source: sasview/sansmodels/src/sans/models/c_extensions/capcyl.c @ 7a8faf8

/*
 * Scattering model for a Capped Cylinder
 */
#include "capcyl.h"
#include <math.h>
#include "GaussWeights.h"
#include "libCylinder.h"

/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the CappedCylinder
 * @param q: q-value
 * @return: function value
 */
double capcyl_analytical_1D(CapCylParameters *pars, double q) {
        double dp[7];
        double result;

        dp[0] = pars->scale;
        dp[1] = pars->rad_cyl;
        dp[2] = pars->len_cyl;
        dp[3] = pars->rad_cap;
        dp[4] = pars->sld_capcyl;
        dp[5] = pars->sld_solv;
        dp[6] = pars->background;

        result = CappedCylinder(dp, q);
        // Make Sure it never goes to inf/nan.
        if ( result == INFINITY || result == NAN){
                result = pars->background;
        }
        return result;
}


double capcyl2d_kernel(double dp[], double q, double alpha) {
        int i,j;
        double Pi;
        double scale,contr,bkg,sldc,slds;
        double len,rad,hDist,endRad;
        int nordj=76;
        double zi=alpha,yyy,answer;                     //running tally of integration
        double summj,vaj,vbj,zij;                       //for the inner integration
        double arg1,arg2,inner,be;


        scale = dp[0];
        rad = dp[1];
        len = dp[2];
        endRad = dp[3];
        sldc = dp[4];
        slds = dp[5];
        bkg = dp[6];

        hDist = -1.0*sqrt(fabs(endRad*endRad-rad*rad));         //by definition for this model

        contr = sldc-slds;

        Pi = 4.0*atan(1.0);
        vaj = -1.0*hDist/endRad;
        vbj = 1.0;              //endpoints of inner integral

        summj=0.0;

        for(j=0;j<nordj;j++) {
                //20 gauss points for the inner integral
                zij = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0;                //the "t" dummy
                yyy = Gauss76Wt[j] * ConvLens_kernel(dp,q,zij,zi);              //uses the same Kernel as the Dumbbell, here L>0
                summj += yyy;
        }
        //now calculate the value of the inner integral
        inner = (vbj-vaj)/2.0*summj;
        inner *= 4.0*Pi*endRad*endRad*endRad;

        //now calculate outer integrand
        arg1 = q*len/2.0*cos(zi);
        arg2 = q*rad*sin(zi);
        yyy = inner;

        if(arg2 == 0) {
                be = 0.5;
        } else {
                be = NR_BessJ1(arg2)/arg2;
        }

        if(arg1 == 0.0) {               //limiting value of sinc(0) is 1; sinc is not defined in math.h
                yyy += Pi*rad*rad*len*2.0*be;
        } else {
                yyy += Pi*rad*rad*len*sin(arg1)/arg1*2.0*be;
        }
        yyy *= yyy;   //sin(zi);
        answer = yyy;


        answer /= Pi*rad*rad*len + 2.0*Pi*(2.0*endRad*endRad*endRad/3.0+endRad*endRad*hDist-hDist*hDist*hDist/3.0);             //divide by volume
        answer *= 1.0e8;                //convert to cm^-1
        answer *= contr*contr;
        answer *= scale;
        answer += bkg;

        return answer;
}


/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the BarBell
 * @param q: q-value
 * @return: function value
 */
double capcyl_analytical_2DXY(CapCylParameters *pars, double qx, double qy){
        double q;
        q = sqrt(qx*qx+qy*qy);
        return capcyl_analytical_2D_scaled(pars, q, qx/q, qy/q);
}

double capcyl_analytical_2D(CapCylParameters *pars, double q, double phi) {
        return capcyl_analytical_2D_scaled(pars, q, cos(phi), sin(phi));
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the BarBell
 * @param q: q-value
 * @param q_x: q_x / q
 * @param q_y: q_y / q
 * @return: function value
 */
double capcyl_analytical_2D_scaled(CapCylParameters *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;
        double dp[7];

        dp[0] = pars->scale;
        dp[1] = pars->rad_cyl;
        dp[2] = pars->len_cyl;
        dp[3] = pars->rad_cap;
        dp[4] = pars->sld_capcyl;
        dp[5] = pars->sld_solv;
        dp[6] = pars->background;

        //convert angle degree to radian
        double pi = 4.0*atan(1.0);
        double theta = pars->theta * pi/180.0;
        double phi = pars->phi * pi/180.0;


        //double Pi = 4.0*atan(1.0);
    // Cylinder orientation
    cyl_x = sin(theta) * cos(phi);
    cyl_y = sin(theta) * sin(phi);
    cyl_z = cos(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 );

        // Call the IGOR library function to get the kernel
        answer = capcyl2d_kernel(dp, q, alpha)/sin(alpha);


        return answer;

}