/*
    * 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;
  
  import org.hipparchus.complex.Complex;
  import org.hipparchus.complex.ComplexFormat;
  import org.hipparchus.complex.FieldComplex;
  import org.hipparchus.distribution.RealDistribution;
  import org.hipparchus.distribution.continuous.ChiSquaredDistribution;
  import org.hipparchus.linear.BlockRealMatrix;
  import org.hipparchus.linear.FieldMatrix;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.linear.RealVector;
  import org.hipparchus.util.Binary64;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.Precision;
  
  import java.io.ByteArrayInputStream;
  import java.io.ByteArrayOutputStream;
  import java.io.IOException;
  import java.io.ObjectInputStream;
  import java.io.ObjectOutputStream;
  import java.text.DecimalFormat;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.HashMap;
  import java.util.List;
  import java.util.Map;
  
  import static org.junit.jupiter.api.Assertions.assertEquals;
  import static org.junit.jupiter.api.Assertions.assertNotNull;
  import static org.junit.jupiter.api.Assertions.assertTrue;
  import static org.junit.jupiter.api.Assertions.fail;
  
  /**
   */
  public class UnitTestUtils {
      /**
       * Collection of static methods used in math unit tests.
       */
      private UnitTestUtils() {
          super();
      }
  
      /**
       * Verifies that expected and actual are within delta, or are both NaN or
       * infinities of the same sign.
       */
      public static void customAssertEquals(double expected, double actual, double delta) {
          assertEquals(expected, actual, delta);
      }
  
      /**
       * Verifies that expected and actual are within delta, or are both NaN or
       * infinities of the same sign.
       */
      public static void customAssertEquals(String msg, double expected, double actual, double delta) {
          // check for NaN
          if(Double.isNaN(expected)){
              assertTrue(Double.isNaN(actual),
                  "" + actual + " is not NaN.");
          } else {
              assertEquals(expected, actual, delta, msg);
          }
      }
  
      /**
       * Verifies that the two arguments are exactly the same, either
       * both NaN or infinities of same sign, or identical floating point values.
       */
      public static void customAssertSame(double expected, double actual) {
       assertEquals(expected, actual, 0);
      }
  
      /**
       * Verifies that real and imaginary parts of the two complex arguments
       * are exactly the same.  Also ensures that NaN / infinite components match.
       */
      public static void customAssertSame(Complex expected, Complex actual) {
         customAssertSame(expected.getRealPart(), actual.getRealPart());
         customAssertSame(expected.getImaginaryPart(), actual.getImaginaryPart());
     }
 
     /**
      * Verifies that real and imaginary parts of the two complex arguments
      * differ by at most delta.  Also ensures that NaN / infinite components match.
      */
     public static void customAssertEquals(Complex expected, Complex actual, double delta) {
         assertEquals(expected.getRealPart(), actual.getRealPart(), delta);
         assertEquals(expected.getImaginaryPart(), actual.getImaginaryPart(), delta);
     }
 
     /**
      * Verifies that real and imaginary parts of the two complex arguments
      * differ by at most delta.  Also ensures that NaN / infinite components match.
      */
     public static void customAssertEquals(FieldComplex<Binary64> expected, FieldComplex<Binary64> actual, double delta) {
         assertEquals(expected.getRealPart().getReal(), actual.getRealPart().getReal(), delta);
         assertEquals(expected.getImaginaryPart().getReal(), actual.getImaginaryPart().getReal(), delta);
     }
 
     /**
      * Verifies that real and imaginary parts of the two complex arguments
      * are exactly the same.  Also ensures that NaN / infinite components match.
      */
     public static void customAssertSame(FieldComplex<Binary64> expected, FieldComplex<Binary64> actual) {
         customAssertSame(expected.getRealPart().getReal(), actual.getRealPart().getReal());
         customAssertSame(expected.getImaginaryPart().getReal(), actual.getImaginaryPart().getReal());
     }
 
     /**
      * Verifies that two double arrays have equal entries, up to tolerance
      */
     public static void customAssertEquals(double[] expected, double[] observed, double tolerance) {
         customAssertEquals("Array comparison failure", expected, observed, tolerance);
     }
 
