org.apache.commons.math3.stat.correlation

## Class PearsonsCorrelation

- java.lang.Object
- - org.apache.commons.math3.stat.correlation.PearsonsCorrelation

-     public class PearsonsCorrelation
      extends Object

  Computes Pearson's product-moment correlation coefficients for pairs of arrays or columns of a matrix.

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

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

  To compute the correlation coefficient for a single pair of arrays, use `PearsonsCorrelation()` to construct an instance with no data and then `correlation(double[], double[])`. Correlation matrices can also be computed directly from an instance with no data using `computeCorrelationMatrix(double[][])`. In order to use `getCorrelationMatrix()`, `getCorrelationPValues()`, or `getCorrelationStandardErrors()`; however, one of the constructors supplying data or a covariance matrix must be used to create the instance.

  Since:
    2.0

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `PearsonsCorrelation()` Create a PearsonsCorrelation instance without data.
    `PearsonsCorrelation(Covariance covariance)` Create a PearsonsCorrelation from a `Covariance`.
    `PearsonsCorrelation(double[][] data)` Create a PearsonsCorrelation from a rectangular array whose columns represent values of variables to be correlated.
    `PearsonsCorrelation(RealMatrix matrix)` Create a PearsonsCorrelation from a RealMatrix whose columns represent variables to be correlated.
    `PearsonsCorrelation(RealMatrix covarianceMatrix, int numberOfObservations)` Create a PearsonsCorrelation from a covariance matrix.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `RealMatrix` | `computeCorrelationMatrix(double[][] data)` Computes the correlation matrix for the columns of the input rectangular array.
    `RealMatrix` | `computeCorrelationMatrix(RealMatrix matrix)` Computes the correlation matrix for the columns of the input matrix, using `correlation(double[], double[])`.
    `double` | `correlation(double[] xArray, double[] yArray)` Computes the Pearson's product-moment correlation coefficient between two arrays.
    `RealMatrix` | `covarianceToCorrelation(RealMatrix covarianceMatrix)` Derives a correlation matrix from a covariance matrix.
    `RealMatrix` | `getCorrelationMatrix()` Returns the correlation matrix.
    `RealMatrix` | `getCorrelationPValues()` Returns a matrix of p-values associated with the (two-sided) null hypothesis that the corresponding correlation coefficient is zero.
    `RealMatrix` | `getCorrelationStandardErrors()` Returns a matrix of standard errors associated with the estimates in the correlation matrix. `getCorrelationStandardErrors().getEntry(i,j)` is the standard error associated with `getCorrelationMatrix.getEntry(i,j)`

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

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

- - ### Constructor Detail

    - #### PearsonsCorrelation

          public PearsonsCorrelation()

      Create a PearsonsCorrelation instance without data.

    - #### PearsonsCorrelation

          public PearsonsCorrelation(double[][] data)

      Create a PearsonsCorrelation from a rectangular array whose columns represent values of variables to be correlated. Throws MathIllegalArgumentException if the input array does not have at least two columns and two rows. Pairwise correlations are set to NaN if one of the correlates has zero variance.
      Parameters:
        `data` - rectangular array with columns representing variables
      Throws:
        `MathIllegalArgumentException` - if the input data array is not rectangular with at least two rows and two columns.
      See Also:
        `correlation(double[], double[])`

    - #### PearsonsCorrelation

          public PearsonsCorrelation(RealMatrix matrix)

      Create a PearsonsCorrelation from a RealMatrix whose columns represent variables to be correlated. Throws MathIllegalArgumentException if the matrix does not have at least two columns and two rows. Pairwise correlations are set to NaN if one of the correlates has zero variance.
      Parameters:
        `matrix` - matrix with columns representing variables to correlate
      Throws:
        `MathIllegalArgumentException` - if the matrix does not contain sufficient data
      See Also:
        `correlation(double[], double[])`

    - #### PearsonsCorrelation

          public PearsonsCorrelation(Covariance covariance)

      Create a PearsonsCorrelation from a `Covariance`. The correlation matrix is computed by scaling the Covariance's covariance matrix. The Covariance instance must have been created from a data matrix with columns representing variable values.
      Parameters:
        `covariance` - Covariance instance

    - #### PearsonsCorrelation

          public PearsonsCorrelation(RealMatrix covarianceMatrix,
                             int numberOfObservations)

      Create a PearsonsCorrelation from a covariance matrix. The correlation matrix is computed by scaling the covariance matrix.
      Parameters:
        `covarianceMatrix` - covariance matrix
        `numberOfObservations` - the number of observations in the dataset used to compute the covariance matrix

  - ### Method Detail

    - #### getCorrelationMatrix

          public RealMatrix getCorrelationMatrix()

      Returns the correlation matrix.

