/*
	libCylinderFit.h -- equates for CylinderFit XOP
*/
#if defined(_MSC_VER)
#include "winFuncs.h"
#endif

/* Prototypes */
/* IGOR Fit Functions */
double CylinderForm(double dp[], double q);
double EllipCyl76(double dp[], double q);
double EllipCyl20(double dp[], double q);
double TriaxialEllipsoid(double dp[], double q);
double Parallelepiped(double dp[], double q);
double HollowCylinder(double dp[], double q);
double EllipsoidForm(double dp[], double q);
double Cyl_PolyRadius(double dp[], double q);
double Cyl_PolyLength(double dp[], double q);
double CoreShellCylinder(double dp[], double q);
double OblateForm(double dp[], double q);
double ProlateForm(double dp[], double q);
double FlexExclVolCyl(double dp[], double q);
double FlexCyl_PolyLen(double dp[], double q);
double FlexCyl_PolyRad(double dp[], double q);
double FlexCyl_Ellip(double dp[], double q);
double PolyCoShCylinder(double dp[], double q);
double StackedDiscs(double dp[], double q);
double LamellarFF(double dp[], double q);
double LamellarFF_HG(double dp[], double q);
double LamellarPS(double dp[], double q);
double LamellarPS_HG(double dp[], double q);
double Lamellar_ParaCrystal(double dp[], double q);
double Spherocylinder(double dp[], double q);
double ConvexLens(double dp[], double q);
double Dumbbell(double dp[], double q);
double CappedCylinder(double dp[], double q);
double Barbell(double dp[], double q);
double PolyCoreBicelle(double dp[], double q);
double CSParallelepiped(double dp[], double q);

/* internal functions */
double CylKernel(double qq, double rr,double h, double theta);
double NR_BessJ1(double x);
double EllipCylKernel(double qq, double ra,double nu, double theta);
double TriaxialKernel(double q, double aa, double bb, double cc, double dx, double dy);
double PPKernel(double aa, double mu, double uu);
double HolCylKernel(double qq, double rcore, double rshell, double length, double dum);
double EllipsoidKernel(double qq, double a, double va, double dum);
double Cyl_PolyRadKernel(double q, double radius, double length, double zz, double delrho, double dumRad);
double SchulzPoint_cpr(double dumRad, double radius, double zz);
double Cyl_PolyLenKernel(double q, double radius, double len_avg, double zz, double delrho, double dumLen);
double CoreShellCylKernel(double qq, double rcore, double thick, double rhoc, double rhos, double rhosolv, double length, double dum);
double gfn4(double xx, double crmaj, double crmin, double trmaj, double trmin, double delpc, double delps, double qq);
double gfn2(double xx, double crmaj, double crmin, double trmaj, double trmin, double delpc, double delps, double qq);
double FlePolyLen_kernel(double q, double radius, double length, double lb, double zz, double delrho, double zi);
double FlePolyRad_kernel(double q, double ravg, double Lc, double Lb, double zz, double delrho, double zi);
double EllipticalCross_fn(double qq, double a, double b);
double CScyl(double qq, double rad, double radthick, double facthick, double rhoc, double rhos, double rhosolv, double length, double dum);
double CSCylIntegration(double qq, double rad, double radthick, double facthick, double rhoc, double rhos, double rhosolv, double length);
double Stackdisc_kern(double qq, double rcore, double rhoc, double rhol, double rhosolv, double length, double thick, double dum, double gsd, double d, double N);
double paraCryst_sn(double ww, double qval, double davg, long nl, double an);
double paraCryst_an(double ww, double qval, double davg, long nl);
double SphCyl_kernel(double w[], double x, double tt, double Theta);
double ConvLens_kernel(double w[], double x, double tt, double theta);
double Dumb_kernel(double w[], double x, double tt, double theta);
double BicelleKernel(double qq, double rad, double radthick, double facthick, double rhoc, double rhoh, double rhor, double rhosolv, double length, double dum);
double BicelleIntegration(double qq, double rad, double radthick, double facthick, double rhoc, double rhoh, double rhor, double rhosolv, double length);
double CSPPKernel(double dp[], double mu, double uu);

