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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * 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.
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  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.XMinus5Function;
  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;
  
  /**
   * Base class for root-finding algorithms tests derived from
   * {@link BaseSecantSolver}.
   *
   */
  public abstract class BaseSecantSolverAbstractTest {
      /** Returns the solver to use to perform the tests.
       * @return the solver to use to perform the tests
       */
      protected abstract UnivariateSolver getSolver();
  
      /** Returns the expected number of evaluations for the
       * {@link #testQuinticZero} unit test. A value of {@code -1} indicates that
       * the test should be skipped for that solver.
       * @return the expected number of evaluations for the
       * {@link #testQuinticZero} unit test
       */
      protected abstract int[] getQuinticEvalCounts();
  
      @Test
      public void testSinZero() {
          // The sinus function is behaved well around the root at pi. The second
          // order derivative is zero, which means linear approximating methods
          // still converge quadratically.
          UnivariateFunction f = new Sin();
          double result;
          UnivariateSolver solver = getSolver();
  
          result = solver.solve(100, f, 3, 4);
          //System.out.println(
          //    "Root: " + result + " Evaluations: " + solver.getEvaluations());
          Assert.assertEquals(result, JdkMath.PI, solver.getAbsoluteAccuracy());
          Assert.assertTrue(solver.getEvaluations() <= 6);
          result = solver.solve(100, f, 1, 4);
          //System.out.println(
          //    "Root: " + result + " Evaluations: " + solver.getEvaluations());
          Assert.assertEquals(result, JdkMath.PI, solver.getAbsoluteAccuracy());
          Assert.assertTrue(solver.getEvaluations() <= 7);
      }
  
      @Test
      public void testQuinticZero() {
          // The quintic function has zeros at 0, +-0.5 and +-1.
          // Around the root of 0 the function is well behaved, with a second
          // derivative of zero a 0.
          // The other roots are less well to find, in particular the root at 1,
          // because the function grows fast for x>1.
          // The function has extrema (first derivative is zero) at 0.27195613
          // and 0.82221643, intervals containing these values are harder for
          // the solvers.
          UnivariateFunction f = new QuinticFunction();
          double result;
          UnivariateSolver solver = getSolver();
          double atol = solver.getAbsoluteAccuracy();
          int[] counts = getQuinticEvalCounts();
  
          // Tests data: initial bounds, and expected solution, per test case.
          double[][] testsData = {{-0.2,  0.2,  0.0},
                                  {-0.1,  0.3,  0.0},
                                  {-0.3,  0.45, 0.0},
                                  { 0.3,  0.7,  0.5},
                                  { 0.2,  0.6,  0.5},
                                  { 0.05, 0.95, 0.5},
                                  { 0.85, 1.25, 1.0},
                                  { 0.8,  1.2,  1.0},
                                  { 0.85, 1.75, 1.0},
                                  { 0.55, 1.45, 1.0},
                                  { 0.85, 5.0,  1.0},
                                 };
          int maxIter = 500;
  
         for(int i = 0; i < testsData.length; i++) {
             // Skip test, if needed.
             if (counts[i] == -1) {
                 continue;
             }
 
             // Compute solution.
             double[] testData = testsData[i];
             result = solver.solve(maxIter, f, testData[0], testData[1]);
             //System.out.println(
             //    "Root: " + result + " Evaluations: " + solver.getEvaluations());
 
             // Check solution.
             Assert.assertEquals(result, testData[2], atol);
             Assert.assertTrue(solver.getEvaluations() <= counts[i] + 1);
         }
     }
 
     @Test
     public void testRootEndpoints() {
         UnivariateFunction f = new XMinus5Function();
         UnivariateSolver solver = getSolver();
 
         // End-point is root. This should be a special case in the solver, and
         // the initial end-point should be returned exactly.
         double result = solver.solve(100, f, 5.0, 6.0);
         Assert.assertEquals(5.0, result, 0.0);
 
         result = solver.solve(100, f, 4.0, 5.0);
         Assert.assertEquals(5.0, result, 0.0);
 
         result = solver.solve(100, f, 5.0, 6.0, 5.5);
         Assert.assertEquals(5.0, result, 0.0);
 
         result = solver.solve(100, f, 4.0, 5.0, 4.5);
         Assert.assertEquals(5.0, result, 0.0);
     }
 
