AdaptiveIntegrator<T> Class

Represents a numerical integrator that uses an adaptive algorithm based on a Gauss-Kronrod integration rule.

Definition

Namespace: Numerics.NET.Calculus.Generic
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1
C#
public class AdaptiveIntegrator<T> : NumericalIntegrator<T>
where T : Object, INumber<T>
Inheritance
Object  →  ManagedIterativeAlgorithm<T, T, SolutionReport<T, T>>  →  IterativeAlgorithm<T>  →  NumericalIntegrator<T>  →  AdaptiveIntegrator<T>

Type Parameters

T

Remarks

The AdaptiveIntegrator<T> class provides the most robust, reliable, and in most cases the fastest numerical integration algorithm. It uses a simple integration rule to approximate the integral over subintervals. In each step, the interval with the largest estimated error is divided in two, and new approximations for these two subintervals are calculated. This process continues until the total estimated error over all intervals is within the desired tolerance.

AdaptiveIntegrator<T> inherits from NumericalIntegrator<T>, the abstract base class for all numerical integration classes. It, in turn, inherits from the [!:IterativeAlgorithm] class. All properties of this class are also available. The [!:IterativeAlgorithm.AbsoluteTolerance] and [!:IterativeAlgorithm.RelativeTolerance] properties set the desired precision as specified by the [!:IterativeAlgorithm.ConvergenceCriterion] property. The default value for both tolerances is SqrtEpsilon (roughly 10-8). MaxIterations sets the maximum number of iterations, which in this case is the maximum number of subintervals. The default value for this property is 5000. IterationsNeeded returns the actual number of iterations performed after the algorithm has completed.

The Integrate(Func<T, T>, T, T, T[]) method does the actual work of numerically integrating an integrand. It takes three parameters. The first parameter is a function of one variable that specifies the function to integrate. The second and third parameters are T values that specify the lower and upper bounds of the integration interval.

The IntegrationRule<T> property lets you specify which integration rule to use to approximate integrals on a subinterval. Integration rules can be obtained by calling static methods of the IntegrationRule<T> class. The default is the 31-point rule for normal integrands, and the 15-point rule when singularities are expected, and when integrating over infinite intervals. For oscillating integrands, the higher order rules will tend to give better results.

Several enhancements make this the integration algorithm of choice, especially for 'difficult' target functions.

An extra property, UseExtrapolation, lets you specify whether special precautions should be taken to deal with singularities. If UseExtrapolation is true, an extrapolation algorithm is used to approximate the integral near a singularity or singularities. Because this option requires extra resources, it is recommended only for integrands that actually have singularities inside or at the boundaries of the integration interval.

The SetSingularities(T[]) and GetSingularities() methods let you specify and retrieve the points inside the integration interval where the integrand has a singularity or a discontinuity. They are returned as a T array containing the problem points. Extrapolation is used once again to approximate the integral near the singularity or singularities. Specifying the problem points in the target function can lead to speed-ups of several orders of magnitude.

Unlike other classes, this integrator can deal successfully with infinite integration intervals. Specify [!:T.NegativeInfinity] or [!:T.PositiveInfinity] for one or both bounds of the integration interval. Internally, the class transforms the infinite interval to a finite interval, and performs the integration of the transformed integrand over the transformed interval.

Constructors

AdaptiveIntegrator<T>() Constructs a new AdaptiveIntegrator<T> object.
AdaptiveIntegrator<T>(Boolean) Constructs a new AdaptiveIntegrator<T> object.
AdaptiveIntegrator<T>(Func<T, T>, T[]) Constructs a new AdaptiveIntegrator<T> object.
AdaptiveIntegrator<T>(IntegrationRule<T>, Boolean) Constructs a new AdaptiveIntegrator<T> object.
AdaptiveIntegrator<T>(Func<T, T>, T, T) Constructs a new AdaptiveIntegrator<T> object.

Properties

AbsoluteTolerance Gets or sets the absolute tolerance used in the convergence test.
(Inherited from IterativeAlgorithm<T>)
ConvergenceCriterion Gets or sets a value specifying the criterion that is to be used in the convergence test for the algorithm.
(Inherited from IterativeAlgorithm<T>)
ConvergenceTest Gets the convergence test for the algorithm.
(Inherited from IterativeAlgorithm<T>)
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<T>)
CurrentResult Gets the approximation of the result at the current iteration.
(Inherited from IterativeAlgorithm<T>)
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.
(Inherited from NumericalIntegrator<T>)
IntegrationRule Gets or sets the integration rule to be used to estimate integrals over subintervals.
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.
(Inherited from NumericalIntegrator<T>)
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>)
MaxIterationsGets 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 Gauss-Kronrod formula used to calculate the integral on subintervals.
(Overrides NumericalIntegrator<T>.Order)
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<T>)
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 whether to throw an exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
TransformedIntegrand Gets or sets the
(Inherited from NumericalIntegrator<T>)
UpperBound Gets or sets the upper bound of the integration interval.
(Inherited from NumericalIntegrator<T>)
UseExtrapolation Gets or sets whether precautions should be taken to deal with singularities on the integration interval.

Methods

Clone Returns a copy of this numerical integrator object.
(Overrides NumericalIntegrator<T>.Clone())
EqualsDetermines 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<T>)
Evaluate Evaluates the integrand and increments the number of function evaluations.
(Inherited from NumericalIntegrator<T>)
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetSingularities Returns an array of T values containing the locations of singularities of the integrand inside the integration interval.
GetTypeGets 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.
(Inherited from NumericalIntegrator<T>)
Integrate(ParallelOptions) Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator<T>)
Integrate(T, T) Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator<T>)
Integrate(Func<T, T>, T, T) Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator<T>)
Integrate(T, T, ParallelOptions) Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator<T>)
Integrate(Func<T, T>, T, T, T[]) Numerically integrates a function of one variable.
Integrate(Func<T, T>, T, T, ParallelOptions) Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator<T>)
Iterate Performs one iteration of the algorithm.
(Overrides ManagedIterativeAlgorithm<T, TError, TReport>.Iterate())
Iterated Performs tasks after the iteration is completed, but before the status of the algorithm is finalized.
(Overrides IterativeAlgorithm<T>.Iterated())
MemberwiseCloneCreates 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 NumericalIntegrator<T>.OnInit())
ReportFailure(AlgorithmStatus) Reports that the algoritm has failed. No further iterations will be performed.
(Inherited from IterativeAlgorithm<T>)
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<T>)
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>)
SetSingularities Sets the locations of singularities of the integrand inside the integration interval.
TestConvergence Checks whether the algorithm has converged.
(Inherited from NumericalIntegrator<T>)
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>)
ToStringReturns a string that represents the current object.
(Inherited from Object)
UpdateCurrentResult Updates the current approximation in a point-wise convergence.
(Inherited from IterativeAlgorithm<T>)
ValueEvaluator Returns the value to compare the estimated error to when testing whether the algorithm has converged.
(Inherited from IterativeAlgorithm<T>)

See Also