/*
    * 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.distribution.continuous;
  
  import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.InputStreamReader;
  
  import org.hipparchus.UnitTestUtils;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.special.Gamma;
  import org.hipparchus.util.FastMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test cases for GammaDistribution.
   */
  public class GammaDistributionTest extends RealDistributionAbstractTest {
  
      //-------------- Implementations for abstract methods -----------------------
  
      /** Creates the default continuous distribution instance to use in tests. */
      @Override
      public GammaDistribution makeDistribution() {
          return new GammaDistribution(4d, 2d);
      }
  
      /** Creates the default cumulative probability distribution test input values */
      @Override
      public double[] makeCumulativeTestPoints() {
          // quantiles computed using R version 2.9.2
          return new double[] {0.857104827257, 1.64649737269, 2.17973074725, 2.7326367935, 3.48953912565,
                  26.1244815584, 20.0902350297, 17.5345461395, 15.5073130559, 13.3615661365};
      }
  
      /** Creates the default cumulative probability density test expected values */
      @Override
      public double[] makeCumulativeTestValues() {
          return new double[] {0.001, 0.01, 0.025, 0.05, 0.1, 0.999, 0.990, 0.975, 0.950, 0.900};
      }
  
      /** Creates the default probability density test expected values */
      @Override
      public double[] makeDensityTestValues() {
          return new double[] {0.00427280075546, 0.0204117166709, 0.0362756163658, 0.0542113174239, 0.0773195272491,
                  0.000394468852816, 0.00366559696761, 0.00874649473311, 0.0166712508128, 0.0311798227954};
      }
  
      // --------------------- Override tolerance  --------------
      @Override
      public void setUp() {
          super.setUp();
          setTolerance(1e-9);
      }
  
      //---------------------------- Additional test cases -------------------------
      @Test
      public void testParameterAccessors() {
          GammaDistribution distribution = (GammaDistribution) getDistribution();
          Assert.assertEquals(4d, distribution.getShape(), 0);
          Assert.assertEquals(2d, distribution.getScale(), 0);
      }
  
      @Test
      public void testPreconditions() {
          try {
              new GammaDistribution(0, 1);
              Assert.fail("Expecting MathIllegalArgumentException for alpha = 0");
          } catch (MathIllegalArgumentException ex) {
              // Expected.
          }
          try {
              new GammaDistribution(1, 0);
              Assert.fail("Expecting MathIllegalArgumentException for alpha = 0");
          } catch (MathIllegalArgumentException ex) {
              // Expected.
          }
     }
 
     @Test
     public void testProbabilities() {
         testProbability(-1.000, 4.0, 2.0, .0000);
         testProbability(15.501, 4.0, 2.0, .9499);
         testProbability(0.504, 4.0, 1.0, .0018);
         testProbability(10.011, 1.0, 2.0, .9933);
         testProbability(5.000, 2.0, 2.0, .7127);
     }
 
     @Test
     public void testValues() {
         testValue(15.501, 4.0, 2.0, .9499);
         testValue(0.504, 4.0, 1.0, .0018);
         testValue(10.011, 1.0, 2.0, .9933);
         testValue(5.000, 2.0, 2.0, .7127);
     }
 
     private void testProbability(double x, double a, double b, double expected) {
         GammaDistribution distribution = new GammaDistribution( a, b );
         double actual = distribution.cumulativeProbability(x);
         Assert.assertEquals("probability for " + x, expected, actual, 10e-4);
     }
 
     private void testValue(double expected, double a, double b, double p) {
         GammaDistribution distribution = new GammaDistribution( a, b );
         double actual = distribution.inverseCumulativeProbability(p);
         Assert.assertEquals("critical value for " + p, expected, actual, 10e-4);
     }
 
