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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.numbers.complex.Complex;
  import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunction;
  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.apache.commons.math4.legacy.TestUtils;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test case for Laguerre solver.
   * <p>
   * Laguerre's method is very efficient in solving polynomials. Test runs
   * show that for a default absolute accuracy of 1E-6, it generally takes
   * less than 5 iterations to find one root, provided solveAll() is not
   * invoked, and 15 to 20 iterations to find all roots for quintic function.
   *
   */
  public final class LaguerreSolverTest {
      /**
       * Test of solver for the linear function.
       */
      @Test
      public void testLinearFunction() {
          double min;
          double max;
          double expected;
          double result;
          double tolerance;
  
          // p(x) = 4x - 1
          double coefficients[] = { -1.0, 4.0 };
          PolynomialFunction f = new PolynomialFunction(coefficients);
          LaguerreSolver solver = new LaguerreSolver();
  
          min = 0.0; max = 1.0; expected = 0.25;
          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 quadratic function.
       */
      @Test
      public void testQuadraticFunction() {
          double min;
          double max;
          double expected;
          double result;
          double tolerance;
  
          // p(x) = 2x^2 + 5x - 3 = (x+3)(2x-1)
          double coefficients[] = { -3.0, 5.0, 2.0 };
          PolynomialFunction f = new PolynomialFunction(coefficients);
          LaguerreSolver solver = new LaguerreSolver();
  
          min = 0.0; max = 2.0; 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);
  
          min = -4.0; max = -1.0; expected = -3.0;
          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() {
          double min;
          double max;
          double expected;
          double result;
          double tolerance;
 
         // p(x) = x^5 - x^4 - 12x^3 + x^2 - x - 12 = (x+1)(x+3)(x-4)(x^2-x+1)
         double coefficients[] = { -12.0, -1.0, 1.0, -12.0, -1.0, 1.0 };
         PolynomialFunction f = new PolynomialFunction(coefficients);
         LaguerreSolver solver = new LaguerreSolver();
 
         min = -2.0; max = 2.0; 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 = -5.0; max = -2.5; expected = -3.0;
         tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                     JdkMath.abs(expected * solver.getRelativeAccuracy()));
         result = solver.solve(100, f, min, max);
         Assert.assertEquals(expected, result, tolerance);
 
         min = 3.0; max = 6.0; expected = 4.0;
         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 using
      * {@link LaguerreSolver#solveAllComplex(double[],double) solveAllComplex}.
      */
     @Test
     public void testQuinticFunction2() {
         // p(x) = x^5 + 4x^3 + x^2 + 4 = (x+1)(x^2-x+1)(x^2+4)
         final double[] coefficients = { 4.0, 0.0, 1.0, 4.0, 0.0, 1.0 };
         final LaguerreSolver solver = new LaguerreSolver();
         final Complex[] result = solver.solveAllComplex(coefficients, 0);
 
         for (Complex expected : new Complex[] { Complex.ofCartesian(0, -2),
                                                 Complex.ofCartesian(0, 2),
                                                 Complex.ofCartesian(0.5, 0.5 * JdkMath.sqrt(3)),
                                                 Complex.ofCartesian(-1, 0),
                                                 Complex.ofCartesian(0.5, -0.5 * JdkMath.sqrt(3.0)) }) {
             final double tolerance = JdkMath.max(solver.getAbsoluteAccuracy(),
                                                   JdkMath.abs(expected.abs() * solver.getRelativeAccuracy()));
             TestUtils.assertContains(result, expected, tolerance);
         }
     }
 
     /**
      * Test of parameters for the solver.
      */
     @Test
     public void testParameters() {
         double coefficients[] = { -3.0, 5.0, 2.0 };
         PolynomialFunction f = new PolynomialFunction(coefficients);
         LaguerreSolver solver = new LaguerreSolver();
 
         try {
             // bad interval
             solver.solve(100, f, 1, -1);
             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
         }
     }
 }