/**
 * Scattering model for a sphere
 */

#include <math.h>
#include "refl.h"
#include <stdio.h>
#include <stdlib.h>

#define lamda 4.62

typedef struct {
	double re;
	double im;
} complex;

typedef struct {
	complex a;
	complex b;
	complex c;
	complex d;
} matrix;

complex cassign(real, imag)
	double real, imag;
{
	complex x;
	x.re = real;
	x.im = imag;
	return x;
}


complex cadd(x,y)
	complex x,y;
{
	complex z;
	z.re = x.re + y.re;
	z.im = x.im + y.im;
	return z;
}

complex rcmult(x,y)
	double x;
    complex y;
{
	complex z;
	z.re = x*y.re;
	z.im = x*y.im;
	return z;
}

complex csub(x,y)
	complex x,y;
{
	complex z;
	z.re = x.re - y.re;
	z.im = x.im - y.im;
	return z;
}


complex cmult(x,y)
	complex x,y;
{
	complex z;
	z.re = x.re*y.re - x.im*y.im;
	z.im = x.re*y.im + x.im*y.re;
	return z;
}

complex cdiv(x,y)
	complex x,y;
{
	complex z;
	z.re = (x.re*y.re + x.im*y.im)/(y.re*y.re + y.im*y.im);
	z.im = (x.im*y.re - x.re*y.im)/(y.re*y.re + y.im*y.im);
	return z;
}

complex cexp(b)
	complex b;
{
	complex z;
	double br,bi;
	br=b.re;
	bi=b.im;
	z.re = exp(br)*cos(bi);
	z.im = exp(br)*sin(bi);
	return z;
}


complex csqrt(z)   /* see Schaum`s Math Handbook p. 22, 6.6 and 6.10 */
	complex z;
{
	complex c;
	double zr,zi,x,y,r,w;

	zr=z.re;
	zi=z.im;

	if (zr==0.0 && zi==0.0)
	{
    c.re=0.0;
	c.im=0.0;
    return c;
	}
	else
	{
		x=fabs(zr);
		y=fabs(zi);
		if (x>y)
		{
			r=y/x;
			w=sqrt(x)*sqrt(0.5*(1.0+sqrt(1.0+r*r)));
		}
		else
		{
			r=x/y;
			w=sqrt(y)*sqrt(0.5*(r+sqrt(1.0+r*r)));
		}
		if (zr >=0.0)
		{
			c.re=w;
			c.im=zi/(2.0*w);
		}
		else
		{
			c.im=(zi >= 0) ? w : -w;
			c.re=zi/(2.0*c.im);
		}
		return c;
	}
}

complex ccos(b)
	complex b;
{
	complex neg,negb,zero,two,z,i,bi,negbi;
	zero = cassign(0.0,0.0);
	two = cassign(2.0,0.0);
	i = cassign(0.0,1.0);
	bi = cmult(b,i);
	negbi = csub(zero,bi);
	z = cdiv(cadd(cexp(bi),cexp(negbi)),two);
	return z;
}

double errfunc(n_sub, i)
	double n_sub;
	int i;
{
	double bin_size, ind, func;
	ind = i;
	// i range = [ -4..4], x range = [ -2.5..2.5]
	bin_size = n_sub/2.0/2.5;  //size of each sub-layer
	// rescale erf so that 0 < erf < 1 in -2.5 <= x <= 2.5
	func = (erf(ind/bin_size)/2.0+0.5);
	return func;
}

double linefunc(n_sub, i)
	double n_sub;
	int i;
{
	double bin_size, ind, func;
	ind = i + 0.5;
	// i range = [ -4..4], x range = [ -2.5..2.5]
	bin_size = 1.0/n_sub;  //size of each sub-layer
	// rescale erf so that 0 < erf < 1 in -2.5 <= x <= 2.5
	func = ((ind + floor(n_sub/2.0))*bin_size);
	return func;
}

double parabolic_r(n_sub, i)
	double n_sub;
	int i;
{
	double bin_size, ind, func;
	ind = i + 0.5;
	// i range = [ -4..4], x range = [ 0..1]
	bin_size = 1.0/n_sub;  //size of each sub-layer; n_sub = 0 is a singular point (error)
	func = ((ind + floor(n_sub/2.0))*bin_size)*((ind + floor(n_sub/2.0))*bin_size);
	return func;
}

double parabolic_l(n_sub, i)
	double n_sub;
	int i;
{
	double bin_size,ind, func;
	ind = i + 0.5;
	bin_size = 1.0/n_sub;  //size of each sub-layer; n_sub = 0 is a singular point (error)
	func =1.0-(((ind + floor(n_sub/2.0))*bin_size) - 1.0) *(((ind + floor(n_sub/2.0))*bin_size) - 1.0);
	return func;
}

