Covariance
org.apache.commons.math3.stat.correlation

## Class Covariance

• Direct Known Subclasses:
StorelessCovariance

`public class Covarianceextends 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`

• ### 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
Modifier and TypeMethod and 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)           throws MathIllegalArgumentException,                  NotStrictlyPositiveException`
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 one column and two rows.

Parameters:
`data` - rectangular array with columns representing covariates
`biasCorrected` - true means covariances are bias-corrected
Throws:
`MathIllegalArgumentException` - if the input data array is not rectangular with at least two rows and one column.
`NotStrictlyPositiveException` - if the input data array is not rectangular with at least one row and one column.
• #### Covariance

`public Covariance(double[][] data)           throws MathIllegalArgumentException,                  NotStrictlyPositiveException`
Create a Covariance matrix from a rectangular array whose columns represent covariates.

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

Parameters:
`data` - rectangular array with columns representing covariates
Throws:
`MathIllegalArgumentException` - if the input data array is not rectangular with at least two rows and one column.
`NotStrictlyPositiveException` - if the input data array is not rectangular with at least one row and one column.
• #### Covariance

`public Covariance(RealMatrix matrix,          boolean biasCorrected)           throws MathIllegalArgumentException`
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 one column and two rows

Parameters:
`matrix` - matrix with columns representing covariates
`biasCorrected` - true means covariances are bias-corrected
Throws:
`MathIllegalArgumentException` - if the input matrix does not have at least two rows and one column
• #### Covariance

`public Covariance(RealMatrix matrix)           throws MathIllegalArgumentException`
Create a covariance matrix from a matrix whose columns represent covariates.

The matrix must have at least one column and two rows

Parameters:
`matrix` - matrix with columns representing covariates
Throws:
`MathIllegalArgumentException` - if the input matrix does not have at least two rows and one column
• ### 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 MathIllegalArgumentException`
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:
`MathIllegalArgumentException` - if the arrays lengths do not match or there is insufficient data
• #### covariance

`public double covariance(double[] xArray,                double[] yArray)                  throws MathIllegalArgumentException`
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:
`MathIllegalArgumentException` - if the arrays lengths do not match or there is insufficient data