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    • AdaptiveIntegrator Class
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  • RightPointIntegrator Class
    • RightPointIntegrator Constructor
    • Properties
    • RightPointIntegrator Methods

RightPointIntegrator Class

Extreme Optimization Numerical Libraries for .NET Professional
Represents a numerical integrator that uses the right-point rule.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble, Double, SolutionReportDouble, Double
    Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble
      Extreme.Mathematics.AlgorithmsIterativeAlgorithm
        Extreme.Mathematics.CalculusNumericalIntegrator
          Extreme.Mathematics.CalculusRightPointIntegrator

Namespace:  Extreme.Mathematics.Calculus
Assembly:  Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
Syntax

C#
VB
C++
F#
Copy
public sealed class RightPointIntegrator : NumericalIntegrator
Public NotInheritable Class RightPointIntegrator
	Inherits NumericalIntegrator
public ref class RightPointIntegrator sealed : public NumericalIntegrator
[<SealedAttribute>]
type RightPointIntegrator =  
    class
        inherit NumericalIntegrator
    end

The RightPointIntegrator type exposes the following members.

Constructors

  NameDescription
Public methodRightPointIntegrator
Constructs a new RightPointIntegrator object.
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Properties

  NameDescription
Public propertyAbsoluteTolerance
Gets or sets the absolute tolerance used in the convergence test.
(Inherited from IterativeAlgorithm.)
Public propertyConvergenceCriterion
Gets or sets a value specifying the criterion that is to be used in the convergence test for the algorithm.
(Inherited from IterativeAlgorithm.)
Public propertyConvergenceTest
Gets the convergence test for the algorithm.
(Inherited from IterativeAlgorithm.)
Public propertyConvergenceTests
Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyEstimatedError
Gets a value indicating the size of the absolute error of the result.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyEvaluationsNeeded
Gets the number of evaluations needed to execute the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyHasSharedDegreeOfParallelism
Indicates whether the degree of parallelism is a property that is shared across instances.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyIntegrand
Gets or sets the function to integrate.
(Inherited from NumericalIntegrator.)
Public propertyIterationsNeeded
Gets the number of iterations needed by the algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyLowerBound
Gets or sets the lower bound of the integration interval.
(Inherited from NumericalIntegrator.)
Public propertyMaxDegreeOfParallelism
Gets or sets the maximum degree of parallelism enabled by this instance.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMaxEvaluations
Gets or sets the maximum number of evaluations during the calculation.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMaxIterations
Gets or sets the maximum number of iterations to use when approximating the roots of the target function.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMinIterations
Gets or sets the minimum iterations that have to be performed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyOrder
Gets the order of the numerical integrator.
(Overrides NumericalIntegratorOrder.)
Public propertyParallelOptions
Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyRelativeTolerance
Gets or sets the relative tolerance used in the convergence test.
(Inherited from IterativeAlgorithm.)
Public propertyResult
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertySolutionReport
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyStatus
Gets the AlgorithmStatus following an execution of the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyThrowExceptionOnFailure
Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyUpperBound
Gets or sets the upper bound of the integration interval.
(Inherited from NumericalIntegrator.)
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Methods

  NameDescription
Public methodClone
Returns a copy of this numerical integrator object.
(Inherited from NumericalIntegrator.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodIntegrate
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Public methodIntegrate(ParallelOptions)
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Public methodIntegrate(Double, Double)
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Public methodIntegrate(Double, Double, ParallelOptions)
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Public methodIntegrate(FuncDouble, Double, Double, Double)
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Public methodIntegrate(FuncDouble, Double, Double, Double, ParallelOptions)
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

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 each 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. 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 monotonically increasing integrands, and a lower bound for monotonically decreasing integrands. Complementary bounds are produced by the LeftPointIntegrator.

See Also

Reference

Extreme.Mathematics.Calculus Namespace

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