     @Test
     public void testDensity() {
         double[] x = new double[]{-0.1, 1e-6, 0.5, 1, 2, 5};
         // R2.5: print(dgamma(x, shape=1, rate=1), digits=10)
         checkDensity(1, 1, x, new double[]{0.000000000000, 0.999999000001, 0.606530659713, 0.367879441171, 0.135335283237, 0.006737946999});
         // R2.5: print(dgamma(x, shape=2, rate=1), digits=10)
         checkDensity(2, 1, x, new double[]{0.000000000000, 0.000000999999, 0.303265329856, 0.367879441171, 0.270670566473, 0.033689734995});
         // R2.5: print(dgamma(x, shape=4, rate=1), digits=10)
         checkDensity(4, 1, x, new double[]{0.000000000e+00, 1.666665000e-19, 1.263605541e-02, 6.131324020e-02, 1.804470443e-01, 1.403738958e-01});
         // R2.5: print(dgamma(x, shape=4, rate=10), digits=10)
         checkDensity(4, 10, x, new double[]{0.000000000e+00, 1.666650000e-15, 1.403738958e+00, 7.566654960e-02, 2.748204830e-05, 4.018228850e-17});
         // R2.5: print(dgamma(x, shape=.1, rate=10), digits=10)
         checkDensity(0.1, 10, x, new double[]{0.000000000e+00, 3.323953832e+04, 1.663849010e-03, 6.007786726e-06, 1.461647647e-10, 5.996008322e-24});
         // R2.5: print(dgamma(x, shape=.1, rate=20), digits=10)
         checkDensity(0.1, 20, x, new double[]{0.000000000e+00, 3.562489883e+04, 1.201557345e-05, 2.923295295e-10, 3.228910843e-19, 1.239484589e-45});
         // R2.5: print(dgamma(x, shape=.1, rate=4), digits=10)
         checkDensity(0.1, 4, x, new double[]{0.000000000e+00, 3.032938388e+04, 3.049322494e-02, 2.211502311e-03, 2.170613371e-05, 5.846590589e-11});
         // R2.5: print(dgamma(x, shape=.1, rate=1), digits=10)
         checkDensity(0.1, 1, x, new double[]{0.000000000e+00, 2.640334143e+04, 1.189704437e-01, 3.866916944e-02, 7.623306235e-03, 1.663849010e-04});
     }
 
     private void checkDensity(double alpha, double rate, double[] x, double[] expected) {
         GammaDistribution d = new GammaDistribution(alpha, 1 / rate);
         for (int i = 0; i < x.length; i++) {
             Assert.assertEquals(expected[i], d.density(x[i]), 1e-5);
         }
     }
 
     @Test
     public void testInverseCumulativeProbabilityExtremes() {
         setInverseCumulativeTestPoints(new double[] {0, 1});
         setInverseCumulativeTestValues(new double[] {0, Double.POSITIVE_INFINITY});
         verifyInverseCumulativeProbabilities();
     }
 
     @Test
     public void testMoments() {
         final double tol = 1e-9;
         GammaDistribution dist;
 
         dist = new GammaDistribution(1, 2);
         Assert.assertEquals(dist.getNumericalMean(), 2, tol);
         Assert.assertEquals(dist.getNumericalVariance(), 4, tol);
 
         dist = new GammaDistribution(1.1, 4.2);
         Assert.assertEquals(dist.getNumericalMean(), 1.1d * 4.2d, tol);
         Assert.assertEquals(dist.getNumericalVariance(), 1.1d * 4.2d * 4.2d, tol);
     }
 
     private static final double HALF_LOG_2_PI = 0.5 * FastMath.log(2.0 * FastMath.PI);
 
     public static double logGamma(double x) {
         /*
          * This is a copy of
          * double Gamma.logGamma(double)
          * prior to MATH-849
          */
         double ret;
 
         if (Double.isNaN(x) || (x <= 0.0)) {
             ret = Double.NaN;
         } else {
             double sum = Gamma.lanczos(x);
             double tmp = x + Gamma.LANCZOS_G + .5;
             ret = ((x + .5) * FastMath.log(tmp)) - tmp +
                 HALF_LOG_2_PI + FastMath.log(sum / x);
         }
 
         return ret;
     }
 
     public static double density(final double x, final double shape,
                                  final double scale) {
         /*
          * This is a copy of
          * double GammaDistribution.density(double)
          * prior to MATH-753.
          */
         if (x < 0) {
             return 0;
         }
         return FastMath.pow(x / scale, shape - 1) / scale *
                FastMath.exp(-x / scale) / FastMath.exp(logGamma(shape));
     }
 
     /*
      * MATH-753: large values of x or shape parameter cause density(double) to
      * overflow. Reference data is generated with the Maxima script
      * gamma-distribution.mac, which can be found in
      * src/test/resources/org.hipparchus/distribution.
      */
 
     private void doTestMath753(final double shape,
         final double meanNoOF, final double sdNoOF,
         final double meanOF, final double sdOF,
         final String resourceName) throws IOException {
         final GammaDistribution distribution = new GammaDistribution(shape, 1.0);
         final UnitTestUtils.SimpleStatistics statOld = new UnitTestUtils.SimpleStatistics();
         final UnitTestUtils.SimpleStatistics statNewNoOF = new UnitTestUtils.SimpleStatistics();
         final UnitTestUtils.SimpleStatistics statNewOF = new UnitTestUtils.SimpleStatistics();
 
         final InputStream resourceAsStream;
         resourceAsStream = this.getClass().getResourceAsStream(resourceName);
         Assert.assertNotNull("Could not find resource " + resourceName,
                              resourceAsStream);
         final BufferedReader in;
         in = new BufferedReader(new InputStreamReader(resourceAsStream));
 
