Class PearsonsCorrelation
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[(x_{i}  E(X))(y_{i}  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.

Constructor Summary
ConstructorDescriptionCreate a PearsonsCorrelation instance without data.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.PearsonsCorrelation
(Covariance covariance) Create a PearsonsCorrelation from aCovariance
. 
Method Summary
Modifier and TypeMethodDescriptioncomputeCorrelationMatrix
(double[][] data) Computes the correlation matrix for the columns of the input rectangular array.computeCorrelationMatrix
(RealMatrix matrix) Computes the correlation matrix for the columns of the input matrix, usingcorrelation(double[], double[])
.double
correlation
(double[] xArray, double[] yArray) Computes the Pearson's productmoment correlation coefficient between two arrays.covarianceToCorrelation
(RealMatrix covarianceMatrix) Derives a correlation matrix from a covariance matrix.Returns the correlation matrix.Returns a matrix of pvalues associated with the (twosided) null hypothesis that the corresponding correlation coefficient is zero.Returns a matrix of standard errors associated with the estimates in the correlation matrix.
getCorrelationStandardErrors().getEntry(i,j)
is the standard error associated withgetCorrelationMatrix.getEntry(i,j)

Constructor Details

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:

PearsonsCorrelation
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:

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


Method Details

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
Returns a matrix of standard errors associated with the estimates in the correlation matrix.
getCorrelationStandardErrors().getEntry(i,j)
is the standard error associated withgetCorrelationMatrix.getEntry(i,j)
The formula used to compute the standard error is
SE_{r} = ((1  r^{2}) / (n  2))^{1/2}
wherer
is the estimated correlation coefficient andn
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
Returns a matrix of pvalues associated with the (twosided) null hypothesis that the corresponding correlation coefficient is zero.getCorrelationPValues().getEntry(i,j)
is the probability that a random variable distributed ast_{n2}
takes a value with absolute value greater than or equal to
r((n  2) / (1  r^{2}))^{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 pvalues
 Throws:
MathIllegalStateException
 if an error occurs estimating probabilitiesNullPointerException
 if this instance was created with no data

computeCorrelationMatrix
Computes the correlation matrix for the columns of the input matrix, usingcorrelation(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:

computeCorrelationMatrix
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
public double correlation(double[] xArray, double[] yArray) Computes the Pearson's productmoment 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 arrayyArray
 second data array Returns:
 Returns Pearson's correlation coefficient for the two arrays
 Throws:
MathIllegalArgumentException
 if the arrays lengths do not matchMathIllegalArgumentException
 if there is insufficient data

covarianceToCorrelation
Derives a correlation matrix from a covariance matrix.Uses the formula
r(X,Y) = cov(X,Y)/s(X)s(Y)
wherer(·,·)
is the correlation coefficient ands(·)
means standard deviation. Parameters:
covarianceMatrix
 the covariance matrix Returns:
 correlation matrix