     @Test
     public void testBadEndpoints() {
         UnivariateFunction f = new Sin();
         UnivariateSolver solver = getSolver();
         try {  // bad interval
             solver.solve(100, f, 1, -1);
             Assert.fail("Expecting NumberIsTooLargeException - bad interval");
         } catch (NumberIsTooLargeException ex) {
             // expected
         }
         try {  // no bracket
             solver.solve(100, f, 1, 1.5);
             Assert.fail("Expecting NoBracketingException - non-bracketing");
         } catch (NoBracketingException ex) {
             // expected
         }
         try {  // no bracket
             solver.solve(100, f, 1, 1.5, 1.2);
             Assert.fail("Expecting NoBracketingException - non-bracketing");
         } catch (NoBracketingException ex) {
             // expected
         }
     }
 
     @Test
     public void testSolutionLeftSide() {
         UnivariateFunction f = new Sin();
         UnivariateSolver solver = getSolver();
         double left = -1.5;
         double right = 0.05;
         for(int i = 0; i < 10; i++) {
             // Test whether the allowed solutions are taken into account.
             double solution = getSolution(solver, 100, f, left, right, AllowedSolution.LEFT_SIDE);
             if (!Double.isNaN(solution)) {
                 Assert.assertTrue(solution <= 0.0);
             }
 
             // Prepare for next test.
             left -= 0.1;
             right += 0.3;
         }
     }
 
     @Test
     public void testSolutionRightSide() {
         UnivariateFunction f = new Sin();
         UnivariateSolver solver = getSolver();
         double left = -1.5;
         double right = 0.05;
         for(int i = 0; i < 10; i++) {
             // Test whether the allowed solutions are taken into account.
             double solution = getSolution(solver, 100, f, left, right, AllowedSolution.RIGHT_SIDE);
             if (!Double.isNaN(solution)) {
                 Assert.assertTrue(solution >= 0.0);
             }
 
             // Prepare for next test.
             left -= 0.1;
             right += 0.3;
         }
     }
     @Test
     public void testSolutionBelowSide() {
         UnivariateFunction f = new Sin();
         UnivariateSolver solver = getSolver();
         double left = -1.5;
         double right = 0.05;
         for(int i = 0; i < 10; i++) {
             // Test whether the allowed solutions are taken into account.
             double solution = getSolution(solver, 100, f, left, right, AllowedSolution.BELOW_SIDE);
             if (!Double.isNaN(solution)) {
                 Assert.assertTrue(f.value(solution) <= 0.0);
             }
 
             // Prepare for next test.
             left -= 0.1;
             right += 0.3;
         }
     }
 
     @Test
     public void testSolutionAboveSide() {
         UnivariateFunction f = new Sin();
         UnivariateSolver solver = getSolver();
         double left = -1.5;
         double right = 0.05;
         for(int i = 0; i < 10; i++) {
             // Test whether the allowed solutions are taken into account.
             double solution = getSolution(solver, 100, f, left, right, AllowedSolution.ABOVE_SIDE);
             if (!Double.isNaN(solution)) {
                 Assert.assertTrue(f.value(solution) >= 0.0);
             }
 
             // Prepare for next test.
             left -= 0.1;
             right += 0.3;
         }
     }
 
     private double getSolution(UnivariateSolver solver, int maxEval, UnivariateFunction f,
                                double left, double right, AllowedSolution allowedSolution) {
         try {
             @SuppressWarnings("unchecked")
             BracketedUnivariateSolver<UnivariateFunction> bracketing =
             (BracketedUnivariateSolver<UnivariateFunction>) solver;
             return bracketing.solve(100, f, left, right, allowedSolution);
         } catch (ClassCastException cce) {
             double baseRoot = solver.solve(maxEval, f, left, right);
             if (baseRoot <= left || baseRoot >= right) {
                 // the solution slipped out of interval
                 return Double.NaN;
             }
             PegasusSolver bracketing =
                     new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy(),
                                       solver.getFunctionValueAccuracy());
             return UnivariateSolverUtils.forceSide(maxEval - solver.getEvaluations(),
                                                        f, bracketing, baseRoot, left, right,
                                                        allowedSolution);
         }
     }
 }