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## org.apache.commons.math.random
Class CorrelatedRandomVectorGenerator

    java.lang.Object
      org.apache.commons.math.random.CorrelatedRandomVectorGenerator

All Implemented Interfaces:
  RandomVectorGenerator

    public class CorrelatedRandomVectorGenerator

extends Object
implements RandomVectorGenerator

A `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.

Since:
  1.2
Version:
  $Revision: 1043908 $ $Date: 2010-12-09 12:53:14 +0100 (jeu. 09 déc. 2010) $

Field Summary
`private NormalizedRandomGenerator` | `generator` Underlying generator.
`private double[]` | `mean` Mean vector.
`private double[]` | `normalized` Storage for the normalized vector.
`private int` | `rank` Rank of the covariance matrix.
`private RealMatrix` | `root` Permutated Cholesky root of the covariance matrix.

Constructor Summary
`CorrelatedRandomVectorGenerator(double[] mean, RealMatrix covariance, double small, NormalizedRandomGenerator generator)` Simple constructor.
`CorrelatedRandomVectorGenerator(RealMatrix covariance, double small, NormalizedRandomGenerator generator)` Simple constructor.

Method Summary
`private void` | `decompose(RealMatrix covariance, double small)` Decompose the original square matrix.
`NormalizedRandomGenerator` | `getGenerator()` Get the underlying normalized components generator.
`int` | `getRank()` Get the rank of the covariance matrix.
`RealMatrix` | `getRootMatrix()` Get the root of the covariance matrix.
`double[]` | `nextVector()` Generate a correlated random vector.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

### mean

    private final double[] mean

  Mean vector.

### generator

    private final NormalizedRandomGenerator generator

  Underlying generator.

### normalized

    private final double[] normalized

  Storage for the normalized vector.

### root

    private RealMatrix root

  Permutated Cholesky root of the covariance matrix.

### rank

    private int rank

  Rank of the covariance matrix.

Constructor Detail

### CorrelatedRandomVectorGenerator

    public CorrelatedRandomVectorGenerator(double[] mean,
                                           RealMatrix covariance,
                                           double small,
                                           NormalizedRandomGenerator generator)
                                    throws NotPositiveDefiniteMatrixException,
                                           DimensionMismatchException

  Simple constructor.

  Build a correlated random vector generator from its mean vector and covariance matrix.

  Parameters:
    `mean` - 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 discarded
    `generator` - underlying generator for uncorrelated normalized components
  Throws:
    `IllegalArgumentException` - if there is a dimension mismatch between the mean vector and the covariance matrix
    `NotPositiveDefiniteMatrixException` - if the covariance matrix is not strictly positive definite
    `DimensionMismatchException` - if the mean and covariance arrays dimensions don't match

### CorrelatedRandomVectorGenerator

    public CorrelatedRandomVectorGenerator(RealMatrix covariance,
                                           double small,
                                           NormalizedRandomGenerator generator)
                                    throws NotPositiveDefiniteMatrixException

  Simple constructor.

  Build a null mean random correlated vector generator from its covariance matrix.

  Parameters:
    `covariance` - covariance matrix
    `small` - diagonal elements threshold under which column are considered to be dependent on previous ones and are discarded
    `generator` - underlying generator for uncorrelated normalized components
  Throws:
    `NotPositiveDefiniteMatrixException` - if the covariance matrix is not strictly positive definite

Method Detail

### getGenerator

    public NormalizedRandomGenerator getGenerator()

  Get the underlying normalized components generator.

  Returns:
    underlying uncorrelated components generator

### getRootMatrix

    public RealMatrix getRootMatrix()

  Get the root of the covariance matrix. The root is the rectangular matrix `B` such that the covariance matrix is equal to `B.BT`

  Returns:
    root of the square matrix
  See Also:
    `getRank()`

### getRank

    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 rectangular matrix of the decomposition.

  Returns:
    rank of the square matrix.
  See Also:
    `getRootMatrix()`

### decompose

    private void decompose(RealMatrix covariance,
                           double small)
                    throws NotPositiveDefiniteMatrixException

  Decompose the original square matrix.

  The decomposition is based on a Choleski decomposition where additional transforms are performed:

  - the rows of the decomposed matrix are permuted
  - columns with the too small diagonal element are discarded
  - the matrix is permuted
  This means that rather than computing M = UT.U where U is an upper triangular matrix, this method computed M=B.BT where B is a rectangular matrix.

  Parameters:
    `covariance` - covariance matrix
    `small` - diagonal elements threshold under which column are considered to be dependent on previous ones and are discarded
  Throws:
    `NotPositiveDefiniteMatrixException` - if the covariance matrix is not strictly positive definite

### nextVector

    public double[] nextVector()

  Generate a correlated random vector.

  Specified by:
    `nextVector` in interface `RandomVectorGenerator`
  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.

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