diff --git a/src/java/org/apache/commons/math/stat/correlation/Covariance.java b/src/java/org/apache/commons/math/stat/correlation/Covariance.java
new file mode 100644
index 000000000..2066fb26a
--- /dev/null
+++ b/src/java/org/apache/commons/math/stat/correlation/Covariance.java
@@ -0,0 +1,205 @@
+/*
+ * 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.math.stat.correlation;
+
+import org.apache.commons.math.MathRuntimeException;
+import org.apache.commons.math.linear.RealMatrix;
+import org.apache.commons.math.linear.DenseRealMatrix;
+import org.apache.commons.math.stat.descriptive.moment.Mean;
+import org.apache.commons.math.stat.descriptive.moment.Variance;
+
+/**
+ * Computes covariances 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.
+ *
+ * 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
+ *
+ * @version $Revision$ $Date$
+ * @since 2.0
+ */
+public class Covariance {
+
+ /** covariance matrix */
+ private final RealMatrix covarianceMatrix;
+
+ public Covariance() {
+ super();
+ covarianceMatrix = null;
+ }
+
+ /**
+ * 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 two columns
+ * and two rows.
+ *
+ * @param data rectangular array with columns representing covariates
+ * @param biasCorrected true means covariances are bias-corrected
+ * @throws IllegalArgumentException if the input data array is not
+ * rectangular with at least two rows and two columns.
+ */
+ public Covariance(double[][] data, boolean biasCorrected) {
+ this(new DenseRealMatrix(data), biasCorrected);
+ }
+
+ /**
+ * Create a Covariance matrix from a rectangular array
+ * whose columns represent covariates.
+ *
+ * The input array must be rectangular with at least two columns
+ * and two rows
+ *
+ * @param data rectangular array with columns representing covariates
+ * @throws IllegalArgumentException if the input data array is not
+ * rectangular with at least two rows and two columns.
+ */
+ public Covariance(double[][] data) {
+ this(data, true);
+ }
+
+ /**
+ * 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 two columns and two rows
+ *
+ * @param matrix matrix with columns representing covariates
+ * @param biasCorrected true means covariances are bias-corrected
+ * @throws IllegalArgumentException if the input matrix does not have
+ * at least two rows and two columns
+ */
+ public Covariance(RealMatrix matrix, boolean biasCorrected) {
+ checkSufficientData(matrix);
+ covarianceMatrix = computeCovariance(matrix, biasCorrected);
+ }
+
+ /**
+ * Create a covariance matrix from a matrix whose columns
+ * represent covariates.
+ *
+ * The matrix must have at least two columns and two rows
+ *
+ * @param matrix matrix with columns representing covariates
+ * @throws IllegalArgumentException if the input matrix does not have
+ * at least two rows and two columns
+ */
+ public Covariance(RealMatrix matrix) {
+ this(matrix, true);
+ }
+
+ /**
+ * Returns the covariance matrix
+ *
+ * @return covariance matrix
+ */
+ public RealMatrix getCovarianceMatrix() {
+ return covarianceMatrix;
+ }
+
+ /**
+ * Create a covariance matrix from a matrix whose columns represent
+ * covariates.
+ *
+ * The input matrix must have at least two columns and two rows
+ *
+ * The biasCorrected parameter determines whether or not
+ * covariance estimates are bias-corrected.
+ *
+ * @return covariance matrix
+ */
+ protected RealMatrix computeCovariance(RealMatrix matrix, boolean biasCorrected) {
+ int dimension = matrix.getColumnDimension();
+ Variance variance = new Variance(biasCorrected);
+ RealMatrix outMatrix = new DenseRealMatrix(dimension, dimension);
+ for (int i = 0; i < dimension; i++) {
+ for (int j = 0; j < i; j++) {
+ double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);
+ outMatrix.setEntry(i, j, cov);
+ outMatrix.setEntry(j, i, cov);
+ }
+ outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));
+ }
+ return outMatrix;
+ }
+
+ /**
+ * Computes the covariance between the two arrays.