     /**
      * Serializes an object to a bytes array and then recovers the object from the bytes array.
      * Returns the deserialized object.
      *
      * @param o  object to serialize and recover
      * @return  the recovered, deserialized object
      */
     public static Object serializeAndRecover(Object o) {
         try {
             // serialize the Object
             ByteArrayOutputStream bos = new ByteArrayOutputStream();
             ObjectOutputStream so = new ObjectOutputStream(bos);
             so.writeObject(o);
 
             // deserialize the Object
             ByteArrayInputStream bis = new ByteArrayInputStream(bos.toByteArray());
             ObjectInputStream si = new ObjectInputStream(bis);
             return si.readObject();
         } catch (IOException ioe) {
             return null;
         } catch (ClassNotFoundException cnfe) {
             return null;
         }
     }
 
     /**
      * Verifies that serialization preserves equals and hashCode.
      * Serializes the object, then recovers it and checks equals and hash code.
      *
      * @param object  the object to serialize and recover
      */
     public static void checkSerializedEquality(Object object) {
         Object object2 = serializeAndRecover(object);
         assertEquals(object, object2, "Equals check");
         assertEquals(object.hashCode(), object2.hashCode(), "HashCode check");
     }
 
     /**
      * Verifies that the relative error in actual vs. expected is less than or
      * equal to relativeError.  If expected is infinite or NaN, actual must be
      * the same (NaN or infinity of the same sign).
      *
      * @param expected expected value
      * @param actual  observed value
      * @param relativeError  maximum allowable relative error
      */
     public static void customAssertRelativelyEquals(double expected, double actual,
                                                     double relativeError) {
         customAssertRelativelyEquals(null, expected, actual, relativeError);
     }
 
     /**
      * Verifies that the relative error in actual vs. expected is less than or
      * equal to relativeError.  If expected is infinite or NaN, actual must be
      * the same (NaN or infinity of the same sign).
      *
      * @param msg  message to return with failure
      * @param expected expected value
      * @param actual  observed value
      * @param relativeError  maximum allowable relative error
      */
     public static void customAssertRelativelyEquals(String msg, double expected,
                                                     double actual, double relativeError) {
         if (Double.isNaN(expected)) {
             assertTrue(Double.isNaN(actual), msg);
         } else if (Double.isNaN(actual)) {
             assertTrue(Double.isNaN(expected), msg);
         } else if (Double.isInfinite(actual) || Double.isInfinite(expected)) {
             assertEquals(expected, actual, relativeError);
         } else if (expected == 0.0) {
             assertEquals(actual, expected, relativeError, msg);
         } else {
             double absError = FastMath.abs(expected) * relativeError;
             assertEquals(expected, actual, absError, msg);
         }
     }
 
     /**
      * Fails iff values does not contain a number within epsilon of z.
      *
      * @param msg  message to return with failure
      * @param values complex array to search
      * @param z  value sought
      * @param epsilon  tolerance
      */
     public static void customAssertContains(String msg, Complex[] values,
                                             Complex z, double epsilon) {
         for (Complex value : values) {
             if (Precision.equals(value.getReal(), z.getReal(), epsilon) &&
                 Precision.equals(value.getImaginary(), z.getImaginary(), epsilon)) {
                 return;
             }
         }
         fail(msg + " Unable to find " + (new ComplexFormat()).format(z));
     }
 
     /**
      * Fails iff values does not contain a number within epsilon of z.
      *
      * @param values complex array to search
      * @param z  value sought
      * @param epsilon  tolerance
      */
     public static void customAssertContains(Complex[] values,
                                             Complex z, double epsilon) {
         customAssertContains(null, values, z, epsilon);
     }
 
     /**
      * Fails iff values does not contain a number within epsilon of x.
      *
      * @param msg  message to return with failure
      * @param values double array to search
      * @param x value sought
      * @param epsilon  tolerance
      */
     public static void customAssertContains(String msg, double[] values,
                                             double x, double epsilon) {
         for (double value : values) {
             if (Precision.equals(value, x, epsilon)) {
                 return;
             }
         }
         fail(msg + " Unable to find " + x);
     }
 
     /**
      * Fails iff values does not contain a number within epsilon of x.
      *
      * @param values double array to search
      * @param x value sought
      * @param epsilon  tolerance
      */
     public static void customAssertContains(double[] values, double x,
                                             double epsilon) {
        customAssertContains(null, values, x, epsilon);
     }
 