/////////functions for WRC implementation of flexible cylinders
static double
gammaln(double xx)
{
	double x,y,tmp,ser;
	static double cof[6]={76.18009172947146,-86.50532032941677,
		24.01409824083091,-1.231739572450155,
		0.1208650973866179e-2,-0.5395239384953e-5};
	int j;

	y=x=xx;
	tmp=x+5.5;
	tmp -= (x+0.5)*log(tmp);
	ser=1.000000000190015;
	for (j=0;j<=5;j++) ser += cof[j]/++y;
	return -tmp+log(2.5066282746310005*ser/x);
}

//
static double
AlphaSquare(double x)
{
    double yy;
    yy = pow( (1.0 + (x/3.12)*(x/3.12) + (x/8.67)*(x/8.67)*(x/8.67)),(0.176/3.0) );

    return (yy);
}

//
static double
Rgsquarezero(double q, double L, double b)
{
    double yy;
    yy = (L*b/6.0) * (1.0 - 1.5*(b/L) + 1.5*pow((b/L),2) - 0.75*pow((b/L),3)*(1.0 - exp(-2.0*(L/b))));

    return (yy);
}

//
static double
Rgsquareshort(double q, double L, double b)
{
    double yy;
    yy = AlphaSquare(L/b) * Rgsquarezero(q,L,b);

    return (yy);
}

//
static double
Rgsquare(double q, double L, double b)
{
    double yy;
    yy = AlphaSquare(L/b)*L*b/6.0;

    return (yy);
}

// ?? funciton is not used - but should the log actually be log10???
static double
miu(double x)
{
    double yy;
    yy = (1.0/8.0)*(9.0*x - 2.0 + 2.0*log(1.0 + x)/x)*exp(1.0/2.565*(1.0/x + (1.0 - 1.0/(x*x))*log(1.0 + x)));

    return (yy);
}

//WR named this w (too generic)
static double
w_WR(double x)
{
    double yy;
    yy = 0.5*(1 + tanh((x - 1.523)/0.1477));

    return (yy);
}

//
static double
u1(double q, double L, double b)
{
    double yy;

    yy = Rgsquareshort(q,L,b)*q*q;

    return (yy);
}

// was named u
static double
u_WR(double q, double L, double b)
{
    double yy;
    yy = Rgsquare(q,L,b)*q*q;
    return (yy);
}


//
static double
Sdebye1(double q, double L, double b)
{
    double yy;
    yy = 2.0*(exp(-u1(q,L,b)) + u1(q,L,b) -1.0)/( pow((u1(q,L,b)),2.0) );

    return (yy);
}


//
static double
Sdebye(double q, double L, double b)
{
    double yy;
    yy = 2.0*(exp(-u_WR(q,L,b)) + u_WR(q,L,b) -1.0)/(pow((u_WR(q,L,b)),2));

    return (yy);
}

//
static double
Sexv(double q, double L, double b)
{
    double yy,C1,C2,C3,miu,Rg2;
    C1=1.22;
    C2=0.4288;
    C3=-1.651;
    miu = 0.585;

    Rg2 = Rgsquare(q,L,b);

    yy = (1.0 - w_WR(q*sqrt(Rg2)))*Sdebye(q,L,b) + w_WR(q*sqrt(Rg2))*(C1*pow((q*sqrt(Rg2)),(-1.0/miu)) +  C2*pow((q*sqrt(Rg2)),(-2.0/miu)) +    C3*pow((q*sqrt(Rg2)),(-3.0/miu)));

    return (yy);
}

// this must be WR modified version
static double
Sexvnew(double q, double L, double b)
{
    double yy,C1,C2,C3,miu;
    double del=1.05,C_star2,Rg2;