         try {
             for (String line = in.readLine(); line != null; line = in.readLine()) {
                 if (line.startsWith("#")) {
                     continue;
                 }
                 final String[] tokens = line.split(", ");
                 Assert.assertTrue("expected two floating-point values",
                                   tokens.length == 2);
                 final double x = Double.parseDouble(tokens[0]);
                 final String msg = "x = " + x + ", shape = " + shape +
                                    ", scale = 1.0";
                 final double expected = Double.parseDouble(tokens[1]);
                 final double ulp = FastMath.ulp(expected);
                 final double actualOld = density(x, shape, 1.0);
                 final double actualNew = distribution.density(x);
                 final double errOld, errNew;
                 errOld = FastMath.abs((actualOld - expected) / ulp);
                 errNew = FastMath.abs((actualNew - expected) / ulp);
 
                 if (Double.isNaN(actualOld) || Double.isInfinite(actualOld)) {
                     Assert.assertFalse(msg, Double.isNaN(actualNew));
                     Assert.assertFalse(msg, Double.isInfinite(actualNew));
                     statNewOF.addValue(errNew);
                 } else {
                     statOld.addValue(errOld);
                     statNewNoOF.addValue(errNew);
                 }
             }
             if (statOld.getN() != 0) {
                 /*
                  * If no overflow occurs, check that new implementation is
                  * better than old one.
                  */
                 final StringBuilder sb = new StringBuilder("shape = ");
                 sb.append(shape);
                 sb.append(", scale = 1.0\n");
                 sb.append("Old implementation\n");
                 sb.append("------------------\n");
                 sb.append(statOld.toString());
                 sb.append("New implementation\n");
                 sb.append("------------------\n");
                 sb.append(statNewNoOF.toString());
                 final String msg = sb.toString();
 
                 final double oldMin = statOld.getMin();
                 final double newMin = statNewNoOF.getMin();
                 Assert.assertTrue(msg, newMin <= oldMin);
 
                 final double oldMax = statOld.getMax();
                 final double newMax = statNewNoOF.getMax();
                 Assert.assertTrue(msg, newMax <= oldMax);
 
                 final double oldMean = statOld.getMean();
                 final double newMean = statNewNoOF.getMean();
                 Assert.assertTrue(msg, newMean <= oldMean);
 
                 final double oldSd = statOld.getStandardDeviation();
                 final double newSd = statNewNoOF.getStandardDeviation();
                 Assert.assertTrue(msg, newSd <= oldSd);
 
                 Assert.assertTrue(msg, newMean <= meanNoOF);
                 Assert.assertTrue(msg, newSd <= sdNoOF);
             }
             if (statNewOF.getN() != 0) {
                 final double newMean = statNewOF.getMean();
                 final double newSd = statNewOF.getStandardDeviation();
 
                 final StringBuilder sb = new StringBuilder("shape = ");
                 sb.append(shape);
                 sb.append(", scale = 1.0");
                 sb.append(", max. mean error (ulps) = ");
                 sb.append(meanOF);
                 sb.append(", actual mean error (ulps) = ");
                 sb.append(newMean);
                 sb.append(", max. sd of error (ulps) = ");
                 sb.append(sdOF);
                 sb.append(", actual sd of error (ulps) = ");
                 sb.append(newSd);
                 final String msg = sb.toString();
 
                 Assert.assertTrue(msg, newMean <= meanOF);
                 Assert.assertTrue(msg, newSd <= sdOF);
             }
         } catch (IOException e) {
             Assert.fail(e.getMessage());
         } finally {
             in.close();
         }
     }
 
 
     @Test
     public void testMath753Shape1() throws IOException {
         doTestMath753(1.0, 1.5, 0.5, 0.0, 0.0, "gamma-distribution-shape-1.csv");
     }
 
     @Test
     public void testMath753Shape8() throws IOException {
         doTestMath753(8.0, 1.5, 1.0, 0.0, 0.0, "gamma-distribution-shape-8.csv");
     }
 
     @Test
     public void testMath753Shape10() throws IOException {
         doTestMath753(10.0, 1.0, 1.0, 0.0, 0.0, "gamma-distribution-shape-10.csv");
     }
 
     @Test
     public void testMath753Shape100() throws IOException {
         doTestMath753(100.0, 1.5, 1.0, 0.0, 0.0, "gamma-distribution-shape-100.csv");
     }
 
     @Test
     public void testMath753Shape142() throws IOException {
         doTestMath753(142.0, 3.3, 1.6, 40.0, 40.0, "gamma-distribution-shape-142.csv");
     }
 
     @Test
     public void testMath753Shape1000() throws IOException {
         doTestMath753(1000.0, 1.0, 1.0, 160.0, 220.0, "gamma-distribution-shape-1000.csv");
     }
 }