double cubic_r(n_sub, i)
	double n_sub;
	int i;
{
	double bin_size,ind, func;
	ind = i + 0.5;
	// i range = [ -4..4], x range = [ 0..1]
	bin_size = 1.0/n_sub;  //size of each sub-layer; n_sub = 0 is a singular point (error)
	func = ((ind+ floor(n_sub/2.0))*bin_size)*((ind + floor(n_sub/2.0))*bin_size)*((ind + floor(n_sub/2.0))*bin_size);
	return func;
}

double cubic_l(n_sub, i)
	double n_sub;
	int i;
{
	double bin_size,ind, func;
	ind = i + 0.5;
	bin_size = 1.0/n_sub;  //size of each sub-layer; n_sub = 0 is a singular point (error)
	func = 1.0+(((ind + floor(n_sub/2.0)))*bin_size - 1.0)*(((ind + floor(n_sub/2.0)))*bin_size - 1.0)*(((ind + floor(n_sub/2.0)))*bin_size - 1.0);
	return func;
}

double interfunc(fun_type, n_sub, i, sld_l, sld_r)
	double n_sub, sld_l, sld_r;
	int fun_type, i;
{
	double sld_i, func;
	switch(fun_type){
		case 1 :
			func = linefunc(n_sub, i);
			break;
		case 2 :
			func = parabolic_r(n_sub, i);
			break;
		case 3 :
			func = parabolic_l(n_sub, i);
			break;
		case 4 :
			func = cubic_r(n_sub, i);
			break;
		case 5 :
			func = cubic_l(n_sub, i);
			break;
		default:
			func = errfunc(n_sub, i);
			break;
	}
	if (sld_r>sld_l){
		sld_i = (sld_r-sld_l)*func+sld_l; //sld_cal(sld[i],sld[i+1],n_sub,dz,thick);
	}
	else if (sld_r<sld_l){
		func = 1.0-func;
		sld_i = (sld_l-sld_r)*func+sld_r; //sld_cal(sld[i],sld[i+1],n_sub,dz,thick);
	}
	else{
		sld_i = sld_r;
	}
	return sld_i;
}

double re_kernel(double dp[], double q) {
	int n = dp[0];
	int i,j,fun_type[n+2];

	double scale = dp[1];
	double thick_inter_sub = dp[2];
	double sld_sub = dp[4];
	double sld_super = dp[5];
	double background = dp[6];

	double sld[n+2],sld_im[n+2],thick_inter[n+2],thick[n+2],total_thick;
	fun_type[0] = dp[3];
	for (i =1; i<=n; i++){
		sld[i] = dp[i+6];
		thick_inter[i]= dp[i+16];
		thick[i] = dp[i+26];
		fun_type[i] = dp[i+36];
		sld_im[i] = dp[i+46];

		total_thick += thick[i] + thick_inter[i];
	}
	sld[0] = sld_sub;
	sld[n+1] = sld_super;
	sld_im[0] = fabs(dp[0+56]);
	sld_im[n+1] = fabs(dp[1+56]);
	thick[0] = total_thick/5.0;
	thick[n+1] = total_thick/5.0;
	thick_inter[0] = thick_inter_sub;
	thick_inter[n+1] = 0.0;

	double nsl=21.0; //nsl = Num_sub_layer:  MUST ODD number in double //no other number works now
	int n_s, floor_nsl;
    double sld_i,sldim_i,dz,phi,R,ko2;
    double sign,erfunc;
    double pi;
	complex  inv_n,phi1,alpha,alpha2,kn,fnm,fnp,rn,Xn,nn,nn2,an,nnp1,one,zero,two,n_sub,n_sup,knp1,Xnp1;
	pi = 4.0*atan(1.0);
    one = cassign(1.0,0.0);
	//zero = cassign(0.0,0.0);
	two= cassign(0.0,-2.0);

	floor_nsl = floor(nsl/2.0);

	//Checking if floor is available.
	//no imaginary sld inputs in this function yet
    n_sub=cassign(1.0-sld_sub*pow(lamda,2.0)/(2.0*pi),pow(lamda,2.0)/(2.0*pi)*sld_im[0]);
    n_sup=cassign(1.0-sld_super*pow(lamda,2.0)/(2.0*pi),pow(lamda,2.0)/(2.0*pi)*sld_im[n+1]);
    ko2 = pow(2.0*pi/lamda,2.0);

    phi = asin(lamda*q/(4.0*pi));
    phi1 = cdiv(rcmult(phi,one),n_sup);
    alpha = cmult(n_sup,ccos(phi1));
	alpha2 = cmult(alpha,alpha);

