Adaptive Integrator ND Class
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2
public class AdaptiveIntegratorND : NumericalIntegratorND
- Inheritance
- Object → ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>> → IterativeAlgorithm<Double> → NumericalIntegratorND → AdaptiveIntegratorND
Remarks
Use the AdaptiveIntegratorND to compute integrals of functions with one or more variables over box shaped regions. This class uses an adaptive algorithm and in most cases far outperforms alternative methods.
AdaptiveIntegratorND inherits from NumericalIntegratorND, the abstract base class for all classes that implement numerical integration in multiple dimensions. It, in turn, inherits from the IterativeAlgorithm<T> 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 subregions. The default value for this property is 5000. IterationsNeeded returns the actual number of iterations performed after the algorithm has completed.
The Integrate() method does the actual work of numerically integrating an integrand. It takes three parameters. The first parameter is a delegate that represents a multivariate function that specifies the function to integrate. The second and third parameters are Double values that specify the lower and upper bounds of the integration region in the X direction. The fourth and fifth parameters are Double values that specify the lower and upper bounds of the integration region in the Y direction.
The IntegrationRule property lets you specify which integration rule to use to approximate integrals on a subregion. For oscillating integrands, the higher order rules will tend to give better results.
Constructors
Adaptive | Initializes a new instance of the AdaptiveIntegratorND class |
Properties
Absolute |
Gets or sets the absolute tolerance used in the
convergence test.
(Inherited from IterativeAlgorithm<T>) |
Convergence |
Gets or sets a value specifying the criterion that is
to be used in the convergence test for the algorithm.
(Inherited from IterativeAlgorithm<T>) |
Convergence |
Gets the convergence test for the algorithm.
(Inherited from IterativeAlgorithm<T>) |
Convergence |
Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Current |
Gets the estimated error of the approximation of the result
at the current iteration.
(Inherited from IterativeAlgorithm<T>) |
Current |
Gets the approximation of the result at the current iteration.
(Inherited from IterativeAlgorithm<T>) |
Estimated |
Gets a value indicating the size of the absolute
error of the result.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Evaluations |
Gets the number of evaluations needed to execute the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Evaluations |
Gets the number of evaluations still available.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Has |
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 NumericalIntegratorND) |
Integration | Gets or sets the integration rule used to evaluate the integral in a simple region. |
Integration | Gets or sets the integration rule used to evaluate the integral in a simple region. |
Iterations |
Gets the number of iterations needed by the
algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Iterations |
Gets the number of iterations remaining.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Lower |
Gets or sets a vector that specifies the lower bounds of the integration region.
(Inherited from NumericalIntegratorND) |
Max |
Gets or sets the maximum degree of parallelism enabled by this instance.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Max |
Gets or sets the maximum number of evaluations during the calculation.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Max | Gets or sets the maximum number of iterations
to use when approximating the roots of the target
function.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Min |
Gets or sets the minimum iterations that have to be performed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Order |
Gets the order of the integration rule.
(Overrides NumericalIntegratorND.Order) |
Parallel |
Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Relative |
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>) |
Solution |
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>) |
Throw |
Gets or sets whether to throw an
exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Upper |
Gets or sets a vector that specifies the upper bounds of the integration region.
(Inherited from NumericalIntegratorND) |
Methods
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
Error |
Returns the estimated error for testing whether the algorithm has converged.
(Inherited from IterativeAlgorithm<T>) |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
Get | Serves as the default hash function. (Inherited from Object) |
Get | Gets the Type of the current instance. (Inherited from Object) |
Increment |
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Increment |
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 NumericalIntegratorND) |
Integrate( |
Numerically integrates a function of one variable.
(Inherited from NumericalIntegratorND) |
Integrate( |
Numerically integrates a function of one variable.
(Inherited from NumericalIntegratorND) |
Integrate( |
Numerically integrates a function of one variable.
(Inherited from NumericalIntegratorND) |
Integrate( |
Numerically integrates a function of one variable.
(Inherited from NumericalIntegratorND) |
Integrate( |
Numerically integrates a function of one variable.
(Inherited from NumericalIntegratorND) |
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.
(Inherited from IterativeAlgorithm<T>) |
Memberwise | Creates a shallow copy of the current Object. (Inherited from Object) |
OnConvergence |
Performs any tasks after the main algorithm has converged.
(Overrides ManagedIterativeAlgorithm<T, TError, TReport>.OnConvergence()) |
OnFailure |
Performs any tasks after the main algorithm has failed to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
OnInit |
Performs initialization before the first iteration.
(Overrides IterativeAlgorithm<T>.OnInit()) |
Report |
Reports that the algoritm has failed. No further iterations will be performed.
(Inherited from IterativeAlgorithm<T>) |
Report |
Records the results of an algorithm in case it fails.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Report |
Records the results of an algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Report |
Reports that the algoritm has succeeded. No further iterations will be performed.
(Inherited from IterativeAlgorithm<T>) |
Report |
Records the results of a algorithm that converged successfully.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Reset |
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( |
Runs the algorithm using the specified parallelization options.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Set |
Sets the results of an algorithm's execution.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Test |
Checks whether the algorithm has converged.
(Inherited from IterativeAlgorithm<T>) |
Thread |
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Thread |
Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Throw |
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) |
Update |
Updates the current approximation in a point-wise convergence.
(Inherited from IterativeAlgorithm<T>) |
Value |
Returns the value to compare the estimated error to
when testing whether the algorithm has converged.
(Inherited from IterativeAlgorithm<T>) |