pmlpp/mlpp/numerical_analysis/numerical_analysis.h

#ifndef MLPP_NUMERICAL_ANALYSIS_H
#define MLPP_NUMERICAL_ANALYSIS_H

//
//  NumericalAnalysis.hpp
//
//

#include <string>
#include <vector>


class NumericalAnalysis {
public:
	/* A numerical method for derivatives is used. This may be subject to change,
	as an analytical method for calculating derivatives will most likely be used in
	the future.
	*/
	double numDiff(double (*function)(double), double x);
	double numDiff_2(double (*function)(double), double x);
	double numDiff_3(double (*function)(double), double x);

	double constantApproximation(double (*function)(double), double c);
	double linearApproximation(double (*function)(double), double c, double x);
	double quadraticApproximation(double (*function)(double), double c, double x);
	double cubicApproximation(double (*function)(double), double c, double x);

	double numDiff(double (*function)(std::vector<double>), std::vector<double> x, int axis);
	double numDiff_2(double (*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2);
	double numDiff_3(double (*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2, int axis3);

	double newtonRaphsonMethod(double (*function)(double), double x_0, double epoch_num);
	double halleyMethod(double (*function)(double), double x_0, double epoch_num);
	double invQuadraticInterpolation(double (*function)(double), std::vector<double> x_0, double epoch_num);

	double eulerianMethod(double (*derivative)(double), std::vector<double> q_0, double p, double h); // Euler's method for solving diffrential equations.
	double eulerianMethod(double (*derivative)(std::vector<double>), std::vector<double> q_0, double p, double h); // Euler's method for solving diffrential equations.

	double growthMethod(double C, double k, double t); // General growth-based diffrential equations can be solved by seperation of variables.

	std::vector<double> jacobian(double (*function)(std::vector<double>), std::vector<double> x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
	std::vector<std::vector<double>> hessian(double (*function)(std::vector<double>), std::vector<double> x);
	std::vector<std::vector<std::vector<double>>> thirdOrderTensor(double (*function)(std::vector<double>), std::vector<double> x);

	double constantApproximation(double (*function)(std::vector<double>), std::vector<double> c);
	double linearApproximation(double (*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
	double quadraticApproximation(double (*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
	double cubicApproximation(double (*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);

	double laplacian(double (*function)(std::vector<double>), std::vector<double> x); // laplacian

	std::string secondPartialDerivativeTest(double (*function)(std::vector<double>), std::vector<double> x);
};


#endif /* NumericalAnalysis_hpp */