/*******************************************************************************
*
* McXtrace, X-ray tracing package
*         Copyright, All rights reserved
*         DTU Physics, Kgs. Lyngby, Denmark
*         Synchrotron SOLEIL, Saint-Aubin, France
*
* Component: SasView_rectangular_prism
*
* %Identification
* Written by: Jose Robledo
* Based on sasmodels from SasView
* Origin: FZJ / DTU / ESS DMSC
*
*
* SasView rectangular_prism model component as sample description.
*
* %Description
*
* SasView_rectangular_prism component, generated from rectangular_prism.c in sasmodels.
*
* Example: 
*  SasView_rectangular_prism_aniso(sld, sld_solvent, length_a, b2a_ratio, c2a_ratio, theta, Phi, Psi, 
*     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_length_a=0.0, pd_theta=0.0, pd_Phi=0.0, pd_Psi=0.0)
*
* %Parameters
* INPUT PARAMETERS:
* sld: [1e-6/Ang^2] ([-inf, inf]) Parallelepiped scattering length density.
* sld_solvent: [1e-6/Ang^2] ([-inf, inf]) Solvent scattering length density.
* length_a: [Ang] ([0, inf]) Shorter side of the parallelepiped.
* b2a_ratio: [] ([0, inf]) Ratio sides b/a.
* c2a_ratio: [] ([0, inf]) Ratio sides c/a.
* 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_length_a: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_theta: [] (0,360) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_Phi: [] (0,360) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_Psi: [] (0,360) defined as (dx/x), where x is de mean value and dx the standard devition of the variable
*
* %Link
* %End
*******************************************************************************/
DEFINE COMPONENT SasView_rectangular_prism_aniso

SETTING PARAMETERS (
        sld=6.3,
        sld_solvent=1,
        length_a=35,
        b2a_ratio=1,
        c2a_ratio=1,
        theta=0,
        Phi=0,
        Psi=0,
        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_length_a=0.0,
        pd_theta=0.0,
        pd_Phi=0.0,
        pd_Psi=0.0)


SHARE %{
%include "sas_kernel_header.c"

/* BEGIN Required header for SASmodel rectangular_prism */
#define HAS_Iqabc
#define FORM_VOL

#ifndef SAS_HAVE_gauss76
#define SAS_HAVE_gauss76

#line 1 "gauss76"
// Created by Andrew Jackson on 4/23/07

 #ifdef GAUSS_N
 # undef GAUSS_N
 # undef GAUSS_Z
 # undef GAUSS_W
 #endif
 #define GAUSS_N 76
 #define GAUSS_Z Gauss76Z
 #define GAUSS_W Gauss76Wt

// Gaussians
constant double Gauss76Wt[76] = {
	.00126779163408536,		//0
	.00294910295364247,
	.00462793522803742,
	.00629918049732845,
	.00795984747723973,
	.00960710541471375,
	.0112381685696677,
	.0128502838475101,
	.0144407317482767,
	.0160068299122486,
	.0175459372914742,		//10
	.0190554584671906,
	.020532847967908,
	.0219756145344162,
	.0233813253070112,
	.0247476099206597,
	.026072164497986,
	.0273527555318275,
	.028587223650054,
	.029773487255905,
	.0309095460374916,		//20
	.0319934843404216,
	.0330234743977917,
	.0339977794120564,
	.0349147564835508,
	.0357728593807139,
	.0365706411473296,
	.0373067565423816,
	.0379799643084053,
	.0385891292645067,
	.0391332242205184,		//30
	.0396113317090621,
	.0400226455325968,
	.040366472122844,
	.0406422317102947,
	.0408494593018285,
	.040987805464794,
	.0410570369162294,
	.0410570369162294,
	.040987805464794,
	.0408494593018285,		//40
	.0406422317102947,
	.040366472122844,
	.0400226455325968,
	.0396113317090621,
	.0391332242205184,
	.0385891292645067,
	.0379799643084053,
	.0373067565423816,
	.0365706411473296,
	.0357728593807139,		//50
	.0349147564835508,
	.0339977794120564,
	.0330234743977917,
	.0319934843404216,
	.0309095460374916,
	.029773487255905,
	.028587223650054,
	.0273527555318275,
	.026072164497986,
	.0247476099206597,		//60
	.0233813253070112,
	.0219756145344162,
	.020532847967908,
	.0190554584671906,
	.0175459372914742,
	.0160068299122486,
	.0144407317482767,
	.0128502838475101,
	.0112381685696677,
	.00960710541471375,		//70
	.00795984747723973,
	.00629918049732845,
	.00462793522803742,
	.00294910295364247,
	.00126779163408536		//75 (indexed from 0)
};