     /**
      * Asserts that all entries of the specified vectors are equal to within a
      * positive {@code delta}.
      *
      * @param message the identifying message for the assertion error (can be
      * {@code null})
      * @param expected expected value
      * @param actual actual value
      * @param delta the maximum difference between the entries of the expected
      * and actual vectors for which both entries are still considered equal
      */
     public static void customAssertEquals(final String message,
                                           final double[] expected, final RealVector actual, final double delta) {
         final String msgAndSep = message.equals("") ? "" : message + ", ";
         assertEquals(expected.length,
             actual.getDimension(),
             msgAndSep + "dimension");
         for (int i = 0; i < expected.length; i++) {
             assertEquals(expected[i],
                 actual.getEntry(i), delta, msgAndSep + "entry #" + i);
         }
     }
 
     /**
      * Asserts that all entries of the specified vectors are equal to within a
      * positive {@code delta}.
      *
      * @param message the identifying message for the assertion error (can be
      * {@code null})
      * @param expected expected value
      * @param actual actual value
      * @param delta the maximum difference between the entries of the expected
      * and actual vectors for which both entries are still considered equal
      */
     public static void customAssertEquals(final String message,
                                           final RealVector expected, final RealVector actual, final double delta) {
         final String msgAndSep = message.equals("") ? "" : message + ", ";
         assertEquals(expected.getDimension(),
             actual.getDimension(),
             msgAndSep + "dimension");
         final int dim = expected.getDimension();
         for (int i = 0; i < dim; i++) {
             assertEquals(expected.getEntry(i), actual.getEntry(i), delta, msgAndSep + "entry #" + i);
         }
     }
 
     /** verifies that two matrices are close (1-norm) */
     public static void customAssertEquals(String msg, RealMatrix expected, RealMatrix observed, double tolerance) {
 
         assertNotNull(observed,msg + "\nObserved should not be null");
 
         if (expected.getColumnDimension() != observed.getColumnDimension() ||
                 expected.getRowDimension() != observed.getRowDimension()) {
             StringBuilder messageBuffer = new StringBuilder(msg);
             messageBuffer.append("\nObserved has incorrect dimensions.");
             messageBuffer.append("\nobserved is " + observed.getRowDimension() +
                     " x " + observed.getColumnDimension());
             messageBuffer.append("\nexpected " + expected.getRowDimension() +
                     " x " + expected.getColumnDimension());
             fail(messageBuffer.toString());
         }
 
         RealMatrix delta = expected.subtract(observed);
         if (delta.getNorm1() >= tolerance) {
             StringBuilder messageBuffer = new StringBuilder(msg);
             messageBuffer.append("\nExpected: " + expected);
             messageBuffer.append("\nObserved: " + observed);
             messageBuffer.append("\nexpected - observed: " + delta);
             fail(messageBuffer.toString());
         }
     }
 
     /** verifies that two matrices are equal */
     public static void customAssertEquals(FieldMatrix<? extends FieldElement<?>> expected,
                                           FieldMatrix<? extends FieldElement<?>> observed) {
 
         assertNotNull(observed,"Observed should not be null");
 
         if (expected.getColumnDimension() != observed.getColumnDimension() ||
                 expected.getRowDimension() != observed.getRowDimension()) {
             StringBuilder messageBuffer = new StringBuilder();
             messageBuffer.append("Observed has incorrect dimensions.");
             messageBuffer.append("\nobserved is " + observed.getRowDimension() +
                     " x " + observed.getColumnDimension());
             messageBuffer.append("\nexpected " + expected.getRowDimension() +
                     " x " + expected.getColumnDimension());
             fail(messageBuffer.toString());
         }
 
         for (int i = 0; i < expected.getRowDimension(); ++i) {
             for (int j = 0; j < expected.getColumnDimension(); ++j) {
                 FieldElement<?> eij = expected.getEntry(i, j);
                 FieldElement<?> oij = observed.getEntry(i, j);
                 assertEquals(eij, oij);
             }
         }
     }
 
