## 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
• ### Constructor Summary

Constructors
Constructor 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

All Methods
Modifier and Type Method Description
`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

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### 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
• #### 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