C# Class Accord.Math.Differentiation.FiniteDifferences

Derivative approximation by finite differences.

Numerical differentiation is a technique of numerical analysis to produce an estimate of the derivative of a mathematical function or function subroutine using values from the function and perhaps other knowledge about the function.

References: Trent F. Guidry, Calculating derivatives of a function numerically. Available on: http://www.trentfguidry.net/post/2009/07/12/Calculate-derivatives-function-numerically.aspx

Show file Open project: accord-net/framework Class Usage Examples

Public Methods

Method	Description
Compute ( ) : double[]	Computes the gradient at the given point `x`.
Compute ( double x, double gradient ) : void	Computes the gradient at the given point x, storing the result at gradient.
CreateCoefficients ( int points ) : ].double[][	Creates the interpolation coefficients.
Derivative ( double>.Func function, double value ) : double	Computes the derivative for a simpler unidimensional function.
Derivative ( double>.Func function, double value, int order ) : double	Computes the derivative for a simpler unidimensional function.
Derivative ( double>.Func function, double value, int order, double stepSize ) : double	Computes the derivative for a simpler unidimensional function.
FiniteDifferences ( int variables ) : System	Initializes a new instance of the FiniteDifferences class.
FiniteDifferences ( int variables, double>.Func function ) : System	Initializes a new instance of the FiniteDifferences class.
FiniteDifferences ( int variables, double>.Func function, int order ) : System	Initializes a new instance of the FiniteDifferences class.
FiniteDifferences ( int variables, double>.Func function, int order, double stepSize ) : System	Initializes a new instance of the FiniteDifferences class.
FiniteDifferences ( int variables, int order ) : System	Initializes a new instance of the FiniteDifferences class.
FiniteDifferences ( int variables, int order, double stepSize ) : System	Initializes a new instance of the FiniteDifferences class.

Private Methods

Method	Description
Interpolate ( double coefficients, double points, int order, int center, double step ) : double	Interpolates the points to obtain an estimative of the derivative at x.
derivative ( double x, int index, double output ) : double	Computes the derivative at point `x_i`.
init ( double>.Func func, int variables, int order, double stepSize ) : void

Method Details

Compute() public method

Computes the gradient at the given point x.

public Compute ( ) : double[]
return	double[]

Compute() public method

Computes the gradient at the given point x, storing the result at gradient.

public Compute ( double x, double gradient ) : void
x	double	The point where to compute the gradient.
gradient	double	The gradient of the function evaluated at point x.
return	void

CreateCoefficients() public static method

Creates the interpolation coefficients.

public static CreateCoefficients ( int points ) : ].double[][
points	int	The number of points in the tableau.
return	].double[][

Derivative() public static method

Computes the derivative for a simpler unidimensional function.

public static Derivative ( double>.Func function, double value ) : double
function	double>.Func	The function to be differentiated.
value	double	The value x at which the derivative should be evaluated.
return	double

Derivative() public static method

Computes the derivative for a simpler unidimensional function.

public static Derivative ( double>.Func function, double value, int order ) : double
function	double>.Func	The function to be differentiated.
value	double	The value x at which the derivative should be evaluated.
order	int	The derivative order that should be obtained. Default is 1.
return	double