source: sasview/sansmodels/src/c_models/pringles.cpp @ a9fec15

/**
 * PringlesModel
 *
 * (c) 2013 / Andrew J Jackson / andrew.jackson@esss.se
 *
 * Model for "pringles" particle from K. Edler @ Bath University
 *
 */
#include <math.h>
#include "parameters.hh"
#include "pringles.h"
using namespace std;

extern "C"
{
#include "GaussWeights.h"
#include "libStructureFactor.h"
}

// Convenience parameter structure
typedef struct {
    double scale;
    double radius;
    double thickness;
    double alpha;
    double beta;
    double sldCyl;
    double sldSolv;
    double background;
    double cyl_theta;
    double cyl_phi;
} PringleParameters;


PringlesModel::PringlesModel() {
        scale = Parameter(1.0);
        radius = Parameter(60.0,true);
        radius.set_min(0.0);
        thickness = Parameter(10.0,true);
        thickness.set_min(0.0);
        alpha = Parameter(0.001,true);
        beta = Parameter(0.02,true);
        sld_pringle = Parameter(1.0e-6);
        sld_solvent = Parameter(6.35e-6);
        background = Parameter(0.0);
}

/**
 * Function to evaluate 1D scattering function
 * @param q: q-value
 * @return: function value
 */
double PringlesModel::operator()(double q) {
        double dp[8];
        // Fill parameter array
        // Add the background after averaging
        dp[0] = scale();
        dp[1] = radius();
        dp[2] = thickness();
        dp[3] = alpha();
        dp[4] = beta();
        dp[5] = sld_pringle();
        dp[6] = sld_solvent();
        dp[7] = 0.0;

        // Get the dispersion points for the radius
        vector<WeightPoint> weights_rad;
        radius.get_weights(weights_rad);

        // Get the dispersion points for the thickness
        vector<WeightPoint> weights_thick;
        thickness.get_weights(weights_thick);

        // Get the dispersion points for alpha
        vector<WeightPoint> weights_alpha;
        alpha.get_weights(weights_alpha);

        // Get the dispersion points for beta
        vector<WeightPoint> weights_beta;
        beta.get_weights(weights_beta);

        // Perform the computation, with all weight points
        double sum = 0.0;
        double norm = 0.0;
        double volnorm = 0.0;
        double vol = 0.0;
        double Pi;

        Pi = 4.0 * atan(1.0);

        // Loop over alpha weight points
        for (size_t i = 0; i < weights_alpha.size(); i++) {
                dp[3] = weights_alpha[i].value;

                //Loop over beta weight points
                for (size_t j = 0; j < weights_beta.size(); j++) {
                        dp[4] = weights_beta[j].value;

                        // Loop over thickness weight points
                        for (size_t k = 0; k < weights_thick.size(); k++) {
                                dp[2] = weights_thick[k].value;

                                // Loop over radius weight points
                                for (size_t l = 0; l < weights_rad.size(); l++) {
                                        dp[1] = weights_rad[l].value;
                                        sum += weights_rad[l].weight * weights_thick[k].weight
                                                        * weights_alpha[i].weight * weights_beta[j].weight
                                                        * pringle_form(dp, q);
                                        //Find average volume
                                        vol += weights_rad[l].weight * weights_thick[k].weight * Pi * pow(weights_rad[l].value, 2) * weights_thick[k].value;
                                        volnorm += weights_rad[l].weight * weights_thick[k].weight;
                                        norm +=  weights_rad[l].weight * weights_thick[k].weight * weights_alpha[i].weight * weights_beta[j].weight;

                                }
                        }
                }
        }

        if (vol > 0.0 && norm > 0.0) {
                //normalize by avg volume
                sum = sum * (vol/volnorm);
                return sum/norm + background();
        } else {
                return 0.0;
        }
}

/**
 * Function to evaluate 2D scattering function
 * @param q_x: value of Q along x
 * @param q_y: value of Q along y
 * @return: function value
 */
double PringlesModel::operator()(double qx, double qy) {
        double q = sqrt(qx * qx + qy * qy);
        return (*this).operator()(q);
}
/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the model
 * @param q: q-value
 * @param phi: angle phi
 * @return: function value
 */
double PringlesModel::evaluate_rphi(double q, double phi) {
        return (*this).operator()(q);
}

/**
 * Function to calculate effective radius
 * @return: effective radius value
 */
double PringlesModel::calculate_ER() {
        PringleParameters dp;

        dp.radius     = radius();
        dp.thickness  = thickness();
        double rad_out = 0.0;

        // Perform the computation, with all weight points
        double sum = 0.0;
        double norm = 0.0;

        // Get the dispersion points for the major shell
        vector<WeightPoint> weights_thick;
        thickness.get_weights(weights_thick);

        // Get the dispersion points for the minor shell
        vector<WeightPoint> weights_radius ;
        radius.get_weights(weights_radius);

