uppsrc/ScatterDraw/Equation.h

#ifndef _ScatterDraw_Equation_h_
#define _ScatterDraw_Equation_h_

#include <plugin/Eigen/Eigen.h>

namespace Upp {

#define FormatCoeff(id, numDigits)		(IsNull(numDigits) ? (String("C") + FormatInt(id)) : FormatDoubleFix(coeff[id], numDigits))

class ExplicitEquation : public DataSource {
public:
	ExplicitEquation() {isExplicit = true;}

	virtual void SetDegree(int num) = 0;
	enum FitError {
		NoError = 1,
		InadequateDataSource = -1,
		SmallDataSource = -2,
		ImproperInputParameters = -3,
		TooManyFunctionEvaluation = -4
	};
	virtual FitError Fit(DataSource &series, double &r2);
	FitError Fit(DataSource &series)		{double dummy; return Fit(series, dummy);}
	virtual void GuessCoeff(DataSource &series)	= 0;

	virtual double f(double ) 				= 0;
	virtual double f(double , double ) 		{NEVER(); return Null;}
	virtual double f(Vector <double> ) 		{NEVER(); return Null;}
	virtual double x(int64 ) 				{NEVER(); return Null;}
	virtual double y(int64 ) 				{NEVER(); return Null;}
	virtual String GetName() = 0;
	virtual String GetFullName()			{return GetName();}
	virtual String GetEquation(int numDigits = 3) = 0;
	virtual inline int64 GetCount() const	{return coeff.GetCount() > 0 ? 0 : int64(Null);}

	void SetMaxFitFunctionEvaluations(int n){maxFitFunctionEvaluations = n;}
	int GetMaxFitFunctionEvaluations()		{return maxFitFunctionEvaluations;}

	friend struct Equation_functor;

	const Vector<double> &GetCoeff()			{return coeff;}
	double GetCoeff(int i)						{return coeff[i];}

	template<class T>
	static void Register(const String& name) {
		classMap().FindAdd(name, __Create<T>);
	}
	static void Unregister(const String& name) {
		int i = NameIndex(name);
		ASSERT(i >= 0);
		classMap().Remove(i);
	}
	static int            	 NameIndex(const String& name) {return classMap().Find(name);}
	static int            	 GetEquationCount()            {return classMap().GetCount();}
	static ExplicitEquation* Create(int i)                 {return classMap()[i]();}

	int GetNumCoeff(int ) 	{return coeff.GetCount();}

	ExplicitEquation &operator=(ExplicitEquation &other) {
		if (this != &other) {
			degree = other.degree;
			coeff = clone(other.coeff);
		}
		return *this;
	}
	double R2Y(DataSource &series, double mean = Null);

protected:
	Vector<double> coeff;
	int degree;
	static int maxFitFunctionEvaluations;

	void SetNumCoeff(int num);
	void SetCoeff(const Vector<double>& c)          {coeff = clone(c);}
	void SetCoeff(double c0, double c1, double c2)	{coeff.Clear();	coeff << c0 << c1 << c2;}
	void SetCoeff(double c0, double c1) 			{coeff.Clear();	coeff << c0 << c1;}
	void SetCoeff(double c0) 						{coeff.Clear();	coeff << c0;}
	void SetCoeffVal(int id, double c) 				{coeff[id] = c;}

	typedef ExplicitEquation* (*CreateFunc)();
	template<class T>
	static ExplicitEquation*                      __Create() {return new T;}
	static VectorMap<String, CreateFunc>& classMap() {static VectorMap<String, CreateFunc> cMap; return cMap;}
};

class AvgEquation : public ExplicitEquation {
public:
	AvgEquation() 						{SetCoeff(0);}
	AvgEquation(double c0)				{SetCoeff(c0);}
	double f(double ) 					{return coeff[0];}
	virtual String GetName() 			{return t_("Average");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s", FormatCoeff(0, _numDigits));
		return ret;
	}
	void SetDegree(int )				{NEVER();}
	virtual void GuessCoeff(DataSource &series)	{coeff[0] = series.AvgY();}
};

