/*
    * 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.math4.legacy.analysis.integration.gauss;
  
  import org.apache.commons.math4.legacy.analysis.function.Power;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Test;
  import org.junit.Assert;
  
  /**
   * Base class for standard testing of Gaussian quadrature rules,
   * which are exact for polynomials up to a certain degree. In this test, each
   * monomial in turn is tested against the specified quadrature rule.
   *
   */
  public abstract class GaussianQuadratureAbstractTest {
      /**
       * The maximum absolute error (for zero testing).
       */
      private final double eps;
      /**
       * The maximum relative error (in ulps).
       */
      private final double numUlps;
      /**
       * The quadrature rule under test.
       */
      private final GaussIntegrator integrator;
      /**
       * Maximum degree of monomials to be tested.
       */
      private final int maxDegree;
  
      /**
       * Creates a new instance of this abstract test with the specified
       * quadrature rule.
       * If the expected value is non-zero, equality of actual and expected values
       * is checked in the relative sense <center>
       * |x<sub>act</sub>&nbsp;-&nbsp;x<sub>exp</sub>|&nbsp;&le;&nbsp; n&nbsp;
       * <code>Math.ulp(</code>x<sub>exp</sub><code>)</code>, </center> where n is
       * the maximum relative error (in ulps). If the expected value is zero, the
       * test checks that <center> |x<sub>act</sub>|&nbsp;&le;&nbsp;&epsilon;,
       * </center> where &epsilon; is the maximum absolute error.
       *
       * @param integrator Quadrature rule under test.
       * @param maxDegree Maximum degree of monomials to be tested.
       * @param eps &epsilon;.
       * @param numUlps Value of the maximum relative error (in ulps).
       */
      public GaussianQuadratureAbstractTest(GaussIntegrator integrator,
                                            int maxDegree,
                                            double eps,
                                            double numUlps) {
          this.integrator = integrator;
          this.maxDegree = maxDegree;
          this.eps = eps;
          this.numUlps = numUlps;
      }
  
      /**
       * Returns the expected value of the integral of the specified monomial.
       * The integration is carried out on the natural interval of the quadrature
       * rule under test.
       *
       * @param n Degree of the monomial.
       * @return the expected value of the integral of x<sup>n</sup>.
       */
      public abstract double getExpectedValue(int n);
  
      /**
       * Checks that the value of the integral of each monomial
       *   <code>x<sup>0</sup>, ... , x<sup>p</sup></code>
       * returned by the quadrature rule under test conforms with the expected
       * value.
       * Here {@code p} denotes the degree of the highest polynomial for which
       * exactness is to be expected.
       */
      @Test
      public void testAllMonomials() {
          for (int n = 0; n <= maxDegree; n++) {
              final double expected = getExpectedValue(n);
  
              final Power monomial = new Power(n);
              final double actual = integrator.integrate(monomial);
  
             // System.out.println(n + "/" + maxDegree + " " + integrator.getNumberOfPoints()
             //                    + " " + expected + " " + actual + " " + Math.ulp(expected));
             if (expected == 0) {
                 Assert.assertEquals("while integrating monomial x**" + n +
                                     " with a " +
                                     integrator.getNumberOfPoints() + "-point quadrature rule",
                                     expected, actual, eps);
             } else {
                 double err = JdkMath.abs(actual - expected) / Math.ulp(expected);
                 Assert.assertEquals("while integrating monomial x**" + n + " with a " +
                                     + integrator.getNumberOfPoints() + "-point quadrature rule, " +
                                     " error was " + err + " ulps",
                                     expected, actual, Math.ulp(expected) * numUlps);
             }
         }
     }
 }