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Java example source code file (PearsonsCorrelation.java)

This example Java source code file (PearsonsCorrelation.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

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Java - Java tags/keywords

blockrealmatrix, pearsonscorrelation, realmatrix, simpleregression, tdistribution

The PearsonsCorrelation.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.stat.correlation;

import org.apache.commons.math3.distribution.TDistribution;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.stat.regression.SimpleRegression;
import org.apache.commons.math3.util.FastMath;

/**
 * Computes Pearson's product-moment correlation coefficients for pairs of arrays
 * or columns of a matrix.
 *
 * <p>The constructors that take RealMatrix or
 * <code>double[][] arguments generate correlation matrices.  The
 * columns of the input matrices are assumed to represent variable values.
 * Correlations are given by the formula</p>
 *
 * <p>cor(X, Y) = Σ[(xi - E(X))(yi - E(Y))] / [(n - 1)s(X)s(Y)]
 * where <code>E(X) is the mean of X, E(Y)
 * is the mean of the <code>Y values and s(X), s(Y) are standard deviations.

* * <p>To compute the correlation coefficient for a single pair of arrays, use {@link #PearsonsCorrelation()} * to construct an instance with no data and then {@link #correlation(double[], double[])}. * Correlation matrices can also be computed directly from an instance with no data using * {@link #computeCorrelationMatrix(double[][])}. In order to use {@link #getCorrelationMatrix()}, * {@link #getCorrelationPValues()}, or {@link #getCorrelationStandardErrors()}; however, one of the * constructors supplying data or a covariance matrix must be used to create the instance.</p> * * @since 2.0 */ public class PearsonsCorrelation { /** correlation matrix */ private final RealMatrix correlationMatrix; /** number of observations */ private final int nObs; /** * Create a PearsonsCorrelation instance without data. */ public PearsonsCorrelation() { super(); correlationMatrix = null; nObs = 0; } /** * 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. * * @param 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 #correlation(double[], double[]) */ public PearsonsCorrelation(double[][] data) { this(new BlockRealMatrix(data)); } /** * 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. * * @param matrix matrix with columns representing variables to correlate * @throws MathIllegalArgumentException if the matrix does not contain sufficient data * @see #correlation(double[], double[]) */ public PearsonsCorrelation(RealMatrix matrix) { nObs = matrix.getRowDimension(); correlationMatrix = computeCorrelationMatrix(matrix); } /** * Create a PearsonsCorrelation from a {@link 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. * * @param covariance Covariance instance */ public PearsonsCorrelation(Covariance covariance) { RealMatrix covarianceMatrix = covariance.getCovarianceMatrix(); if (covarianceMatrix == null) { throw new NullArgumentException(LocalizedFormats.COVARIANCE_MATRIX); } nObs = covariance.getN(); correlationMatrix = covarianceToCorrelation(covarianceMatrix); } /** * Create a PearsonsCorrelation from a covariance matrix. The correlation * matrix is computed by scaling the covariance matrix. * * @param covarianceMatrix covariance matrix * @param numberOfObservations the number of observations in the dataset used to compute * the covariance matrix */ public PearsonsCorrelation(RealMatrix covarianceMatrix, int numberOfObservations) { nObs = numberOfObservations; correlationMatrix = covarianceToCorrelation(covarianceMatrix); } /** * Returns the correlation matrix. * * <p>This method will return null if the argumentless constructor was used * to create this instance, even if {@link #computeCorrelationMatrix(double[][])} * has been called before it is activated.</p> * * @return correlation matrix */ public RealMatrix getCorrelationMatrix() { return correlationMatrix; } /** * Returns a matrix of standard errors associated with the estimates * in the correlation matrix.<br/> * <code>getCorrelationStandardErrors().getEntry(i,j) is the standard * error associated with <code>getCorrelationMatrix.getEntry(i,j) * * <p>The formula used to compute the standard error is
* <code>SEr = ((1 - r2) / (n - 2))1/2 * where <code>r is the estimated correlation coefficient and * <code>n is the number of observations in the source dataset.

* * <p>To use this method, one of the constructors that supply an input * matrix must have been used to create this instance.</p> * * @return matrix of correlation standard errors * @throws NullPointerException if this instance was created with no data */ public RealMatrix getCorrelationStandardErrors() { int nVars = correlationMatrix.getColumnDimension(); double[][] out = new double[nVars][nVars]; for (int i = 0; i < nVars; i++) { for (int j = 0; j < nVars; j++) { double r = correlationMatrix.getEntry(i, j); out[i][j] = FastMath.sqrt((1 - r * r) /(nObs - 2)); } } return new BlockRealMatrix(out); } /** * Returns a matrix of p-values associated with the (two-sided) null * hypothesis that the corresponding correlation coefficient is zero. * * <p>getCorrelationPValues().getEntry(i,j) is the probability * that a random variable distributed as <code>tn-2 takes * a value with absolute value greater than or equal to <br> * <code>|r|((n - 2) / (1 - r2))1/2

* * <p>The values in the matrix are sometimes referred to as the * <i>significance of the corresponding correlation coefficients.

