C# Class Accord.Math.Integration.RombergMethod

Romberg's method for numerical integration.

In numerical analysis, Romberg's method (Romberg 1955) is used to estimate the definite integral ∫_a^b(x) dx by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The estimates generate a triangular array. Romberg's method is a Newton–Cotes formula – it evaluates the integrand at equally spaced points. The integrand must have continuous derivatives, though fairly good results may be obtained if only a few derivatives exist. If it is possible to evaluate the integrand at unequally spaced points, then other methods such as Gaussian quadrature and Clenshaw–Curtis quadrature are generally more accurate.

References: Wikipedia, The Free Encyclopedia. Romberg's method. Available on: http://en.wikipedia.org/wiki/Romberg's_method

Inheritance: IUnivariateIntegration, INumericalIntegration

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

Public Methods

Method	Description
Clone ( ) : object	Creates a new object that is a copy of the current instance.
Compute ( ) : bool	Computes the area of the function under the selected Range. The computed value will be available at this object's Area.
Integrate ( double>.Func func, double a, double b ) : double	Computes the area under the integral for the given function, in the given integration interval, using Romberg's method.
Integrate ( double>.Func func, double a, double b, int steps ) : double	Computes the area under the integral for the given function, in the given integration interval, using Romberg's method.
RombergMethod ( ) : System	Constructs a new Romberg's integration method.
RombergMethod ( double>.Func function ) : System	Constructs a new Romberg's integration method.
RombergMethod ( double>.Func function, double a, double b ) : System	Constructs a new Romberg's integration method.
RombergMethod ( int steps ) : System	Constructs a new Romberg's integration method.
RombergMethod ( int steps, double>.Func function ) : System	Constructs a new Romberg's integration method.
RombergMethod ( int steps, double>.Func function, double a, double b ) : System	Constructs a new Romberg's integration method.

Method Details

Clone() public method

Creates a new object that is a copy of the current instance.

public Clone ( ) : object
return	object

Compute() public method

Computes the area of the function under the selected Range. The computed value will be available at this object's Area.

public Compute ( ) : bool
return	bool

Integrate() public static method

Computes the area under the integral for the given function, in the given integration interval, using Romberg's method.

public static Integrate ( double>.Func func, double a, double b ) : double
func	double>.Func	The unidimensional function whose integral should be computed.
a	double	The beginning of the integration interval.
b	double	The ending of the integration interval.
return	double

Integrate() public static method

Computes the area under the integral for the given function, in the given integration interval, using Romberg's method.

public static Integrate ( double>.Func func, double a, double b, int steps ) : double
func	double>.Func	The unidimensional function whose integral should be computed.
a	double	The beginning of the integration interval.
b	double	The ending of the integration interval.
steps	int	The number of steps used in Romberg's method. Default is 6.
return	double