Click or drag to resize
HyperRectangleQuadrature Class
HyperRectangleQuadrature integrates a function over a hypercube.
Inheritance Hierarchy
SystemObject
  Imsl.MathHyperRectangleQuadrature

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
[SerializableAttribute]
public class HyperRectangleQuadrature

The HyperRectangleQuadrature type exposes the following members.

Constructors
  NameDescription
Public methodHyperRectangleQuadrature(Int32)
Constructs a HyperRectangleQuadrature object.
Public methodHyperRectangleQuadrature(IRandomSequence)
Constructs a HyperRectangleQuadrature object.
Top
Methods
  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodEval(HyperRectangleQuadratureIFunction)
Returns the value of the integral over the unit cube.
Public methodEval(HyperRectangleQuadratureIFunction, Double, Double)
Returns the value of the integral over a cube.
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 a hash function for a particular type.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Top
Properties
  NameDescription
Public propertyAbsoluteError
Sets the absolute error tolerance.
Public propertyErrorEstimate
Returns an estimate of the relative error in the computed result.
Public propertyNumberOfProcessors
Perform the parallel calculations with the maximum possible number of processors set to NumberOfProcessors.
Public propertyParallel
Enable or disable performing HyperRectangleQuadrature.IFunction.F in parallel.
Public propertyRelativeError
Sets the relative error tolerance.
Top
Remarks

This class is used to evaluate integrals of the form:

\int_{a_{n-1}}^{b_{n-1}} \cdots 
            \int_{a_0}^{b_0} f(x_0,\ldots,x_{n-1}) \, dx_0 \ldots dx_{n-1}

Integration of functions over hypercubes by Monte Carlo, in which the integral is evaluated as the value of the function averaged over a sequence of randomly chosen points. Under mild assumptions on the function, this method will converge like 1 / \sqrt{n}
            , where n is the number of points at which the function is evaluated.

It is possible to improve on the performance of Monte Carlo by carefully choosing the points at which the function is to be evaluated. Randomly distributed points tend to be non-uniformly distributed. The alternative to a sequence of random points is a low-discrepancy sequence. A low-discrepancy sequence is one that is highly uniform.

This function is based on the low-discrepancy Faure sequence as computed by FaureSequence.

See Also

Reference

Other Resources