source: sasview/sansmodels/src/sans/models/c_extensions/pearlnecklace.c @ 43aef76

/**
 * pearl necklace model
 */
#include <math.h>
#include "pearlnecklace.h"
#include "libmultifunc/libfunc.h"
#include <stdio.h>
#include <stdlib.h>


double pearl_necklace_kernel(double dp[], double q) {
        // fit parameters
        double scale = dp[0];
        double radius = dp[1];
        double edge_separation = dp[2];
        double thick_string = dp[3];
        double num_pearls = dp[4];
        double sld_pearl = dp[5];
        double sld_string = dp[6];
        double sld_solv = dp[7];
        double background = dp[8];

        //relative slds
        double contrast_pearl = sld_pearl - sld_solv;
        double contrast_string = sld_string - sld_solv;

        // number of string segments
        double num_strings = num_pearls - 1.0;

        //Pi
        double pi = 4.0*atan(1.0);

        // each volumes
        double string_vol = edge_separation * pi * pow((thick_string / 2.0), 2);
        double pearl_vol = 4.0 /3.0 * pi * pow(radius, 3);

        //total volume
        double tot_vol;
        tot_vol = num_strings * string_vol;
        tot_vol += num_pearls * pearl_vol;

        //each masses
        double m_r= contrast_string * string_vol;
        double m_s= contrast_pearl * pearl_vol;

        //sine functions of a pearl
        double psi;
        psi = sin(q*radius);
        psi -= q * radius * cos(q * radius);
        psi /= pow((q * radius), 3);
        psi *= 3.0;

        // Note take only 20 terms in Si series: 10 terms may be enough though.
        double gamma;
        gamma = Si(q* edge_separation);
        gamma /= (q* edge_separation);
        double beta;
        beta = Si(q * (edge_separation + radius));
        beta -= Si(q * radius);
        beta /= (q* edge_separation);

        //form factors
        double sss; //pearls
        double srr; //strings
        double srs; //cross
        // center to center distance between the neighboring pearls
        double A_s = edge_separation + 2.0 * radius;

        // form factor for num_pearls
        sss = 1.0 - pow(sinc(q*A_s), num_pearls );
        sss /= pow((1.0-sinc(q*A_s)), 2);
        sss *= -sinc(q*A_s);
        sss -= num_pearls/2.0;
        sss += num_pearls/(1.0-sinc(q*A_s));
        sss *= 2.0 * pow((m_s*psi), 2);

        // form factor for num_strings (like thin rods)
        double srr_1;
        srr_1 = -pow(sinc(q*edge_separation/2.0), 2);

        srr_1 += 2.0 * gamma;
        srr_1 *= num_strings;
        double srr_2;
        srr_2 = 2.0/(1.0-sinc(q*A_s));
        srr_2 *= num_strings;
        srr_2 *= pow(beta, 2);
        double srr_3;
        srr_3 = 1.0 - pow(sinc(q*A_s), num_strings);
        srr_3 /= pow((1.0-sinc(q*A_s)), 2);
        srr_3 *= pow(beta, 2);
        srr_3 *= -2.0;

        // total srr
        srr = srr_1 + srr_2 + srr_3;
        srr *= pow(m_r, 2);

        // form factor for correlations
        srs = 1.0;
        srs -= pow(sinc(q*A_s), num_strings);
        srs /= pow((1.0-sinc(q*A_s)), 2);
        srs *= -sinc(q*A_s);
        srs += (num_strings/(1.0-sinc(q*A_s)));
        srs *= 4.0;
        srs *= (m_r * m_s * beta * psi);

        double form_factor;
        form_factor = sss + srr + srs;
        form_factor /= (tot_vol * 1.0e-8); // norm by volume and A^-1 to cm^-1

        // scale and background
        form_factor *= scale;
        form_factor += background;
    return (form_factor);
}

/**
 * Function to evaluate pearlnecklace function
 * @param pars: parameters of pearlnecklace
 * @param q: q-value
 * @return: function value
 */

double pearl_necklace_analytical_1D(PeralNecklaceParameters *pars, double q) {
        double dp[9];

        dp[0] = pars->scale;
        dp[1] = pars->radius;
        dp[2] = pars->edge_separation;
        dp[3] = pars->thick_string;
        dp[4] = pars->num_pearls;
        dp[5] = pars->sld_pearl;
        dp[6] = pars->sld_string;
        dp[7] = pars->sld_solv;
        dp[8] = pars->background;

        return pearl_necklace_kernel(dp, q);
}

/**
 * Function to evaluate pearl_necklace function
 * @param pars: parameters of PeralNecklace
 * @param q: q-value
 * @return: function value
 */
double pearl_necklace_analytical_2D(PeralNecklaceParameters *pars, double q, double phi) {
        return pearl_necklace_analytical_1D(pars,q);
}

double pearl_necklace_analytical_2DXY(PeralNecklaceParameters *pars, double qx, double qy){
        return pearl_necklace_analytical_1D(pars,sqrt(qx*qx+qy*qy));
}