[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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| 51 | double temp2 = pow( 1.0-exp(-1.0*temp1) ,3); |
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| 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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| 56 | double integrand = temp2*sc_eval(yy,xx,temp3,temp4,temp5); |
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| 57 | integrand *= 2.0/M_PI; |
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| 58 | |
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| 59 | return(integrand); |
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| 60 | } |
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| 61 | |
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| 62 | static |
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| 63 | double sc_crystal_kernel(double q, |
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| 64 | double dnn, |
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| 65 | double d_factor, |
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| 66 | double radius, |
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| 67 | double sphere_sld, |
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| 68 | double solvent_sld) |
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| 69 | { |
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| 70 | const double va = 0.0; |
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| 71 | const double vb = M_PI/2.0; //orientation average, outer integral |
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| 72 | |
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| 73 | double summ=0.0; |
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| 74 | double answer=0.0; |
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| 75 | |
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| 76 | for(int i=0;i<150;i++) { |
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| 77 | //setup inner integral over the ellipsoidal cross-section |
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| 78 | double summj=0.0; |
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| 79 | double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; |
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| 80 | for(int j=0;j<150;j++) { |
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| 81 | //150 gauss points for the inner integral |
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| 82 | double zij = ( Gauss150Z[j]*(vb-va) + va + vb )/2.0; |
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| 83 | double tmp = Gauss150Wt[j] * sc_integrand(dnn,d_factor,q,zi,zij); |
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| 84 | summj += tmp; |
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| 85 | } |
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| 86 | //now calculate the value of the inner integral |
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| 87 | answer = (vb-va)/2.0*summj; |
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| 88 | |
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| 89 | //now calculate outer integral |
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| 90 | double tmp = Gauss150Wt[i] * answer; |
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| 91 | summ += tmp; |
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| 92 | } //final scaling is done at the end of the function, after the NT_FP64 case |
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| 93 | |
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| 94 | answer = (vb-va)/2.0*summ; |
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| 95 | |
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| 96 | //Volume fraction calculated from lattice symmetry and sphere radius |
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[ad90df9] | 97 | // NB: 4/3 pi r^3 / dnn^3 = 4/3 pi(r/dnn)^3 |
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| 98 | const double latticeScale = sphere_volume(radius/dnn); |
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[9aac25d] | 99 | |
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| 100 | answer *= sphere_form(q, radius, sphere_sld, solvent_sld)*latticeScale; |
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| 101 | |
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| 102 | return answer; |
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| 103 | } |
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| 104 | |
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| 105 | static |
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| 106 | double sc_crystal_kernel_2d(double q, double q_x, double q_y, |
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| 107 | double dnn, |
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| 108 | double d_factor, |
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| 109 | double radius, |
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| 110 | double sphere_sld, |
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| 111 | double solvent_sld, |
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| 112 | double theta, |
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| 113 | double phi, |
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| 114 | double psi) |
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| 115 | { |
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| 116 | //convert angle degree to radian |
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| 117 | theta = theta * M_PI_180; |
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| 118 | phi = phi * M_PI_180; |
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| 119 | psi = psi * M_PI_180; |
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| 120 | |
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| 121 | const double qda_2 = pow(q*d_factor*dnn,2.0); |
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| 122 | |
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| 123 | double snt, cnt; |
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| 124 | SINCOS(theta, snt, cnt); |
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| 125 | |
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| 126 | double snp, cnp; |
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| 127 | SINCOS(phi, snp, cnp); |
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| 128 | |
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| 129 | double sns, cns; |
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| 130 | SINCOS(psi, sns, cns); |
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| 131 | |
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| 132 | /// Angles here are respect to detector coordinate instead of against |
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| 133 | // q coordinate(PRB 36, 3, 1754) |
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| 134 | // a3 axis orientation |
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| 135 | |
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| 136 | const double a3_x = cnt * cnp; |
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| 137 | const double a3_y = snt; |
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| 138 | |
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| 139 | // Compute the angle btw vector q and the a3 axis |