+ *
+ * Array lengths must match and the common length must be at least 2.
+ *
+ * @param xArray first data array
+ * @param yArray second data array
+ * @param biasCorrected if true, returned value will be bias-corrected
+ * @return returns the covariance for the two arrays
+ * @throws IllegalArgumentException if the arrays lengths do not match or
+ * there is insufficient data
+ */
+ public double covariance(final double[] xArray, final double[] yArray, boolean biasCorrected)
+ throws IllegalArgumentException {
+ Mean mean = new Mean();
+ double result = 0d;
+ long length = xArray.length;
+ if(length == yArray.length && length > 1) {
+ double xMean = mean.evaluate(xArray);
+ double yMean = mean.evaluate(yArray);
+ for (int i = 0; i < xArray.length; i++) {
+ double xDev = xArray[i] - xMean;
+ double yDev = yArray[i] - yMean;
+ result += (xDev * yDev - result) / (i + 1);
+ }
+ }
+ else {
+ throw MathRuntimeException.createIllegalArgumentException(
+ "Arrays must have the same length and both must have at " +
+ "least two elements. xArray has size {0}, yArray has {1} elements",
+ new Object[] {xArray.length, yArray.length});
+ }
+ return biasCorrected ? result * ((double) length / (double)(length - 1)) : result;
+ }
+
+ /**
+ * Throws IllegalArgumentException of the matrix does not have at least
+ * two columns and two rows
+ */
+ private void checkSufficientData(final RealMatrix matrix) {
+ int nRows = matrix.getRowDimension();
+ int nCols = matrix.getColumnDimension();
+ if (nRows < 2 || nCols < 2) {
+ throw MathRuntimeException.createIllegalArgumentException(
+ "Insufficient data: only {0} rows and {1} columns.",
+ new Object[]{nRows, nCols});
+ }
+ }
+}
diff --git a/src/site/xdoc/changes.xml b/src/site/xdoc/changes.xml
index e222a1f31..6802795c5 100644
--- a/src/site/xdoc/changes.xml
+++ b/src/site/xdoc/changes.xml
@@ -39,9 +39,16 @@ The type attribute can be add,update,fix,remove.
+
+ Added Covariance class to compute variance-covariance matrices in new
+ correlation package.
+
Improved fast Fourier transform efficiency.
+
+ Added a SparseRealVector class that implements a sparse vector for the RealVector interface.
+
Added factory methods to create Chebyshev, Hermite, Laguerre and Legendre polynomials.
@@ -303,9 +310,6 @@ The type attribute can be add,update,fix,remove.
Added root checks for the endpoints.
-
- Added a SparseRealVector class that implements a sparse vector for the RealVector interface.
-
")
+#
+#------------------------------------------------------------------------------
+tol <- 1E-9 # error tolerance for tests
+#------------------------------------------------------------------------------
+# Function definitions
+
+source("testFunctions") # utility test functions
+options(digits=16) # override number of digits displayed
+
+# function to verify covariance computations
+verifyCovariance <- function(matrix, expectedCovariance, name) {
+ covariance <- cov(matrix)
+ output <- c("Covariance test dataset = ", name)
