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 covariance 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.
| Modifier and Type | Field and Description |
|---|---|
| private final NormalizedRandomGenerator | generator
Underlying generator. |
| private final double[] | mean
Mean vector. |
| private final double[] | normalized
Storage for the normalized vector. |
| private final RealMatrix | root
Root of the covariance matrix. |
| Access | Constructor and Description |
|---|---|
| public | CorrelatedRandomVectorGenerator(double[]
Expected mean values for all components. mean, RealMatrix Covariance matrix. covariance, double Diagonal elements threshold under which column are
considered to be dependent on previous ones and are discarded small, NormalizedRandomGenerator underlying generator for uncorrelated normalized
components. generator)Builds a correlated random vector generator from its mean vector and covariance matrix. |
| public | CorrelatedRandomVectorGenerator(RealMatrix
Covariance matrix. covariance, double Diagonal elements threshold under which column are
considered to be dependent on previous ones and are discarded. small, NormalizedRandomGenerator Underlying generator for uncorrelated normalized
components. generator)Builds a null mean random correlated vector generator from its covariance matrix. |
| Modifier and Type | Method and Description |
|---|---|
| public NormalizedRandomGenerator | Returns: underlying uncorrelated components generatorGet the underlying normalized components generator. |
| public int | |
| public RealMatrix | |
| public double[] | Returns: a random vector as an array of double. The returned array is created at each call, the caller can do what it wants with it.Implements org. Generate a correlated random vector. |
| generator | back to summary |
|---|---|
| private final NormalizedRandomGenerator generator Underlying generator. | |
| mean | back to summary |
|---|---|
| private final double[] mean Mean vector. | |
| normalized | back to summary |
|---|---|
| private final double[] normalized Storage for the normalized vector. | |
| root | back to summary |
|---|---|
| private final RealMatrix root Root of the covariance matrix. | |
| CorrelatedRandomVectorGenerator | back to summary |
|---|---|
| public CorrelatedRandomVectorGenerator(double[] mean, RealMatrix covariance, double small, NormalizedRandomGenerator generator) Builds a correlated random vector generator from its mean vector and covariance matrix.
| |
| CorrelatedRandomVectorGenerator | back to summary |
|---|---|
| public CorrelatedRandomVectorGenerator(RealMatrix covariance, double small, NormalizedRandomGenerator generator) Builds a null mean random correlated vector generator from its covariance matrix.
| |
| getGenerator | back to summary |
|---|---|
| public NormalizedRandomGenerator getGenerator() Get the underlying normalized components generator.
| |
| getRank | back to summary |
|---|---|
| public int getRank() Get the rank of the covariance matrix. The rank is the number of independent rows in the covariance matrix, it is also the number of columns of the root matrix.
| |
| getRootMatrix | back to summary |
|---|---|
| public RealMatrix getRootMatrix() Get the root of the covariance matrix.
The root is the rectangular matrix
| |
| nextVector | back to summary |
|---|---|
| public double[] nextVector() Implements org. Generate a correlated random vector.
| |