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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * 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.solvers;
  
  import org.apache.commons.math4.legacy.analysis.QuinticFunction;
  import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
  import org.apache.commons.math4.legacy.analysis.function.Expm1;
  import org.apache.commons.math4.legacy.analysis.function.Sin;
  import org.apache.commons.math4.legacy.exception.NoBracketingException;
  import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test case for {@link MullerSolver Muller} solver.
   * <p>
   * Muller's method converges almost quadratically near roots, but it can
   * be very slow in regions far away from zeros. Test runs show that for
   * reasonably good initial values, for a default absolute accuracy of 1E-6,
   * it generally takes 5 to 10 iterations for the solver to converge.
   * <p>
   * Tests for the exponential function illustrate the situations where
   * Muller solver performs poorly.
   *
   */
  public final class MullerSolverTest {
      /**
       * Test of solver for the sine function.
       */
      @Test
      public void testSinFunction() {
          UnivariateFunction f = new Sin();
          UnivariateSolver solver = new MullerSolver();
          double min;
          double max;
          double expected;
          double result;
          double tolerance;
  
          min = 3.0; max = 4.0; expected = JdkMath.PI;
          tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                      JdkMath.abs(expected * solver.getRelativeAccuracy()));
          result = solver.solve(100, f, min, max);
          Assert.assertEquals(expected, result, tolerance);
  
          min = -1.0; max = 1.5; expected = 0.0;
          tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                      JdkMath.abs(expected * solver.getRelativeAccuracy()));
          result = solver.solve(100, f, min, max);
          Assert.assertEquals(expected, result, tolerance);
      }
  
      /**
       * Test of solver for the quintic function.
       */
      @Test
      public void testQuinticFunction() {
          UnivariateFunction f = new QuinticFunction();
          UnivariateSolver solver = new MullerSolver();
          double min;
          double max;
          double expected;
          double result;
          double tolerance;
  
          min = -0.4; max = 0.2; expected = 0.0;
          tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                      JdkMath.abs(expected * solver.getRelativeAccuracy()));
          result = solver.solve(100, f, min, max);
          Assert.assertEquals(expected, result, tolerance);
  
          min = 0.75; max = 1.5; expected = 1.0;
          tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                      JdkMath.abs(expected * solver.getRelativeAccuracy()));
          result = solver.solve(100, f, min, max);
          Assert.assertEquals(expected, result, tolerance);
  
          min = -0.9; max = -0.2; expected = -0.5;
          tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                      JdkMath.abs(expected * solver.getRelativeAccuracy()));
          result = solver.solve(100, f, min, max);
          Assert.assertEquals(expected, result, tolerance);
      }
  
     /**
      * Test of solver for the exponential function.
      * <p>
      * It takes 10 to 15 iterations for the last two tests to converge.
      * In fact, if not for the bisection alternative, the solver would
      * exceed the default maximal iteration of 100.
      */
     @Test
     public void testExpm1Function() {
         UnivariateFunction f = new Expm1();
         UnivariateSolver solver = new MullerSolver();
         double min;
         double max;
         double expected;
         double result;
         double tolerance;
 
         min = -1.0; max = 2.0; expected = 0.0;
         tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                     JdkMath.abs(expected * solver.getRelativeAccuracy()));
         result = solver.solve(100, f, min, max);
         Assert.assertEquals(expected, result, tolerance);
 
         min = -20.0; max = 10.0; expected = 0.0;
         tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                     JdkMath.abs(expected * solver.getRelativeAccuracy()));
         result = solver.solve(100, f, min, max);
         Assert.assertEquals(expected, result, tolerance);
 
         min = -50.0; max = 100.0; expected = 0.0;
         tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                     JdkMath.abs(expected * solver.getRelativeAccuracy()));
         result = solver.solve(100, f, min, max);
         Assert.assertEquals(expected, result, tolerance);
     }
 
     /**
      * Test of parameters for the solver.
      */
     @Test
     public void testParameters() {
         UnivariateFunction f = new Sin();
         UnivariateSolver solver = new MullerSolver();
 
         try {
             // bad interval
             double root = solver.solve(100, f, 1, -1);
             System.out.println("root=" + root);
             Assert.fail("Expecting NumberIsTooLargeException - bad interval");
         } catch (NumberIsTooLargeException ex) {
             // expected
         }
         try {
             // no bracketing
             solver.solve(100, f, 2, 3);
             Assert.fail("Expecting NoBracketingException - no bracketing");
         } catch (NoBracketingException ex) {
             // expected
         }
     }
 }