Changeset 7e0b281 in sasmodels for sasmodels/models/fcc_paracrystal.c
- Timestamp:
- Apr 17, 2017 4:34:52 PM (7 years ago)
- Branches:
- master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- 64ca163
- Parents:
- cb038a2
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
sasmodels/models/fcc_paracrystal.c
r2a0b2b1 r7e0b281 1 1 static double 2 _sq_fcc(double qa, double qb, double qc, double dnn, double d_factor)2 fcc_Zq(double qa, double qb, double qc, double dnn, double d_factor) 3 3 { 4 // Rewriting equations for efficiency, accuracy and readability, and so 5 // code is reusable between 1D and 2D models. 6 const double a1 = qb + qa; 7 const double a2 = qa + qc; 8 const double a3 = qb + qc; 9 10 const double half_dnn = 0.5*dnn; 11 const double arg = 0.5*square(half_dnn*d_factor)*(a1*a1 + a2*a2 + a3*a3); 4 #if 0 // Equations as written in Matsuoka 5 const double a1 = ( qa + qb)/2.0; 6 const double a2 = (-qa + qc)/2.0; 7 const double a3 = (-qa + qb)/2.0; 8 #else 9 const double a1 = ( qa + qb)/2.0; 10 const double a2 = ( qa + qc)/2.0; 11 const double a3 = ( qb + qc)/2.0; 12 #endif 12 13 13 14 // Numerator: (1 - exp(a)^2)^3 14 15 // => (-(exp(2a) - 1))^3 15 16 // => -expm1(2a)^3 16 // Denominator: prod(1 - 2 cos(xk) exp(a) + exp(a)^2) 17 // => exp(a)^2 - 2 cos(xk) exp(a) + 1 18 // => (exp(a) - 2 cos(xk)) * exp(a) + 1 19 const double exp_arg = exp(-arg); 20 const double Sq = -cube(expm1(-2.0*arg)) 21 / ( ((exp_arg - 2.0*cos(half_dnn*a1))*exp_arg + 1.0) 22 * ((exp_arg - 2.0*cos(half_dnn*a2))*exp_arg + 1.0) 23 * ((exp_arg - 2.0*cos(half_dnn*a3))*exp_arg + 1.0)); 17 // Denominator: prod(1 - 2 cos(d ak) exp(a) + exp(2a)) 18 // => prod(exp(a)^2 - 2 cos(d ak) exp(a) + 1) 19 // => prod((exp(a) - 2 cos(d ak)) * exp(a) + 1) 20 const double arg = -0.5*square(dnn*d_factor)*(a1*a1 + a2*a2 + a3*a3); 21 const double exp_arg = exp(arg); 22 const double Zq = -cube(expm1(2.0*arg)) 23 / ( ((exp_arg - 2.0*cos(dnn*a1))*exp_arg + 1.0) 24 * ((exp_arg - 2.0*cos(dnn*a2))*exp_arg + 1.0) 25 * ((exp_arg - 2.0*cos(dnn*a3))*exp_arg + 1.0)); 24 26 25 return Sq;27 return Zq; 26 28 } 27 29 … … 29 31 // occupied volume fraction calculated from lattice symmetry and sphere radius 30 32 static double 31 _fcc_volume_fraction(double radius, double dnn)33 fcc_volume_fraction(double radius, double dnn) 32 34 { 33 35 return 4.0*sphere_volume(M_SQRT1_2*radius/dnn); … … 66 68 const double qa = qab*cos_phi; 67 69 const double qb = qab*sin_phi; 68 const double f q = _sq_fcc(qa, qb, qc, dnn, d_factor);69 inner_sum += Gauss150Wt[j] * f q;70 const double form = fcc_Zq(qa, qb, qc, dnn, d_factor); 71 inner_sum += Gauss150Wt[j] * form; 70 72 } 71 73 inner_sum *= phi_m; // sum(f(x)dx) = sum(f(x)) dx … … 73 75 } 74 76 outer_sum *= theta_m; 75 const double Sq = outer_sum/(4.0*M_PI);77 const double Zq = outer_sum/(4.0*M_PI); 76 78 const double Pq = sphere_form(q, radius, sld, solvent_sld); 77 79 78 return _fcc_volume_fraction(radius, dnn) * Pq * Sq;80 return fcc_volume_fraction(radius, dnn) * Pq * Zq; 79 81 } 80 82 … … 93 95 q = sqrt(qa*qa + qb*qb + qc*qc); 94 96 const double Pq = sphere_form(q, radius, sld, solvent_sld); 95 const double Sq = _sq_fcc(qa, qb, qc, dnn, d_factor);96 return _fcc_volume_fraction(radius, dnn) * Pq * Sq;97 const double Zq = fcc_Zq(qa, qb, qc, dnn, d_factor); 98 return fcc_volume_fraction(radius, dnn) * Pq * Zq; 97 99 }
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