[becded3] | 1 | static double |
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| 2 | form_volume(double length_a, double length_b, double length_c) |
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[c5b7d07] | 3 | { |
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[a807206] | 4 | return length_a * length_b * length_c; |
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[c5b7d07] | 5 | } |
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| 6 | |
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[d277229] | 7 | static double |
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[99658f6] | 8 | radius_from_excluded_volume(double length_a, double length_b, double length_c) |
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| 9 | { |
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| 10 | double r_equiv, length; |
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| 11 | double lengths[3] = {length_a, length_b, length_c}; |
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| 12 | double lengthmax = fmax(lengths[0],fmax(lengths[1],lengths[2])); |
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| 13 | double length_1 = lengthmax; |
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| 14 | double length_2 = lengthmax; |
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| 15 | double length_3 = lengthmax; |
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| 16 | |
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| 17 | for(int ilen=0; ilen<3; ilen++) { |
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| 18 | if (lengths[ilen] < length_1) { |
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| 19 | length_2 = length_1; |
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| 20 | length_1 = lengths[ilen]; |
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| 21 | } else { |
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| 22 | if (lengths[ilen] < length_2) { |
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| 23 | length_2 = lengths[ilen]; |
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| 24 | } |
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| 25 | } |
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| 26 | } |
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| 27 | if(length_2-length_1 > length_3-length_2) { |
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| 28 | r_equiv = sqrt(length_2*length_3/M_PI); |
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| 29 | length = length_1; |
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| 30 | } else { |
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| 31 | r_equiv = sqrt(length_1*length_2/M_PI); |
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| 32 | length = length_3; |
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| 33 | } |
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| 34 | |
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| 35 | return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length + (r_equiv + length)*(M_PI*r_equiv + length))); |
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| 36 | } |
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| 37 | |
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| 38 | static double |
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[d277229] | 39 | effective_radius(int mode, double length_a, double length_b, double length_c) |
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| 40 | { |
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[ee60aa7] | 41 | switch (mode) { |
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[d42dd4a] | 42 | default: |
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[99658f6] | 43 | case 1: // equivalent cylinder excluded volume |
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| 44 | return radius_from_excluded_volume(length_a,length_b,length_c); |
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| 45 | case 2: // equivalent volume sphere |
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[6d5601c] | 46 | return cbrt(length_a*length_b*length_c/M_4PI_3); |
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[99658f6] | 47 | case 3: // half length_a |
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[d277229] | 48 | return 0.5 * length_a; |
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[99658f6] | 49 | case 4: // half length_b |
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[d277229] | 50 | return 0.5 * length_b; |
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[99658f6] | 51 | case 5: // half length_c |
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[d277229] | 52 | return 0.5 * length_c; |
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[99658f6] | 53 | case 6: // equivalent circular cross-section |
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[d277229] | 54 | return sqrt(length_a*length_b/M_PI); |
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[99658f6] | 55 | case 7: // half ab diagonal |
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[d277229] | 56 | return 0.5*sqrt(length_a*length_a + length_b*length_b); |
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[99658f6] | 57 | case 8: // half diagonal |
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[d277229] | 58 | return 0.5*sqrt(length_a*length_a + length_b*length_b + length_c*length_c); |
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| 59 | } |
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| 60 | } |
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| 61 | |
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[71b751d] | 62 | static void |
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| 63 | Fq(double q, |
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| 64 | double *F1, |
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| 65 | double *F2, |
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[c5b7d07] | 66 | double sld, |
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| 67 | double solvent_sld, |
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[a807206] | 68 | double length_a, |
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| 69 | double length_b, |
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| 70 | double length_c) |
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[c5b7d07] | 71 | { |
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[14838a3] | 72 | const double mu = 0.5 * q * length_b; |