     /** verifies that two arrays are close (sup norm) */
     public static void customAssertEquals(String msg, double[] expected, double[] observed, double tolerance) {
         StringBuilder out = new StringBuilder(msg);
         if (expected.length != observed.length) {
             out.append("\n Arrays not same length. \n");
             out.append("expected has length ");
             out.append(expected.length);
             out.append(" observed length = ");
             out.append(observed.length);
             fail(out.toString());
         }
         boolean failure = false;
         for (int i=0; i < expected.length; i++) {
             if (!Precision.equalsIncludingNaN(expected[i], observed[i], tolerance)) {
                 failure = true;
                 out.append("\n Elements at index ");
                 out.append(i);
                 out.append(" differ. ");
                 out.append(" expected = ");
                 out.append(expected[i]);
                 out.append(" observed = ");
                 out.append(observed[i]);
             }
         }
         if (failure) {
             fail(out.toString());
         }
     }
 
     /** verifies that two int arrays are equal */
     public static void customAssertEquals(int[] expected, int[] observed) {
         StringBuilder out = new StringBuilder();
         if (expected.length != observed.length) {
             out.append("\n Arrays not same length. \n");
             out.append("expected has length ");
             out.append(expected.length);
             out.append(" observed length = ");
             out.append(observed.length);
             fail(out.toString());
         }
         boolean failure = false;
         for (int i=0; i < expected.length; i++) {
             if (expected[i] != observed[i]) {
                 failure = true;
                 out.append("\n Elements at index ");
                 out.append(i);
                 out.append(" differ. ");
                 out.append(" expected = ");
                 out.append(expected[i]);
                 out.append(" observed = ");
                 out.append(observed[i]);
             }
         }
         if (failure) {
             fail(out.toString());
         }
     }
 
     /**
      * verifies that for i = 0,..., observed.length, observed[i] is within epsilon of one of the values in expected[i]
      * or observed[i] is NaN and expected[i] contains a NaN.
      */
     public static void customAssertContains(double[][] expected, double[] observed, double epsilon) {
         StringBuilder out = new StringBuilder();
         if (expected.length != observed.length) {
             out.append("\n Arrays not same length. \n");
             out.append("expected has length ");
             out.append(expected.length);
             out.append(" observed length = ");
             out.append(observed.length);
             fail(out.toString());
         }
         boolean failure = false;
         for (int i = 0; i < expected.length; i++) {
             boolean found = false;
             for (int j = 0; j < expected[i].length; j++) {
                 if (Precision.equalsIncludingNaN(expected[i][j], observed[i], epsilon)) {
                     found = true;
                     break;
                 }
             }
             if (!found) {
                 out.append("\n Observed element at index ");
                 out.append(i);
                 out.append(" is not among the expected values. ");
                 out.append(" expected = " + Arrays.toString(expected[i]));
                 out.append(" observed = ");
                 out.append(observed[i]);
                 failure = true;
             }
         }
         if (failure) {
             fail(out.toString());
         }
     }
 
 
 
     /** verifies that two int arrays are equal */
     public static void customAssertEquals(long[] expected, long[] observed) {
         StringBuilder out = new StringBuilder();
         if (expected.length != observed.length) {
             out.append("\n Arrays not same length. \n");
             out.append("expected has length ");
             out.append(expected.length);
             out.append(" observed length = ");
             out.append(observed.length);
             fail(out.toString());
         }
         boolean failure = false;
         for (int i=0; i < expected.length; i++) {
             if (expected[i] != observed[i]) {
                 failure = true;
                 out.append("\n Elements at index ");
                 out.append(i);
                 out.append(" differ. ");
                 out.append(" expected = ");
                 out.append(expected[i]);
                 out.append(" observed = ");
                 out.append(observed[i]);
             }
         }
         if (failure) {
             fail(out.toString());
         }
     }
 
     /** verifies that two arrays are equal */
     public static <T extends FieldElement<T>> void customAssertEquals(T[] m, T[] n) {
         if (m.length != n.length) {
             fail("vectors not same length");
         }
         for (int i = 0; i < m.length; i++) {
             assertEquals(m[i],n[i]);
         }
     }
 
     /**
      * Computes the sum of squared deviations of <values> from <target>
      * @param values array of deviates
      * @param target value to compute deviations from
      *
      * @return sum of squared deviations
      */
     public static double sumSquareDev(double[] values, double target) {
         double sumsq = 0d;
         for (int i = 0; i < values.length; i++) {
             final double dev = values[i] - target;
             sumsq += (dev * dev);
         }
         return sumsq;
     }
 
