Octahedron - octahedron_h_mi.c

```    ```#include <math.h>
#include <stdio.h>
static double
form_volume(double length_a, double b2a_ratio, double c2a_ratio)
{
//octehedron volume formula
// length_a is the half height along the a axis of the octahedron
return (4/3) * length_a * (length_a*b2a_ratio) * (length_a*c2a_ratio);
}

static double
Iq(double q,
double sld,
double solvent_sld,
double length_a,
double b2a_ratio,
double c2a_ratio)
{
const double length_b = length_a * b2a_ratio;
const double length_c = length_a * c2a_ratio;

//Integration limits to use in Gaussian quadrature
const double v1a = 0.0;
const double v1b = M_PI_2;  //theta integration limits
const double v2a = 0.0;
const double v2b = M_PI_2;  //phi integration limits

double outer_sum = 0.0;
for(int i=0; i<GAUSS_N; i++) {
const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
double sin_theta, cos_theta;
SINCOS(theta, sin_theta, cos_theta);

double inner_sum = 0.0;
for(int j=0; j<GAUSS_N; j++) {
double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
double sin_phi, cos_phi;
SINCOS(phi, sin_phi, cos_phi);

//HERE: Octahedron formula
const double Qx = q * sin_theta * cos_phi;
const double Qy = q * sin_theta * sin_phi;
const double Qz = q * cos_theta;
const double qx = Qx * length_a;
const double qy = Qy * length_b;
const double qz = Qz * length_c;

const double A = 8.*(qy*sin(qy)-qz*sin(qz))/(qy*qy-qz*qz);
const double B = 8.*(qz*sin(qz)-qx*sin(qx))/(qx*qx-qz*qz);

// normalisation to 1. of AP at q = 0. Division by a Factor 4/3.
const double AP = (3./4.)*(A+B)/(qx*qx-qy*qy);

inner_sum += GAUSS_W[j] * AP * AP;
}
inner_sum = 0.5 * (v2b-v2a) * inner_sum;
outer_sum += GAUSS_W[i] * inner_sum * sin_theta;
}

double answer = 0.5*(v1b-v1a)*outer_sum;

// Normalize by Pi (Eqn. 16).
// The factor 2 appears because the theta integral has been defined between
// 0 and pi/2, instead of 0 to pi.
answer /= M_PI_2; //Form factor P(q)

// Multiply by contrast^2 and volume^2
// volume of octahedron
const double volume = (4./3.)*length_a * length_b * length_c;

// Convert from [1e-12 A-1] to [cm-1]

}

static void
Fq(double q,
double *F1,
double *F2,
double sld,
double solvent_sld,
double length_a,
double b2a_ratio,
double c2a_ratio)
{
const double length_b = length_a * b2a_ratio;
const double length_c = length_a * c2a_ratio;

//Integration limits to use in Gaussian quadrature
const double v1a = 0.0;
const double v1b = M_PI_2;  //theta integration limits
const double v2a = 0.0;
const double v2b = M_PI_2;  //phi integration limits

double outer_sum_F1 = 0.0;
double outer_sum_F2 = 0.0;
for(int i=0; i<GAUSS_N; i++) {
const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
double sin_theta, cos_theta;
SINCOS(theta, sin_theta, cos_theta);

double inner_sum_F1 = 0.0;
double inner_sum_F2 = 0.0;
for(int j=0; j<GAUSS_N; j++) {
double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
double sin_phi, cos_phi;
SINCOS(phi, sin_phi, cos_phi);

//HERE: Octahedron formula
const double Qx = q * sin_theta * cos_phi;
const double Qy = q * sin_theta * sin_phi;
const double Qz = q * cos_theta;
const double qx = Qx * length_a;
const double qy = Qy * length_b;
const double qz = Qz * length_c;

const double A = 8.*(qy*sin(qy)-qz*sin(qz))/(qy*qy-qz*qz);
const double B = 8.*(qz*sin(qz)-qx*sin(qx))/(qx*qx-qz*qz);

// normalisation to 1. of AP at q = 0. Division by a Factor 4/3.
const double AP = (3./4.)*(A+B)/(qx*qx-qy*qy);

inner_sum_F1 += GAUSS_W[j] * AP;
inner_sum_F2 += GAUSS_W[j] * AP * AP;
}
inner_sum_F1 = 0.5 * (v2b-v2a) * inner_sum_F1;
inner_sum_F2 = 0.5 * (v2b-v2a) * inner_sum_F2;
outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta;
outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta;
}

outer_sum_F1 *= 0.5*(v1b-v1a);
outer_sum_F2 *= 0.5*(v1b-v1a);

// Normalize by Pi (Eqn. 16).
// The factor 2 appears because the theta integral has been defined between
// 0 and pi/2, instead of 0 to pi.
outer_sum_F1 /= M_PI_2;
outer_sum_F2 /= M_PI_2;

// Multiply by contrast and volume
// volume of octahedron
const double s = (sld-solvent_sld) * (4./3.) * (length_a * length_b * length_c);

// Convert from [1e-12 A-1] to [cm-1]
*F1 = 1e-2 * s * outer_sum_F1;
*F2 = 1e-4 * s * s * outer_sum_F2;
}

static double
Iqabc(double qa, double qb, double qc,
double sld,
double solvent_sld,
double length_a,
double b2a_ratio,
double c2a_ratio)
{
const double length_b = length_a * b2a_ratio;
const double length_c = length_a * c2a_ratio;

//HERE: Octahedron formula
const double qx = qa * length_a;
const double qy = qb * length_b;
const double qz = qc * length_c;

const double A = 8.*(qy*sin(qy)-qz*sin(qz))/(qy*qy-qz*qz);
const double B = 8.*(qz*sin(qz)-qx*sin(qx))/(qx*qx-qz*qz);
// normalisation to 1. of AP at q = 0. Division by a Factor 4/3.
const double AP = (3./4.)*(A+B)/(qx*qx-qy*qy);

// Multiply by contrast and volume
const double s = (sld-solvent_sld) *(4./3.)* (length_a * length_b * length_c);

// Convert from [1e-12 A-1] to [cm-1]
return 1.0e-4 * square(s * AP);
}
```
```