+ if (assertEquals(expectedCovariance,covariance,tol,"Covariances")) {
+ displayPadded(output, SUCCEEDED, WIDTH)
+ } else {
+ displayPadded(output, FAILED, WIDTH)
+ }
+}
+
+#--------------------------------------------------------------------------
+cat("Covariance test cases\n")
+
+# Longley
+
+longley <- matrix(c(60323,83.0,234289,2356,1590,107608,1947,
+ 61122,88.5,259426,2325,1456,108632,1948,
+ 60171,88.2,258054,3682,1616,109773,1949,
+ 61187,89.5,284599,3351,1650,110929,1950,
+ 63221,96.2,328975,2099,3099,112075,1951,
+ 63639,98.1,346999,1932,3594,113270,1952,
+ 64989,99.0,365385,1870,3547,115094,1953,
+ 63761,100.0,363112,3578,3350,116219,1954,
+ 66019,101.2,397469,2904,3048,117388,1955,
+ 67857,104.6,419180,2822,2857,118734,1956,
+ 68169,108.4,442769,2936,2798,120445,1957,
+ 66513,110.8,444546,4681,2637,121950,1958,
+ 68655,112.6,482704,3813,2552,123366,1959,
+ 69564,114.2,502601,3931,2514,125368,1960,
+ 69331,115.7,518173,4806,2572,127852,1961,
+ 70551,116.9,554894,4007,2827,130081,1962),
+ nrow = 16, ncol = 7, byrow = TRUE)
+
+expectedCovariance <- matrix(c(
+ 12333921.73333333246, 3.679666000000000e+04, 343330206.333333313,
+ 1649102.666666666744, 1117681.066666666651, 23461965.733333334, 16240.93333333333248,
+ 36796.66000000000, 1.164576250000000e+02, 1063604.115416667,
+ 6258.666250000000, 3490.253750000000, 73503.000000000, 50.92333333333334,
+ 343330206.33333331347, 1.063604115416667e+06, 9879353659.329166412,
+ 56124369.854166664183, 30880428.345833335072, 685240944.600000024, 470977.90000000002328,
+ 1649102.66666666674, 6.258666250000000e+03, 56124369.854166664,
+ 873223.429166666698, -115378.762499999997, 4462741.533333333, 2973.03333333333330,
+ 1117681.06666666665, 3.490253750000000e+03, 30880428.345833335,
+ -115378.762499999997, 484304.095833333326, 1764098.133333333, 1382.43333333333339,
+ 23461965.73333333433, 7.350300000000000e+04, 685240944.600000024,
+ 4462741.533333333209, 1764098.133333333302, 48387348.933333330, 32917.40000000000146,
+ 16240.93333333333, 5.092333333333334e+01, 470977.900000000,
+ 2973.033333333333, 1382.433333333333, 32917.40000000, 22.66666666666667),
+ nrow = 7, ncol = 7, byrow = TRUE)
+
+ verifyCovariance(longley, expectedCovariance, "longley")
+
+ # Swiss Fertility
+
+ fertility <- matrix(c(80.2,17.0,15,12,9.96,
+ 83.1,45.1,6,9,84.84,
+ 92.5,39.7,5,5,93.40,
+ 85.8,36.5,12,7,33.77,
+ 76.9,43.5,17,15,5.16,
+ 76.1,35.3,9,7,90.57,
+ 83.8,70.2,16,7,92.85,
+ 92.4,67.8,14,8,97.16,
+ 82.4,53.3,12,7,97.67,
+ 82.9,45.2,16,13,91.38,
+ 87.1,64.5,14,6,98.61,
+ 64.1,62.0,21,12,8.52,
+ 66.9,67.5,14,7,2.27,
+ 68.9,60.7,19,12,4.43,
+ 61.7,69.3,22,5,2.82,
+ 68.3,72.6,18,2,24.20,
+ 71.7,34.0,17,8,3.30,
+ 55.7,19.4,26,28,12.11,
+ 54.3,15.2,31,20,2.15,
+ 65.1,73.0,19,9,2.84,
+ 65.5,59.8,22,10,5.23,
+ 65.0,55.1,14,3,4.52,
+ 56.6,50.9,22,12,15.14,
+ 57.4,54.1,20,6,4.20,
+ 72.5,71.2,12,1,2.40,
+ 74.2,58.1,14,8,5.23,
+ 72.0,63.5,6,3,2.56,
+ 60.5,60.8,16,10,7.72,
+ 58.3,26.8,25,19,18.46,
+ 65.4,49.5,15,8,6.10,