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| 140 | double cos_val_a3 = a3_x*q_x + a3_y*q_y; |
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| 141 | |
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| 142 | // a1 axis orientation |
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| 143 | const double a1_x = -cnp*sns * snt+snp*cns; |
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| 144 | const double a1_y = sns*cnt; |
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| 145 | |
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| 146 | double cos_val_a1 = a1_x*q_x + a1_y*q_y; |
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| 147 | |
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| 148 | // a2 axis orientation |
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| 149 | const double a2_x = -snt*cns*cnp-sns*snp; |
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| 150 | const double a2_y = cnt*cns; |
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| 151 | |
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| 152 | // a2 axis |
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| 153 | const double cos_val_a2 = a2_x*q_x + a2_y*q_y; |
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| 154 | |
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| 155 | // The following test should always pass |
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| 156 | if (fabs(cos_val_a3)>1.0) { |
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| 157 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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| 158 | cos_val_a3 = 1.0; |
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| 159 | } |
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| 160 | if (fabs(cos_val_a1)>1.0) { |
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| 161 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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| 162 | cos_val_a1 = 1.0; |
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| 163 | } |
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| 164 | if (fabs(cos_val_a2)>1.0) { |
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| 165 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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| 166 | cos_val_a3 = 1.0; |
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| 167 | } |
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| 168 | |
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| 169 | const double a3_dot_q = dnn*q*cos_val_a3; |
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| 170 | const double a1_dot_q = dnn*q*cos_val_a1; |
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| 171 | const double a2_dot_q = dnn*q*cos_val_a2; |
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| 172 | |
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| 173 | // Call Zq=Z1*Z2*Z3 |
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| 174 | double Zq = (1.0-exp(-qda_2))/(1.0-2.0*exp(-0.5*qda_2)*cos(a1_dot_q)+exp(-qda_2)); |
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| 175 | Zq *= (1.0-exp(-qda_2))/(1.0-2.0*exp(-0.5*qda_2)*cos(a2_dot_q)+exp(-qda_2)); |
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| 176 | Zq *= (1.0-exp(-qda_2))/(1.0-2.0*exp(-0.5*qda_2)*cos(a3_dot_q)+exp(-qda_2)); |
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| 177 | |
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| 178 | // Use SphereForm directly from libigor |
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| 179 | double answer = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq; |
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| 180 | |
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| 181 | //consider scales |
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[ad90df9] | 182 | const double latticeScale = sphere_volume(radius/dnn); |
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[9aac25d] | 183 | answer *= latticeScale; |
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| 184 | |
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| 185 | return answer; |
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| 186 | } |
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| 187 | |
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| 188 | double Iq(double q, |
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| 189 | double dnn, |
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| 190 | double d_factor, |
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| 191 | double radius, |
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| 192 | double sphere_sld, |
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| 193 | double solvent_sld) |
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| 194 | { |
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| 195 | return sc_crystal_kernel(q, |
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| 196 | dnn, |
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| 197 | d_factor, |
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| 198 | radius, |
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| 199 | sphere_sld, |
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| 200 | solvent_sld); |
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| 201 | } |
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| 202 | |
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| 203 | // Iqxy is never called since no orientation or magnetic parameters. |
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| 204 | double Iqxy(double qx, double qy, |
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| 205 | double dnn, |
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| 206 | double d_factor, |
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| 207 | double radius, |
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| 208 | double sphere_sld, |
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| 209 | double solvent_sld, |
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| 210 | double theta, |
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| 211 | double phi, |
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| 212 | double psi) |
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| 213 | { |
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| 214 | double q = sqrt(qx*qx + qy*qy); |
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| 215 | |
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| 216 | |
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| 217 | return sc_crystal_kernel_2d(q, qx/q, qy/q, |
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| 218 | dnn, |
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| 219 | d_factor, |
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| 220 | radius, |
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| 221 | sphere_sld, |
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| 222 | solvent_sld, |
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| 223 | theta, |
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| 224 | phi, |
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| 225 | psi); |
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| 226 | |
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| 227 | } |
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| 228 | |
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