source: sasmodels/sasmodels/models/barbell.c @ 26141cb

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 26141cb was 26141cb, checked in by wojciech, 8 years ago

A few extra models fixed

  • Property mode set to 100644
File size: 4.4 KB
Line 
1double form_volume(double bell_radius, double radius, double length);
2double Iq(double q, double sld, double solvent_sld,
3        double bell_radius, double radius, double length);
4double Iqxy(double qx, double qy, double sld, double solvent_sld,
5        double bell_radius, double radius, double length,
6        double theta, double phi);
7
8//barbell kernel - same as dumbell
9static double
10_bell_kernel(double q, double h, double bell_radius,
11             double half_length, double sin_alpha, double cos_alpha)
12{
13    // translate a point in [-1,1] to a point in [lower,upper]
14    const double upper = 1.0;
15    const double lower = h/bell_radius;
16    const double zm = 0.5*(upper-lower);
17    const double zb = 0.5*(upper+lower);
18
19    // cos term in integral is:
20    //    cos (q (R t - h + L/2) cos(alpha))
21    // so turn it into:
22    //    cos (m t + b)
23    // where:
24    //    m = q R cos(alpha)
25    //    b = q(L/2-h) cos(alpha)
26    const double m = q*bell_radius*cos_alpha; // cos argument slope
27    const double b = q*(half_length-h)*cos_alpha; // cos argument intercept
28    const double qrst = q*bell_radius*sin_alpha; // Q*R*sin(theta)
29    double total = 0.0;
30    for (int i = 0; i < 76; i++){
31        const double t = Gauss76Z[i]*zm + zb;
32        const double radical = 1.0 - t*t;
33        const double bj = sas_J1c(qrst*sqrt(radical));
34        const double Fq = cos(m*t + b) * radical * bj;
35        total += Gauss76Wt[i] * Fq;
36    }
37    // translate dx in [-1,1] to dx in [lower,upper]
38    const double integral = total*zm;
39    const double bell_Fq = 2*M_PI*cube(bell_radius)*integral;
40    return bell_Fq;
41}
42
43double form_volume(double bell_radius,
44        double radius,
45        double length)
46{
47
48    // bell radius should never be less than radius when this is called
49    const double hdist = sqrt(square(bell_radius) - square(radius));
50    const double p1 = 2.0/3.0*cube(bell_radius);
51    const double p2 = square(bell_radius)*hdist;
52    const double p3 = cube(hdist)/3.0;
53
54    return M_PI*square(radius)*length + 2.0*M_PI*(p1+p2-p3);
55}
56
57double Iq(double q, double sld, double solvent_sld,
58          double bell_radius, double radius, double length)
59{
60    // Exclude invalid inputs.
61    if (bell_radius < radius) return NAN;
62    const double h = -sqrt(bell_radius*bell_radius - radius*radius);
63    const double half_length = 0.5*length;
64
65    // translate a point in [-1,1] to a point in [0, pi/2]
66    const double zm = M_PI_4;
67    const double zb = M_PI_4;
68    double total = 0.0;
69    for (int i = 0; i < 76; i++){
70        const double alpha= Gauss76Z[i]*zm + zb;
71        double sin_alpha, cos_alpha; // slots to hold sincos function output
72        SINCOS(alpha, sin_alpha, cos_alpha);
73
74        const double bell_Fq = _bell_kernel(q, h, bell_radius, half_length, sin_alpha, cos_alpha);
75        const double bj = sas_J1c(q*radius*sin_alpha);
76        const double si = sinc(q*half_length*cos_alpha);
77        const double cyl_Fq = M_PI*radius*radius*length*bj*si;
78        const double Aq = bell_Fq + cyl_Fq;
79        total += Gauss76Wt[i] * Aq * Aq * sin_alpha;
80    }
81    // translate dx in [-1,1] to dx in [lower,upper]
82    const double form = total*zm;
83
84    //Contrast
85    const double s = (sld - solvent_sld);
86    return 1.0e-4 * s * s * form;
87}
88
89
90double Iqxy(double qx, double qy,
91        double sld, double solvent_sld,
92        double bell_radius, double radius, double length,
93        double theta, double phi)
94{
95    // Compute angle alpha between q and the cylinder axis
96    double sn, cn; // slots to hold sincos function output
97    SINCOS(theta*M_PI_180, sn, cn);
98    const double q = sqrt(qx*qx+qy*qy);
99    const double cos_val = cn*cos(phi*M_PI_180)*(qx/q) + sn*(qy/q);
100    const double alpha = acos(cos_val); // rod angle relative to q
101
102    // Exclude invalid inputs.
103    if (bell_radius < radius) return NAN;
104    const double h = -sqrt(square(bell_radius) - square(radius));
105    const double half_length = 0.5*length;
106
107    double sin_alpha, cos_alpha; // slots to hold sincos function output
108    SINCOS(alpha, sin_alpha, cos_alpha);
109    const double bell_Fq = _bell_kernel(q, h, bell_radius, half_length, sin_alpha, cos_alpha);
110    const double bj = sas_J1c(q*radius*sin_alpha);
111    const double si = sinc(q*half_length*cos_alpha);
112    const double cyl_Fq = M_PI*radius*radius*length*bj*si;
113    const double Aq = cyl_Fq + bell_Fq;
114
115    // Multiply by contrast^2 and convert to cm-1
116    const double s = (sld - solvent_sld);
117    return 1.0e-4 * square(s * Aq);
118}
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