#include <Core/Core.h>

using namespace Upp;

#include <plugin/Eigen/Eigen.h>
#include <plugin/Eigen/unsupported/Eigen/NonLinearOptimization>

using namespace Eigen;

#define VerifyIsApprox(a, b)	(fabs(a-(b)) < 0.0001)

// Generic functor
template<typename _Scalar, int nx = Dynamic, int ny = Dynamic>
struct Functor {
	typedef _Scalar Scalar;
	enum {
		InputsAtCompileTime = nx,
		ValuesAtCompileTime = ny
	};
	typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
	typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
	typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
	
	const int m_inputs, m_values;
	
	Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
	Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
	
	int inputs() const {return m_inputs;}
	int values() const {return m_values;}

	// you should define that in the subclass :
	virtual  void operator() (const InputType& x, ValueType* v, JacobianType* _j=0) const {};
};

struct eckerle4_functor : Functor<double> {
	eckerle4_functor() : Functor<double>(3,35) {}
	static const double x[35];
	static const double y[35];
	int operator()(const VectorXd &b, VectorXd &fvec) const {
		ASSERT(b.size()==3);
		ASSERT(fvec.size()==35);
		for(int i=0; i<35; i++)
			fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];
		return 0;
	}
};
const double eckerle4_functor::x[35] = {400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};
const double eckerle4_functor::y[35] = {0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };

struct thurber_functor : Functor<double>
{
	thurber_functor(int unk, int equat) : Functor<double>(unk, equat) {}
	static const double _x[37];
	static const double _y[37];
	int operator()(const VectorXd &b, VectorXd &fvec) const {
		ASSERT(b.size()==7);
		ASSERT(fvec.size()==37);
		for(int i=0; i<37; i++) {
			double x = _x[i], xx=x*x, xxx=xx*x;
			fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i];
		}
		return 0;
	}
};
const double thurber_functor::_x[37] = {-3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 };
const double thurber_functor::_y[37] = {80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0};


void NonLinearOptimization() {
	Cout() << "\n\nNon linear equations optimization using Levenberg Marquardt based on Minpack\n"
	     "(Given a set of non linear equations and a set of data longer than the equations, "
	     "the program finds the equation coefficients that better fit with the equations)";
	
	{
		Cout() << "\n\nEckerle4 equation\nSee: http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml";
		
		VectorXd x(3);
		
		x << 1., 10., 500.;		// Initial values
		
		eckerle4_functor functor;
		NumericalDiff<eckerle4_functor> numDiff(functor);
		LevenbergMarquardt<NumericalDiff<eckerle4_functor> > lm(numDiff);
		int ret = lm.minimize(x);
		if (ret == LevenbergMarquardtSpace::ImproperInputParameters || 
			ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation)
			Cout() << "\nNo convergence!: " << ret;
		else {
			if (VerifyIsApprox(lm.fvec.squaredNorm(), 1.4635887487E-03))
				Cout() << "\nNorm^2 is right";
			if (VerifyIsApprox(x[0], 1.5543827178) &&
				VerifyIsApprox(x[1], 4.0888321754) &&
				VerifyIsApprox(x[2], 4.5154121844E+02))
				Cout() << "\nNon-linear function optimization is right!";
		}
	}
	{
		Cout() << "\n\nThurber equation\nSee: http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml\n";
		
		int numVars = 7;
		
		VectorXd x(7);
		
		x << 1000, 1000, 400, 40, 0.7, 0.3, 0.0;
		
		int numEquations = 37;
		thurber_functor functor(numVars, numEquations);	// Vars and equations known at run time
		NumericalDiff<thurber_functor> numDiff(functor);
		LevenbergMarquardt<NumericalDiff<thurber_functor> > lm(numDiff);
		lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
		lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
		int ret = lm.minimize(x);
		if (ret == LevenbergMarquardtSpace::ImproperInputParameters || 
			ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation)
			Cout() << "\nNo convergence!: " << ret;
		else {
			if (VerifyIsApprox(lm.fvec.squaredNorm(), 5.6427082397E+03))
				Cout() << "\nNorm^2 is right";
			if (VerifyIsApprox(x[0], 1.2881396800E+03) &&
			    VerifyIsApprox(x[1], 1.4910792535E+03) &&
			    VerifyIsApprox(x[2], 5.8323836877E+02) &&
			    VerifyIsApprox(x[3], 7.5416644291E+01) &&
			    VerifyIsApprox(x[4], 9.6629502864E-01) &&
			    VerifyIsApprox(x[5], 3.9797285797E-01) &&
			    VerifyIsApprox(x[6], 4.9727297349E-02))
				Cout() << "\nNon-linear function optimization is right!";
		}
	}
}

struct hybrd_functor : Functor<double>
{
	hybrd_functor(void) : Functor<double>(9,9) {}
	int operator()(const VectorXd &x, VectorXd &fvec) const {
		double temp, temp1, temp2;
		const int n = x.size();
		
		ASSERT(fvec.size()==n);
		for (int k=0; k < n; k++) {
			temp = (3. - 2.*x[k])*x[k];
			temp1 = 0.;
			if (k) 
				temp1 = x[k-1];
			temp2 = 0.;
			if (k != n-1) 
				temp2 = x[k+1];
			fvec[k] = temp - temp1 - 2.*temp2 + 1.;
		}
		return 0;
	}
};

void NonLinearSolving() {
	Cout() << "\n\nNon linear equation solving using the Powell hybrid method (\"dogleg\") based on Minpack. "
	       << "(Finds a zero of a system of n nonlinear equations in n variables)";
	
	const int n = 9;
	VectorXd x;
	
	x.setConstant(n, -1.);		// Initial values
	
	hybrd_functor functor;
	HybridNonLinearSolver<hybrd_functor> solver(functor);
	int ret = solver.solveNumericalDiff(x);
	if (ret == HybridNonLinearSolverSpace::ImproperInputParameters ||
	    ret == HybridNonLinearSolverSpace::TooManyFunctionEvaluation ||
	    ret == HybridNonLinearSolverSpace::NotMakingProgressJacobian ||
	    ret == HybridNonLinearSolverSpace::NotMakingProgressIterations)
		Cout() << "\nNo convergence!: " << ret;
	else {
		if (solver.nfev != 14)
			Cout() << "\nError with nfev!";
		if (VerifyIsApprox(solver.fvec.blueNorm(), 1.192636e-08))
			Cout() << "\nNorm is right";
		if (VerifyIsApprox(x[0], -0.5706545) && 
		    VerifyIsApprox(x[1], -0.6816283) &&     
		    VerifyIsApprox(x[2], -0.7017325) && 
		    VerifyIsApprox(x[3], -0.7042129) &&  
		    VerifyIsApprox(x[4], -0.701369) && 
		    VerifyIsApprox(x[5], -0.6918656) && 
		    VerifyIsApprox(x[6], -0.665792) && 
		    VerifyIsApprox(x[7], -0.5960342) &&  
		    VerifyIsApprox(x[8], -0.4164121))
			Cout() << "\nEquation solving is right!";
	}
}

void NonLinearTests() {
	NonLinearSolving();
	NonLinearOptimization();
}