Enhanced Ellipsoid Models for SasView - core_shell_ellipsoid_high_res.c

    
// Converted from Igor function gfn4, using the same pattern as ellipsoid
// for evaluating the parts of the integral.
//     FUNCTION gfn4:    CONTAINS F(Q,A,B,MU)**2  AS GIVEN
//                       BY (53) & (58-59) IN CHEN AND
//                       KOTLARCHYK REFERENCE
//
//       <OBLATE ELLIPSOID>
static double
_cs_ellipsoid_kernel(double qab, double qc,
    double equat_core, double polar_core,
    double equat_shell, double polar_shell,
    double sld_core_shell, double sld_shell_solvent)
{
    const double qr_core = sqrt(square(equat_core*qab) + square(polar_core*qc));
    const double si_core = sas_3j1x_x(qr_core);
    const double volume_core = M_4PI_3*equat_core*equat_core*polar_core;
    const double fq_core = si_core*volume_core*sld_core_shell;

    const double qr_shell = sqrt(square(equat_shell*qab) + square(polar_shell*qc));
    const double si_shell = sas_3j1x_x(qr_shell);
    const double volume_shell = M_4PI_3*equat_shell*equat_shell*polar_shell;
    const double fq_shell = si_shell*volume_shell*sld_shell_solvent;

    return fq_core + fq_shell;
}

static double
form_volume(double radius_equat_core,
    double x_core,
    double thick_shell,
    double x_polar_shell)
{
    const double equat_shell = radius_equat_core + thick_shell;
    const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;
    double vol = M_4PI_3*equat_shell*equat_shell*polar_shell;
    return vol;
}

static double
radius_from_volume(double radius_equat_core, double x_core, double thick_shell, double x_polar_shell)
{
    const double volume_ellipsoid = form_volume(radius_equat_core, x_core, thick_shell, x_polar_shell);
    return cbrt(volume_ellipsoid/M_4PI_3);
}

static double
radius_from_curvature(double radius_equat_core, double x_core, double thick_shell, double x_polar_shell)
{
    // Trivial cases
    if (1.0 == x_core && 1.0 == x_polar_shell) return radius_equat_core + thick_shell;
    if ((radius_equat_core + thick_shell)*(radius_equat_core*x_core + thick_shell*x_polar_shell) == 0.)  return 0.;

    // see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449
    const double radius_equat_tot = radius_equat_core + thick_shell;
    const double radius_polar_tot = radius_equat_core*x_core + thick_shell*x_polar_shell;
    const double ratio = (radius_polar_tot < radius_equat_tot
                          ? radius_polar_tot / radius_equat_tot
                          : radius_equat_tot / radius_polar_tot);
    const double e1 = sqrt(1.0 - ratio*ratio);
    const double b1 = 1.0 + asin(e1) / (e1 * ratio);
    const double bL = (1.0 + e1) / (1.0 - e1);
    const double b2 = 1.0 + 0.5 * ratio * ratio / e1 * log(bL);
    const double delta = 0.75 * b1 * b2;
    const double ddd = 2.0 * (delta + 1.0) * radius_polar_tot * radius_equat_tot * radius_equat_tot;
    return 0.5 * cbrt(ddd);
}

static double
radius_effective(int mode, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell)
{
    const double radius_equat_tot = radius_equat_core + thick_shell;
    const double radius_polar_tot = radius_equat_core*x_core + thick_shell*x_polar_shell;

    switch (mode) {
    default:
    case 1: // average outer curvature
        return radius_from_curvature(radius_equat_core, x_core, thick_shell, x_polar_shell);
    case 2: // equivalent volume sphere
        return radius_from_volume(radius_equat_core, x_core, thick_shell, x_polar_shell);
    case 3: // min outer radius
        return (radius_polar_tot < radius_equat_tot ? radius_polar_tot : radius_equat_tot);
    case 4: // max outer radius
        return (radius_polar_tot > radius_equat_tot ? radius_polar_tot : radius_equat_tot);
    }
}


