org.apache.commons.math.stat.correlation

## Class Covariance

- java.lang.Object
- - org.apache.commons.math.stat.correlation.Covariance

    public class Covariance
    extends java.lang.Object

Computes covariances for pairs of arrays or columns of a matrix.

The constructors that take `RealMatrix` or `double[][]` arguments generate covariance matrices. The columns of the input matrices are assumed to represent variable values.

The constructor argument `biasCorrected` determines whether or not computed covariances are bias-corrected.

Unbiased covariances are given by the formula

`cov(X, Y) = Σ[(xi - E(X))(yi - E(Y))] / (n - 1)` where `E(X)` is the mean of `X` and `E(Y)` is the mean of the `Y` values.

Non-bias-corrected estimates use `n` in place of `n - 1`

Since:
  2.0
Version:
  $Revision: 983921 $ $Date: 2010-08-10 12:46:06 +0200 (mar. 10 août 2010) $

### Field Summary

Fields
`private RealMatrix` `covarianceMatrix` covariance matrix
`private int` `n` Number of observations (length of covariate vectors)

### Constructor Summary

Constructors
Constructor and Description
`Covariance()` Create a Covariance with no data
`Covariance(double[][] data)` Create a Covariance matrix from a rectangular array whose columns represent covariates.
`Covariance(double[][] data, boolean biasCorrected)` Create a Covariance matrix from a rectangular array whose columns represent covariates.
`Covariance(RealMatrix matrix)` Create a covariance matrix from a matrix whose columns represent covariates.
`Covariance(RealMatrix matrix, boolean biasCorrected)` Create a covariance matrix from a matrix whose columns represent covariates.

### Method Summary

Methods
`private void` `checkSufficientData(RealMatrix matrix)` Throws IllegalArgumentException of the matrix does not have at least two columns and two rows
`protected RealMatrix` `computeCovarianceMatrix(double[][] data)` Create a covariance matrix from a rectangual array whose columns represent covariates.
`protected RealMatrix` `computeCovarianceMatrix(double[][] data, boolean biasCorrected)` Compute a covariance matrix from a rectangular array whose columns represent covariates.
`protected RealMatrix` `computeCovarianceMatrix(RealMatrix matrix)` Create a covariance matrix from a matrix whose columns represent covariates.
`protected RealMatrix` `computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected)` Compute a covariance matrix from a matrix whose columns represent covariates.
`double` `covariance(double[] xArray, double[] yArray)` Computes the covariance between the two arrays, using the bias-corrected formula.
`double` `covariance(double[] xArray, double[] yArray, boolean biasCorrected)` Computes the covariance between the two arrays.
`RealMatrix` `getCovarianceMatrix()` Returns the covariance matrix
`int` `getN()` Returns the number of observations (length of covariate vectors)

### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

### Field Detail

#### covarianceMatrix

    private final RealMatrix covarianceMatrix

covariance matrix

#### n

    private final int n

Number of observations (length of covariate vectors)

### Constructor Detail

#### Covariance

    public Covariance()

Create a Covariance with no data

#### Covariance

    public Covariance(double[][] data,
              boolean biasCorrected)

Create a Covariance matrix from a rectangular array whose columns represent covariates.

The `biasCorrected` parameter determines whether or not covariance estimates are bias-corrected.

The input array must be rectangular with at least two columns and two rows.

Parameters:
  `data` - rectangular array with columns representing covariates
  `biasCorrected` - true means covariances are bias-corrected
Throws:
  `java.lang.IllegalArgumentException` - if the input data array is not rectangular with at least two rows and two columns.

#### Covariance

    public Covariance(double[][] data)

Create a Covariance matrix from a rectangular array whose columns represent covariates.

The input array must be rectangular with at least two columns and two rows

Parameters:
  `data` - rectangular array with columns representing covariates
Throws:
  `java.lang.IllegalArgumentException` - if the input data array is not rectangular with at least two rows and two columns.