        // Loop over major shell weight points
        for(int i=0; i< (int)weights_thick.size(); i++) {
                dp.thickness = weights_thick[i].value;
                for(int k=0; k< (int)weights_radius.size(); k++) {
                        dp.radius = weights_radius[k].value;
                        //Note: output of "DiamCyl(dp.thick,dp.radius)" is DIAMETER.
                        sum +=weights_thick[i].weight
                                * weights_radius[k].weight*DiamCyl(dp.thickness,dp.radius)/2.0;
                        norm += weights_thick[i].weight* weights_radius[k].weight;
                }
        }
        if (norm != 0){
                //return the averaged value
                rad_out =  sum/norm;}
        else{
                //return normal value
                //Note: output of "DiamCyl(dp.length,dp.radius)" is DIAMETER.
                rad_out = DiamCyl(dp.thickness,dp.radius)/2.0;}

        return rad_out;
}
/**
 * Function to calculate particle volume/total volume for shape models:
 *    Most case returns 1 but for example for the vesicle model it is
 *    (total volume - core volume)/total volume
 *    (< 1 depending on the thickness).
 * @return: effective radius value
 */
double PringlesModel::calculate_VR() {
        return 1.0;
}

/*
 * Useful work functions start here!
 *
 */

static double pringle_form(double dp[], double q) {

        double Pi;
        int nord = 76, i=0;                     //order of integration
        double uplim, lolim;            //upper and lower integration limits
        double summ, phi, yyy, answer, vcyl;                    //running tally of integration
        double delrho;

        Pi = 4.0 * atan(1.0);
        lolim = 0.0;
        uplim = Pi / 2.0;

        summ = 0.0;                     //initialize integral

        delrho = dp[5] - dp[6] ; //make contrast term

        for (i = 0; i < nord; i++) {
                phi = (Gauss76Z[i] * (uplim - lolim) + uplim + lolim) / 2.0;
                yyy = Gauss76Wt[i] * pringle_kernel(dp, q, phi);
                summ += yyy;
        }

        answer = (uplim - lolim) / 2.0 * summ;

        answer *= delrho*delrho;

    //normalize by cylinder volume
        //vcyl=Pi*dp[1]*dp[1]*dp[2];
        //answer *= vcyl;

    //convert to [cm-1]
        answer *= 1.0e8;

    //Scale by volume fraction
        answer *= dp[0];

        return answer;
}

static double pringle_kernel(double dp[], double q, double phi) {

        double sumterm, sincarg, sincterm, nn, retval;

        sincarg = q * dp[2] * cos(phi) / 2.0; //dp[2] = thickness
        sincterm = pow(sin(sincarg) / sincarg, 2.0);

        //calculate sum term from n = -3 to 3
        sumterm = 0;
        for (nn = -3; nn <= 3; nn = nn + 1) {
                sumterm = sumterm
                                + (pow(pringleC(dp, q, phi, nn), 2.0)
                                                + pow(pringleS(dp, q, phi, nn), 2.0));
        }

        retval = 4.0 * sin(phi) * sumterm * sincterm;

        return retval;

}

static double pringleC(double dp[], double q, double phi, double n) {

        double nord, va, vb, summ;
        double bessargs, cosarg, bessargcb;
        double r, retval, yyy;
        int ii;
        // set up the integration
        // end points and weights
        nord = 76;
        va = 0;
        vb = dp[1]; //radius

        // evaluate at Gauss points
        // remember to index from 0,size-1

        summ = 0.0;             // initialize integral
        ii = 0;
        do {
                // Using 76 Gauss points
                r = (Gauss76Z[ii] * (vb - va) + vb + va) / 2.0;

                bessargs = q * r * sin(phi);
                cosarg = q * r * r * dp[3] * cos(phi);
                bessargcb = q * r * r * dp[4] * cos(phi);

                yyy = Gauss76Wt[ii] * r * cos(cosarg) * jn(n, bessargcb)
                                * jn(2 * n, bessargs);
                summ += yyy;

                ii += 1;
        } while (ii < nord);                    // end of loop over quadrature points
        //
        // calculate value of integral to return

        retval = (vb - va) / 2.0 * summ;

        retval = retval / pow(r, 2.0);

        return retval;
}

static double pringleS(double dp[], double q, double phi, double n) {

        double nord, va, vb, summ;
        double bessargs, sinarg, bessargcb;
        double r, retval, yyy;
        int ii;
        // set up the integration
        // end points and weights
        nord = 76;
        va = 0;
        vb = dp[1]; //radius

        // evaluate at Gauss points
        // remember to index from 0,size-1

        summ = 0.0;             // initialize integral
        ii = 0;
        do {
                // Using 76 Gauss points
                r = (Gauss76Z[ii] * (vb - va) + vb + va) / 2.0;

                bessargs = q * r * sin(phi);
                sinarg = q * r * r * dp[3] * cos(phi);
                bessargcb = q * r * r * dp[4] * cos(phi);

                yyy = Gauss76Wt[ii] * r * sin(sinarg) * jn(n, bessargcb)
                                * jn(2 * n, bessargs);

                summ += yyy;

                ii += 1;
        } while (ii < nord);                    // end of loop over quadrature points
        //
        // calculate value of integral to return

        retval = (vb - va) / 2.0 * summ;

        retval = retval / pow(r, 2.0);

        return retval;
}