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[2a0b2b1] | 73 | |
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[c5b7d07] | 74 | // Scale sides by B |
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[14838a3] | 75 | const double a_scaled = length_a / length_b; |
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| 76 | const double c_scaled = length_c / length_b; |
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[2a0b2b1] | 77 | |
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[14838a3] | 78 | // outer integral (with gauss points), integration limits = 0, 1 |
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[71b751d] | 79 | double outer_total_F1 = 0.0; //initialize integral |
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| 80 | double outer_total_F2 = 0.0; //initialize integral |
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[74768cb] | 81 | for( int i=0; i<GAUSS_N; i++) { |
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| 82 | const double sigma = 0.5 * ( GAUSS_Z[i] + 1.0 ); |
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[14838a3] | 83 | const double mu_proj = mu * sqrt(1.0-sigma*sigma); |
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| 84 | |
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| 85 | // inner integral (with gauss points), integration limits = 0, 1 |
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| 86 | // corresponding to angles from 0 to pi/2. |
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[71b751d] | 87 | double inner_total_F1 = 0.0; |
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| 88 | double inner_total_F2 = 0.0; |
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[74768cb] | 89 | for(int j=0; j<GAUSS_N; j++) { |
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| 90 | const double uu = 0.5 * ( GAUSS_Z[j] + 1.0 ); |
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[14838a3] | 91 | double sin_uu, cos_uu; |
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| 92 | SINCOS(M_PI_2*uu, sin_uu, cos_uu); |
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[1e7b0db0] | 93 | const double si1 = sas_sinx_x(mu_proj * sin_uu * a_scaled); |
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| 94 | const double si2 = sas_sinx_x(mu_proj * cos_uu); |
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[71b751d] | 95 | const double fq = si1 * si2; |
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| 96 | inner_total_F1 += GAUSS_W[j] * fq; |
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| 97 | inner_total_F2 += GAUSS_W[j] * fq * fq; |
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[c5b7d07] | 98 | } |
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[dbf1a60] | 99 | // now complete change of inner integration variable (1-0)/(1-(-1))= 0.5 |
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[71b751d] | 100 | inner_total_F1 *= 0.5; |
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| 101 | inner_total_F2 *= 0.5; |
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[c5b7d07] | 102 | |
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[1e7b0db0] | 103 | const double si = sas_sinx_x(mu * c_scaled * sigma); |
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[71b751d] | 104 | outer_total_F1 += GAUSS_W[i] * inner_total_F1 * si; |
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| 105 | outer_total_F2 += GAUSS_W[i] * inner_total_F2 * si * si; |
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[14838a3] | 106 | } |
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[dbf1a60] | 107 | // now complete change of outer integration variable (1-0)/(1-(-1))= 0.5 |
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[71b751d] | 108 | outer_total_F1 *= 0.5; |
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| 109 | outer_total_F2 *= 0.5; |
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[14838a3] | 110 | |
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| 111 | // Multiply by contrast^2 and convert from [1e-12 A-1] to [cm-1] |
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| 112 | const double V = form_volume(length_a, length_b, length_c); |
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[71b751d] | 113 | const double contrast = (sld-solvent_sld); |
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| 114 | const double s = contrast * V; |
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| 115 | *F1 = 1.0e-2 * s * outer_total_F1; |
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| 116 | *F2 = 1.0e-4 * s * s * outer_total_F2; |
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[c5b7d07] | 117 | } |
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| 118 | |
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[becded3] | 119 | static double |
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[108e70e] | 120 | Iqabc(double qa, double qb, double qc, |
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[c5b7d07] | 121 | double sld, |
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| 122 | double solvent_sld, |
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[a807206] | 123 | double length_a, |
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| 124 | double length_b, |
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[becded3] | 125 | double length_c) |
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[c5b7d07] | 126 | { |
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[2a0b2b1] | 127 | const double siA = sas_sinx_x(0.5*length_a*qa); |
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| 128 | const double siB = sas_sinx_x(0.5*length_b*qb); |
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| 129 | const double siC = sas_sinx_x(0.5*length_c*qc); |
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[14838a3] | 130 | const double V = form_volume(length_a, length_b, length_c); |
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| 131 | const double drho = (sld - solvent_sld); |
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| 132 | const double form = V * drho * siA * siB * siC; |
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| 133 | // Square and convert from [1e-12 A-1] to [cm-1] |
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| 134 | return 1.0e-4 * form * form; |
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[c5b7d07] | 135 | } |
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