class LinearEquation : public ExplicitEquation {
public:
	LinearEquation() 					{SetCoeff(0, 0);}
	LinearEquation(double c0, double c1){SetCoeff(c0, c1);}
	double f(double x) 					{
		return coeff[0] + x*coeff[1];
	}
	virtual String GetName() 			{return t_("Linear");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s + %s*x", FormatCoeff(0, _numDigits), FormatCoeff(1, _numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	void SetDegree(int )				{NEVER();}
	virtual void GuessCoeff(DataSource &series)	{coeff[0] = series.AvgY();}
};

class PolynomialEquation : public ExplicitEquation {
public:
	PolynomialEquation() 				       	{}
	PolynomialEquation(const Vector<double>& c) {SetCoeff(c);}
	double f(double x);
	virtual String GetName() 			       	{return t_("Polynomial");}
	virtual String GetFullName() 		       	{return t_("Polynomial") + String(" n = ") + FormatInt(degree);}
	virtual String GetEquation(int numDigits = 3);
	void SetDegree(int num)				       	{degree = num;	SetNumCoeff(num + 1);}
	virtual void GuessCoeff(DataSource &series) {
		coeff[0] = series.AvgY();
		int realDegree = degree;
		for (degree = 2; degree < realDegree; degree++)
			Fit(series);
	}
};

class PolynomialEquation2 : public PolynomialEquation {
public:
	PolynomialEquation2() {SetDegree(2);}
};

class PolynomialEquation3 : public PolynomialEquation {
public:
	PolynomialEquation3() {SetDegree(3);}
};

class PolynomialEquation4 : public PolynomialEquation {
public:
	PolynomialEquation4() {SetDegree(4);}
};

class PolynomialEquation5 : public PolynomialEquation {
public:
	PolynomialEquation5() {SetDegree(5);}
};

class SinEquation : public ExplicitEquation {
public:
	SinEquation() 					{coeff.Clear();	coeff << 0. << 0.1 << 0.1 << 0.1;}
	SinEquation(double offset, double A, double w, double phi) 	{Init(offset, A, w, phi);}
	void Init(double offset, double A, double w, double phi) 	{coeff.Clear();	coeff << offset << A << w << phi;}
	double f(double x)				{return coeff[0] + coeff[1]*sin(coeff[2]*x + coeff[3]);}
	virtual String GetName() 		{return t_("Sine");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s + %s*sin(%s*t + %s)", FormatCoeff(0, _numDigits), FormatCoeff(1, _numDigits)
													, FormatCoeff(2, _numDigits), FormatCoeff(3, _numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	void SetDegree(int )				{NEVER();}
	virtual void GuessCoeff(DataSource &series)	{
		coeff[0] = series.AvgY();
		coeff[1] = series.SinEstim_Amplitude(coeff[0]);
		double frequency, phase;
		if (series.SinEstim_FreqPhase(frequency, phase, coeff[0])) {
			coeff[2] = frequency;
			coeff[3] = phase;
		}
	}
};

class DampedSinEquation : public ExplicitEquation {
public:
	DampedSinEquation() 					{coeff.Clear();	coeff << 0. << 0.1 << 0.1 << 0.1 << 0.1;}
	DampedSinEquation(double offset, double A, double lambda, double w, double phi) {Init(offset, A, lambda, w, phi);}
	void Init(double offset, double A, double lambda, double w, double phi) 	{coeff.Clear();	coeff << offset << A << lambda << w << phi;}
	double f(double x)				{return coeff[0] + coeff[1]*exp(-coeff[2]*x)*cos(coeff[3]*x + coeff[4]);}
	virtual String GetName() 		{return t_("DampedSinusoidal");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s + %s*e^(-%s*t)*cos(%s*t + %s)", FormatCoeff(0, _numDigits),
			FormatCoeff(1, _numDigits), FormatCoeff(2, _numDigits), FormatCoeff(3, _numDigits), FormatCoeff(4, _numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	void SetDegree(int )						{NEVER();}
	virtual void GuessCoeff(DataSource &series)	{
		coeff[0] = series.AvgY();
		coeff[2] = series.SinEstim_Amplitude(coeff[0]);
		double frequency, phase;
		if (series.SinEstim_FreqPhase(frequency, phase, coeff[0])) {
			coeff[3] = frequency;
			coeff[4] = phase;
		}
	}
};

