Represents a numerical integrator that uses an adaptive
algorithm based on a GaussKronrod integration rule.
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
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.
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 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.) 
 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 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 GaussKronrod formula used to
calculate the integral on subintervals.
(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  (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.) 
 UseExtrapolation 
Gets or sets a value indicating whether precautions
should be taken to deal with singularities on the
integration interval.

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 Name  Description 

 Clone 
Returns a copy of this numerical integrator object.
(Overrides NumericalIntegratorClone.) 
 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.) 
 GetSingularities 
Returns an array of Double values
containing the locations of singularities of the
integrand inside the integration interval.

 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, Double) 
Numerically integrates a function of one variable.

 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.
(Overrides IterativeAlgorithmIterated.) 
 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.) 
 SetSingularities 
Sets the locations of singularities of the
integrand inside the integration interval.

 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  (Inherited from ManagedIterativeAlgorithmT, TError, TReport.) 
 ToString  Returns a string that represents the current object. (Inherited from Object.) 
 UpdateCurrentResult 
Updates the current approximation in a pointwise convergence.
(Inherited from IterativeAlgorithm.) 
 ValueEvaluator 
Returns the value to compare the estimated error to
when testing whether the algorithm has converged.
(Inherited from IterativeAlgorithm.) 
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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 31point rule
for normal integrands, and the
15point 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 speedups 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.
Reference