     /**
      * Asserts the null hypothesis for a ChiSquare test.  Fails and dumps arguments and test
      * statistics if the null hypothesis can be rejected with confidence 100 * (1 - alpha)%
      *
      * @param valueLabels labels for the values of the discrete distribution under test
      * @param expected expected counts
      * @param observed observed counts
      * @param alpha significance level of the test
      */
     public static void customAssertChiSquareAccept(String[] valueLabels, double[] expected, long[] observed, double alpha) {
 
         // Fail if we can reject null hypothesis that distributions are the same
         if (chiSquareTest(expected, observed) <= alpha) {
             StringBuilder msgBuffer = new StringBuilder();
             DecimalFormat df = new DecimalFormat("#.##");
             msgBuffer.append("Chisquare test failed");
             msgBuffer.append(" p-value = ");
             msgBuffer.append(chiSquareTest(expected, observed));
             msgBuffer.append(" chisquare statistic = ");
             msgBuffer.append(chiSquare(expected, observed));
             msgBuffer.append(". \n");
             msgBuffer.append("value\texpected\tobserved\n");
             for (int i = 0; i < expected.length; i++) {
                 msgBuffer.append(valueLabels[i]);
                 msgBuffer.append("\t");
                 msgBuffer.append(df.format(expected[i]));
                 msgBuffer.append("\t\t");
                 msgBuffer.append(observed[i]);
                 msgBuffer.append("\n");
             }
             msgBuffer.append("This test can fail randomly due to sampling error with probability ");
             msgBuffer.append(alpha);
             msgBuffer.append(".");
             fail(msgBuffer.toString());
         }
     }
 
     /**
      * Asserts the null hypothesis for a ChiSquare test.  Fails and dumps arguments and test
      * statistics if the null hypothesis can be rejected with confidence 100 * (1 - alpha)%
      *
      * @param values integer values whose observed and expected counts are being compared
      * @param expected expected counts
      * @param observed observed counts
      * @param alpha significance level of the test
      */
     public static void customAssertChiSquareAccept(int[] values, double[] expected, long[] observed, double alpha) {
         String[] labels = new String[values.length];
         for (int i = 0; i < values.length; i++) {
             labels[i] = Integer.toString(values[i]);
         }
         customAssertChiSquareAccept(labels, expected, observed, alpha);
     }
 
     /**
      * Asserts the null hypothesis for a ChiSquare test.  Fails and dumps arguments and test
      * statistics if the null hypothesis can be rejected with confidence 100 * (1 - alpha)%
      *
      * @param expected expected counts
      * @param observed observed counts
      * @param alpha significance level of the test
      */
     public static void customAssertChiSquareAccept(double[] expected, long[] observed, double alpha) {
         String[] labels = new String[expected.length];
         for (int i = 0; i < labels.length; i++) {
             labels[i] = Integer.toString(i + 1);
         }
         customAssertChiSquareAccept(labels, expected, observed, alpha);
     }
 
     /**
      * Asserts the null hypothesis that the sample follows the given distribution, using a G-test
      *
      * @param expectedDistribution distribution values are supposed to follow
      * @param values sample data
      * @param alpha significance level of the test
      */
     public static void customAssertGTest(final RealDistribution expectedDistribution, final double[] values, double alpha) {
         final int numBins = values.length / 30;
         final double[] breaks = new double[numBins];
         for (int b = 0; b < breaks.length; b++) {
             breaks[b] = expectedDistribution.inverseCumulativeProbability((double) b / numBins);
         }
 
         final long[] observed = new long[numBins];
         for (final double value : values) {
             int b = 0;
             do {
                 b++;
             } while (b < numBins && value >= breaks[b]);
 
             observed[b - 1]++;
         }
 
         final double[] expected = new double[numBins];
         Arrays.fill(expected, (double) values.length / numBins);
 