class Sin_DampedSinEquation : public ExplicitEquation {
public:
	Sin_DampedSinEquation() 			{coeff.Clear();	coeff << 0. << 0.1 << 0.1 << 0.1 << 0.1 << 0.1 << 0.1 << 0.1;}
	Sin_DampedSinEquation(double offset, double A1, double w1, double phi1, double A2,
			double lambda, double w2, double phi2) {Init(offset, A1, w1, phi1, A2, lambda, w2, phi2);}
	void Init(double offset, double A1, double w1, double phi1, double A2, double lambda,
		double w2, double phi2) {coeff.Clear();
								coeff << offset << A1 << w1 << phi1 << A2 << lambda << w2 << phi2;}
	double f(double x)				{return coeff[0] + coeff[1]*cos(coeff[2]*x + coeff[3]) + coeff[4]*exp(-coeff[5]*x)*cos(coeff[6]*x + coeff[7]);}
	virtual String GetName() 		{return t_("Sin_DampedSinusoidal");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s + %s*cos(%s*t + %s) + %s*e^(-%s*t)*cos(%s*t + %s)",
			FormatCoeff(0, _numDigits), FormatCoeff(1, _numDigits), FormatCoeff(2, _numDigits),
			FormatCoeff(3, _numDigits), FormatCoeff(4, _numDigits), FormatCoeff(5, _numDigits),
			FormatCoeff(6, _numDigits), FormatCoeff(7, _numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	void SetDegree(int )				{NEVER();}
	virtual void GuessCoeff(DataSource &series)	{
		coeff[0] = series.AvgY();
		coeff[1] = series.SinEstim_Amplitude(coeff[0]);
		double frequency, phase;
		if (series.SinEstim_FreqPhase(frequency, phase, coeff[0])) {
			coeff[2] = frequency;
			coeff[3] = phase;
		}
	}
};

class FourierEquation : public ExplicitEquation {
public:
	FourierEquation() 					        {}
	FourierEquation(const Vector<double>& c) 	{SetCoeff(c);}
	double f(double x);
	virtual String GetName() 			        {return t_("Fourier");}
	virtual String GetFullName() 		        {return t_("Fourier") + String(" n = ") + FormatInt(degree);}
	virtual String GetEquation(int numDigits = 3);
	virtual void GuessCoeff(DataSource &series) {coeff[0] = series.AvgY();}
	void SetDegree(int num)				        {degree = num;	SetNumCoeff(2*num + 2);}
};

class FourierEquation1 : public FourierEquation {
public:
	FourierEquation1() {SetDegree(1);}
};

class FourierEquation2 : public FourierEquation {
public:
	FourierEquation2() {SetDegree(2);}
};

class FourierEquation3 : public FourierEquation {
public:
	FourierEquation3() {SetDegree(3);}
};

class FourierEquation4 : public FourierEquation {
public:
	FourierEquation4() {SetDegree(4);}
};

class ExponentialEquation : public ExplicitEquation {
public:
	ExponentialEquation() 						{SetCoeff(1, 0);}
	ExponentialEquation(double c0, double c1)	{SetCoeff(c0, c1);}
	double f(double x) 							{return coeff[0]*exp(-x) + coeff[1];}
	virtual String GetName() 					{return t_("Exponential");}
	virtual String GetEquation(int numDigits = 3) {
		String ret = Format("%s*e^-x + %s", FormatCoeff(0, numDigits), FormatCoeff(1, numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	virtual void GuessCoeff(DataSource &) {}
	void SetDegree(int )				{NEVER();}
};

class RealExponentEquation : public ExplicitEquation {
public:
	RealExponentEquation() 						{SetCoeff(1, 1);}
	RealExponentEquation(double a, double b)	{SetCoeff(a, b);}
	double f(double x) 							{
		if (x < 0)
			return Null;
		return coeff[0]*pow(x, coeff[1]);
	}
	virtual String GetName() 					{return t_("RealExponent");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s*x^%s", FormatCoeff(0, _numDigits), FormatCoeff(1, _numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	virtual void GuessCoeff(DataSource &) {}
	void SetDegree(int )				{NEVER();}
};