+ 75.5,85.9,3,2,99.71,
+ 69.3,84.9,7,6,99.68,
+ 77.3,89.7,5,2,100.00,
+ 70.5,78.2,12,6,98.96,
+ 79.4,64.9,7,3,98.22,
+ 65.0,75.9,9,9,99.06,
+ 92.2,84.6,3,3,99.46,
+ 79.3,63.1,13,13,96.83,
+ 70.4,38.4,26,12,5.62,
+ 65.7,7.7,29,11,13.79,
+ 72.7,16.7,22,13,11.22,
+ 64.4,17.6,35,32,16.92,
+ 77.6,37.6,15,7,4.97,
+ 67.6,18.7,25,7,8.65,
+ 35.0,1.2,37,53,42.34,
+ 44.7,46.6,16,29,50.43,
+ 42.8,27.7,22,29,58.33),
+ nrow = 47, ncol = 5, byrow = TRUE)
+
+ expectedCovariance <- matrix(c(
+ 156.0424976873265, 100.1691489361702, -64.36692876965772, -79.7295097132285, 241.5632030527289,
+ 100.169148936170251, 515.7994172062905, -124.39283071230344, -139.6574005550416, 379.9043755781684,
+ -64.3669287696577, -124.3928307123034, 63.64662349676226, 53.5758556891767, -190.5606105457909,
+ -79.7295097132285, -139.6574005550416, 53.57585568917669, 92.4560592044403, -61.6988297872340,
+ 241.5632030527289, 379.9043755781684, -190.56061054579092, -61.6988297872340, 1739.2945371877890),
+ nrow = 5, ncol = 5, byrow = TRUE)
+
+ verifyCovariance(fertility, expectedCovariance, "swiss fertility")
+
+ displayDashes(WIDTH)
\ No newline at end of file
diff --git a/src/test/R/testAll b/src/test/R/testAll
index e7f66bf29..1e63a144e 100644
--- a/src/test/R/testAll
+++ b/src/test/R/testAll
@@ -47,6 +47,9 @@ source("descriptiveTestCases")
# multiple regression
source("multipleOLSRegressionTestCases")
+# covariance
+source("covarianceTestCases")
+
#------------------------------------------------------------------------------
# if output has been diverted, change it back
if (sink.number()) {
diff --git a/src/test/org/apache/commons/math/stat/correlation/CovarianceTest.java b/src/test/org/apache/commons/math/stat/correlation/CovarianceTest.java
new file mode 100644
index 000000000..59a6e397d
--- /dev/null
+++ b/src/test/org/apache/commons/math/stat/correlation/CovarianceTest.java
@@ -0,0 +1,225 @@
+/*
+ * 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.math.stat.correlation;
+
+import org.apache.commons.math.TestUtils;
+import org.apache.commons.math.linear.RealMatrix;
+import org.apache.commons.math.linear.RealMatrixImpl;
+import org.apache.commons.math.stat.descriptive.moment.Variance;
+
+import junit.framework.TestCase;
+
+public class CovarianceTest extends TestCase {
+
+ protected final double[] longleyData = new double[] {
+ 60323,83.0,234289,2356,1590,107608,1947,
+ 61122,88.5,259426,2325,1456,108632,1948,
+ 60171,88.2,258054,3682,1616,109773,1949,
+ 61187,89.5,284599,3351,1650,110929,1950,
+ 63221,96.2,328975,2099,3099,112075,1951,
+ 63639,98.1,346999,1932,3594,113270,1952,
+ 64989,99.0,365385,1870,3547,115094,1953,
+ 63761,100.0,363112,3578,3350,116219,1954,
+ 66019,101.2,397469,2904,3048,117388,1955,
+ 67857,104.6,419180,2822,2857,118734,1956,
+ 68169,108.4,442769,2936,2798,120445,1957,
+ 66513,110.8,444546,4681,2637,121950,1958,
+ 68655,112.6,482704,3813,2552,123366,1959,
+ 69564,114.2,502601,3931,2514,125368,1960,
+ 69331,115.7,518173,4806,2572,127852,1961,
