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65 lines
3.1 KiB
C++
65 lines
3.1 KiB
C++
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#ifndef MLPP_NUMERICAL_ANALYSIS_H
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#define MLPP_NUMERICAL_ANALYSIS_H
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//
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// NumericalAnalysis.hpp
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//
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//
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#include "core/math/math_defs.h"
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#include "core/object/reference.h"
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#include <string>
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#include <vector>
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class MLPPNumericalAnalysis : public Reference {
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GDCLASS(MLPPNumericalAnalysis, Reference);
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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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real_t numDiff(real_t (*function)(real_t), real_t x);
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real_t numDiff_2(real_t (*function)(real_t), real_t x);
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real_t numDiff_3(real_t (*function)(real_t), real_t x);
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real_t constantApproximation(real_t (*function)(real_t), real_t c);
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real_t linearApproximation(real_t (*function)(real_t), real_t c, real_t x);
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real_t quadraticApproximation(real_t (*function)(real_t), real_t c, real_t x);
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real_t cubicApproximation(real_t (*function)(real_t), real_t c, real_t x);
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real_t numDiff(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis);
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real_t numDiff_2(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis1, int axis2);
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real_t numDiff_3(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis1, int axis2, int axis3);
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real_t newtonRaphsonMethod(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
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real_t halleyMethod(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
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real_t invQuadraticInterpolation(real_t (*function)(real_t), std::vector<real_t> x_0, int epoch_num);
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real_t eulerianMethod(real_t (*derivative)(real_t), std::vector<real_t> q_0, real_t p, real_t h); // Euler's method for solving diffrential equations.
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real_t eulerianMethod(real_t (*derivative)(std::vector<real_t>), std::vector<real_t> q_0, real_t p, real_t h); // Euler's method for solving diffrential equations.
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real_t growthMethod(real_t C, real_t k, real_t t); // General growth-based diffrential equations can be solved by seperation of variables.
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std::vector<real_t> jacobian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
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std::vector<std::vector<real_t>> hessian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x);
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std::vector<std::vector<std::vector<real_t>>> thirdOrderTensor(real_t (*function)(std::vector<real_t>), std::vector<real_t> x);
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real_t constantApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c);
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real_t linearApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x);
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real_t quadraticApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x);
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real_t cubicApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x);
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real_t laplacian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x); // laplacian
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std::string secondPartialDerivativeTest(real_t (*function)(std::vector<real_t>), std::vector<real_t> x);
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protected:
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static void _bind_methods();
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};
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#endif /* NumericalAnalysis_hpp */
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