source: sasmodels/sasmodels/models/hollow_rectangular_prism.c @ 6f676fb

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Last change on this file since 6f676fb was 6f676fb, checked in by Paul Kienzle <pkienzle@…>, 6 years ago

hollow_rectangular_prism: code cleanup, and 2x faster with precomputed trig.

  • Property mode set to 100644
File size: 3.2 KB
Line 
1double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness);
2double Iq(double q, double sld, double solvent_sld, double length_a, 
3          double b2a_ratio, double c2a_ratio, double thickness);
4
5double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness)
6{
7    double length_b = length_a * b2a_ratio;
8    double length_c = length_a * c2a_ratio;
9    double a_core = length_a - 2.0*thickness;
10    double b_core = length_b - 2.0*thickness;
11    double c_core = length_c - 2.0*thickness;
12    double vol_core = a_core * b_core * c_core;
13    double vol_total = length_a * length_b * length_c;
14    double vol_shell = vol_total - vol_core;
15    return vol_shell;
16}
17
18double Iq(double q,
19    double sld,
20    double solvent_sld,
21    double length_a,
22    double b2a_ratio,
23    double c2a_ratio,
24    double thickness)
25{
26    const double length_b = length_a * b2a_ratio;
27    const double length_c = length_a * c2a_ratio;
28    const double a_half = 0.5 * length_a;
29    const double b_half = 0.5 * length_b;
30    const double c_half = 0.5 * length_c;
31    const double vol_total = length_a * length_b * length_c;
32    const double vol_core = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness);
33
34    //Integration limits to use in Gaussian quadrature
35    const double v1a = 0.0;
36    const double v1b = M_PI_2;  //theta integration limits
37    const double v2a = 0.0;
38    const double v2b = M_PI_2;  //phi integration limits
39   
40    double outer_sum = 0.0;
41    for(int i=0; i<76; i++) {
42
43        const double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b );
44        double sin_theta, cos_theta;
45        SINCOS(theta, sin_theta, cos_theta);
46
47        const double termC1 = sinc(q * c_half * cos(theta));
48        const double termC2 = sinc(q * (c_half-thickness)*cos(theta));
49
50        double inner_sum = 0.0;
51        for(int j=0; j<76; j++) {
52
53            const double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b );
54            double sin_phi, cos_phi;
55            SINCOS(phi, sin_phi, cos_phi);
56
57            // Amplitude AP from eqn. (13), rewritten to avoid round-off effects when arg=0
58
59            const double termA1 = sinc(q * a_half * sin_theta * sin_phi);
60            const double termA2 = sinc(q * (a_half-thickness) * sin_theta * sin_phi);
61
62            const double termB1 = sinc(q * b_half * sin_theta * cos_phi);
63            const double termB2 = sinc(q * (b_half-thickness) * sin_theta * cos_phi);
64
65            const double AP1 = vol_total * termA1 * termB1 * termC1;
66            const double AP2 = vol_core * termA2 * termB2 * termC2;
67
68            inner_sum += Gauss76Wt[j] * square(AP1-AP2);
69        }
70        inner_sum *= 0.5 * (v2b-v2a);
71
72        outer_sum += Gauss76Wt[i] * inner_sum * sin(theta);
73    }
74    outer_sum *= 0.5*(v1b-v1a);
75
76    // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization)
77    // The factor 2 is due to the different theta integration limit (pi/2 instead of pi)
78    const double form = outer_sum/M_PI_2;
79
80    // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization.
81    const double delrho = sld - solvent_sld;
82
83    // Convert from [1e-12 A-1] to [cm-1]
84    return 1.0e-4 * delrho * delrho * form;
85}
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