+ 70551,116.9,554894,4007,2827,130081,1962
+ };
+
+ protected final double[] swissData = new double[] {
+ 80.2,17.0,15,12,9.96,
+ 83.1,45.1,6,9,84.84,
+ 92.5,39.7,5,5,93.40,
+ 85.8,36.5,12,7,33.77,
+ 76.9,43.5,17,15,5.16,
+ 76.1,35.3,9,7,90.57,
+ 83.8,70.2,16,7,92.85,
+ 92.4,67.8,14,8,97.16,
+ 82.4,53.3,12,7,97.67,
+ 82.9,45.2,16,13,91.38,
+ 87.1,64.5,14,6,98.61,
+ 64.1,62.0,21,12,8.52,
+ 66.9,67.5,14,7,2.27,
+ 68.9,60.7,19,12,4.43,
+ 61.7,69.3,22,5,2.82,
+ 68.3,72.6,18,2,24.20,
+ 71.7,34.0,17,8,3.30,
+ 55.7,19.4,26,28,12.11,
+ 54.3,15.2,31,20,2.15,
+ 65.1,73.0,19,9,2.84,
+ 65.5,59.8,22,10,5.23,
+ 65.0,55.1,14,3,4.52,
+ 56.6,50.9,22,12,15.14,
+ 57.4,54.1,20,6,4.20,
+ 72.5,71.2,12,1,2.40,
+ 74.2,58.1,14,8,5.23,
+ 72.0,63.5,6,3,2.56,
+ 60.5,60.8,16,10,7.72,
+ 58.3,26.8,25,19,18.46,
+ 65.4,49.5,15,8,6.10,
+ 75.5,85.9,3,2,99.71,
+ 69.3,84.9,7,6,99.68,
+ 77.3,89.7,5,2,100.00,
+ 70.5,78.2,12,6,98.96,
+ 79.4,64.9,7,3,98.22,
+ 65.0,75.9,9,9,99.06,
+ 92.2,84.6,3,3,99.46,
+ 79.3,63.1,13,13,96.83,
+ 70.4,38.4,26,12,5.62,
+ 65.7,7.7,29,11,13.79,
+ 72.7,16.7,22,13,11.22,
+ 64.4,17.6,35,32,16.92,
+ 77.6,37.6,15,7,4.97,
+ 67.6,18.7,25,7,8.65,
+ 35.0,1.2,37,53,42.34,
+ 44.7,46.6,16,29,50.43,
+ 42.8,27.7,22,29,58.33
+ };
+
+
+ /**
+ * Test Longley dataset against R.
+ * Data Source: J. Longley (1967) "An Appraisal of Least Squares
+ * Programs for the Electronic Computer from the Point of View of the User"
+ * Journal of the American Statistical Association, vol. 62. September,
+ * pp. 819-841.
+ *
+ * Data are from NIST:
+ * http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Longley.dat
+ */
+ public void testLongly() {
+ RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
+ RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
+ double[] rData = new double[] {
+ 12333921.73333333246, 3.679666000000000e+04, 343330206.333333313,
+ 1649102.666666666744, 1117681.066666666651, 23461965.733333334, 16240.93333333333248,
+ 36796.66000000000, 1.164576250000000e+02, 1063604.115416667,
+ 6258.666250000000, 3490.253750000000, 73503.000000000, 50.92333333333334,
+ 343330206.33333331347, 1.063604115416667e+06, 9879353659.329166412,
+ 56124369.854166664183, 30880428.345833335072, 685240944.600000024, 470977.90000000002328,
+ 1649102.66666666674, 6.258666250000000e+03, 56124369.854166664,
+ 873223.429166666698, -115378.762499999997, 4462741.533333333, 2973.03333333333330,
+ 1117681.06666666665, 3.490253750000000e+03, 30880428.345833335,
+ -115378.762499999997, 484304.095833333326, 1764098.133333333, 1382.43333333333339,
+ 23461965.73333333433, 7.350300000000000e+04, 685240944.600000024,
+ 4462741.533333333209, 1764098.133333333302, 48387348.933333330, 32917.40000000000146,
+ 16240.93333333333, 5.092333333333334e+01, 470977.900000000,
+ 2973.033333333333, 1382.433333333333, 32917.40000000, 22.66666666666667
+ };
+
+ TestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 7, 7), covarianceMatrix, 10E-9);
+
+ }
+
+ /**
+ * Test R Swiss fertility dataset against R.
