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  • Extreme.Mathematics.Calculus
    • AdaptiveIntegrator Class
    • AdaptiveIntegrator2D Class
    • AdaptiveIntegrator2DRule Enumeration
    • AdaptiveIntegrator3DRule Enumeration
    • AdaptiveIntegratorND Class
    • AdaptiveIntegratorNDRule Enumeration
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    • Repeated1DIntegratorDirection Enumeration
    • RightPointIntegrator Class
    • RombergIntegrator Class
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  • AdaptiveIntegrator Class
    • AdaptiveIntegrator Constructors
    • Properties
    • Methods

AdaptiveIntegrator Class

Extreme Optimization Numerical Libraries for .NET Professional
Represents a numerical integrator that uses an adaptive algorithm based on a Gauss-Kronrod integration rule.
Inheritance Hierarchy

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

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

C#
VB
C++
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public class AdaptiveIntegrator : NumericalIntegrator
Public Class AdaptiveIntegrator
	Inherits NumericalIntegrator
public ref class AdaptiveIntegrator : public NumericalIntegrator
type AdaptiveIntegrator =  
    class
        inherit NumericalIntegrator
    end

The AdaptiveIntegrator type exposes the following members.

Constructors

  NameDescription
Public methodAdaptiveIntegrator
Constructs a new AdaptiveIntegrator object.
Public methodAdaptiveIntegrator(Boolean)
Constructs a new AdaptiveIntegrator object.
Public methodAdaptiveIntegrator(FuncDouble, Double, Double)
Constructs a new AdaptiveIntegrator object.
Public methodAdaptiveIntegrator(IntegrationRule, Boolean)
Constructs a new AdaptiveIntegrator object.
Public methodAdaptiveIntegrator(FuncDouble, Double, Double, Double)
Constructs a new AdaptiveIntegrator 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.)
Protected propertyCurrentError
Gets the estimated error of the approximation of the result at the current iteration.
(Inherited from IterativeAlgorithm.)
Protected propertyCurrentResult
Gets the approximation of the result at the current iteration.
(Inherited from IterativeAlgorithm.)
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.)
Protected propertyEvaluationsRemaining
Gets the number of evaluations still available.
(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 propertyIntegrationRule
Gets or sets the integration rule to be used to estimate integrals over subintervals.
Public propertyIterationsNeeded
Gets the number of iterations needed by the algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected propertyIterationsRemaining
Gets the number of iterations remaining.
(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 Gauss-Kronrod formula used to calculate the integral on subintervals.
(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.)
Protected propertyTransformedIntegrand
Gets or sets the
(Inherited from NumericalIntegrator.)
Public propertyUpperBound
Gets or sets the upper bound of the integration interval.
(Inherited from NumericalIntegrator.)
Public propertyUseExtrapolation
Gets or sets a value indicating whether precautions should be taken to deal with singularities on the integration interval.
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Methods

  NameDescription
Public methodClone
Returns a copy of this numerical integrator object.
(Overrides NumericalIntegratorClone.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodErrorEvaluator
Returns the estimated error for testing whether the algorithm has converged.
(Inherited from IterativeAlgorithm.)
Protected methodEvaluate
Evaluates the integrand and increments the number of function evaluations.
(Inherited from NumericalIntegrator.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetSingularities
Returns an array of Double values containing the locations of singularities of the integrand inside the integration interval.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodIncrementEvaluations
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodIncrementEvaluations(Int32)
Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
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, Double)
Numerically integrates a function of one variable.
Public methodIntegrate(FuncDouble, Double, Double, Double, ParallelOptions)
Numerically integrates a function of one variable.
(Inherited from NumericalIntegrator.)
Protected methodIterate
Performs one iteration of the algorithm.
(Overrides ManagedIterativeAlgorithmT, TError, TReportIterate.)
Protected methodIterated
Performs tasks after the iteration is completed, but before the status of the algorithm is finalized.
(Overrides IterativeAlgorithmIterated.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Protected methodOnConvergence
Performs any tasks after the main algorithm has converged.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodOnFailure
Performs any tasks after the main algorithm has failed to converge.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodOnInit
Initializes the algorithm.
(Overrides NumericalIntegratorOnInit.)
Protected methodReportFailure(AlgorithmStatus)
Reports that the algoritm has failed. No further iterations will be performed.
(Inherited from IterativeAlgorithm.)
Protected methodReportFailure(T, TError, AlgorithmStatus)
Records the results of an algorithm in case it fails.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodReportResult
Records the results of an algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodReportSuccess
Reports that the algoritm has succeeded. No further iterations will be performed.
(Inherited from IterativeAlgorithm.)
Protected methodReportSuccess(T, TError)
Records the results of a algorithm that converged successfully.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodResetEvaluations
Resets the number of evaluations to zero.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodRestart
Prepares the algorithm to be run again with possibly different inputs.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodRun
Runs the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodRun(ParallelOptions)
Runs the algorithm using the specified parallelization options.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodSetResult
Sets the results of an algorithm's execution.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public methodSetSingularities
Sets the locations of singularities of the integrand inside the integration interval.
Protected methodTestConvergence
Checks whether the algorithm has converged.
(Inherited from NumericalIntegrator.)
Protected methodThreadSafeIncrementEvaluations
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodThreadSafeIncrementEvaluations(Int32)
Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodThrowConvergenceException
Interprets the AlgorithmStatus and throws the appropriate exception.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Protected methodUpdateCurrentResult
Updates the current approximation in a point-wise convergence.
(Inherited from IterativeAlgorithm.)
Protected methodValueEvaluator
Returns the value to compare the estimated error to when testing whether the algorithm has converged.
(Inherited from IterativeAlgorithm.)
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Remarks

The AdaptiveIntegrator 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 inherits from NumericalIntegrator, the base class for all numerical integration classes. It, in turn, inherits from the IterativeAlgorithm class. All properties of this class are also available. The AbsoluteTolerance and RelativeTolerance properties set the desired precision as specified by the 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(FuncDouble, Double, Double, Double, Double) 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 Double values that specify the lower and upper bounds of the integration interval.

The IntegrationRule 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 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(Double) 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 Double 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 NegativeInfinity or 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.

See Also

Reference

Extreme.Mathematics.Calculus Namespace

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