/*******************************************************************************
*
* McXtrace, X-ray tracing package
*         Copyright, All rights reserved
*         DTU Physics, Kgs. Lyngby, Denmark
*         Synchrotron SOLEIL, Saint-Aubin, France
*
* Component: SasView_pearl_necklace
*
* %Identification
* Written by: Jose Robledo
* Based on sasmodels from SasView
* Origin: FZJ / DTU / ESS DMSC
*
*
* SasView pearl_necklace model component as sample description.
*
* %Description
*
* SasView_pearl_necklace component, generated from pearl_necklace.c in sasmodels.
*
* Example: 
*  SasView_pearl_necklace(radius, edge_sep, thick_string, num_pearls, sld, sld_string, sld_solvent, 
*     model_scale=1.0, model_abs=0.0, xwidth=0.01, yheight=0.01, zdepth=0.005, R=0, 
*     int target_index=1, target_x=0, target_y=0, target_z=1,
*     focus_xw=0.5, focus_yh=0.5, focus_aw=0, focus_ah=0, focus_r=0, 
*     pd_radius=0.0, pd_thick_string=0.0)
*
* %Parameters
* INPUT PARAMETERS:
* radius: [Ang] ([0, inf]) Mean radius of the chained spheres.
* edge_sep: [Ang] ([0, inf]) Mean separation of chained particles.
* thick_string: [Ang] ([0, inf]) Thickness of the chain linkage.
* num_pearls: [none] ([1, inf]) Number of pearls in the necklace (must be integer).
* sld: [1e-6/Ang^2] ([-inf, inf]) Scattering length density of the chained spheres.
* sld_string: [1e-6/Ang^2] ([-inf, inf]) Scattering length density of the chain linkage.
* sld_solvent: [1e-6/Ang^2] ([-inf, inf]) Scattering length density of the solvent.
* Optional parameters:
* model_abs: [ ] Absorption cross section density at 2200 m/s.
* model_scale: [ ] Global scale factor for scattering kernel. For systems without inter-particle interference, the form factors can be related to the scattering intensity by the particle volume fraction.
* xwidth: [m] ([-inf, inf]) Horiz. dimension of sample, as a width.
* yheight: [m] ([-inf, inf]) vert . dimension of sample, as a height for cylinder/box
* zdepth: [m] ([-inf, inf]) depth of sample
* R: [m] Outer radius of sample in (x,z) plane for cylinder/sphere.
* target_x: [m] relative focus target position.
* target_y: [m] relative focus target position.
* target_z: [m] relative focus target position.
* target_index: [ ] Relative index of component to focus at, e.g. next is +1.
* focus_xw: [m] horiz. dimension of a rectangular area.
* focus_yh: [m], vert. dimension of a rectangular area.
* focus_aw: [deg], horiz. angular dimension of a rectangular area.
* focus_ah: [deg], vert. angular dimension of a rectangular area.
* focus_r: [m] case of circular focusing, focusing radius.
* pd_radius: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_thick_string: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable
*
* %Link
* %End
*******************************************************************************/
DEFINE COMPONENT SasView_pearl_necklace
DEFINITION PARAMETERS ()
SETTING PARAMETERS (
        radius=80.0,
        edge_sep=350.0,
        thick_string=2.5,
        num_pearls=3,
        sld=1.0,
        sld_string=1.0,
        sld_solvent=6.3,
        model_scale=1.0,
        model_abs=0.0,
        xwidth=0.01,
        yheight=0.01,
        zdepth=0.005,
        R=0,
        target_x=0,
        target_y=0,
        target_z=1,
        int target_index=1,
        focus_xw=0.5,
        focus_yh=0.5,
        focus_aw=0,
        focus_ah=0,
        focus_r=0,
        pd_radius=0.0,
        pd_thick_string=0.0)


SHARE %{
%include "sas_kernel_header.c"

/* BEGIN Required header for SASmodel pearl_necklace */
#define HAS_Iq
#define FORM_VOL

#ifndef SAS_HAVE_sas_Si
#define SAS_HAVE_sas_Si

#line 1 "sas_Si"
// integral of sin(x)/x Taylor series approximated to w/i 0.1%
double sas_Si(double x);