class WeibullCumulativeEquation : public ExplicitEquation {
public:
	WeibullCumulativeEquation() 						{SetCoeff(1, 1);}
	WeibullCumulativeEquation(double k, double lambda)	{ASSERT(k > 0);	ASSERT(lambda > 0);	SetCoeff(k, lambda);}
	double f(double x) {
		if (x < 0)
			return 0;
		double k =  coeff[0];
		double lambda = coeff[1];
		return 1 - exp(double(-pow(x/lambda, k)));
	}
	virtual String GetName() 					{return t_("Weibull cumulative");}
	virtual String GetEquation(int numDigits = 3) {
		String k =  FormatCoeff(0, numDigits);
		String lambda = FormatCoeff(1, numDigits);
		String ret = Format("1 - e^(-((x/%s)^%s))", lambda, k);
		ret.Replace("+ -", "- ");
		return ret;
	}
	virtual void GuessCoeff(DataSource &) {}
	void SetDegree(int )				{NEVER();}
};

class WeibullEquation : public ExplicitEquation {
public:
	WeibullEquation() 							{SetCoeff(1, 1, 1);}
	WeibullEquation(double k, double lambda, double factor)	{ASSERT(k > 0);	ASSERT(lambda > 0);	SetCoeff(k, lambda, factor);}
	double f(double x) {
		if (x < 0)
			return 0;
		double k =  coeff[0];
		double lambda = coeff[1];
		double factor = coeff[2];
		return factor*(k/lambda)*(pow(x/lambda, k-1))*exp(double(-pow(x/lambda, k)));
	}
	virtual String GetName() 					{return t_("Weibull");}
	virtual String GetEquation(int numDigits = 3) {
		String k =  FormatCoeff(0, numDigits);
		String lambda = FormatCoeff(1, numDigits);
		String sfactor = FormatCoeff(2, numDigits);
		String ret = Format("%s*(%s/%s)*(x/%s)^(%s-1)*e^(-((x/%s)^%s))", sfactor, k, lambda, lambda, k, lambda, k);
		ret.Replace("+ -", "- ");
		return ret;
	}
	virtual void GuessCoeff(DataSource &) {}
	virtual void _GuessCoeff(DataSource &series) {
		Vector<Pointf> cumulative = series.CumulativeY();
		double fac = cumulative.Top().y;
		for (int i = 0; i < cumulative.GetCount(); ++i)
			cumulative[i].y /= fac;
		VectorPointf data(cumulative);
		WeibullCumulativeEquation weibullCumulative;
		ExplicitEquation::FitError error = weibullCumulative.Fit(data);
		if (error == ExplicitEquation::NoError) {
			double k = weibullCumulative.GetCoeff()[0];
			double lambda = weibullCumulative.GetCoeff()[1];
			SetCoeff(k, lambda, 1);
		}
	}
	FitError Fit(DataSource &series, double &r2) {
		_GuessCoeff(series);
		return ExplicitEquation::Fit(series, r2);
	}
	FitError Fit(DataSource &series)		{double dummy; return Fit(series, dummy);}
	void SetDegree(int )					{NEVER();}
};

class NormalEquation : public ExplicitEquation {
public:
	NormalEquation() 						{SetCoeff(1, 1, 1);}
	NormalEquation(double c, double mean, double std)	{SetCoeff(c, mean, std);}
	double f(double x) {
		double c    = coeff[0];
		double mean = coeff[1];
		double std  = coeff[2];
		return c*exp(-0.5*sqr((x - mean)/std))/(std*sqrt(2*M_PI));
	}
	virtual String GetName() 					{return t_("Normal");}
	virtual String GetEquation(int numDigits = 3) {
		String c = FormatCoeff(0, numDigits);
		String mean = FormatCoeff(1, numDigits);
		String std = FormatCoeff(2, numDigits);
		String ret = Format("%s/(%s*sqrt(2*PI))*e^(-1/2((x-%s)/%s))", c, std, mean, std);
		ret.Replace("+ -", "- ");
		return ret;
	}
	virtual void GuessCoeff(DataSource &) {}
	virtual void _GuessCoeff(DataSource &series) {
		double mean = series.AvgX();
		double std = series.StdDevX();
		double c = series.MaxY()*std*sqrt(2*M_PI);
		SetCoeff(c, mean, std);
	}
	FitError Fit(DataSource &series, double &r2) {
		_GuessCoeff(series);
		return ExplicitEquation::Fit(series, r2);
	}
	FitError Fit(DataSource &series)		{double dummy; return Fit(series, dummy);}
	void SetDegree(int )					{NEVER();}
};