         customAssertGTest(expected, observed, alpha);
     }
 
     /**
      * Asserts the null hypothesis that the observed counts follow the given distribution implied by expected,
      * using a G-test
      *
      * @param expected expected counts
      * @param observed observed counts
      * @param alpha significance level of the test
      */
     public static void customAssertGTest(final double[] expected, long[] observed, double alpha) {
         if (gTest(expected, observed) <  alpha) {
             StringBuilder msgBuffer = new StringBuilder();
             DecimalFormat df = new DecimalFormat("#.##");
             msgBuffer.append("G test failed");
             msgBuffer.append(" p-value = ");
             msgBuffer.append(gTest(expected, observed));
             msgBuffer.append(". \n");
             msgBuffer.append("value\texpected\tobserved\n");
             for (int i = 0; i < expected.length; i++) {
                 msgBuffer.append(df.format(expected[i]));
                 msgBuffer.append("\t\t");
                 msgBuffer.append(observed[i]);
                 msgBuffer.append("\n");
             }
             msgBuffer.append("This test can fail randomly due to sampling error with probability ");
             msgBuffer.append(alpha);
             msgBuffer.append(".");
             fail(msgBuffer.toString());
         }
     }
 
     /**
      * Computes the 25th, 50th and 75th percentiles of the given distribution and returns
      * these values in an array.
      */
     public static double[] getDistributionQuartiles(RealDistribution distribution) {
         double[] quantiles = new double[3];
         quantiles[0] = distribution.inverseCumulativeProbability(0.25d);
         quantiles[1] = distribution.inverseCumulativeProbability(0.5d);
         quantiles[2] = distribution.inverseCumulativeProbability(0.75d);
         return quantiles;
     }
 
     /**
      * Updates observed counts of values in quartiles.
      * counts[0] ↔ 1st quartile ... counts[3] ↔ top quartile
      */
     public static void updateCounts(double value, long[] counts, double[] quartiles) {
         if (value < quartiles[0]) {
             counts[0]++;
         } else if (value > quartiles[2]) {
             counts[3]++;
         } else if (value > quartiles[1]) {
             counts[2]++;
         } else {
             counts[1]++;
         }
     }
 
     /**
      * Eliminates points with zero mass from densityPoints and densityValues parallel
      * arrays.  Returns the number of positive mass points and collapses the arrays so
      * that the first <returned value> elements of the input arrays represent the positive
      * mass points.
      */
     public static int eliminateZeroMassPoints(int[] densityPoints, double[] densityValues) {
         int positiveMassCount = 0;
         for (int i = 0; i < densityValues.length; i++) {
             if (densityValues[i] > 0) {
                 positiveMassCount++;
             }
         }
         if (positiveMassCount < densityValues.length) {
             int[] newPoints = new int[positiveMassCount];
             double[] newValues = new double[positiveMassCount];
             int j = 0;
             for (int i = 0; i < densityValues.length; i++) {
                 if (densityValues[i] > 0) {
                     newPoints[j] = densityPoints[i];
                     newValues[j] = densityValues[i];
                     j++;
                 }
             }
             System.arraycopy(newPoints,0,densityPoints,0,positiveMassCount);
             System.arraycopy(newValues,0,densityValues,0,positiveMassCount);
         }
         return positiveMassCount;
     }
 
     /*************************************************************************************
      * Stripped-down implementations of some basic statistics borrowed from hipparchus-stat.
      * NOTE: These implementations are NOT intended for reuse.  They are neither robust,
      * nor efficient; nor do they handle NaN, infinity or other corner cases in
      * a predictable way. They DO NOT CHECK PARAMETERS - the assumption is that incorrect
      * or meaningless results from bad parameters will trigger test failures in unit
      * tests using these methods.
      ************************************************************************************/
 
     /**
      * Returns p-value associated with null hypothesis that observed counts follow
      * expected distribution.  Will normalize inputs if necessary.
      *
      * @param expected expected counts
      * @param observed observed counts
      * @return p-value of Chi-square test
      */
     public static double chiSquareTest(final double[] expected, final long[] observed) {
             final org.hipparchus.distribution.continuous.ChiSquaredDistribution distribution =
                 new ChiSquaredDistribution(expected.length - 1.0);
             return 1.0 - distribution.cumulativeProbability(chiSquare(expected, observed));
     }
 
