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