MidpointIntegrator Class

public sealed class MidpointIntegrator : NumericalIntegrator

Public NotInheritable Class MidpointIntegrator
	Inherits NumericalIntegrator

public ref class MidpointIntegrator sealed : public NumericalIntegrator

[<SealedAttribute>]
type MidpointIntegrator =  
    class
        inherit NumericalIntegrator
    end

The MidpointIntegrator type exposes the following members.

	Name	Description
	MidpointIntegrator	Constructs a new MidpointIntegrator object.

	Name	Description
	AbsoluteTolerance	Gets or sets the absolute tolerance used in the convergence test. (Inherited from IterativeAlgorithm.)
	ConvergenceCriterion	Gets or sets a value specifying the criterion that is to be used in the convergence test for the algorithm. (Inherited from IterativeAlgorithm.)
	ConvergenceTest	Gets the convergence test for the algorithm. (Inherited from IterativeAlgorithm.)
	ConvergenceTests	Gets the collection of convergence tests for the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	EstimatedError	Gets a value indicating the size of the absolute error of the result. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	HasSharedDegreeOfParallelism	Indicates whether the degree of parallelism is a property that is shared across instances. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Integrand	Gets or sets the function to integrate. (Inherited from NumericalIntegrator.)
	IterationsNeeded	Gets the number of iterations needed by the algorithm to reach the desired accuracy. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	LowerBound	Gets or sets the lower bound of the integration interval. (Inherited from NumericalIntegrator.)
	MaxDegreeOfParallelism	Gets or sets the maximum degree of parallelism enabled by this instance. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxEvaluations	Gets or sets the maximum number of evaluations during the calculation. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxIterations	Gets or sets the maximum number of iterations to use when approximating the roots of the target function. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MinIterations	Gets or sets the minimum iterations that have to be performed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Order	Gets the order of the numerical integrator. (Overrides NumericalIntegratorOrder.)
	ParallelOptions	Gets or sets the configuration for the parallel behavior of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	RelativeTolerance	Gets or sets the relative tolerance used in the convergence test. (Inherited from IterativeAlgorithm.)
	Result	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SolutionReport	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ThrowExceptionOnFailure	Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	UpperBound	Gets or sets the upper bound of the integration interval. (Inherited from NumericalIntegrator.)

	Name	Description
	Clone	Returns a copy of this numerical integrator object. (Inherited from NumericalIntegrator.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Integrate	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(ParallelOptions)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(Double, Double)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(Double, Double, ParallelOptions)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(FuncDouble, Double, Double, Double)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(FuncDouble, Double, Double, Double, ParallelOptions)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

The right point rule is one of the simplest numerical integration algorithms around. The interval is divided into smaller intervals, and the function value in the middle of the subinterval is taken as an approximation for the function over the entire subinterval.

This algorithm is of order 1. In each iteration, the number of points is doubled. The difference between successive approximations is taken as the estimate for the integration error.

Because the order of the algorithm is so low, use of this algorithm is not generally recommended for general use. The fact that previous integration points are not re-used makes this algorithm extra inefficient. However, it does provide a unique feature in that can produce absolute bounds on the value of the integral of some functions. It produces an upper bound for concave integrands, and a lower bound for convex integrands. Complementary bounds are produced by the TrapezoidIntegrator.

Reference