source: sasview/sansmodels/src/sans/models/c_extensions/sc.c @ 30ccad1

/*
 * Scattering model for a SC_ParaCrystal
 */
#include "sc.h"
#include "libSphere.h"
#include <math.h>


/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the SC_ParaCrystal
 * @param q: q-value
 * @return: function value
 */
double sc_analytical_1D(SCParameters *pars, double q) {
        double dp[7];
        double result;

        dp[0] = pars->scale;
        dp[1] = pars->dnn;
        dp[2] = pars->d_factor;
        dp[3] = pars->radius;
        dp[4] = pars->sldSph;
        dp[5] = pars->sldSolv;
        dp[6] = pars->background;

        result = SC_ParaCrystal(dp, q);
        // This FIXES a singualrity the kernel in libigor.
        if ( result == INFINITY || result == NAN){
                result = pars->background;
        }
        return result;
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the SC_ParaCrystal
 * @param q: q-value
 * @return: function value
 */
double sc_analytical_2DXY(SCParameters *pars, double qx, double qy){
        double q;
        q = sqrt(qx*qx+qy*qy);
        return sc_analytical_2D_scaled(pars, q, qx/q, qy/q);
}

double sc_analytical_2D(SCParameters *pars, double q, double phi) {
        return sc_analytical_2D_scaled(pars, q, cos(phi), sin(phi));
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the SCCrystalModel
 * @param q: q-value
 * @param q_x: q_x / q
 * @param q_y: q_y / q
 * @return: function value
 */
double sc_analytical_2D_scaled(SCParameters *pars, double q, double q_x, double q_y) {
        double a3_x, a3_y, a3_z, a2_x, a2_y, a1_x, a1_y, a1_z;
        double q_z;
        double alpha, vol, cos_val_a3, cos_val_a2, cos_val_a1;
        double a1_dot_q, a2_dot_q,a3_dot_q;
        double answer;
        double Pi = 4.0*atan(1.0);
        double aa, Da, qDa_2, latticeScale, Zq;

        double dp[5];
        dp[0] = 1.0;
        dp[1] = pars->radius;
        dp[2] = pars->sldSph;
        dp[3] = pars->sldSolv;
        dp[4] = 0.0;

        //convert angle degree to radian
        double theta = pars->theta * Pi/180.0;
        double phi = pars->phi * Pi/180.0;
        double psi = pars->psi * Pi/180.0;

        aa = pars->dnn;
        Da = pars->d_factor*aa;
        qDa_2 = pow(q*Da,2.0);

        latticeScale = (4.0/3.0)*Pi*(dp[1]*dp[1]*dp[1])/pow(aa,3.0);
        /// Angles here are respect to detector coordinate instead of against q coordinate(PRB 36, 3, 1754)
    // a3 axis orientation
    a3_x = sin(theta) * cos(phi);//negative sign here???
    a3_y = sin(theta) * sin(phi);
    a3_z = cos(theta);

    // q vector
    q_z = 0.0;

    // Compute the angle btw vector q and the a3 axis
    cos_val_a3 = a3_x*q_x + a3_y*q_y + a3_z*q_z;
    alpha = acos(cos_val_a3);
    //alpha = acos(cos_val_a3);
    a3_dot_q = aa*q*cos_val_a3;
    // a1 axis orientation
    a1_x = sin(psi);
    a1_y = cos(psi);

    cos_val_a1 = a1_x*q_x + a1_y*q_y;
    a1_dot_q = aa*q*cos_val_a1*sin(alpha);

    // a2 axis orientation
    a2_x = sqrt(1.0-sin(theta)*cos(phi))*cos(psi);
    a2_y = sqrt(1.0-sin(theta)*cos(phi))*sin(psi);
    // a2 axis
    cos_val_a2 =  sin(acos(cos_val_a1));//a2_x*q_x + a2_y*q_y;
    a2_dot_q = aa*q*cos_val_a2*sin(alpha);

    // The following test should always pass
    if (fabs(cos_val_a3)>1.0) {
        printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n");
        return 0;
    }
    // Call Zq=Z1*Z2*Z3
    Zq = (1.0-exp(-qDa_2))/(1.0-2.0*exp(-0.5*qDa_2)*cos(a1_dot_q)+exp(-qDa_2));
    Zq = Zq * (1.0-exp(-qDa_2))/(1.0-2.0*exp(-0.5*qDa_2)*cos(a2_dot_q)+exp(-qDa_2));
    Zq = Zq * (1.0-exp(-qDa_2))/(1.0-2.0*exp(-0.5*qDa_2)*cos(a3_dot_q)+exp(-qDa_2));

        // Use SphereForm directly from libigor
        answer = SphereForm(dp,q)*Zq;

        //consider scales
        answer *= latticeScale * pars->scale;

        // This FIXES a singualrity the kernel in libigor.
        if ( answer == INFINITY || answer == NAN){
                answer = 0.0;
        }

        // add background
        answer += pars->background;

        return answer;
}