    
#pragma acc routine seq
double sas_Si(double x)
{
    if (x >= M_PI*6.2/4.0) {
        const double xxinv = 1./(x*x);
        // Explicitly writing factorial values triples the speed of the calculation
        const double out_cos = (((-720.*xxinv + 24.)*xxinv - 2.)*xxinv + 1.)/x;
        const double out_sin = (((-5040.*xxinv + 120.)*xxinv - 6.)*xxinv + 1)*xxinv;

        double sin_x, cos_x;
        SINCOS(x, sin_x, cos_x);
        return M_PI_2 - cos_x*out_cos - sin_x*out_sin;
    } else {
        const double xx = x*x;
        // Explicitly writing factorial values triples the speed of the calculation
        return (((((-1./439084800.*xx
            + 1./3265920.)*xx
            - 1./35280.)*xx
            + 1./600.)*xx
            - 1./18.)*xx
            + 1.)*x;
    }
}


#endif // SAS_HAVE_sas_Si


#ifndef SAS_HAVE_sas_3j1x_x
#define SAS_HAVE_sas_3j1x_x

#line 1 "sas_3j1x_x"
/**
* Spherical Bessel function 3*j1(x)/x
*
* Used for low q to avoid cancellation error.
* Note that the values differ from sasview ~ 5e-12 rather than 5e-14, but
* in this case it is likely cancellation errors in the original expression
* using double precision that are the source.
*/
double sas_3j1x_x(double q);

// The choice of the number of terms in the series and the cutoff value for
// switching between series and direct calculation depends on the numeric
// precision.
//
// Point where direct calculation reaches machine precision:
//
//   single machine precision eps 3e-8 at qr=1.1 **
//   double machine precision eps 4e-16 at qr=1.1
//
// Point where Taylor series reaches machine precision (eps), where taylor
// series matches direct calculation (cross) and the error at that point:
//
//   prec   n eps  cross  error
//   single 3 0.28  0.4   6.2e-7
//   single 4 0.68  0.7   2.3e-7
//   single 5 1.18  1.2   7.5e-8
//   double 3 0.01  0.03  2.3e-13
//   double 4 0.06  0.1   3.1e-14
//   double 5 0.16  0.2   5.0e-15
//
// ** Note: relative error on single precision starts increase on the direct
// method at qr=1.1, rising from 3e-8 to 5e-5 by qr=1e3.  This should be
// safe for the sans range, with objects of 100 nm supported to a q of 0.1
// while maintaining 5 digits of precision.  For usans/sesans, the objects
// are larger but the q is smaller, so again it should be fine.
//
// See explore/sph_j1c.py for code to explore these ranges.

// Use 4th order series
#if FLOAT_SIZE>4
#define SPH_J1C_CUTOFF 0.1
#else
#define SPH_J1C_CUTOFF 0.7
#endif
#pragma acc routine seq
double sas_3j1x_x(double q)
{
    // 2017-05-18 PAK - support negative q
    if (fabs(q) < SPH_J1C_CUTOFF) {
        const double q2 = q*q;
        return (1.0 + q2*(-3./30. + q2*(3./840. + q2*(-3./45360.))));// + q2*(3./3991680.)))));
    } else {
        double sin_q, cos_q;
        SINCOS(q, sin_q, cos_q);
        return 3.0*(sin_q/q - cos_q)/(q*q);
    }
}


#endif // SAS_HAVE_sas_3j1x_x


#ifndef SAS_HAVE_pearl_necklace
#define SAS_HAVE_pearl_necklace

#line 1 "pearl_necklace"
double form_volume_pearl_necklace(double radius, double edge_sep,
    double thick_string, double fp_num_pearls);
double Iq_pearl_necklace(double q, double radius, double edge_sep,
    double thick_string, double fp_num_pearls, double sld,
    double string_sld, double solvent_sld);

// From Igor library
static double
pearl_necklace_kernel(double q, double radius, double edge_sep, double thick_string,
    int num_pearls, double sld_pearl, double sld_string, double sld_solv)
{
    // number of string segments
    const int num_strings = num_pearls - 1;

    //each masses: contrast * volume
    const double contrast_pearl = sld_pearl - sld_solv;
    const double contrast_string = sld_string - sld_solv;
    const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string;
    const double pearl_vol = M_4PI_3 * radius * radius * radius;
    const double m_string = contrast_string * string_vol;
    const double m_pearl = contrast_pearl * pearl_vol;

    // center to center distance between the neighboring pearls
    const double A_s = edge_sep + 2.0 * radius;

    //sine functions of a pearl
    // Note: lim_(q->0) Si(q*a)/(q*b) = a/b
    // So therefore:
    //    beta = q==0. ? 1.0 : (Si(q*(A_s-radius)) - Si(q*radius))/q_edge;
    //    gamma = q==0. ? 1.0 : Si(q_edge)/q_edge;
    // But there is a 1/(1-sinc) term below which blows up so don't bother
    const double q_edge = q * edge_sep;
    const double beta = (sas_Si(q*(A_s-radius)) - sas_Si(q*radius)) / q_edge;
    const double gamma = sas_Si(q_edge) / q_edge;
    const double psi = sas_3j1x_x(q*radius);