    C1=1.22;
    C2=0.4288;
    C3=-1.651;
    miu = 0.585;

    //calculating the derivative to decide on the corection (cutoff) term?
    // I have modified this from WRs original code

    if( (Sexv(q*del,L,b)-Sexv(q,L,b))/(q*del - q) >= 0.0 ) {
        C_star2 = 0.0;
    } else {
        C_star2 = 1.0;
    }

    Rg2 = Rgsquare(q,L,b);

	yy = (1.0 - w_WR(q*sqrt(Rg2)))*Sdebye(q,L,b) + C_star2*w_WR(q*sqrt(Rg2))*(C1*pow((q*sqrt(Rg2)),(-1.0/miu)) + C2*pow((q*sqrt(Rg2)),(-2.0/miu)) + C3*pow((q*sqrt(Rg2)),(-3.0/miu)));

    return (yy);
}

// these are the messy ones
static double
a2short(double q, double L, double b, double p1short, double p2short, double q0)
{
    double yy,Rg2_sh;
    double t1,E,Rg2_sh2,Et1,Emt1,q02,q0p;
    double pi;

    E = 2.718281828459045091;
	pi = 4.0*atan(1.0);
    Rg2_sh = Rgsquareshort(q,L,b);
    Rg2_sh2 = Rg2_sh*Rg2_sh;
    t1 = ((q0*q0*Rg2_sh)/(b*b));
    Et1 = pow(E,t1);
    Emt1 =pow(E,-t1);
    q02 = q0*q0;
    q0p = pow(q0,(-4.0 + p2short) );

    //E is the number e
    yy = ((-(1.0/(L*((p1short - p2short))*Rg2_sh2)*((b*Emt1*q0p*((8.0*b*b*b*L - 8.0*b*b*b*Et1*L - 2.0*b*b*b*L*p1short + 2.0*b*b*b*Et1*L*p1short + 4.0*b*L*q02*Rg2_sh + 4.0*b*Et1*L*q02*Rg2_sh - 2.0*b*Et1*L*p1short*q02*Rg2_sh - Et1*pi*q02*q0*Rg2_sh2 + Et1*p1short*pi*q02*q0*Rg2_sh2)))))));

    return (yy);
}

//
static double
a1short(double q, double L, double b, double p1short, double p2short, double q0)
{
    double yy,Rg2_sh;
    double t1,E,Rg2_sh2,Et1,Emt1,q02,q0p,b3;
	double pi;

    E = 2.718281828459045091;
	pi = 4.0*atan(1.0);
    Rg2_sh = Rgsquareshort(q,L,b);
    Rg2_sh2 = Rg2_sh*Rg2_sh;
    b3 = b*b*b;
    t1 = ((q0*q0*Rg2_sh)/(b*b));
    Et1 = pow(E,t1);
    Emt1 =pow(E,-t1);
    q02 = q0*q0;
    q0p = pow(q0,(-4.0 + p1short) );

    yy = ((1.0/(L*((p1short - p2short))*Rg2_sh2)*((b*Emt1*q0p*((8.0*b3*L - 8.0*b3*Et1*L - 2.0*b3*L*p2short + 2.0*b3*Et1*L*p2short + 4.0*b*L*q02*Rg2_sh + 4.0*b*Et1*L*q02*Rg2_sh - 2.0*b*Et1*L*p2short*q02*Rg2_sh - Et1*pi*q02*q0*Rg2_sh2 + Et1*p2short*pi*q02*q0*Rg2_sh2))))));

    return(yy);
}


//need to define this on my own
static double
sech_WR(double x)
{
	return(1/cosh(x));
}

// this one will be lots of trouble
static double
a2long(double q, double L, double b, double p1, double p2, double q0)
{
    double yy,C1,C2,C3,C4,C5,miu,C,Rg2;
    double t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,pi;
    double E,b2,b3,b4,q02,q03,q04,q05,Rg22;

    pi = 4.0*atan(1.0);
    E = 2.718281828459045091;
    if( L/b > 10.0) {
        C = 3.06/pow((L/b),0.44);
    } else {
        C = 1.0;
    }

