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    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.stat.correlation;
  
  import org.hipparchus.UnitTestUtils;
  import org.hipparchus.distribution.continuous.TDistribution;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.linear.BlockRealMatrix;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.util.FastMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  
  public class PearsonsCorrelationTest {
  
      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.
      */
     @Test
     public void testLongly() {
         RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
         RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
         double[] rData = new double[] {
                 1.000000000000000, 0.9708985250610560, 0.9835516111796693, 0.5024980838759942,
                 0.4573073999764817, 0.960390571594376, 0.9713294591921188,
                 0.970898525061056, 1.0000000000000000, 0.9915891780247822, 0.6206333925590966,
                 0.4647441876006747, 0.979163432977498, 0.9911491900672053,
                 0.983551611179669, 0.9915891780247822, 1.0000000000000000, 0.6042609398895580,
                 0.4464367918926265, 0.991090069458478, 0.9952734837647849,
                 0.502498083875994, 0.6206333925590966, 0.6042609398895580, 1.0000000000000000,
                 -0.1774206295018783, 0.686551516365312, 0.6682566045621746,
                 0.457307399976482, 0.4647441876006747, 0.4464367918926265, -0.1774206295018783,
                 1.0000000000000000, 0.364416267189032, 0.4172451498349454,
                 0.960390571594376, 0.9791634329774981, 0.9910900694584777, 0.6865515163653120,
                 0.3644162671890320, 1.000000000000000, 0.9939528462329257,
                 0.971329459192119, 0.9911491900672053, 0.9952734837647849, 0.6682566045621746,
                 0.4172451498349454, 0.993952846232926, 1.0000000000000000
         };
         UnitTestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 7, 7), correlationMatrix, 10E-15);
 
         double[] rPvalues = new double[] {
                 4.38904690369668e-10,
                 8.36353208910623e-12, 7.8159700933611e-14,
                 0.0472894097790304, 0.01030636128354301, 0.01316878049026582,
                 0.0749178049642416, 0.06971758330341182, 0.0830166169296545, 0.510948586323452,
                 3.693245043123738e-09, 4.327782576751815e-11, 1.167954621905665e-13, 0.00331028281967516, 0.1652293725106684,
                 3.95834476307755e-10, 1.114663916723657e-13, 1.332267629550188e-15, 0.00466039138541463, 0.1078477071581498, 7.771561172376096e-15
         };
         RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 7);
         fillUpper(rPMatrix, 0d);
         UnitTestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
     }
 
     /**
      * Test R Swiss fertility dataset against R.
      */
     @Test
     public void testSwissFertility() {
          RealMatrix matrix = createRealMatrix(swissData, 47, 5);
          PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
          RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
          double[] rData = new double[] {
                1.0000000000000000, 0.3530791836199747, -0.6458827064572875, -0.6637888570350691,  0.4636847006517939,
                  0.3530791836199747, 1.0000000000000000,-0.6865422086171366, -0.6395225189483201, 0.4010950530487398,
                 -0.6458827064572875, -0.6865422086171366, 1.0000000000000000, 0.6984152962884830, -0.5727418060641666,
                 -0.6637888570350691, -0.6395225189483201, 0.6984152962884830, 1.0000000000000000, -0.1538589170909148,
                  0.4636847006517939, 0.4010950530487398, -0.5727418060641666, -0.1538589170909148, 1.0000000000000000
          };
          UnitTestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 5, 5), correlationMatrix, 10E-15);
 
          double[] rPvalues = new double[] {
                  0.01491720061472623,
                  9.45043734069043e-07, 9.95151527133974e-08,
                  3.658616965962355e-07, 1.304590105694471e-06, 4.811397236181847e-08,
                  0.001028523190118147, 0.005204433539191644, 2.588307925380906e-05, 0.301807756132683
          };
          RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 5);
          fillUpper(rPMatrix, 0d);
          UnitTestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
     }
 
     /**
      * Test p-value near 0. JIRA: MATH-371
      */
     @Test
     public void testPValueNearZero() {
         /*
          * Create a dataset that has r -> 1, p -> 0 as dimension increases.
          * Prior to the fix for MATH-371, p vanished for dimension >= 14.
          * Post fix, p-values diminish smoothly, vanishing at dimension = 127.
          * Tested value is ~1E-303.
          */
         int dimension = 120;
         double[][] data = new double[dimension][2];
         for (int i = 0; i < dimension; i++) {
             data[i][0] = i;
             data[i][1] = i + 1/((double)i + 1);
         }
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(data);
         Assert.assertTrue(corrInstance.getCorrelationPValues().getEntry(0, 1) > 0);
     }
 
