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JMSLTM Numerical Library 4.0 | ||||||||
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java.lang.Object com.imsl.math.HyperRectangleQuadrature
HyperRectangleQuadrature integrates a function over a hypercube. 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
.
Nested Class Summary | |
static interface |
HyperRectangleQuadrature.Function
Public interface function for the HyperRectangleQuadrature class. |
Constructor Summary | |
HyperRectangleQuadrature(int dim)
Constructs a HyperRectangleQuadrature object. |
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HyperRectangleQuadrature(RandomSequence sequence)
Constructs a HyperRectangleQuadrature object. |
Method Summary | |
double |
eval(HyperRectangleQuadrature.Function objectF)
Returns the value of the integral over the unit cube. |
double |
eval(HyperRectangleQuadrature.Function objectF,
double[] a,
double[] b)
Returns the value of the integral over a cube. |
double |
getErrorEstimate()
Returns an estimate of the relative error in the computed result. |
void |
setAbsoluteError(double errorAbsolute)
Sets the absolute error tolerance. |
void |
setRelativeError(double errorRelative)
Sets the relative error tolerance. |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
public HyperRectangleQuadrature(int dim)
public HyperRectangleQuadrature(RandomSequence sequence)
Method Detail |
public double eval(HyperRectangleQuadrature.Function objectF)
objectF
- Function
containing the function to be integratedpublic double eval(HyperRectangleQuadrature.Function objectF, double[] a, double[] b)
objectF
- Function
containing the function to be integrateda
- is a double
specifying the lower limit of integration.
If null all of the lower limits default to 0.b
- is a double
specifying the upper limit of integration.
If null all of the upper limits default to 1.public double getErrorEstimate()
double
specifying an estimate of the relative
error in the computed resultpublic void setAbsoluteError(double errorAbsolute)
errorAbsolute
- a double
scalar value specifying the
absolute errorpublic void setRelativeError(double errorRelative)
errorRelative
- a double
scalar value specifying the
relative error
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JMSLTM Numerical Library 4.0 | ||||||||
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