    C1 = 1.22;
    C2 = 0.4288;
    C3 = -1.651;
    C4 = 1.523;
    C5 = 0.1477;
    miu = 0.585;

    Rg2 = Rgsquare(q,L,b);
    Rg22 = Rg2*Rg2;
    b2 = b*b;
    b3 = b*b*b;
    b4 = b3*b;
    q02 = q0*q0;
    q03 = q0*q0*q0;
    q04 = q03*q0;
    q05 = q04*q0;

    t1 = (1.0/(b* p1*pow(q0,((-1.0) - p1 - p2)) - b*p2*pow(q0,((-1.0) - p1 - p2)) ));

    t2 = (b*C*(((-1.0*((14.0*b3)/(15.0*q03*Rg2))) + (14.0*b3*pow(E,(-((q02*Rg2)/b2))))/(15.0*q03*Rg2) + (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*((11.0/15.0 + (7*b2)/(15.0*q02*Rg2)))*Rg2)/b)))/L;

    t3 = (sqrt(Rg2)*((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2.0))/(2.0*C5);

    t4 = (b4*sqrt(Rg2)*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2))/(C5*q04*Rg22);

    t5 = (2.0*b4*(((2.0*q0*Rg2)/b - (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*Rg2)/b))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))/(q04*Rg22);

    t6 = (8.0*b4*b*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))/(q05*Rg22);

    t7 = (((-((3.0*C3*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 3.0/miu)))/miu)) - (2.0*C2*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 2.0/miu)))/miu - (C1*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 1.0/miu)))/miu));

    t8 = ((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)));

    t9 = (b*C*((4.0/15.0 - pow(E,(-((q02*Rg2)/b2)))*((11.0/15.0 + (7.0*b2)/(15*q02*Rg2))) + (7.0*b2)/(15.0*q02*Rg2))))/L;

    t10 = (2.0*b4*(((-1) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))/(q04*Rg22);


    yy = ((-1.0*(t1* ((-pow(q0,-p1)*(((b2*pi)/(L*q02) + t2 + t3 - t4 + t5 - t6 + 1.0/2.0*t7*t8)) - b*p1*pow(q0,((-1.0) - p1))*(((-((b*pi)/(L*q0))) + t9 + t10 + 1.0/2.0*((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))))*((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))))));

    return (yy);
}
//
static double
a1long(double q, double L, double b, double p1, double p2, double q0)
{
    double yy,C,C1,C2,C3,C4,C5,miu,Rg2;
    double t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15;
    double E,pi;
    double b2,b3,b4,q02,q03,q04,q05,Rg22;

    pi = 4.0*atan(1.0);
    E = 2.718281828459045091;

    if( L/b > 10.0) {
        C = 3.06/pow((L/b),0.44);
    } else {
        C = 1.0;
    }

    C1 = 1.22;
    C2 = 0.4288;
    C3 = -1.651;
    C4 = 1.523;
    C5 = 0.1477;
    miu = 0.585;

    Rg2 = Rgsquare(q,L,b);
    Rg22 = Rg2*Rg2;
    b2 = b*b;
    b3 = b*b*b;
    b4 = b3*b;
    q02 = q0*q0;
    q03 = q0*q0*q0;
    q04 = q03*q0;
    q05 = q04*q0;

    t1 = (b*C*((4.0/15.0 - pow(E,(-((q02*Rg2)/b2)))*((11.0/15.0 + (7.0*b2)/(15.0*q02*Rg2))) + (7.0*b2)/(15.0*q02*Rg2))));

    t2 = (2.0*b4*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))));

    t3 = ((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))));

    t4 = ((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)));

    t5 = (1.0/(b*p1*pow(q0,((-1.0) - p1 - p2)) - b*p2*pow(q0,((-1.0) - p1 - p2))));