    nnp1=n_sub;
    knp1=csqrt(rcmult(ko2,csub(cmult(nnp1,nnp1),alpha2)));  //nnp1*ko*sin(phinp1)
    Xnp1=cassign(0.0,0.0);
    dz = 0.0;
    // iteration for # of layers +sub from the top
    for (i=1;i<=n+1; i++){
		//iteration for 9 sub-layers
		for (j=0;j<2;j++){
			for (n_s=-floor_nsl;n_s<=floor_nsl; n_s++){
				if (j==1){
					if (i==n+1)
						break;
					dz = thick[i];
					sld_i = sld[i];
					sldim_i = sld_im[i];
				}
				else{
					dz = thick_inter[i-1]/nsl;
					if (sld[i-1] == sld[i]){
						sld_i = sld[i];
					}
					else{
						sld_i = interfunc(fun_type[i-1],nsl, n_s, sld[i-1], sld[i]);
					}
					if (sld_im[i-1] == sld_im[i]){
						sldim_i = sld_im[i];
					}
					else{
						sldim_i = interfunc(fun_type[i-1],nsl, n_s, sld_im[i-1], sld_im[i]);
					}
				}
				nn = cassign(1.0-sld_i*pow(lamda,2.0)/(2.0*pi),pow(lamda,2.0)/(2.0*pi)*sldim_i);
				nn2=cmult(nn,nn);

				kn=csqrt(rcmult(ko2,csub(nn2,alpha2)));        //nn*ko*sin(phin)
				an=cexp(rcmult(dz,cmult(two,kn)));

				fnm=csub(kn,knp1);
				fnp=cadd(kn,knp1);
				rn=cdiv(fnm,fnp);
				Xn=cmult(an,cdiv(cadd(rn,Xnp1),cadd(one,cmult(rn,Xnp1))));    //Xn=an*((rn+Xnp1*anp1)/(1+rn*Xnp1*anp1))

				Xnp1=Xn;
				knp1=kn;

				if (j==1)
					break;
			}
		}
    }
    R=pow(Xn.re,2.0)+pow(Xn.im,2.0);
    // This temperarily fixes the total reflection for Rfunction and linear.
    // ToDo: Show why it happens that Xn.re=0 and Xn.im >1!
    if (Xn.im == 0.0){
    	R=1.0;
    }
    R *= scale;
    R += background;

    return R;

}
/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the sphere
 * @param q: q-value
 * @return: function value
 */
double refl_analytical_1D(ReflParameters *pars, double q) {
	double dp[59];

	dp[0] = pars->n_layers;
	dp[1] = pars->scale;
	dp[2] = pars->thick_inter0;
	dp[3] = pars->func_inter0;
	dp[4] = pars->sld_sub0;
	dp[5] = pars->sld_medium;
	dp[6] = pars->background;

	dp[7] = pars->sld_flat1;
	dp[8] = pars->sld_flat2;
	dp[9] = pars->sld_flat3;
	dp[10] = pars->sld_flat4;
	dp[11] = pars->sld_flat5;
	dp[12] = pars->sld_flat6;
	dp[13] = pars->sld_flat7;
	dp[14] = pars->sld_flat8;
	dp[15] = pars->sld_flat9;
	dp[16] = pars->sld_flat10;

	dp[17] = pars->thick_inter1;
	dp[18] = pars->thick_inter2;
	dp[19] = pars->thick_inter3;
	dp[20] = pars->thick_inter4;
	dp[21] = pars->thick_inter5;
	dp[22] = pars->thick_inter6;
	dp[23] = pars->thick_inter7;
	dp[24] = pars->thick_inter8;
	dp[25] = pars->thick_inter9;
	dp[26] = pars->thick_inter10;

	dp[27] = pars->thick_flat1;
	dp[28] = pars->thick_flat2;
	dp[29] = pars->thick_flat3;
	dp[30] = pars->thick_flat4;
	dp[31] = pars->thick_flat5;
	dp[32] = pars->thick_flat6;
	dp[33] = pars->thick_flat7;
	dp[34] = pars->thick_flat8;
	dp[35] = pars->thick_flat9;
	dp[36] = pars->thick_flat10;

	dp[37] = pars->func_inter1;
	dp[38] = pars->func_inter2;
	dp[39] = pars->func_inter3;
	dp[40] = pars->func_inter4;
	dp[41] = pars->func_inter5;
	dp[42] = pars->func_inter6;
	dp[43] = pars->func_inter7;
	dp[44] = pars->func_inter8;
	dp[45] = pars->func_inter9;
	dp[46] = pars->func_inter10;

	dp[47] = pars->sldIM_flat1;
	dp[48] = pars->sldIM_flat2;
	dp[49] = pars->sldIM_flat3;
	dp[50] = pars->sldIM_flat4;
	dp[51] = pars->sldIM_flat5;
	dp[52] = pars->sldIM_flat6;
	dp[53] = pars->sldIM_flat7;
	dp[54] = pars->sldIM_flat8;
	dp[55] = pars->sldIM_flat9;
	dp[56] = pars->sldIM_flat10;

	dp[57] = pars->sldIM_sub0;
	dp[58] = pars->sldIM_medium;

	return re_kernel(dp, q);
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the sphere
 * @param q: q-value
 * @return: function value
 */
double refl_analytical_2D(ReflParameters *pars, double q, double phi) {
	return refl_analytical_1D(pars,q);
}

double refl_analytical_2DXY(ReflParameters *pars, double qx, double qy){
	return refl_analytical_1D(pars,sqrt(qx*qx+qy*qy));
}