class Rational1Equation : public ExplicitEquation {
public:
	Rational1Equation() 				{SetCoeff(1, 0, 0);}
	Rational1Equation(double c0, double c1, double c2)	{SetCoeff(c0, c1, c2);}
	double f(double x) 					{return coeff[0]/(x + coeff[1]) + coeff[2];}
	virtual String GetName() 			{return t_("Rational_1");}
	virtual String GetEquation(int _numDigits = 3) {
		String ret = Format("%s/(x + %s) + %s", FormatCoeff(0, _numDigits), FormatCoeff(1, _numDigits), FormatCoeff(2, _numDigits));
		ret.Replace("+ -", "- ");
		return ret;
	}
	virtual void GuessCoeff(DataSource &) {}
	void SetDegree(int )				{NEVER();}
};

class Spline {
public:
	Spline()													 {}
	Spline(const Vector<double> &x, const Vector<double> &y)	 {Fit(x, y);}
	Spline(const Eigen::VectorXd &x, const Eigen::VectorXd &y) 	 {Fit(x, y);}
	Spline(const double *x, const double *y, int n)				 {Fit(x, y, n);}
	void Fit(const Vector<double> &x, const Vector<double> &y)	 {Fit(x.begin(), y.begin(), x.GetCount());}
	void Fit(const Eigen::VectorXd &x, const Eigen::VectorXd &y) {Fit(x.data(), y.data(), int(x.size()));}
	void Fit(const double *x, const double *y, int n);
	double f(double x) const;

private:
	struct Coeff {double a, b, c, d, x;};
    Buffer<Coeff> scoeff;
    int nscoeff = 0;
};

class SplineEquation : public ExplicitEquation, public Spline {
public:
	SplineEquation() 					{}
	double f(double x)					{return Spline::f(x);}
	virtual String GetName() 			{return t_("Spline");}
	void SetDegree(int )				{NEVER();}
	void GuessCoeff(DataSource &)		{NEVER();}
	String GetEquation(int)				{return t_("Spline");}
	FitError Fit(DataSource &series, double &r2);
	FitError Fit(DataSource &series)	{double dummy; return Fit(series, dummy);}
};

class Unit : public Moveable<Unit> {
public:
	Unit() 							{SetNull();}
	Unit(const Nuller&)	: Unit()	{}
	Unit(double _m, double _l, double _t) : m(_m), l(_l), t(_t) {}
	String GetString() {
		if (IsNullInstance())
			return String();
		String ret;
		if (m != 0) {
			ret << "Kg";
			if (m != 1)
				ret << "^" << m;
		}
		if (l != 0) {
			if (!ret.IsEmpty())
				ret << "*";
			ret << "m";
			if (l != 1)
				ret << "^" << l;
		}
		if (t != 0) {
			if (!ret.IsEmpty())
				ret << "*";
			ret << "sec";
			if (t != 1)
				ret << "^" << t;
		}
		return ret;
	}
	bool IsEqual(const Unit &un) {return m == un.m && l == un.l && t == un.t;}
	void Mult(const Unit &un) {
		m += un.m;
		l += un.l;
		t += un.t;
	}
	void Div(const Unit &un) {
		m -= un.m;
		l -= un.l;
		t -= un.t;
	}
	void Exp(double exp) {
		m *= exp;
		l *= exp;
		t *= exp;
	}
	void Sqrt() {
		m /= 2.;
		l /= 2.;
		t /= 2.;
	}

	void SetNull()             	{m = Null;}
	bool IsNullInstance() const	{return Upp::IsNull(m);}
	bool IsAdim() const			{return (m == 0) && (l == 0) && (t == 0);}

	double m, l, t;
};

class doubleUnit : public Moveable<doubleUnit> {
public:
	doubleUnit() : doubleUnit(0)						{}
	doubleUnit(double _val) : val(_val), sval(String::GetVoid()), unit(0, 0, 0)	{}
	doubleUnit(const Nuller&) 							{SetNull();}