constant double Gauss76Z[76] = {
	-.999505948362153,		//0
	-.997397786355355,
	-.993608772723527,
	-.988144453359837,
	-.981013938975656,
	-.972229228520377,
	-.961805126758768,
	-.949759207710896,
	-.936111781934811,
	-.92088586125215,
	-.904107119545567,		//10
	-.885803849292083,
	-.866006913771982,
	-.844749694983342,
	-.822068037328975,
	-.7980001871612,
	-.77258672828181,
	-.74587051350361,
	-.717896592387704,
	-.688712135277641,
	-.658366353758143,		//20
	-.626910417672267,
	-.594397368836793,
	-.560882031601237,
	-.526420920401243,
	-.491072144462194,
	-.454895309813726,
	-.417951418780327,
	-.380302767117504,
	-.342012838966962,
	-.303146199807908,		//30
	-.263768387584994,
	-.223945802196474,
	-.183745593528914,
	-.143235548227268,
	-.102483975391227,
	-.0615595913906112,
	-.0205314039939986,
	.0205314039939986,
	.0615595913906112,
	.102483975391227,			//40
	.143235548227268,
	.183745593528914,
	.223945802196474,
	.263768387584994,
	.303146199807908,
	.342012838966962,
	.380302767117504,
	.417951418780327,
	.454895309813726,
	.491072144462194,		//50
	.526420920401243,
	.560882031601237,
	.594397368836793,
	.626910417672267,
	.658366353758143,
	.688712135277641,
	.717896592387704,
	.74587051350361,
	.77258672828181,
	.7980001871612,	//60
	.822068037328975,
	.844749694983342,
	.866006913771982,
	.885803849292083,
	.904107119545567,
	.92088586125215,
	.936111781934811,
	.949759207710896,
	.961805126758768,
	.972229228520377,		//70
	.981013938975656,
	.988144453359837,
	.993608772723527,
	.997397786355355,
	.999505948362153		//75
};


#pragma acc declare copyin(Gauss76Wt[0:76], Gauss76Z[0:76])

#endif // SAS_HAVE_gauss76


#ifndef SAS_HAVE_rectangular_prism
#define SAS_HAVE_rectangular_prism

#line 1 "rectangular_prism"
static double
form_volume_rectangular_prism(double length_a, double b2a_ratio, double c2a_ratio)
{
    return length_a * (length_a*b2a_ratio) * (length_a*c2a_ratio);
}

static double
radius_from_excluded_volume_rectangular_prism(double length_a, double b2a_ratio, double c2a_ratio)
{
    double const r_equiv   = sqrt(length_a*length_a*b2a_ratio/M_PI);
    double const length_c  = c2a_ratio*length_a;
    return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length_c + (r_equiv + length_c)*(M_PI*r_equiv + length_c)));
}

static double
radius_effective_rectangular_prism(int mode, double length_a, double b2a_ratio, double c2a_ratio)
{
    switch (mode) {
    default:
    case 1: // equivalent cylinder excluded volume
        return radius_from_excluded_volume_rectangular_prism(length_a,b2a_ratio,c2a_ratio);
    case 2: // equivalent volume sphere
        return cbrt(cube(length_a)*b2a_ratio*c2a_ratio/M_4PI_3);
    case 3: // half length_a
        return 0.5 * length_a;
    case 4: // half length_b
        return 0.5 * length_a*b2a_ratio;
    case 5: // half length_c
        return 0.5 * length_a*c2a_ratio;
    case 6: // equivalent circular cross-section
        return length_a*sqrt(b2a_ratio/M_PI);
    case 7: // half ab diagonal
        return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio)));
    case 8: // half diagonal
        return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio) + square(c2a_ratio)));
    }
}

static double
Iq_rectangular_prism(double q,
    double sld,
    double solvent_sld,
    double length_a,
    double b2a_ratio,
    double c2a_ratio)
{
    const double length_b = length_a * b2a_ratio;
    const double length_c = length_a * c2a_ratio;
    const double a_half = 0.5 * length_a;
    const double b_half = 0.5 * length_b;
    const double c_half = 0.5 * length_c;

   //Integration limits to use in Gaussian quadrature
    const double v1a = 0.0;
    const double v1b = M_PI_2;  //theta integration limits
    const double v2a = 0.0;
    const double v2b = M_PI_2;  //phi integration limits

    double outer_sum = 0.0;
    for(int i=0; i<GAUSS_N; i++) {
        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
        double sin_theta, cos_theta;
        SINCOS(theta, sin_theta, cos_theta);

        const double termC = sas_sinx_x(q * c_half * cos_theta);

        double inner_sum = 0.0;
        for(int j=0; j<GAUSS_N; j++) {
            double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
            double sin_phi, cos_phi;
            SINCOS(phi, sin_phi, cos_phi);

            // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0
            const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi);
            const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi);
            const double AP = termA * termB * termC;
            inner_sum += GAUSS_W[j] * AP * AP;
        }
        inner_sum = 0.5 * (v2b-v2a) * inner_sum;
        outer_sum += GAUSS_W[i] * inner_sum * sin_theta;
    }

    double answer = 0.5*(v1b-v1a)*outer_sum;

    // Normalize by Pi (Eqn. 16).
    // The term (ABC)^2 does not appear because it was introduced before on
    // the definitions of termA, termB, termC.
    // The factor 2 appears because the theta integral has been defined between
    // 0 and pi/2, instead of 0 to pi.
    answer /= M_PI_2; //Form factor P(q)