    // Precomputed sinc terms
    const double si = sas_sinx_x(q*A_s);
    const double omsi = 1.0 - si;
    const double pow_si = pown(si, num_pearls);

    // form factor for num_pearls
    const double sss = 2.0*square(m_pearl*psi) * (
        - si * (1.0 - pow_si) / (omsi*omsi)
        + num_pearls / omsi
        - 0.5 * num_pearls
        );

    // form factor for num_strings (like thin rods)
    const double srr = m_string * m_string * (
        - 2.0 * (1.0 - pow_si/si)*beta*beta / (omsi*omsi)
        + 2.0 * num_strings*beta*beta / omsi
        + num_strings * (2.0*gamma - square(sas_sinx_x(q_edge/2.0)))
        );

    // form factor for correlations
    const double srs = 4.0 * m_string * m_pearl * beta * psi * (
        - si * (1.0 - pow_si/si) / (omsi*omsi)
        + num_strings / omsi
        );

    const double form = sss + srr + srs;

    return 1.0e-4 * form;
}

double form_volume_pearl_necklace(double radius, double edge_sep, double thick_string, double fp_num_pearls)
{
    const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls
    const int num_strings = num_pearls - 1;
    const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string;
    const double pearl_vol = M_4PI_3 * radius * radius * radius;
    const double volume = num_strings*string_vol + num_pearls*pearl_vol;

    return volume;
}

static double
radius_from_volume_pearl_necklace(double radius, double edge_sep, double thick_string, double fp_num_pearls)
{
    const double vol_tot = form_volume_pearl_necklace(radius, edge_sep, thick_string, fp_num_pearls);
    return cbrt(vol_tot/M_4PI_3);
}

static double
radius_effective_pearl_necklace(int mode, double radius, double edge_sep, double thick_string, double fp_num_pearls)
{
    switch (mode) {
    default:
    case 1:
        return radius_from_volume_pearl_necklace(radius, edge_sep, thick_string, fp_num_pearls);
    }
}

double Iq_pearl_necklace(double q, double radius, double edge_sep,
    double thick_string, double fp_num_pearls, double sld,
    double string_sld, double solvent_sld)
{
    const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls
    const double form = pearl_necklace_kernel(q, radius, edge_sep,
        thick_string, num_pearls, sld, string_sld, solvent_sld);

    return form;
}


#endif // SAS_HAVE_pearl_necklace



/* END Required header for SASmodel pearl_necklace */
%}
    DECLARE
%{
  double shape;
  double my_a_k;
%}

INITIALIZE
%{
shape=-1;  /* -1:no shape, 0:cyl, 1:box, 2:sphere  */
if (xwidth && yheight && zdepth)
    shape=1;
  else if (R > 0 && yheight)
    shape=0;
  else if (R > 0 && !yheight)
    shape=2;
  if (shape < 0)
    exit(fprintf(stderr, "SasView_model: %s: sample has invalid dimensions.\n"
                         "ERROR     Please check parameter values.\n", NAME_CURRENT_COMP));

  /* now compute target coords if a component index is supplied */
  if (!target_index && !target_x && !target_y && !target_z) target_index=1;
  if (target_index)
  {
    Coords ToTarget;
    ToTarget = coords_sub(POS_A_COMP_INDEX(INDEX_CURRENT_COMP+target_index),POS_A_CURRENT_COMP);
    ToTarget = rot_apply(ROT_A_CURRENT_COMP, ToTarget);
    coords_get(ToTarget, &target_x, &target_y, &target_z);
  }

  if (!(target_x || target_y || target_z)) {
    printf("SasView_model: %s: The target is not defined. Using direct beam (Z-axis).\n",
      NAME_CURRENT_COMP);
    target_z=1;
  }

  /*TODO fix absorption*/
  my_a_k = model_abs; /* assume absorption is given in 1/m */

%}


TRACE
%{
  double l0, l1, k, l_full, l, dl, d_Phi;
  double aim_x=0, aim_y=0, aim_z=1, axis_x, axis_y, axis_z;
  double f, solid_angle, kx_i, ky_i, kz_i, q, qx, qy, qz;
  char intersect=0;