     /**
      * Returns chi-square test statistic for expected and observed arrays. Rescales arrays
      * if necessary.
      *
      * @param expected expected counts
      * @param observed observed counts
      * @return chi-square statistic
      */
     public static double chiSquare(final double[] expected, final long[] observed) {
             double sumExpected = 0d;
             double sumObserved = 0d;
             for (int i = 0; i < observed.length; i++) {
                 sumExpected += expected[i];
                 sumObserved += observed[i];
             }
             double ratio = 1.0d;
             boolean rescale = false;
             if (FastMath.abs(sumExpected - sumObserved) > 10E-6) {
                 ratio = sumObserved / sumExpected;
                 rescale = true;
             }
             double sumSq = 0.0d;
             for (int i = 0; i < observed.length; i++) {
                 if (rescale) {
                     final double dev = observed[i] - ratio * expected[i];
                     sumSq += dev * dev / (ratio * expected[i]);
                 } else {
                     final double dev = observed[i] - expected[i];
                     sumSq += dev * dev / expected[i];
                 }
             }
             return sumSq;
 
         }
 
     /**
      * Computes G-test statistic for expected, observed counts.
      * @param expected expected counts
      * @param observed observed counts
      * @return G statistic
      */
     private static double g(final double[] expected, final long[] observed) {
         double sumExpected = 0d;
         double sumObserved = 0d;
         for (int i = 0; i < observed.length; i++) {
             sumExpected += expected[i];
             sumObserved += observed[i];
         }
         double ratio = 1d;
         boolean rescale = false;
         if (FastMath.abs(sumExpected - sumObserved) > 10E-6) {
             ratio = sumObserved / sumExpected;
             rescale = true;
         }
         double sum = 0d;
         for (int i = 0; i < observed.length; i++) {
             final double dev = rescale ?
                     FastMath.log(observed[i] / (ratio * expected[i])) :
                         FastMath.log(observed[i] / expected[i]);
             sum += (observed[i]) * dev;
         }
         return 2d * sum;
     }
 
     /**
      * Computes p-value for G-test.
      *
      * @param expected expected counts
      * @param observed observed counts
      * @return p-value
      */
     private static double gTest(final double[] expected, final long[] observed) {
         final ChiSquaredDistribution distribution =
                 new ChiSquaredDistribution(expected.length - 1.0);
         return 1.0 - distribution.cumulativeProbability(g(expected, observed));
     }
 
     /**
      * Computes the mean of the values in the array.
      *
      * @param values input values
      * @return arithmetic mean
      */
     public static double mean(final double[] values) {
         double sum = 0;
         for (double val : values) {
             sum += val;
         }
         return sum / values.length;
     }
 
     /**
      * Computes the (bias-adjusted) variance of the values in the input array.
      *
      * @param values input values
      * @return bias-adjusted variance
      */
     public static double variance(final double[] values) {
         final int length = values.length;
         final double mean = mean(values);
         double var = Double.NaN;
         if (length == 1) {
             var = 0.0;
         } else if (length > 1) {
             double accum = 0.0;
             double dev = 0.0;
             double accum2 = 0.0;
             for (int i = 0; i < length; i++) {
                 dev = values[i] - mean;
                 accum += dev * dev;
                 accum2 += dev;
             }
             final double len = length;
             var = (accum - (accum2 * accum2 / len)) / (len - 1.0);
         }
         return var;
     }
 
     /**
      * Computes the standard deviation of the values in the input array.
      *
      * @param values input values
      * @return standard deviation
      */
     public static double standardDeviation(final double[] values) {
         return FastMath.sqrt(variance(values));
     }
 
     /**
      * Computes the median of the values in the input array.
      *
      * @param values input values
      * @return estimated median
      */
     public static double median(final double[] values) {
         final int len = values.length;
         final double[] sortedValues = Arrays.copyOf(values, len);
         Arrays.sort(sortedValues);
         if (len % 2 == 0) {
             return ((double)sortedValues[len/2] + (double)sortedValues[len/2 - 1])/2;
         } else {
             return (double) sortedValues[len/2];
         }
     }
 
     /**
      * Computes the covariance of the two input arrays.
      *
      * @param xArray first covariate
      * @param yArray second covariate
      * @return covariance
      */
     public static double covariance(final double[] xArray, final double[] yArray) {
         double result = 0d;
         final int length = xArray.length;
         final double xMean = mean(xArray);
         final double yMean = mean(yArray);
         for (int i = 0; i < length; i++) {
             final double xDev = xArray[i] - xMean;
             final double yDev = yArray[i] - yMean;
             result += (xDev * yDev - result) / (i + 1);
         }
         return result * ((double) length / (double)(length - 1));
     }
 
