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# ifndef MLPP_NUMERICAL_ANALYSIS_H
# define MLPP_NUMERICAL_ANALYSIS_H
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//
// NumericalAnalysis.hpp
//
//
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# include "core/math/math_defs.h"
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# include "core/object/reference.h"
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# include "core/containers/vector.h"
# include "core/string/ustring.h"
class MLPPVector ;
class MLPPMatrix ;
class MLPPTensor3 ;
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class MLPPNumericalAnalysis : public Reference {
GDCLASS ( MLPPNumericalAnalysis , Reference ) ;
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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 .
*/
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real_t num_diffr ( real_t ( * function ) ( real_t ) , real_t x ) ;
real_t num_diff_2r ( real_t ( * function ) ( real_t ) , real_t x ) ;
real_t num_diff_3r ( real_t ( * function ) ( real_t ) , real_t x ) ;
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real_t constant_approximationr ( real_t ( * function ) ( real_t ) , real_t c ) ;
real_t linear_approximationr ( real_t ( * function ) ( real_t ) , real_t c , real_t x ) ;
real_t quadratic_approximationr ( real_t ( * function ) ( real_t ) , real_t c , real_t x ) ;
real_t cubic_approximationr ( real_t ( * function ) ( real_t ) , real_t c , real_t x ) ;
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real_t num_diffv ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & , int axis ) ;
real_t num_diff_2v ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & , int axis1 , int axis2 ) ;
real_t num_diff_3v ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & , int axis1 , int axis2 , int axis3 ) ;
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real_t newton_raphson_method ( real_t ( * function ) ( real_t ) , real_t x_0 , real_t epoch_num ) ;
real_t halley_method ( real_t ( * function ) ( real_t ) , real_t x_0 , real_t epoch_num ) ;
real_t inv_quadratic_interpolation ( real_t ( * function ) ( real_t ) , const Ref < MLPPVector > & x_0 , int epoch_num ) ;
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real_t eulerian_methodr ( real_t ( * derivative ) ( real_t ) , real_t q_0 , real_t q_1 , real_t p , real_t h ) ; // Euler's method for solving diffrential equations.
real_t eulerian_methodv ( real_t ( * derivative ) ( const Ref < MLPPVector > & ) , real_t q_0 , real_t q_1 , real_t p , real_t h ) ; // Euler's method for solving diffrential equations.
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real_t growth_method ( 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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Ref < MLPPVector > jacobian ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & x ) ; // Indeed, for functions with scalar outputs the Jacobians will be vectors.
Ref < MLPPMatrix > hessian ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & x ) ;
Ref < MLPPTensor3 > third_order_tensor ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & x ) ;
Vector < Ref < MLPPMatrix > > third_order_tensorvt ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & x ) ;
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real_t constant_approximationv ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & c ) ;
real_t linear_approximationv ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & c , const Ref < MLPPVector > & x ) ;
real_t quadratic_approximationv ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & c , const Ref < MLPPVector > & x ) ;
real_t cubic_approximationv ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & c , const Ref < MLPPVector > & x ) ;
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real_t laplacian ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & x ) ; // laplacian
String second_partial_derivative_test ( real_t ( * function ) ( const Ref < MLPPVector > & ) , const Ref < MLPPVector > & x ) ;
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protected :
static void _bind_methods ( ) ;
} ;
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# endif /* NumericalAnalysis_hpp */