 
     /**
      * Constant column
      */
     @Test
     public void testConstant() {
         double[] noVariance = new double[] {1, 1, 1, 1};
         double[] values = new double[] {1, 2, 3, 4};
         Assert.assertTrue(Double.isNaN(new PearsonsCorrelation().correlation(noVariance, values)));
         Assert.assertTrue(Double.isNaN(new PearsonsCorrelation().correlation(values, noVariance)));
     }
 
 
     /**
      * Insufficient data
      */
 
     @Test
     public void testInsufficientData() {
         double[] one = new double[] {1};
         double[] two = new double[] {2};
         try {
             new PearsonsCorrelation().correlation(one, two);
             Assert.fail("Expecting MathIllegalArgumentException");
         } catch (MathIllegalArgumentException ex) {
             // Expected
         }
         RealMatrix matrix = new BlockRealMatrix(new double[][] {{0},{1}});
         try {
             new PearsonsCorrelation(matrix);
             Assert.fail("Expecting MathIllegalArgumentException");
         } catch (MathIllegalArgumentException ex) {
             // Expected
         }
     }
 
     /**
      * Verify that direct t-tests using standard error estimates are consistent
      * with reported p-values
      */
     @Test
     public void testStdErrorConsistency() {
         TDistribution tDistribution = new TDistribution(45);
         RealMatrix matrix = createRealMatrix(swissData, 47, 5);
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
         RealMatrix rValues = corrInstance.getCorrelationMatrix();
         RealMatrix pValues = corrInstance.getCorrelationPValues();
         RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
         for (int i = 0; i < 5; i++) {
             for (int j = 0; j < i; j++) {
                 double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
                 double p = 2 * (1 - tDistribution.cumulativeProbability(t));
                 Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
             }
         }
     }
 
     /**
      * Verify that creating correlation from covariance gives same results as
      * direct computation from the original matrix
      */
     @Test
     public void testCovarianceConsistency() {
         RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
         Covariance covInstance = new Covariance(matrix);
         PearsonsCorrelation corrFromCovInstance = new PearsonsCorrelation(covInstance);
         UnitTestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
                 corrFromCovInstance.getCorrelationMatrix(), 10E-15);
         UnitTestUtils.assertEquals("p values", corrInstance.getCorrelationPValues(),
                 corrFromCovInstance.getCorrelationPValues(), 10E-15);
         UnitTestUtils.assertEquals("standard errors", corrInstance.getCorrelationStandardErrors(),
                 corrFromCovInstance.getCorrelationStandardErrors(), 10E-15);
 
         PearsonsCorrelation corrFromCovInstance2 =
             new PearsonsCorrelation(covInstance.getCovarianceMatrix(), 16);
         UnitTestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
                 corrFromCovInstance2.getCorrelationMatrix(), 10E-15);
         UnitTestUtils.assertEquals("p values", corrInstance.getCorrelationPValues(),
                 corrFromCovInstance2.getCorrelationPValues(), 10E-15);
         UnitTestUtils.assertEquals("standard errors", corrInstance.getCorrelationStandardErrors(),
                 corrFromCovInstance2.getCorrelationStandardErrors(), 10E-15);
     }
 
 
     @Test
     public void testConsistency() {
         RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
         double[][] data = matrix.getData();
         double[] x = matrix.getColumn(0);
         double[] y = matrix.getColumn(1);
         Assert.assertEquals(new PearsonsCorrelation().correlation(x, y),
                 corrInstance.getCorrelationMatrix().getEntry(0, 1), Double.MIN_VALUE);
         UnitTestUtils.assertEquals("Correlation matrix", corrInstance.getCorrelationMatrix(),
                 new PearsonsCorrelation().computeCorrelationMatrix(data), Double.MIN_VALUE);
     }
 
     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 BlockRealMatrix(matrixData);
     }
 
     protected RealMatrix createLowerTriangularRealMatrix(double[] data, int dimension) {
         int ptr = 0;
         RealMatrix result = new BlockRealMatrix(dimension, dimension);
         for (int i = 1; i < dimension; i++) {
             for (int j = 0; j < i; j++) {
                 result.setEntry(i, j, data[ptr]);
                 ptr++;
             }
         }
         return result;
     }
 
     protected void fillUpper(RealMatrix matrix, double diagonalValue) {
         int dimension = matrix.getColumnDimension();
         for (int i = 0; i < dimension; i++) {
             matrix.setEntry(i, i, diagonalValue);
             for (int j = i+1; j < dimension; j++) {
                 matrix.setEntry(i, j, matrix.getEntry(j, i));
             }
         }
     }
 }