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58 lines
3.2 KiB
C++
58 lines
3.2 KiB
C++
//
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// NumericalAnalysis.hpp
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//
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//
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#ifndef MLPP_NUMERICAL_ANALYSIS_H
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#define MLPP_NUMERICAL_ANALYSIS_H
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#include <vector>
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#include <string>
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namespace MLPP{
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class NumericalAnalysis{
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public:
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/* A numerical method for derivatives is used. This may be subject to change,
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as an analytical method for calculating derivatives will most likely be used in
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the future.
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*/
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double numDiff(double(*function)(double), double x);
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double numDiff_2(double(*function)(double), double x);
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double numDiff_3(double(*function)(double), double x);
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double constantApproximation(double(*function)(double), double c);
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double linearApproximation(double(*function)(double), double c, double x);
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double quadraticApproximation(double(*function)(double), double c, double x);
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double cubicApproximation(double(*function)(double), double c, double x);
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double numDiff(double(*function)(std::vector<double>), std::vector<double> x, int axis);
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double numDiff_2(double(*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2);
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double numDiff_3(double(*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2, int axis3);
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double newtonRaphsonMethod(double(*function)(double), double x_0, double epoch_num);
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double halleyMethod(double(*function)(double), double x_0, double epoch_num);
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double invQuadraticInterpolation(double (*function)(double), std::vector<double> x_0, double epoch_num);
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double eulerianMethod(double(*derivative)(double), std::vector<double> q_0, double p, double h); // Euler's method for solving diffrential equations.
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double eulerianMethod(double(*derivative)(std::vector<double>), std::vector<double> q_0, double p, double h); // Euler's method for solving diffrential equations.
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double growthMethod(double C, double k, double t); // General growth-based diffrential equations can be solved by seperation of variables.
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std::vector<double> jacobian(double(*function)(std::vector<double>), std::vector<double> x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
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std::vector<std::vector<double>> hessian(double(*function)(std::vector<double>), std::vector<double> x);
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std::vector<std::vector<std::vector<double>>> thirdOrderTensor(double(*function)(std::vector<double>), std::vector<double> x);
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double constantApproximation(double(*function)(std::vector<double>), std::vector<double> c);
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double linearApproximation(double(*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
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double quadraticApproximation(double(*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
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double cubicApproximation(double(*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
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double laplacian(double(*function)(std::vector<double>), std::vector<double> x); // laplacian
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std::string secondPartialDerivativeTest(double(*function)(std::vector<double>), std::vector<double> x);
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};
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}
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#endif /* NumericalAnalysis_hpp */
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