StorelessCovariance (Apache Commons Math 3.3 API)

org.apache.commons.math3.stat.correlation

## Class StorelessCovariance

- java.lang.Object
- - org.apache.commons.math3.stat.correlation.Covariance
  - - org.apache.commons.math3.stat.correlation.StorelessCovariance

-     public class StorelessCovariance
      extends Covariance

  Covariance implementation that does not require input data to be stored in memory. The size of the covariance matrix is specified in the constructor. Specific elements of the matrix are incrementally updated with calls to incrementRow() or increment Covariance().

  This class is based on a paper written by Philippe Pébay: Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments, 2008, Technical Report SAND2008-6212, Sandia National Laboratories.

  Note: the underlying covariance matrix is symmetric, thus only the upper triangular part of the matrix is stored and updated each increment.

  Since:
    3.0
  Version:
    $Id: StorelessCovariance.java 1519851 2013-09-03 21:16:35Z tn $

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `StorelessCovariance(int dim)` Create a bias corrected covariance matrix with a given dimension.
    `StorelessCovariance(int dim, boolean biasCorrected)` Create a covariance matrix with a given number of rows and columns and the indicated bias correction.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `void` | `append(StorelessCovariance sc)` Appends `sc` to this, effectively aggregating the computations in `sc` with this.
    `double` | `getCovariance(int xIndex, int yIndex)` Get the covariance for an individual element of the covariance matrix.
    `RealMatrix` | `getCovarianceMatrix()` Returns the covariance matrix
    `double[][]` | `getData()` Return the covariance matrix as two-dimensional array.
    `int` | `getN()` This `Covariance` method is not supported by a `StorelessCovariance`, since the number of bivariate observations does not have to be the same for different pairs of covariates - i.e., N as defined in `Covariance.getN()` is undefined.
    `void` | `increment(double[] data)` Increment the covariance matrix with one row of data.

    - ### Methods inherited from class org.apache.commons.math3.stat.correlation.Covariance

      `computeCovarianceMatrix, computeCovarianceMatrix, computeCovarianceMatrix, computeCovarianceMatrix, covariance, covariance`

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

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

- - ### Constructor Detail

    - #### StorelessCovariance

          public StorelessCovariance(int dim)

      Create a bias corrected covariance matrix with a given dimension.
      Parameters:
        `dim` - the dimension of the square covariance matrix

    - #### StorelessCovariance

          public StorelessCovariance(int dim,
                             boolean biasCorrected)

      Create a covariance matrix with a given number of rows and columns and the indicated bias correction.
      Parameters:
        `dim` - the dimension of the covariance matrix
        `biasCorrected` - if `true` the covariance estimate is corrected for bias, i.e. n-1 in the denominator, otherwise there is no bias correction, i.e. n in the denominator.

  - ### Method Detail

    - #### getCovariance

          public double getCovariance(int xIndex,
                             int yIndex)
                               throws NumberIsTooSmallException

      Get the covariance for an individual element of the covariance matrix.
      Parameters:
        `xIndex` - row index in the covariance matrix
        `yIndex` - column index in the covariance matrix
      Returns:
        the covariance of the given element
      Throws:
        `NumberIsTooSmallException` - if the number of observations in the cell is < 2

    - #### increment

          public void increment(double[] data)
                         throws DimensionMismatchException

      Increment the covariance matrix with one row of data.
      Parameters:
        `data` - array representing one row of data.
      Throws:
        `DimensionMismatchException` - if the length of `rowData` does not match with the covariance matrix

    - #### append

          public void append(StorelessCovariance sc)
                      throws DimensionMismatchException

      Appends `sc` to this, effectively aggregating the computations in `sc` with this. After invoking this method, covariances returned should be close to what would have been obtained by performing all of the `increment(double[])` operations in `sc` directly on this.
      Parameters:
        `sc` - externally computed StorelessCovariance to add to this
      Throws:
        `DimensionMismatchException` - if the dimension of sc does not match this
      Since:
        3.3

    - #### getCovarianceMatrix

          public RealMatrix getCovarianceMatrix()
                                         throws NumberIsTooSmallException

      Returns the covariance matrix
      Overrides:
        `getCovarianceMatrix` in class `Covariance`
      Returns:
        covariance matrix
      Throws:
        `NumberIsTooSmallException` - if the number of observations in a cell is < 2

    - #### getData

          public double[][] getData()
                             throws NumberIsTooSmallException

      Return the covariance matrix as two-dimensional array.
      Returns:
        a two-dimensional double array of covariance values
      Throws:
        `NumberIsTooSmallException` - if the number of observations for a cell is < 2

    - #### getN

          public int getN()
                   throws MathUnsupportedOperationException

      This `Covariance` method is not supported by a `StorelessCovariance`, since the number of bivariate observations does not have to be the same for different pairs of covariates - i.e., N as defined in `Covariance.getN()` is undefined.
      Overrides:
        `getN` in class `Covariance`
      Returns:
        nothing as this implementation always throws a `MathUnsupportedOperationException`
      Throws:
        `MathUnsupportedOperationException` - in all cases

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