	double val;
	String sval;
	Unit unit;

	void Sum(const doubleUnit &d) {
		if (!(unit.IsEqual(d.unit) || IsNull(unit) || IsNull(d.unit)))
			throw Exc(t_("Units does not match in summation"));
		val += d.val;
	}
	void Sub(const doubleUnit &d) {
		if (!(unit.IsEqual(d.unit) || IsNull(unit) || IsNull(d.unit)))
			throw Exc(t_("Units does not match in substraction"));
		val -= d.val;
	}
	void Mult(const doubleUnit &d) {
		unit.Mult(d.unit);
		val *= d.val;
	}
	void Div(const doubleUnit &d) {
		if (abs(d.val) < 1e-100)
			throw Exc(t_("Division by zero"));
		unit.Div(d.unit);
		val /= d.val;
	}
	void Neg() {
		val = -val;
	}
	void Exp(const doubleUnit &d) {
		if (!(IsNull(d.unit) || d.unit.IsAdim()))
			throw Exc(t_("Exponent cannot have units"));
		unit.Mult(d.unit);
		val = pow(val, d.val);
	}
	void Sqrt() {
		if (val < 0)
			throw Exc(t_("Negative number sqrt"));
		val = sqrt(val);
		unit.Sqrt();
	}
	void ResParallel(const doubleUnit &d) {
		if (abs(val + d.val) < 1e-100 && abs(val*d.val) > 1e-100)
			throw Exc(t_("Division by zero"));
		if (!(unit.IsEqual(d.unit) || IsNull(unit) || IsNull(d.unit)))
			throw Exc(t_("Units does not match in resistor parallel"));
		if (abs(val*d.val) < 1e-100)
			val = 0.0;
		else
			val = val*d.val/(val + d.val);
	}
	void SetNull()                 {val = Null;}
	bool IsNullInstance() const    {return IsNull(unit) && IsNull(val);}
};

template<> inline bool IsNull(const doubleUnit& r)  {return r.val < DOUBLE_NULL_LIM;}

class CParserPP : public CParser {
public:
	CParserPP() : CParser() {}
	CParserPP(const char *ptr) : CParser(ptr) {}

	String ReadIdPP() {
		if(!IsId())
			ThrowError("missing id");
		String result;
		const char *b = term;
		const char *p = b;

		while (true) {
			while (iscid(*p))
				p++;
			if ((*p) == '[') {
				p++;
				const char *p0 = p;
				while ((*p) >= '0' && (*p) <= '9')
					p++;
				if (p0 == p)
					ThrowError("empty vector index");
				if ((*p) != ']')
					ThrowError("wrong token found closing vector index");
				else
					p++;
			} else if ((*p) == '.')
				p++;
			else
				break;
		}
		term = p;
		DoSpaces();
		return String(b, (int)(uintptr_t)(p - b));
	}
};

class EvalExpr {
public:
	EvalExpr();
	void Clear()									  		{variables.Clear();}
	doubleUnit Eval(String line);
	doubleUnit AssignVariable(String var, String expr);
	doubleUnit AssignVariable(String var, double d);
	String EvalStr(String line, int numDigits = 3);
	EvalExpr &SetCaseSensitivity(bool val = true) 			{noCase = !val;				return *this;}
	EvalExpr &SetErrorUndefined(bool val = true)  			{errorIfUndefined = val;	return *this;}
	EvalExpr &SetAllowString(bool val = true)  				{allowString = val;			return *this;}

	const String &GetFunction(int id) 						{return functions.GetKey(id);}
	int GetFunctionsCount() 								{return functions.GetCount();}

	void SetConstant(String name, doubleUnit value)			{constants.GetAdd(name) = value;}
	void SetConstant(int id, doubleUnit value)				{constants[id] = value;}
	const doubleUnit &GetConstant(String name) 				{return constants.Get(name, doubleUnit(Null));}
	void GetConstant(int id, String &name, doubleUnit &val)	{name = constants.GetKey(id); val = constants[id];}
	int GetConstantId(String &name)							{return constants.Find(name);}
	int GetConstantsCount() 								{return constants.GetCount();}

	doubleUnit &GetVariable(String name) {
		int id = FindVariable(name);
		if (id >= 0)
			return variables[id];
		if (errorIfUndefined)
			EvalThrowError(p, Format(t_("Unknown identifier '%s'"), name));
		return variables.Add(name, Null);
	}
	doubleUnit &GetVariable(int id)							{return variables[id];}
	void GetVariable(int id, String &name, doubleUnit &val)	{name = variables.GetKey(id); val = variables[id];}
	int GetVariablesCount() 								{return variables.GetCount();}
	void ClearVariables();
	String &GetLastError()									{return lastError;}