      This method will return null if the argumentless constructor was used to create this instance, even if `computeCorrelationMatrix(double[][])` has been called before it is activated.

      Returns:
        correlation matrix

    - #### getCorrelationStandardErrors

          public RealMatrix getCorrelationStandardErrors()

      Returns a matrix of standard errors associated with the estimates in the correlation matrix.
      `getCorrelationStandardErrors().getEntry(i,j)` is the standard error associated with `getCorrelationMatrix.getEntry(i,j)`

      The formula used to compute the standard error is
      `SEr = ((1 - r2) / (n - 2))1/2` where `r` is the estimated correlation coefficient and `n` is the number of observations in the source dataset.

      To use this method, one of the constructors that supply an input matrix must have been used to create this instance.

      Returns:
        matrix of correlation standard errors
      Throws:
        `NullPointerException` - if this instance was created with no data

    - #### getCorrelationPValues

          public RealMatrix getCorrelationPValues()

      Returns a matrix of p-values associated with the (two-sided) null hypothesis that the corresponding correlation coefficient is zero.

      `getCorrelationPValues().getEntry(i,j)` is the probability that a random variable distributed as `tn-2` takes a value with absolute value greater than or equal to
      `|r|((n - 2) / (1 - r2))1/2`

      The values in the matrix are sometimes referred to as the significance of the corresponding correlation coefficients.

      To use this method, one of the constructors that supply an input matrix must have been used to create this instance.

      Returns:
        matrix of p-values
      Throws:
        `MaxCountExceededException` - if an error occurs estimating probabilities
        `NullPointerException` - if this instance was created with no data

    - #### computeCorrelationMatrix

          public RealMatrix computeCorrelationMatrix(RealMatrix matrix)

      Computes the correlation matrix for the columns of the input matrix, using `correlation(double[], double[])`. Throws MathIllegalArgumentException if the matrix does not have at least two columns and two rows. Pairwise correlations are set to NaN if one of the correlates has zero variance.
      Parameters:
        `matrix` - matrix with columns representing variables to correlate
      Returns:
        correlation matrix
      Throws:
        `MathIllegalArgumentException` - if the matrix does not contain sufficient data
      See Also:
        `correlation(double[], double[])`

    - #### computeCorrelationMatrix

          public RealMatrix computeCorrelationMatrix(double[][] data)

      Computes the correlation matrix for the columns of the input rectangular array. The columns of the array represent values of variables to be correlated. Throws MathIllegalArgumentException if the matrix does not have at least two columns and two rows or if the array is not rectangular. Pairwise correlations are set to NaN if one of the correlates has zero variance.
      Parameters:
        `data` - matrix with columns representing variables to correlate
      Returns:
        correlation matrix
      Throws:
        `MathIllegalArgumentException` - if the array does not contain sufficient data
      See Also:
        `correlation(double[], double[])`

    - #### correlation

          public double correlation(double[] xArray,
                           double[] yArray)

      Computes the Pearson's product-moment correlation coefficient between two arrays.

      Throws MathIllegalArgumentException if the arrays do not have the same length or their common length is less than 2. Returns `NaN` if either of the arrays has zero variance (i.e., if one of the arrays does not contain at least two distinct values).

      Parameters:
        `xArray` - first data array
        `yArray` - second data array
      Returns:
        Returns Pearson's correlation coefficient for the two arrays
      Throws:
        `DimensionMismatchException` - if the arrays lengths do not match
        `MathIllegalArgumentException` - if there is insufficient data

    - #### covarianceToCorrelation

          public RealMatrix covarianceToCorrelation(RealMatrix covarianceMatrix)

      Derives a correlation matrix from a covariance matrix.

      Uses the formula
      `r(X,Y) = cov(X,Y)/s(X)s(Y)` where `r(·,·)` is the correlation coefficient and `s(·)` means standard deviation.

      Parameters:
        `covarianceMatrix` - the covariance matrix
      Returns:
        correlation matrix

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