NumericalIntegrator Class

Serves as an abstract base class for classes that represent an implementation of a numerical integration algorithm.

Definition

Namespace: Extreme.Mathematics.Calculus
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

public abstract class NumericalIntegrator : IterativeAlgorithm

Visual Basic

Public MustInherit Class NumericalIntegrator
	Inherits IterativeAlgorithm

C++/CLI

public ref class NumericalIntegrator abstract : public IterativeAlgorithm

[<AbstractClassAttribute>]
type NumericalIntegrator = 
    class
        inherit IterativeAlgorithm
    end

Inheritance: Object → ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>> → ManagedIterativeAlgorithm<Double> → IterativeAlgorithm → NumericalIntegrator

Derived: Extreme.Mathematics.Calculus.AdaptiveIntegrator
Extreme.Mathematics.Calculus.DoubleExponentialIntegrator
Extreme.Mathematics.Calculus.LeftPointIntegrator
Extreme.Mathematics.Calculus.MidpointIntegrator
Extreme.Mathematics.Calculus.NonAdaptiveGaussKronrodIntegrator
Extreme.Mathematics.Calculus.RightPointIntegrator
Extreme.Mathematics.Calculus.RombergIntegrator
Extreme.Mathematics.Calculus.SimpsonIntegrator
Extreme.Mathematics.Calculus.TrapezoidIntegrator
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Remarks

NumericalIntegrator is the abstract base class for classes that implement numerical integration algorithms. It cannot be instantiated directly. Instead, use one of the derived classes:

Class	Description
SimpsonIntegrator	Represents a numerical integrator that uses Simpson's rule.
RombergIntegrator	Represents a numerical integrator that uses Romberg's method.
NonAdaptiveGaussKronrodIntegrator	Represents a numerical integrator that uses a non-adaptive 87-point Gauss-Kronrod algorithm.
AdaptiveIntegrator	Represents a numerical integrator that uses an adaptive algorithm based on a Gauss-Kronrod integration rule.

Constructors

NumericalIntegrator()	Constructs a new NumericalIntegrator object.
NumericalIntegrator(Func<Double, Double>, Double, Double)	Constructs a new NumericalIntegrator object.

Properties

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 ManagedIterativeAlgorithm<T, TError, TReport>)
CurrentError	Gets the estimated error of the approximation of the result at the current iteration. (Inherited from IterativeAlgorithm)
CurrentResult	Gets the approximation of the result at the current iteration. (Inherited from IterativeAlgorithm)
EstimatedError	Gets a value indicating the size of the absolute error of the result. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsRemaining	Gets the number of evaluations still available. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
HasSharedDegreeOfParallelism	Indicates whether the degree of parallelism is a property that is shared across instances. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Integrand	Gets or sets the function to integrate.
IterationsNeeded	Gets the number of iterations needed by the algorithm to reach the desired accuracy. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IterationsRemaining	Gets the number of iterations remaining. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
LowerBound	Gets or sets the lower bound of the integration interval.
MaxDegreeOfParallelism	Gets or sets the maximum degree of parallelism enabled by this instance. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxEvaluations	Gets or sets the maximum number of evaluations during the calculation. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxIterations	Gets or sets the maximum number of iterations to use when approximating the roots of the target function. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MinIterations	Gets or sets the minimum iterations that have to be performed. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Order	Gets the order of the numerical integrator.
ParallelOptions	Gets or sets the configuration for the parallel behavior of the algorithm. (Inherited from ManagedIterativeAlgorithm<T, 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 ManagedIterativeAlgorithm<T, TError, TReport>)
SolutionReport	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThrowExceptionOnFailure	Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
TransformedIntegrand	Gets or sets the
UpperBound	Gets or sets the upper bound of the integration interval.

Methods

Clone	Returns a copy of this numerical integrator object.
Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
ErrorEvaluator	Returns the estimated error for testing whether the algorithm has converged. (Inherited from IterativeAlgorithm)
Evaluate	Evaluates the integrand and increments the number of function evaluations.
Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
GetHashCode	Serves as the default hash function. (Inherited from Object)
GetType	Gets the Type of the current instance. (Inherited from Object)
IncrementEvaluations()	Increments the number of evaluations by one. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IncrementEvaluations(Int32)	Increments the number of evaluations by the specified amount. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Integrate()	Numerically integrates a function of one variable.
Integrate(ParallelOptions)	Numerically integrates a function of one variable.
Integrate(Double, Double)	Numerically integrates a function of one variable.
Integrate(Double, Double, ParallelOptions)	Numerically integrates a function of one variable.
Integrate(Func<Double, Double>, Double, Double)	Numerically integrates a function of one variable.
Integrate(Func<Double, Double>, Double, Double, ParallelOptions)	Numerically integrates a function of one variable.
Iterate	Performs one iteration of the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Iterated	Performs tasks after the iteration is completed, but before the status of the algorithm is finalized. (Inherited from IterativeAlgorithm)
MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
OnConvergence	Performs any tasks after the main algorithm has converged. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
OnFailure	Performs any tasks after the main algorithm has failed to converge. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
OnInit	Initializes the algorithm. (Overrides IterativeAlgorithm.OnInit())
ReportFailure(AlgorithmStatus)	Reports that the algoritm has failed. No further iterations will be performed. (Inherited from IterativeAlgorithm)
ReportFailure(T, TError, AlgorithmStatus)	Records the results of an algorithm in case it fails. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ReportResult	Records the results of an algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ReportSuccess()	Reports that the algoritm has succeeded. No further iterations will be performed. (Inherited from IterativeAlgorithm)
ReportSuccess(T, TError)	Records the results of a algorithm that converged successfully. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ResetEvaluations	Resets the number of evaluations to zero. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Restart	Prepares the algorithm to be run again with possibly different inputs. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Run()	Runs the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Run(ParallelOptions)	Runs the algorithm using the specified parallelization options. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SetResult	Sets the results of an algorithm's execution. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
TestConvergence	Checks whether the algorithm has converged. (Overrides IterativeAlgorithm.TestConvergence())
ThreadSafeIncrementEvaluations()	Increments the number of evaluations by one. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThreadSafeIncrementEvaluations(Int32)	Increments the number of evaluations by the specified amount. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThrowConvergenceException	Interprets the AlgorithmStatus and throws the appropriate exception. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ToString	Returns a string that represents the current object. (Inherited from Object)
UpdateCurrentResult	Updates the current approximation in a point-wise convergence. (Inherited from IterativeAlgorithm)
ValueEvaluator	Returns the value to compare the estimated error to when testing whether the algorithm has converged. (Inherited from IterativeAlgorithm)