+ * Data Source: R datasets package
+ */
+ public void testSwissFertility() {
+ RealMatrix matrix = createRealMatrix(swissData, 47, 5);
+ RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
+ double[] rData = new double[] {
+ 156.0424976873265, 100.1691489361702, -64.36692876965772, -79.7295097132285, 241.5632030527289,
+ 100.169148936170251, 515.7994172062905, -124.39283071230344, -139.6574005550416, 379.9043755781684,
+ -64.3669287696577, -124.3928307123034, 63.64662349676226, 53.5758556891767, -190.5606105457909,
+ -79.7295097132285, -139.6574005550416, 53.57585568917669, 92.4560592044403, -61.6988297872340,
+ 241.5632030527289, 379.9043755781684, -190.56061054579092, -61.6988297872340, 1739.2945371877890
+ };
+
+ TestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 5, 5), covarianceMatrix, 10E-13);
+ }
+
+ /**
+ * Constant column
+ */
+ public void testConstant() {
+ double[] noVariance = new double[] {1, 1, 1, 1};
+ double[] values = new double[] {1, 2, 3, 4};
+ assertEquals(0d, new Covariance().covariance(noVariance, values, true), Double.MIN_VALUE);
+ assertEquals(0d, new Covariance().covariance(noVariance, noVariance, true), Double.MIN_VALUE);
+ }
+
+
+ /**
+ * Insufficient data
+ */
+ public void testInsufficientData() {
+ double[] one = new double[] {1};
+ double[] two = new double[] {2};
+ try {
+ new Covariance().covariance(one, two, false);
+ fail("Expecting IllegalArgumentException");
+ } catch (IllegalArgumentException ex) {
+ // Expected
+ }
+ RealMatrix matrix = new RealMatrixImpl(new double[][] {{0},{1}});
+ try {
+ new Covariance(matrix);
+ fail("Expecting IllegalArgumentException");
+ } catch (IllegalArgumentException ex) {
+ // Expected
+ }
+ }
+
+ /**
+ * Verify that diagonal entries are consistent with Variance computation and matrix matches
+ * column-by-column covariances
+ */
+ public void testConsistency() {
+ RealMatrix matrix = createRealMatrix(swissData, 47, 5);
+ RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
+
+ // Variances on the diagonal
+ Variance variance = new Variance();
+ for (int i = 0; i < 5; i++) {
+ assertEquals(variance.evaluate(matrix.getColumn(i)), covarianceMatrix.getEntry(i,i), 10E-14);
+ }
+
+ // Symmetry, column-consistency
+ assertEquals(covarianceMatrix.getEntry(2, 3),
+ new Covariance().covariance(matrix.getColumn(2), matrix.getColumn(3), true), 10E-14);
+ assertEquals(covarianceMatrix.getEntry(2, 3), covarianceMatrix.getEntry(3, 2), Double.MIN_VALUE);
+
+ // All columns same -> all entries = column variance
+ RealMatrix repeatedColumns = new RealMatrixImpl(47, 3);
+ for (int i = 0; i < 3; i++) {
+ repeatedColumns.setColumnMatrix(i, matrix.getColumnMatrix(0));
+ }
+ covarianceMatrix = new Covariance(repeatedColumns).getCovarianceMatrix();
+ double columnVariance = variance.evaluate(matrix.getColumn(0));
+ for (int i = 0; i < 3; i++) {
+ for (int j = 0; j < 3; j++) {
+ assertEquals(columnVariance, covarianceMatrix.getEntry(i, j), 10E-14);
+ }
+ }
+
+ }
+
+ protected RealMatrix createRealMatrix(double[] data, int nRows, int nCols) {
+ double[][] matrixData = new double[nRows][nCols];
+ int ptr = 0;
+ for (int i = 0; i < nRows; i++) {
+ System.arraycopy(data, ptr, matrixData[i], 0, nCols);
+ ptr += nCols;
+ }
+ return new RealMatrixImpl(matrixData);
+ }
+}