public class UniformlyCorrelatedRandomVectorGenerator extends Object implements RandomVectorGenerator
RandomVectorGenerator
that generates vectors with with
correlated components.
Random vectors with correlated components are built by combining the uncorrelated components of another random vector in such a way that the resulting correlations are the ones specified by a positive definite correlation matrix.
The main use for correlated random vector generation is for Monte-Carlo simulation of physical problems with several
variables, for example to generate error vectors to be added to a nominal vector. A particularly interesting case is
when the generated vector should be drawn from a Multivariate Normal Distribution. The
approach using a Cholesky decomposition is quite usual in this case. However, it can be extended to other cases as
long as the underlying random generator provides normalized values
like
GaussianRandomGenerator
or UniformRandomGenerator
.
Sometimes, the covariance matrix for a given simulation is not strictly positive definite. This means that the
correlations are not all independent from each other. In this case, however, the non strictly positive elements found
during the Cholesky decomposition of the covariance matrix should not be negative either, they should be null.
Another non-conventional extension handling this case is used here. Rather than computing
C = UT.U
where C
is the covariance matrix and U
is an
upper-triangular matrix, we compute C = B.BT
where B
is a rectangular matrix
having more rows than columns. The number of columns of B
is the rank of the covariance matrix, and it
is the dimension of the uncorrelated random vector that is needed to compute the component of the correlated vector.
This class handles this situation automatically.
Constructor and Description |
---|
UniformlyCorrelatedRandomVectorGenerator(double[] aMean,
RealMatrix covariance,
double small,
NormalizedRandomGenerator aGenerator)
Builds a correlated random vector generator from its mean vector and covariance matrix.
|
UniformlyCorrelatedRandomVectorGenerator(RealMatrix covariance,
double small,
NormalizedRandomGenerator aGenerator)
Builds a null mean random correlated vector generator from its covariance matrix.
|
Modifier and Type | Method and Description |
---|---|
NormalizedRandomGenerator |
getGenerator()
Get the underlying normalized components generator.
|
int |
getRank()
Get the rank of the covariance matrix.
|
RealMatrix |
getRootMatrix()
Get the root of the correlation matrix.
|
double[] |
getStandardDeviationVector()
Get the standard deviation vector.
|
double[] |
nextVector()
Generate a correlated random vector.
|
public UniformlyCorrelatedRandomVectorGenerator(double[] aMean, RealMatrix covariance, double small, NormalizedRandomGenerator aGenerator)
aMean
- Expected mean values for all components.covariance
- Covariance matrix.small
- Diagonal elements threshold under which column are
considered to be dependent on previous ones and are discardedaGenerator
- underlying generator for uncorrelated normalized components.DimensionMismatchException
- thrown if mean vector is not of the same dimension as covariance matrixNonSquareMatrixException
- if the covariance matrix is not squareNonSymmetricMatrixException
- if the covariance matrix is not symmetricpublic UniformlyCorrelatedRandomVectorGenerator(RealMatrix covariance, double small, NormalizedRandomGenerator aGenerator)
covariance
- Covariance matrix.small
- Diagonal elements threshold under which column are
considered to be dependent on previous ones and are discarded.aGenerator
- Underlying generator for uncorrelated normalized components.public NormalizedRandomGenerator getGenerator()
public int getRank()
getRootMatrix()
public RealMatrix getRootMatrix()
B
such that
the correlation matrix is equal to B.BT
getRank()
public double[] getStandardDeviationVector()
public double[] nextVector()
nextVector
in interface RandomVectorGenerator
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