source: sasmodels/sasmodels/models/triaxial_ellipsoid.c @ 68dd6a9

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Last change on this file since 68dd6a9 was 68dd6a9, checked in by Paul Kienzle <pkienzle@…>, 3 years ago

triaxial ellipsoid: adjust to new asymmetric orientation definition; reimplement 1D model from Finnigan and Jacobs, 1971. Refs #890.

  • Property mode set to 100644
File size: 2.8 KB
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1double form_volume(double radius_equat_minor, double radius_equat_major, double radius_polar);
2double Iq(double q, double sld, double sld_solvent,
3    double radius_equat_minor, double radius_equat_major, double radius_polar);
4double Iqxy(double qx, double qy, double sld, double sld_solvent,
5    double radius_equat_minor, double radius_equat_major, double radius_polar, double theta, double phi, double psi);
6
7//#define INVALID(v) (v.radius_equat_minor > v.radius_equat_major || v.radius_equat_major > v.radius_polar)
8
9
10double form_volume(double radius_equat_minor, double radius_equat_major, double radius_polar)
11{
12    return M_4PI_3*radius_equat_minor*radius_equat_major*radius_polar;
13}
14
15double Iq(double q,
16    double sld,
17    double sld_solvent,
18    double radius_equat_minor,
19    double radius_equat_major,
20    double radius_polar)
21{
22    const double pa = square(radius_equat_minor/radius_equat_major) - 1.0;
23    const double pc = square(radius_polar/radius_equat_major) - 1.0;
24    // translate a point in [-1,1] to a point in [0, pi/2]
25    const double zm = M_PI_4;
26    const double zb = M_PI_4;
27    double outer = 0.0;
28    for (int i=0;i<76;i++) {
29        //const double u = Gauss76Z[i]*(upper-lower)/2 + (upper + lower)/2;
30        const double phi = Gauss76Z[i]*zm + zb;
31        const double pa_sinsq_phi = pa*square(sin(phi));
32
33        double inner = 0.0;
34        const double um = 0.5;
35        const double ub = 0.5;
36        for (int j=0;j<76;j++) {
37            // translate a point in [-1,1] to a point in [0, 1]
38            const double usq = square(Gauss76Z[j]*um + ub);
39            const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq);
40            const double fq = sas_3j1x_x(q*r);
41            inner += Gauss76Wt[j] * fq * fq;
42        }
43        outer += Gauss76Wt[i] * inner;  // correcting for dx later
44    }
45    // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi
46    const double fqsq = outer/4.0;  // = outer*um*zm*8.0/(4.0*M_PI);
47    const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar);
48    return 1.0e-4 * s * s * fqsq;
49}
50
51double Iqxy(double qx, double qy,
52    double sld,
53    double sld_solvent,
54    double radius_equat_minor,
55    double radius_equat_major,
56    double radius_polar,
57    double theta,
58    double phi,
59    double psi)
60{
61    double q, xhat, yhat, zhat;
62    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat);
63
64    const double r = sqrt(square(radius_equat_minor*xhat)
65                          + square(radius_equat_major*yhat)
66                          + square(radius_polar*zhat));
67    const double fq = sas_3j1x_x(q*r);
68    const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar);
69
70    return 1.0e-4 * square(s * fq);
71}
72
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