[9aac25d] | 1 | double form_volume(double radius); |
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| 2 | |
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| 3 | double Iq(double q, |
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| 4 | double dnn, |
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| 5 | double d_factor, |
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| 6 | double radius, |
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| 7 | double sphere_sld, |
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| 8 | double solvent_sld); |
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| 9 | |
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| 10 | double Iqxy(double qx, double qy, |
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| 11 | double dnn, |
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| 12 | double d_factor, |
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| 13 | double radius, |
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| 14 | double sphere_sld, |
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| 15 | double solvent_sld, |
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| 16 | double theta, |
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| 17 | double phi, |
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| 18 | double psi); |
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| 19 | |
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| 20 | double form_volume(double radius) |
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| 21 | { |
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[ad90df9] | 22 | return sphere_volume(radius); |
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[9aac25d] | 23 | } |
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| 24 | |
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| 25 | static double |
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| 26 | sc_eval(double theta, double phi, double temp3, double temp4, double temp5) |
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| 27 | { |
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| 28 | double cnt, snt; |
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| 29 | SINCOS(theta, cnt, snt); |
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| 30 | |
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| 31 | double cnp, snp; |
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| 32 | SINCOS(phi, cnp, snp); |
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| 33 | |
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| 34 | double temp6 = snt; |
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| 35 | double temp7 = -1.0*temp3*snt*cnp; |
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| 36 | double temp8 = temp3*snt*snp; |
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| 37 | double temp9 = temp3*cnt; |
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| 38 | double result = temp6/((1.0-temp4*cos((temp7))+temp5)* |
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| 39 | (1.0-temp4*cos((temp8))+temp5)* |
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| 40 | (1.0-temp4*cos((temp9))+temp5)); |
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| 41 | return (result); |
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| 42 | } |
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| 43 | |
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| 44 | static double |
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| 45 | sc_integrand(double dnn, double d_factor, double qq, double xx, double yy) |
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| 46 | { |
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| 47 | //Function to calculate integrand values for simple cubic structure |
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| 48 | |
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| 49 | double da = d_factor*dnn; |
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| 50 | double temp1 = qq*qq*da*da; |
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[4962519] | 51 | double temp2 = cube(-expm1(-temp1)); |
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[9aac25d] | 52 | double temp3 = qq*dnn; |
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| 53 | double temp4 = 2.0*exp(-0.5*temp1); |
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| 54 | double temp5 = exp(-1.0*temp1); |
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| 55 | |
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[4962519] | 56 | double integrand = temp2*sc_eval(yy,xx,temp3,temp4,temp5)/M_PI_2; |
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[9aac25d] | 57 | |
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| 58 | return(integrand); |
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| 59 | } |
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| 60 | |
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[11ca2ab] | 61 | double Iq(double q, |
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[9aac25d] | 62 | double dnn, |
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| 63 | double d_factor, |
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| 64 | double radius, |
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| 65 | double sphere_sld, |
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| 66 | double solvent_sld) |
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| 67 | { |
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| 68 | const double va = 0.0; |
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[3a48772] | 69 | const double vb = M_PI_2; //orientation average, outer integral |
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[9aac25d] | 70 | |
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| 71 | double summ=0.0; |
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| 72 | double answer=0.0; |
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| 73 | |
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| 74 | for(int i=0;i<150;i++) { |
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| 75 | //setup inner integral over the ellipsoidal cross-section |
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| 76 | double summj=0.0; |
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| 77 | double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; |
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| 78 | for(int j=0;j<150;j++) { |
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| 79 | //150 gauss points for the inner integral |
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| 80 | double zij = ( Gauss150Z[j]*(vb-va) + va + vb )/2.0; |
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| 81 | double tmp = Gauss150Wt[j] * sc_integrand(dnn,d_factor,q,zi,zij); |
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| 82 | summj += tmp; |
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| 83 | } |
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| 84 | //now calculate the value of the inner integral |
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| 85 | answer = (vb-va)/2.0*summj; |
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| 86 | |
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| 87 | //now calculate outer integral |
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| 88 | double tmp = Gauss150Wt[i] * answer; |
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| 89 | summ += tmp; |
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| 90 | } //final scaling is done at the end of the function, after the NT_FP64 case |
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| 91 | |
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| 92 | answer = (vb-va)/2.0*summ; |
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| 93 | |
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| 94 | //Volume fraction calculated from lattice symmetry and sphere radius |
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[ad90df9] | 95 | // NB: 4/3 pi r^3 / dnn^3 = 4/3 pi(r/dnn)^3 |
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| 96 | const double latticeScale = sphere_volume(radius/dnn); |
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[9aac25d] | 97 | |
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| 98 | answer *= sphere_form(q, radius, sphere_sld, solvent_sld)*latticeScale; |
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| 99 | |
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| 100 | return answer; |
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| 101 | } |
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| 102 | |
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[11ca2ab] | 103 | double Iqxy(double qx, double qy, |
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[9aac25d] | 104 | double dnn, |
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| 105 | double d_factor, |
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| 106 | double radius, |
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| 107 | double sphere_sld, |
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| 108 | double solvent_sld, |
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| 109 | double theta, |
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| 110 | double phi, |
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| 111 | double psi) |
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| 112 | { |
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[50beefe] | 113 | double q, zhat, yhat, xhat; |
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| 114 | ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); |
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[11ca2ab] | 115 | |
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| 116 | const double qd = q*dnn; |
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[0b717c5] | 117 | const double arg = 0.5*square(qd*d_factor); |
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| 118 | const double tanh_qd = tanh(arg); |
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| 119 | const double cosh_qd = cosh(arg); |
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[50beefe] | 120 | const double Zq = tanh_qd/(1. - cos(qd*zhat)/cosh_qd) |
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| 121 | * tanh_qd/(1. - cos(qd*yhat)/cosh_qd) |
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| 122 | * tanh_qd/(1. - cos(qd*xhat)/cosh_qd); |
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[11ca2ab] | 123 | |
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| 124 | const double Fq = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq; |
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| 125 | //the occupied volume of the lattice |
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| 126 | const double lattice_scale = sphere_volume(radius/dnn); |
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| 127 | return lattice_scale * Fq; |
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[9aac25d] | 128 | } |
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