DoubleExponentialIntegrator Class

public class DoubleExponentialIntegrator : NumericalIntegrator

Public Class DoubleExponentialIntegrator
	Inherits NumericalIntegrator

public ref class DoubleExponentialIntegrator : public NumericalIntegrator

type DoubleExponentialIntegrator =  
    class
        inherit NumericalIntegrator
    end

The DoubleExponentialIntegrator type exposes the following members.

	Name	Description
	DoubleExponentialIntegrator	Constructs a new NumericalIntegrator object.
	DoubleExponentialIntegrator(FuncDouble, Double, Double, Double)	Constructs a new NumericalIntegrator 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.)
	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 ManagedIterativeAlgorithmT, TError, TReport.)
	EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	EvaluationsRemaining	Gets the number of evaluations still available. (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.)
	IterationsRemaining	Gets the number of iterations remaining. (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 integration rule. (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.)
	TransformedIntegrand	Gets or sets the (Inherited from NumericalIntegrator.)
	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.)
	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. (Inherited from NumericalIntegrator.)
	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 ManagedIterativeAlgorithmT, TError, TReport.)
	IncrementEvaluations(Int32)	Increments the number of evaluations by the specified amount. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	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.)
	Iterate	Performs one iteration of the algorithm. (Overrides ManagedIterativeAlgorithmT, TError, TReportIterate.)
	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 ManagedIterativeAlgorithmT, TError, TReport.)
	OnFailure	Performs any tasks after the main algorithm has failed to converge. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	OnInit	Initializes the algorithm. (Overrides NumericalIntegratorOnInit.)
	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 ManagedIterativeAlgorithmT, TError, TReport.)
	ReportResult	Records the results of an algorithm. (Inherited from ManagedIterativeAlgorithmT, 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 ManagedIterativeAlgorithmT, TError, TReport.)
	ResetEvaluations	Resets the number of evaluations to zero. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Restart	Prepares the algorithm to be run again with possibly different inputs. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Run	Runs the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Run(ParallelOptions)	Runs the algorithm using the specified parallelization options. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SetResult	Sets the results of an algorithm's execution. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	TestConvergence	Checks whether the algorithm has converged. (Inherited from NumericalIntegrator.)
	ThreadSafeIncrementEvaluations	Increments the number of evaluations by one. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ThreadSafeIncrementEvaluations(Int32)	Increments the number of evaluations by the specified amount. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ThrowConvergenceException	Interprets the AlgorithmStatus and throws the appropriate exception. (Inherited from ManagedIterativeAlgorithmT, 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.)

The DoubleExponentialIntegrator class provides a robust, general purpose numerical integration algorithm. It uses a transformation that emphasises the regions closest to but not including the end points, which allows it to handle most integrands with singularities at the end points.

DoubleExponentialIntegrator 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 stages in which the number of evaluation points is doubled. The default value for this property is 8. IterationsNeeded returns the actual number of iterations performed after the algorithm has completed.

The Integrate(FuncDouble, 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 argument specify the lower and upper bound of the integration interval.

This integrator can handle 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.

Reference