1 | static double |
---|
2 | form_volume(double radius_minor, double r_ratio, double length) |
---|
3 | { |
---|
4 | return M_PI * radius_minor * radius_minor * r_ratio * length; |
---|
5 | } |
---|
6 | |
---|
7 | static double |
---|
8 | radius_from_excluded_volume(double radius_minor, double r_ratio, double length) |
---|
9 | { |
---|
10 | const double r_equiv = sqrt(radius_minor*radius_minor*r_ratio); |
---|
11 | return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length + (r_equiv + length)*(M_PI*r_equiv + length))); |
---|
12 | } |
---|
13 | |
---|
14 | static double |
---|
15 | radius_from_volume(double radius_minor, double r_ratio, double length) |
---|
16 | { |
---|
17 | const double volume_ellcyl = form_volume(radius_minor,r_ratio,length); |
---|
18 | return cbrt(volume_ellcyl/M_4PI_3); |
---|
19 | } |
---|
20 | |
---|
21 | static double |
---|
22 | radius_from_min_dimension(double radius_minor, double r_ratio, double hlength) |
---|
23 | { |
---|
24 | const double rad_min = (r_ratio > 1.0 ? radius_minor : r_ratio*radius_minor); |
---|
25 | return (rad_min < hlength ? rad_min : hlength); |
---|
26 | } |
---|
27 | |
---|
28 | static double |
---|
29 | radius_from_max_dimension(double radius_minor, double r_ratio, double hlength) |
---|
30 | { |
---|
31 | const double rad_max = (r_ratio < 1.0 ? radius_minor : r_ratio*radius_minor); |
---|
32 | return (rad_max > hlength ? rad_max : hlength); |
---|
33 | } |
---|
34 | |
---|
35 | static double |
---|
36 | radius_from_diagonal(double radius_minor, double r_ratio, double length) |
---|
37 | { |
---|
38 | const double radius_max = (r_ratio > 1.0 ? radius_minor*r_ratio : radius_minor); |
---|
39 | return sqrt(radius_max*radius_max + 0.25*length*length); |
---|
40 | } |
---|
41 | |
---|
42 | static double |
---|
43 | effective_radius(int mode, double radius_minor, double r_ratio, double length) |
---|
44 | { |
---|
45 | switch (mode) { |
---|
46 | default: |
---|
47 | case 1: // equivalent cylinder excluded volume |
---|
48 | return radius_from_excluded_volume(radius_minor, r_ratio, length); |
---|
49 | case 2: // equivalent volume sphere |
---|
50 | return radius_from_volume(radius_minor, r_ratio, length); |
---|
51 | case 3: // average radius |
---|
52 | return 0.5*radius_minor*(1.0 + r_ratio); |
---|
53 | case 4: // min radius |
---|
54 | return (r_ratio > 1.0 ? radius_minor : r_ratio*radius_minor); |
---|
55 | case 5: // max radius |
---|
56 | return (r_ratio < 1.0 ? radius_minor : r_ratio*radius_minor); |
---|
57 | case 6: // equivalent circular cross-section |
---|
58 | return sqrt(radius_minor*radius_minor*r_ratio); |
---|
59 | case 7: // half length |
---|
60 | return 0.5*length; |
---|
61 | case 8: // half min dimension |
---|
62 | return radius_from_min_dimension(radius_minor,r_ratio,0.5*length); |
---|
63 | case 9: // half max dimension |
---|
64 | return radius_from_max_dimension(radius_minor,r_ratio,0.5*length); |
---|
65 | case 10: // half diagonal |
---|
66 | return radius_from_diagonal(radius_minor,r_ratio,length); |
---|
67 | } |
---|
68 | } |
---|
69 | |
---|
70 | static void |
---|
71 | Fq(double q, double *F1, double *F2, double radius_minor, double r_ratio, double length, |
---|
72 | double sld, double solvent_sld) |
---|
73 | { |
---|
74 | // orientational average limits |
---|
75 | const double va = 0.0; |
---|
76 | const double vb = 1.0; |
---|
77 | // inner integral limits |
---|
78 | const double vaj=0.0; |
---|
79 | const double vbj=M_PI; |
---|
80 | |
---|
81 | const double radius_major = r_ratio * radius_minor; |
---|
82 | const double rA = 0.5*(square(radius_major) + square(radius_minor)); |
---|
83 | const double rB = 0.5*(square(radius_major) - square(radius_minor)); |
---|
84 | |
---|
85 | //initialize integral |
---|
86 | double outer_sum_F1 = 0.0; |
---|
87 | double outer_sum_F2 = 0.0; |
---|
88 | for(int i=0;i<GAUSS_N;i++) { |
---|
89 | //setup inner integral over the ellipsoidal cross-section |
---|
90 | const double cos_val = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0; |
---|
91 | const double sin_val = sqrt(1.0 - cos_val*cos_val); |
---|
92 | //const double arg = radius_minor*sin_val; |
---|
93 | double inner_sum_F1 = 0.0; |
---|
94 | double inner_sum_F2 = 0.0; |
---|
95 | for(int j=0;j<GAUSS_N;j++) { |
---|
96 | const double theta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0; |
---|
97 | const double r = sin_val*sqrt(rA - rB*cos(theta)); |
---|
98 | const double be = sas_2J1x_x(q*r); |
---|
99 | inner_sum_F1 += GAUSS_W[j] * be; |
---|
100 | inner_sum_F2 += GAUSS_W[j] * be * be; |
---|
101 | } |
---|
102 | //now calculate the value of the inner integral |
---|
103 | inner_sum_F1 *= 0.5*(vbj-vaj); |
---|
104 | inner_sum_F2 *= 0.5*(vbj-vaj); |
---|
105 | |
---|
106 | //now calculate outer integral |
---|
107 | const double si = sas_sinx_x(q*0.5*length*cos_val); |
---|
108 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * si; |
---|
109 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * si * si; |
---|
110 | } |
---|
111 | // correct limits and divide integral by pi |
---|
112 | outer_sum_F1 *= 0.5*(vb-va)/M_PI; |
---|
113 | outer_sum_F2 *= 0.5*(vb-va)/M_PI; |
---|
114 | |
---|
115 | // scale by contrast and volume, and convert to to 1/cm units |
---|
116 | const double volume = form_volume(radius_minor, r_ratio, length); |
---|
117 | const double contrast = sld - solvent_sld; |
---|
118 | const double s = contrast*volume; |
---|
119 | *F1 = 1.0e-2*s*outer_sum_F1; |
---|
120 | *F2 = 1.0e-4*s*s*outer_sum_F2; |
---|
121 | } |
---|
122 | |
---|
123 | |
---|
124 | static double |
---|
125 | Iqabc(double qa, double qb, double qc, |
---|
126 | double radius_minor, double r_ratio, double length, |
---|
127 | double sld, double solvent_sld) |
---|
128 | { |
---|
129 | // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) |
---|
130 | // Given: radius_major = r_ratio * radius_minor |
---|
131 | const double qr = radius_minor*sqrt(square(r_ratio*qb) + square(qa)); |
---|
132 | const double be = sas_2J1x_x(qr); |
---|
133 | const double si = sas_sinx_x(qc*0.5*length); |
---|
134 | const double fq = be * si; |
---|
135 | const double contrast = sld - solvent_sld; |
---|
136 | const double volume = form_volume(radius_minor, r_ratio, length); |
---|
137 | return 1.0e-4 * square(contrast * volume * fq); |
---|
138 | } |
---|