/*
    * 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.analysis.integration.gauss;
  
  import org.hipparchus.analysis.CalculusFieldUnivariateFunction;
  import org.hipparchus.util.Binary64;
  import org.hipparchus.util.Binary64Field;
  import org.hipparchus.util.FastMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test of the {@link HermiteRuleFactory}.
   *
   */
  public class FieldHermiteTest {
      private static final FieldGaussIntegratorFactory<Binary64> factory = new FieldGaussIntegratorFactory<>(Binary64Field.getInstance());
  
      @Test
      public void testNormalDistribution() {
          final Binary64 oneOverSqrtPi = new Binary64(1 / FastMath.sqrt(Math.PI));
  
          // By defintion, Gauss-Hermite quadrature readily provides the
          // integral of the normal distribution density.
          final int numPoints = 1;
  
          // Change of variable:
          //   y = (x - mu) / (sqrt(2) *  sigma)
          // such that the integrand
          //   N(x, mu, sigma)
          // is transformed to
          //   f(y) * exp(-y^2)
          final CalculusFieldUnivariateFunction<Binary64> f = y -> oneOverSqrtPi;
  
          final FieldGaussIntegrator<Binary64> integrator = factory.hermite(numPoints);
          final double result = integrator.integrate(f).getReal();
          final double expected = 1;
          Assert.assertEquals(expected, result, FastMath.ulp(expected));
      }
  
      @Test
      public void testNormalMean() {
          final Binary64 sqrtTwo = new Binary64(FastMath.sqrt(2));
          final Binary64 oneOverSqrtPi = new Binary64(1 / FastMath.sqrt(Math.PI));
  
          final Binary64 mu = new Binary64(12345.6789);
          final Binary64 sigma = new Binary64(987.654321);
          final int numPoints = 6;
  
          // Change of variable:
          //   y = (x - mu) / (sqrt(2) *  sigma)
          // such that the integrand
          //   x * N(x, mu, sigma)
          // is transformed to
          //   f(y) * exp(-y^2)
          final CalculusFieldUnivariateFunction<Binary64> f =
                          y ->  oneOverSqrtPi.multiply(sqrtTwo.multiply(sigma).multiply(y).add(mu));
  
          final FieldGaussIntegrator<Binary64> integrator = factory.hermite(numPoints);
          final double result = integrator.integrate(f).getReal();
          final double expected = mu.getReal();
          Assert.assertEquals(expected, result, 5 * FastMath.ulp(expected));
      }
  
      @Test
      public void testNormalVariance() {
          final Binary64 twoOverSqrtPi = new Binary64(2 / FastMath.sqrt(Math.PI));
  
          final Binary64 sigma = new Binary64(987.654321);
          final Binary64 sigma2 = sigma.multiply(sigma);
          final int numPoints = 5;
  
          // Change of variable:
          //   y = (x - mu) / (sqrt(2) *  sigma)
          // such that the integrand
          //   (x - mu)^2 * N(x, mu, sigma)
          // is transformed to
          //   f(y) * exp(-y^2)
          final CalculusFieldUnivariateFunction<Binary64> f =
                          y -> twoOverSqrtPi.multiply(sigma2).multiply(y).multiply(y);
 
         final FieldGaussIntegrator<Binary64> integrator = factory.hermite(numPoints);
         final double result = integrator.integrate(f).getReal();
         final double expected = sigma2.getReal();
         Assert.assertEquals(expected, result, 10 * FastMath.ulp(expected));
     }
 }