/**
 * Scattering model for a cylinder with elliptical cross-section
 */

#include "elliptical_cylinder.h"
#include <math.h>
#include "libCylinder.h"
#include <stdio.h>
#include <stdlib.h>


/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @return: function value
 */
double elliptical_cylinder_analytical_1D(EllipticalCylinderParameters *pars, double q) {
	double dp[6];
	
	// Fill paramater array
	dp[0] = pars->scale;
	dp[1] = pars->r_minor;
	dp[2] = pars->r_ratio;
	dp[3] = pars->length;
	dp[4] = pars->contrast;
	dp[5] = pars->background;
	
	// Call library function to evaluate model
	return EllipCyl20(dp, q);	
}

double elliptical_cylinder_kernel(EllipticalCylinderParameters *pars, double q, double alpha, double psi) {
	double qr;
	double qL;
	double r_major;
	double kernel;
	
	r_major = pars->r_ratio * pars->r_minor;

	qr = q*sin(alpha)*sqrt( r_major*r_major*sin(psi)*sin(psi) + pars->r_minor*pars->r_minor*cos(psi)*cos(psi) );
	qL = q*pars->length*cos(alpha)/2.0;
	
	kernel = 2.0*NR_BessJ1(qr)/qr * sin(qL)/qL;
	return kernel*kernel;
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @return: function value
 */
double elliptical_cylinder_analytical_2DXY(EllipticalCylinderParameters *pars, double qx, double qy) {
	double q;
	q = sqrt(qx*qx+qy*qy);
    return elliptical_cylinder_analytical_2D_scaled(pars, q, qx/q, qy/q);
} 

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @param phi: angle phi
 * @return: function value
 */
double elliptical_cylinder_analytical_2D(EllipticalCylinderParameters *pars, double q, double phi) {
    return elliptical_cylinder_analytical_2D_scaled(pars, q, cos(phi), sin(phi));
} 

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @param q_x: q_x / q
 * @param q_y: q_y / q
 * @return: function value
 */
double elliptical_cylinder_analytical_2D_scaled(EllipticalCylinderParameters *pars, double q, double q_x, double q_y) {
	double cyl_x, cyl_y, cyl_z;
	double q_z;
	double alpha, vol, cos_val;
	double answer;
        
    // Cylinder orientation
    cyl_x = sin(pars->cyl_theta) * cos(pars->cyl_phi);
    cyl_y = sin(pars->cyl_theta) * sin(pars->cyl_phi);
    cyl_z = cos(pars->cyl_theta);
     
    // q vector
    q_z = 0;
        
    // Compute the angle btw vector q and the
    // axis of the cylinder
    cos_val = cyl_x*q_x + cyl_y*q_y + cyl_z*q_z;
    
    // The following test should always pass
    if (fabs(cos_val)>1.0) {
    	printf("cyl_ana_2D: Unexpected error: cos(alpha)>1\n");
     	return 0;
    }
    
    // Note: cos(alpha) = 0 and 1 will get an
    // undefined value from CylKernel
	alpha = acos( cos_val );
	
	answer = elliptical_cylinder_kernel(pars, q, alpha, pars->cyl_psi);
	
	// Multiply by contrast^2
	answer *= pars->contrast*pars->contrast;
	
	//normalize by cylinder volume
	//NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl
    vol = acos(-1.0) * pars->r_minor * pars->r_minor * pars->r_ratio * pars->length;
	answer *= vol;
	
	//convert to [cm-1]
	answer *= 1.0e8;
	
	//Scale
	answer *= pars->scale;
	
	// add in the background
	answer += pars->background;
	
	return answer;
}