    t6 = (b*C*(((-((14.0*b3)/(15.0*q03*Rg2))) + (14.0*b3*pow(E,(-((q02*Rg2)/b2))))/(15.0*q03*Rg2) + (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*((11.0/15.0 + (7.0*b2)/(15.0*q02*Rg2)))*Rg2)/b)));

    t7 = (sqrt(Rg2)*((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2));

    t8 = (b4*sqrt(Rg2)*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2));

    t9 = (2.0*b4*(((2.0*q0*Rg2)/b - (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*Rg2)/b))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))));

    t10 = (8.0*b4*b*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))));

    t11 = (((-((3.0*C3*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 3.0/miu)))/miu)) - (2.0*C2*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 2.0/miu)))/miu - (C1*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 1.0/miu)))/miu));

    t12 = ((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)));

    t13 = (b*C*((4.0/15.0 - pow(E,(-((q02*Rg2)/b2)))*((11.0/15.0 + (7.0*b2)/(15.0*q02* Rg2))) + (7.0*b2)/(15.0*q02*Rg2))));

    t14 = (2.0*b4*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))));

    t15 = ((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))));


    yy = (pow(q0,p1)*(((-((b*pi)/(L*q0))) +t1/L +t2/(q04*Rg22) + 1.0/2.0*t3*t4)) + (t5*((pow(q0,(p1 - p2))*(((-pow(q0,(-p1)))*(((b2*pi)/(L*q02) +t6/L +t7/(2.0*C5) -t8/(C5*q04*Rg22) +t9/(q04*Rg22) -t10/(q05*Rg22) + 1.0/2.0*t11*t12)) - b*p1*pow(q0,((-1.0) - p1))*(((-((b*pi)/(L*q0))) +t13/L +t14/(q04*Rg22) + 1.0/2.0*t15*((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)))))))))));

    return (yy);
}


static double
Sk_WR(double q, double L, double b)
{
	//
	double p1,p2,p1short,p2short,q0;
	double C,ans,q0short,Sexvmodify,pi;

	pi = 4.0*atan(1.0);

	p1 = 4.12;
	p2 = 4.42;
	p1short = 5.36;
	p2short = 5.62;
	q0 = 3.1;
	//
	q0short = fmax(1.9/sqrt(Rgsquareshort(q,L,b)),3.0);

	//
	if(L/b > 10.0) {
		C = 3.06/pow((L/b),0.44);
	} else {
		C = 1.0;
	}
	//

	if( L > 4*b ) { // Longer Chains
		if (q*b <= 3.1) {		//Modified by Yun on Oct. 15,
			Sexvmodify = Sexvnew(q, L, b);
			ans = Sexvmodify + C * (4.0/15.0 + 7.0/(15.0*u_WR(q,L,b)) - (11.0/15.0 + 7.0/(15.0*u_WR(q,L,b)))*exp(-u_WR(q,L,b)))*(b/L);
		} else { //q(i)*b > 3.1
			ans = a1long(q, L, b, p1, p2, q0)/(pow((q*b),p1)) + a2long(q, L, b, p1, p2, q0)/(pow((q*b),p2)) + pi/(q*L);
		}
	} else { //L <= 4*b Shorter Chains
		if (q*b <= fmax(1.9/sqrt(Rgsquareshort(q,L,b)),3.0) ) {
			if (q*b<=0.01) {
				ans = 1.0 - Rgsquareshort(q,L,b)*(q*q)/3.0;
			} else {
				ans = Sdebye1(q,L,b);
			}
		} else {	//q*b > max(1.9/sqrt(Rgsquareshort(q(i),L,b)),3)
			ans = a1short(q,L,b,p1short,p2short,q0short)/(pow((q*b),p1short)) + a2short(q,L,b,p1short,p2short,q0short)/(pow((q*b),p2short)) + pi/(q*L);
		}
	}

	return(ans);
	//return(a2long(q, L, b, p1, p2, q0));
}