HyperRectangleQuadrature Class |
Namespace: Imsl.Math
The HyperRectangleQuadrature type exposes the following members.
Name | Description | |
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HyperRectangleQuadrature(Int32) |
Constructs a HyperRectangleQuadrature object.
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HyperRectangleQuadrature(IRandomSequence) |
Constructs a HyperRectangleQuadrature object.
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Name | Description | |
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Eval(HyperRectangleQuadratureIFunction) |
Returns the value of the integral over the unit cube.
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Eval(HyperRectangleQuadratureIFunction, Double, Double) |
Returns the value of the integral over a cube.
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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 a hash function for a particular type. (Inherited from Object.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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AbsoluteError |
Sets the absolute error tolerance.
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ErrorEstimate |
Returns an estimate of the relative error in the computed result.
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NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
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Parallel |
Enable or disable performing HyperRectangleQuadrature.IFunction.F in parallel.
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RelativeError |
Sets the relative error tolerance.
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This class is used to evaluate integrals of the form:
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 , 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.