	VectorMap<String, doubleUnit> constants;
	VectorMap<String, doubleUnit (*)(doubleUnit)> functions;

	CParserPP p;

	static void EvalThrowError(CParserPP &p, const char *s);

	virtual int FindVariable(String strId) 					{return variables.Find(strId);}

protected:
	doubleUnit Exp(CParserPP& p);

	void SetVariable(String name, doubleUnit value)	{
		lastVariableSetId = variables.FindAdd(name);
		variables[lastVariableSetId] = value;
	}
	void SetVariable(int id, doubleUnit value) {
		lastVariableSetId = id;
		variables[id] = value;
	}
	int FindAddVariable(String name) {
		return lastVariableSetId = variables.FindAdd(name);
	}
	void RemoveVariable(int id) {
		variables.Remove(id);
	}
	bool noCase;
	String lastError;
	VectorMap<String, doubleUnit> variables;
	bool errorIfUndefined;
	bool allowString;
	int lastVariableSetId = -1;

	bool IsFunction(String str)								{return functions.Get(str, 0);}
	bool IsConstant(String str)								{return !IsNull(GetConstant(str));}

private:
	void *Functions_Get(CParserPP& p);
	doubleUnit Term(CParserPP& p);
	doubleUnit Pow(CParserPP& p);
	doubleUnit Mul(CParserPP& p);

	String TermStr(CParserPP& p, int numDigits);
	String PowStr(CParserPP& p, int numDigits);
	String MulStr(CParserPP& p, int numDigits);
	String ExpStr(CParserPP& p, int numDigits);
};

class UserEquation : public ExplicitEquation {
public:
	UserEquation() {}
	UserEquation(String _name, String _strEquation, String varHoriz = "x")	{Init(_name, _strEquation, varHoriz);}
	void Init(String _name, String _strEquation, String varHoriz = "x") {
		name = _name;
		_strEquation.Replace(" ", "");
		StringStream str(_strEquation);
		Vector<String> parts = GetCsvLine(str, ';', CHARSET_DEFAULT);
		if (parts.IsEmpty())
			return;
		strEquation = parts[0];
		eval.Clear();
		eval.SetConstant(varHoriz, doubleUnit(23));
		idx = eval.GetConstantsCount() - 1;
		eval.EvalStr(strEquation);
		coeff.Clear();
		varNames.Clear();
		if (eval.GetVariablesCount() == 0)
			coeff.SetCount(1);
		else {
			for (int i = 0; i < eval.GetVariablesCount(); ++i) {
				String varName;
				doubleUnit dummy;
				eval.GetVariable(i, varName, dummy);
				varNames << varName;
				int istr;
				for (istr = 1; istr < parts.GetCount(); ++istr) {
					String strVar = varName + "=";
					int ifound = parts[istr].Find(strVar);
					if (ifound >= 0) {
						double val = ScanDouble(parts[istr].Mid(strVar.GetCount()));
						coeff << val;
						break;
					}
				}
				if (istr == parts.GetCount())
					coeff << 0.1;
			}
		}
	}
	double f(double x)  {
		eval.SetConstant(idx, doubleUnit(x));
		for (int i = 0; i < varNames.GetCount(); ++i)
			eval.AssignVariable(varNames[i], coeff[i]);
		return eval.Eval(strEquation).val;
	}
	void SetName(String _name) 					    {name = _name;}
	virtual String GetName() 						{return name;}
	virtual String GetEquation(int numDigits = 3)	{return eval.EvalStr(strEquation, numDigits);}
	virtual void GuessCoeff(DataSource &)		 	{}
	void SetDegree(int)								{NEVER();}

private:
	String name;
	String strEquation;
	Vector<String> varNames;
	EvalExpr eval;
	int idx;
};

}

#endif