, r_ratio, length); |
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| 128 | return 1.0e-4 * square(contrast * volume * fq); |
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[a8b3cdb] | 129 | } |
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