  /* Intersection photon trajectory / sample (sample surface) */
  if (shape == 0){
    intersect = cylinder_intersect(&l0, &l1, x, y, z, kx, ky, kz, R, yheight);}
  else if (shape == 1){
    intersect = box_intersect(&l0, &l1, x, y, z, kx, ky, kz, xwidth, yheight, zdepth);}
  else if (shape == 2){
    intersect = sphere_intersect(&l0, &l1, x, y, z, kx, ky, kz, R);}
  if(intersect)
  {
    if(l0 < 0)
      ABSORB;

    /* Photon enters at l0. */
    k = sqrt(kx*kx + ky*ky + kz*kz);
    l_full = (l1 - l0);          /* Length of full path through sample */
    dl = rand01()*(l1 - l0) + l0;    /* Point of scattering */
    PROP_DL(dl);                     /* Point of scattering */
    l = (dl-l0);                   /* Penetration in sample */

    kx_i=kx;
    ky_i=ky;
    kz_i=kz;
    if ((target_x || target_y || target_z)) {
      aim_x = target_x-x;            /* Vector pointing at target (anal./det.) */
      aim_y = target_y-y;
      aim_z = target_z-z;
    }
    if(focus_aw && focus_ah) {
      randvec_target_rect_angular(&kx, &ky, &kz, &solid_angle,
        aim_x, aim_y, aim_z, focus_aw, focus_ah, ROT_A_CURRENT_COMP);
    } else if(focus_xw && focus_yh) {
      randvec_target_rect(&kx, &ky, &kz, &solid_angle,
        aim_x, aim_y, aim_z, focus_xw, focus_yh, ROT_A_CURRENT_COMP);
    } else {
      randvec_target_circle(&kx, &ky, &kz, &solid_angle, aim_x, aim_y, aim_z, focus_r);
    }
    NORM(kx, ky, kz);
    kx *= k;
    ky *= k;
    kz *= k;
    qx = (kx_i-kx);
    qy = (ky_i-ky);
    qz = (kz_i-kz);
    q = sqrt(qx*qx+qy*qy+qz*qz);
    
    double trace_radius=radius;
    double trace_thick_string=thick_string;
    if ( pd_radius!=0.0 || pd_thick_string!=0.0 ){
    trace_radius = (randnorm()*pd_radius+1.0)*radius;
    trace_thick_string = (randnorm()*pd_thick_string+1.0)*thick_string;
    }

        


    // Sample dependent. Retrieved from SasView./////////////////////
    float Iq_out;
    Iq_out = 1;

    Iq_out = Iq_pearl_necklace(q, trace_radius, edge_sep, trace_thick_string, num_pearls, sld, sld_string, sld_solvent);


    float vol;
    vol = 1;

    // Scale by 1.0E2 [SasView: 1/cm  ->   McXtrace: 1/m]
    Iq_out = model_scale*Iq_out / vol * 1.0E2;

    
    p *= l_full*solid_angle/(4*PI)*Iq_out*exp(-my_a_k*(l+l1));


    SCATTER;
  }
%}

MCDISPLAY
%{

  if (shape == 0) {	/* cylinder */
    circle("xz", 0,  yheight/2.0, 0, R);
    circle("xz", 0, -yheight/2.0, 0, R);
    line(-R, -yheight/2.0, 0, -R, +yheight/2.0, 0);
    line(+R, -yheight/2.0, 0, +R, +yheight/2.0, 0);
    line(0, -yheight/2.0, -R, 0, +yheight/2.0, -R);
    line(0, -yheight/2.0, +R, 0, +yheight/2.0, +R);
  }
  else if (shape == 1) { 	/* box */
    double xmin = -0.5*xwidth;
    double xmax =  0.5*xwidth;
    double ymin = -0.5*yheight;
    double ymax =  0.5*yheight;
    double zmin = -0.5*zdepth;
    double zmax =  0.5*zdepth;
    multiline(5, xmin, ymin, zmin,
                 xmax, ymin, zmin,
                 xmax, ymax, zmin,
                 xmin, ymax, zmin,
                 xmin, ymin, zmin);
    multiline(5, xmin, ymin, zmax,
                 xmax, ymin, zmax,
                 xmax, ymax, zmax,
                 xmin, ymax, zmax,
                 xmin, ymin, zmax);
    line(xmin, ymin, zmin, xmin, ymin, zmax);
    line(xmax, ymin, zmin, xmax, ymin, zmax);
    line(xmin, ymax, zmin, xmin, ymax, zmax);
    line(xmax, ymax, zmin, xmax, ymax, zmax);
  }
  else if (shape == 2) {	/* sphere */
    circle("xy", 0,  0.0, 0, R);
    circle("xz", 0,  0.0, 0, R);
    circle("yz", 0,  0.0, 0, R);
  }
%}
END