     /**
      * Computes a covariance matrix from a matrix whose columns represent covariates.
      *
      * @param matrix input matrix
      * @return covariance matrix
      */
     public static RealMatrix covarianceMatrix(RealMatrix matrix) {
         int dimension = matrix.getColumnDimension();
         final RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);
         for (int i = 0; i < dimension; i++) {
             for (int j = 0; j < i; j++) {
                 final double cov = covariance(matrix.getColumn(i), matrix.getColumn(j));
                 outMatrix.setEntry(i, j, cov);
                 outMatrix.setEntry(j, i, cov);
             }
             outMatrix.setEntry(i, i, variance(matrix.getColumn(i)));
         }
         return outMatrix;
     }
 
     public static double min(final double[] values) {
         double min = values[0];
         for (int i = 1; i < values.length; i++) {
             if (values[i] < min) {
                 min = values[i];
             }
         }
         return min;
     }
 
     /**
      * Computes the maximum of the values in the input array.
      *
      * @param values input array
      * @return the maximum value
      */
     public static double max(final double[] values) {
         double max = values[0];
         for (int i = 1; i < values.length; i++) {
             if (values[i] > max) {
                 max = values[i];
             }
         }
         return max;
     }
 
     /**
      * Unpacks a list of Doubles into a double[].
      *
      * @param values list of Double
      * @return double array
      */
     private static double[] unpack(List<Double> values) {
         int n = values.size();
         if (values == null || n == 0) {
             return new double[] {};
         }
         double[] out = new double[n];
         for (int i = 0; i < n; i++) {
             out[i] = values.get(i);
         }
         return out;
     }
 
     /**
      * Keeps track of the number of occurrences of distinct T instances
      * added via {@link #addValue(Object)}.
      *
      * @param <T> type of objects being tracked
      */
     public static class Frequency<T> {
         private Map<T, Integer> counts = new HashMap<>();
         public void addValue(T value) {
            Integer old = counts.put(value, 0);
            if (old != null) {
                counts.put(value, old++);
            }
         }
         public int getCount(T value) {
            Integer ret = counts.get(value);
            return ret == null ? 0 : ret;
         }
     }
 
     /**
      * Stripped down implementation of StreamingStatistics from o.h.stat.descriptive.
      * Actually holds all values in memory, so not suitable for very large streams of data.
      */
     public static class SimpleStatistics {
         private final List<Double> values = new ArrayList<>();
         public void addValue(double value) {
             values.add(value);
         }
         public double getMean() {
             return mean(unpack(values));
         }
         public double getStandardDeviation() {
             return standardDeviation(unpack(values));
         }
         public double getMin() {
             return min(unpack(values));
         }
         public double getMax() {
             return max(unpack(values));
         }
         public double getMedian() {
             return median(unpack(values));
         }
         public double getVariance() {
             return variance(unpack(values));
         }
         public long getN() {
             return values.size();
         }
     }
 
     /**
      * Stripped-down version of the bivariate regression class with the same name
      * in o.h.stat.regression.
      * Always estimates the model with an intercept term.
      */
     public static class SimpleRegression {
         private double sumX = 0d;
         private double sumXX = 0d;
         private double sumY = 0d;
         private double sumXY = 0d;
         private long n = 0;
         private double xbar = 0;
         private double ybar = 0;
 
         public void addData(double x, double y) {
             if (n == 0) {
                 xbar = x;
                 ybar = y;
             } else {
                 final double fact1 = 1.0 + n;
                 final double fact2 = n / (1.0 + n);
                 final double dx = x - xbar;
                 final double dy = y - ybar;
                 sumXX += dx * dx * fact2;
                 sumXY += dx * dy * fact2;
                 xbar += dx / fact1;
                 ybar += dy / fact1;
             }
             sumX += x;
             sumY += y;
             n++;
         }
 
         public double getSlope() {
             if (n < 2) {
                 return Double.NaN; //not enough data
             }
             if (FastMath.abs(sumXX) < 10 * Double.MIN_VALUE) {
                 return Double.NaN; //not enough variation in x
             }
             return sumXY / sumXX;
         }
 
         public double getIntercept() {
             return (sumY - getSlope() * sumX) / n;
         }
     }
 }