    // Multiply by contrast^2 and volume^2
    const double volume = length_a * length_b * length_c;
    answer *= square((sld-solvent_sld)*volume);

    // Convert from [1e-12 A-1] to [cm-1]
    answer *= 1.0e-4;

    return answer;
}

static void
Fq_rectangular_prism(double q,
    double *F1,
    double *F2,
    double sld,
    double solvent_sld,
    double length_a,
    double b2a_ratio,
    double c2a_ratio)
{
    const double length_b = length_a * b2a_ratio;
    const double length_c = length_a * c2a_ratio;
    const double a_half = 0.5 * length_a;
    const double b_half = 0.5 * length_b;
    const double c_half = 0.5 * length_c;

   //Integration limits to use in Gaussian quadrature
    const double v1a = 0.0;
    const double v1b = M_PI_2;  //theta integration limits
    const double v2a = 0.0;
    const double v2b = M_PI_2;  //phi integration limits

    double outer_sum_F1 = 0.0;
    double outer_sum_F2 = 0.0;
    for(int i=0; i<GAUSS_N; i++) {
        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
        double sin_theta, cos_theta;
        SINCOS(theta, sin_theta, cos_theta);

        const double termC = sas_sinx_x(q * c_half * cos_theta);

        double inner_sum_F1 = 0.0;
        double inner_sum_F2 = 0.0;
        for(int j=0; j<GAUSS_N; j++) {
            double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
            double sin_phi, cos_phi;
            SINCOS(phi, sin_phi, cos_phi);

            // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0
            const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi);
            const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi);
            const double AP = termA * termB * termC;
            inner_sum_F1 += GAUSS_W[j] * AP;
            inner_sum_F2 += GAUSS_W[j] * AP * AP;
        }
        inner_sum_F1 = 0.5 * (v2b-v2a) * inner_sum_F1;
        inner_sum_F2 = 0.5 * (v2b-v2a) * inner_sum_F2;
        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta;
        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta;
    }

    outer_sum_F1 *= 0.5*(v1b-v1a);
    outer_sum_F2 *= 0.5*(v1b-v1a);

    // Normalize by Pi (Eqn. 16).
    // The term (ABC)^2 does not appear because it was introduced before on
    // the definitions of termA, termB, termC.
    // The factor 2 appears because the theta integral has been defined between
    // 0 and pi/2, instead of 0 to pi.
    outer_sum_F1 /= M_PI_2;
    outer_sum_F2 /= M_PI_2;

    // Multiply by contrast and volume
    const double s = (sld-solvent_sld) * (length_a * length_b * length_c);

    // Convert from [1e-12 A-1] to [cm-1]
    *F1 = 1e-2 * s * outer_sum_F1;
    *F2 = 1e-4 * s * s * outer_sum_F2;
}


static double
Iqabc_rectangular_prism(double qa, double qb, double qc,
    double sld,
    double solvent_sld,
    double length_a,
    double b2a_ratio,
    double c2a_ratio)
{
    const double length_b = length_a * b2a_ratio;
    const double length_c = length_a * c2a_ratio;
    const double a_half = 0.5 * length_a;
    const double b_half = 0.5 * length_b;
    const double c_half = 0.5 * length_c;

    // Amplitude AP from eqn. (13)
    const double termA = sas_sinx_x(qa * a_half);
    const double termB = sas_sinx_x(qb * b_half);
    const double termC = sas_sinx_x(qc * c_half);
    const double AP = termA * termB * termC;

    // Multiply by contrast and volume
    const double s = (sld-solvent_sld) * (length_a * length_b * length_c);

    // Convert from [1e-12 A-1] to [cm-1]
    return 1.0e-4 * square(s * AP);
}


#endif // SAS_HAVE_rectangular_prism



/* END Required header for SASmodel rectangular_prism */
%}
    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_length_a=length_a;
    if ( pd_length_a!=0.0 ){
    trace_length_a = (randnorm()*pd_length_a+1.0)*length_a;
    }

        
    double trace_theta=theta, dtheta=0.0;
    double trace_Phi=Phi, dPhi=0.0;
    double trace_Psi=Psi, dPsi=0.0;
    if ( pd_theta!=0.0 || pd_Phi!=0.0 || pd_Psi!=0.0 ){
    trace_theta = ((rand01()-0.5)*pd_theta + 1.0)*theta;
    dtheta = trace_theta-theta;
    trace_Phi = ((rand01()-0.5)*pd_Phi + 1.0)*Phi;
    dPhi = trace_Phi-Phi;
    trace_Psi = ((rand01()-0.5)*pd_Psi + 1.0)*Psi;
    dPsi = trace_Psi-Psi;
    }


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

    double qa=0.0, qb=0.0, qc=0.0;
    QABCRotation rotation;

    qabc_rotation(&rotation, trace_theta, trace_Phi, trace_Psi, dtheta, dPhi, dPsi);
    qabc_apply(&rotation, qx, qy, &qa, &qb, &qc);
    Iq_out = Iqabc_rectangular_prism(qa, qb, qc, sld, sld_solvent, trace_length_a, b2a_ratio, c2a_ratio  );


    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