#### Covariance

    public Covariance(RealMatrix matrix,
              boolean biasCorrected)

Create a covariance matrix from a matrix whose columns represent covariates.

The `biasCorrected` parameter determines whether or not covariance estimates are bias-corrected.

The matrix must have at least two columns and two rows

Parameters:
  `matrix` - matrix with columns representing covariates
  `biasCorrected` - true means covariances are bias-corrected
Throws:
  `java.lang.IllegalArgumentException` - if the input matrix does not have at least two rows and two columns

#### Covariance

    public Covariance(RealMatrix matrix)

Create a covariance matrix from a matrix whose columns represent covariates.

The matrix must have at least two columns and two rows

Parameters:
  `matrix` - matrix with columns representing covariates
Throws:
  `java.lang.IllegalArgumentException` - if the input matrix does not have at least two rows and two columns

### Method Detail

#### getCovarianceMatrix

    public RealMatrix getCovarianceMatrix()

Returns the covariance matrix

Returns:
  covariance matrix

#### getN

    public int getN()

Returns the number of observations (length of covariate vectors)

Returns:
  number of observations

#### computeCovarianceMatrix

    protected RealMatrix computeCovarianceMatrix(RealMatrix matrix,
                                     boolean biasCorrected)

Compute a covariance matrix from a matrix whose columns represent covariates.

Parameters:
  `matrix` - input matrix (must have at least two columns and two rows)
  `biasCorrected` - determines whether or not covariance estimates are bias-corrected
Returns:
  covariance matrix

#### computeCovarianceMatrix

    protected RealMatrix computeCovarianceMatrix(RealMatrix matrix)

Create a covariance matrix from a matrix whose columns represent covariates. Covariances are computed using the bias-corrected formula.

Parameters:
  `matrix` - input matrix (must have at least two columns and two rows)
Returns:
  covariance matrix
See Also:
  `Covariance(org.apache.commons.math.linear.RealMatrix)`

#### computeCovarianceMatrix

    protected RealMatrix computeCovarianceMatrix(double[][] data,
                                     boolean biasCorrected)

Compute a covariance matrix from a rectangular array whose columns represent covariates.

Parameters:
  `data` - input array (must have at least two columns and two rows)
  `biasCorrected` - determines whether or not covariance estimates are bias-corrected
Returns:
  covariance matrix

#### computeCovarianceMatrix

    protected RealMatrix computeCovarianceMatrix(double[][] data)

Create a covariance matrix from a rectangual array whose columns represent covariates. Covariances are computed using the bias-corrected formula.

Parameters:
  `data` - input array (must have at least two columns and two rows)
Returns:
  covariance matrix
See Also:
  `Covariance(org.apache.commons.math.linear.RealMatrix)`

#### covariance

    public double covariance(double[] xArray,
                    double[] yArray,
                    boolean biasCorrected)
                      throws java.lang.IllegalArgumentException

Computes the covariance between the two arrays.

Array lengths must match and the common length must be at least 2.

Parameters:
  `xArray` - first data array
  `yArray` - second data array
  `biasCorrected` - if true, returned value will be bias-corrected
Returns:
  returns the covariance for the two arrays
Throws:
  `java.lang.IllegalArgumentException` - if the arrays lengths do not match or there is insufficient data

#### covariance

    public double covariance(double[] xArray,
                    double[] yArray)
                      throws java.lang.IllegalArgumentException

Computes the covariance between the two arrays, using the bias-corrected formula.

Array lengths must match and the common length must be at least 2.

Parameters:
  `xArray` - first data array
  `yArray` - second data array
Returns:
  returns the covariance for the two arrays
Throws:
  `java.lang.IllegalArgumentException` - if the arrays lengths do not match or there is insufficient data

#### checkSufficientData

    private void checkSufficientData(RealMatrix matrix)

Throws IllegalArgumentException of the matrix does not have at least two columns and two rows

Parameters:
  `matrix` - matrix to check