* * <p>To use this method, one of the constructors that supply an input * matrix must have been used to create this instance.</p> * * @return matrix of p-values * @throws org.apache.commons.math3.exception.MaxCountExceededException * if an error occurs estimating probabilities * @throws NullPointerException if this instance was created with no data */ public RealMatrix getCorrelationPValues() { TDistribution tDistribution = new TDistribution(nObs - 2); int nVars = correlationMatrix.getColumnDimension(); double[][] out = new double[nVars][nVars]; for (int i = 0; i < nVars; i++) { for (int j = 0; j < nVars; j++) { if (i == j) { out[i][j] = 0d; } else { double r = correlationMatrix.getEntry(i, j); double t = FastMath.abs(r * FastMath.sqrt((nObs - 2)/(1 - r * r))); out[i][j] = 2 * tDistribution.cumulativeProbability(-t); } } } return new BlockRealMatrix(out); } /** * Computes the correlation matrix for the columns of the * input matrix, using {@link #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. * * @param matrix matrix with columns representing variables to correlate * @return correlation matrix * @throws MathIllegalArgumentException if the matrix does not contain sufficient data * @see #correlation(double[], double[]) */ public RealMatrix computeCorrelationMatrix(RealMatrix matrix) { checkSufficientData(matrix); int nVars = matrix.getColumnDimension(); RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars); for (int i = 0; i < nVars; i++) { for (int j = 0; j < i; j++) { double corr = correlation(matrix.getColumn(i), matrix.getColumn(j)); outMatrix.setEntry(i, j, corr); outMatrix.setEntry(j, i, corr); } outMatrix.setEntry(i, i, 1d); } return outMatrix; } /** * 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. * * @param data matrix with columns representing variables to correlate * @return correlation matrix * @throws MathIllegalArgumentException if the array does not contain sufficient data * @see #correlation(double[], double[]) */ public RealMatrix computeCorrelationMatrix(double[][] data) { return computeCorrelationMatrix(new BlockRealMatrix(data)); } /** * Computes the Pearson's product-moment correlation coefficient between two arrays. * * <p>Throws MathIllegalArgumentException if the arrays do not have the same length * or their common length is less than 2. Returns {@code NaN} if either of the arrays * has zero variance (i.e., if one of the arrays does not contain at least two distinct * values).</p> * * @param xArray first data array * @param yArray second data array * @return Returns Pearson's correlation coefficient for the two arrays * @throws DimensionMismatchException if the arrays lengths do not match * @throws MathIllegalArgumentException if there is insufficient data */ public double correlation(final double[] xArray, final double[] yArray) { SimpleRegression regression = new SimpleRegression(); if (xArray.length != yArray.length) { throw new DimensionMismatchException(xArray.length, yArray.length); } else if (xArray.length < 2) { throw new MathIllegalArgumentException(LocalizedFormats.INSUFFICIENT_DIMENSION, xArray.length, 2); } else { for(int i=0; i<xArray.length; i++) { regression.addData(xArray[i], yArray[i]); } return regression.getR(); } } /** * Derives a correlation matrix from a covariance matrix. * * <p>Uses the formula
* <code>r(X,Y) = cov(X,Y)/s(X)s(Y) where * <code>r(·,·) is the correlation coefficient and * <code>s(·) means standard deviation.

* * @param covarianceMatrix the covariance matrix * @return correlation matrix */ public RealMatrix covarianceToCorrelation(RealMatrix covarianceMatrix) { int nVars = covarianceMatrix.getColumnDimension(); RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars); for (int i = 0; i < nVars; i++) { double sigma = FastMath.sqrt(covarianceMatrix.getEntry(i, i)); outMatrix.setEntry(i, i, 1d); for (int j = 0; j < i; j++) { double entry = covarianceMatrix.getEntry(i, j) / (sigma * FastMath.sqrt(covarianceMatrix.getEntry(j, j))); outMatrix.setEntry(i, j, entry); outMatrix.setEntry(j, i, entry); } } return outMatrix; } /** * Throws MathIllegalArgumentException if the matrix does not have at least * two columns and two rows. * * @param matrix matrix to check for sufficiency * @throws MathIllegalArgumentException if there is insufficient data */ private void checkSufficientData(final RealMatrix matrix) { int nRows = matrix.getRowDimension(); int nCols = matrix.getColumnDimension(); if (nRows < 2 || nCols < 2) { throw new MathIllegalArgumentException(LocalizedFormats.INSUFFICIENT_ROWS_AND_COLUMNS, nRows, nCols); } } }

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