static void
integrand_core_shell_ellipsoid(
    const double x,
    const double q,
    const double radius_equat_core,
    const double polar_core,
    const double equat_shell,
    const double polar_shell,
    const double sld_core_shell,
    const double sld_shell_solvent,
    double* res1,
    double* res2,
    int n,
    int i){

    double sin_theta, cos_theta;
    get_sin_x(n, i, &sin_theta);
    get_cos_x(n, i, &cos_theta);

    const double qab = q*sin_theta;
    const double qc = q*cos_theta;
    const double fq = _cs_ellipsoid_kernel(q*sin_theta, q*cos_theta,
            radius_equat_core, polar_core,
            equat_shell, polar_shell,
            sld_core_shell, sld_shell_solvent);
    *res1 = fq * sin_theta;
    *res2 = fq * fq * sin_theta;
}

void integrate_core_shell_ellipsoid(
    const double a,
    const double b,
    const double q,
    const double radius_equat_core,
    const double polar_core,
    const double equat_shell,
    const double polar_shell,
    const double sld_core_shell,
    const double sld_shell_solvent,
    double* res1,
    double* res2
    ){


    const double A = radius_equat_core;
    const double B = polar_core;
    const double C = equat_shell;
    const double D = polar_shell;

    int expo = (int)(eval_poly(log2m(max(limits[0][0],min(limits[0][1], q))), log2m(max(limits[1][0],min(limits[1][1], A))), log2m(max(limits[2][0],min(limits[2][1], B))), log2m(max(limits[3][0],min(limits[3][1], C))), log2m(max(limits[4][0],min(limits[4][1], D)))) + 1);
    int n = (int)(pow(2, max(1, min(15, expo))));

    double *xg, *wg;
    get_gauss_points(n, &xg, &wg);

    // Perform the integration
    *res1 = 0;
    *res2 = 0;

    for (int i = 0; i < n; i++){
        double t1, t2;
        integrand_core_shell_ellipsoid(a + (b - a) * 0.5 * (xg[i] + 1), q, radius_equat_core, polar_core, equat_shell, polar_shell, sld_core_shell, sld_shell_solvent, &t1, &t2, n, i);
        *res1 += t1 * wg[i];
        *res2 += t2 * wg[i];
    }

    *res1 *= (b - a) * 0.5;
    *res2 *= (b - a) * 0.5;


}


static void
Fq(double q,
    double *F1,
    double *F2,
    double radius_equat_core,
    double x_core,
    double thick_shell,
    double x_polar_shell,
    double core_sld,
    double shell_sld,
    double solvent_sld)
{
    const double sld_core_shell = core_sld - shell_sld;
    const double sld_shell_solvent = shell_sld - solvent_sld;

    const double polar_core = radius_equat_core*x_core;
    const double equat_shell = radius_equat_core + thick_shell;
    const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;


    double total_F1, total_F2;
    integrate_core_shell_ellipsoid(0, M_PI_2, q, radius_equat_core, polar_core, equat_shell, polar_shell, sld_core_shell, sld_shell_solvent, &total_F1, &total_F2);

    // convert to [cm-1]
    *F1 = 1.0e-2 * total_F1;
    *F2 = 1.0e-4 * total_F2;
}


static double
Iqac(double qab, double qc,
    double radius_equat_core,
    double x_core,
    double thick_shell,
    double x_polar_shell,
    double core_sld,
    double shell_sld,
    double solvent_sld)
{
    const double sld_core_shell = core_sld - shell_sld;
    const double sld_shell_solvent = shell_sld - solvent_sld;

    const double polar_core = radius_equat_core*x_core;
    const double equat_shell = radius_equat_core + thick_shell;
    const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;

    double fq = _cs_ellipsoid_kernel(qab, qc,
                  radius_equat_core, polar_core,
                  equat_shell, polar_shell,
                  sld_core_shell, sld_shell_solvent);

    //convert to [cm-1]
    return 1.0e-4 * fq * fq;
}
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