/*
    * 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.
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  package org.apache.commons.math4.legacy.optim.nonlinear.scalar.noderiv;
  
  import org.apache.commons.math4.legacy.analysis.MultivariateFunction;
  import org.apache.commons.math4.legacy.analysis.SumSincFunction;
  import org.apache.commons.math4.legacy.exception.MathUnsupportedOperationException;
  import org.apache.commons.math4.legacy.optim.InitialGuess;
  import org.apache.commons.math4.legacy.optim.MaxEval;
  import org.apache.commons.math4.legacy.optim.PointValuePair;
  import org.apache.commons.math4.legacy.optim.SimpleBounds;
  import org.apache.commons.math4.legacy.optim.nonlinear.scalar.GoalType;
  import org.apache.commons.math4.legacy.optim.nonlinear.scalar.ObjectiveFunction;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test for {@link PowellOptimizer}.
   */
  public class PowellOptimizerTest {
      @Test(expected=MathUnsupportedOperationException.class)
      public void testBoundsUnsupported() {
          final MultivariateFunction func = new SumSincFunction(-1);
          final PowellOptimizer optim = new PowellOptimizer(1e-8, 1e-5,
                                                            1e-4, 1e-4);
  
          optim.optimize(new MaxEval(100),
                         new ObjectiveFunction(func),
                         GoalType.MINIMIZE,
                         new InitialGuess(new double[] { -3, 0 }),
                         new SimpleBounds(new double[] { -5, -1 },
                                          new double[] { 5, 1 }));
      }
  
      @Test
      public void testSumSinc() {
          final MultivariateFunction func = new SumSincFunction(-1);
  
          int dim = 2;
          final double[] minPoint = new double[dim];
          for (int i = 0; i < dim; i++) {
              minPoint[i] = 0;
          }
  
          double[] init = new double[dim];
  
          // Initial is minimum.
          for (int i = 0; i < dim; i++) {
              init[i] = minPoint[i];
          }
          doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9);
  
          // Initial is far from minimum.
          for (int i = 0; i < dim; i++) {
              init[i] = minPoint[i] + 3;
          }
          doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-5);
          // More stringent line search tolerance enhances the precision
          // of the result.
          doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9, 1e-7);
      }
  
      @Test
      public void testQuadratic() {
          final MultivariateFunction func = new MultivariateFunction() {
                  @Override
                  public double value(double[] x) {
                      final double a = x[0] - 1;
                      final double b = x[1] - 1;
                      return a * a + b * b + 1;
                  }
              };
  
          int dim = 2;
          final double[] minPoint = new double[dim];
          for (int i = 0; i < dim; i++) {
              minPoint[i] = 1;
          }
  
          double[] init = new double[dim];
  
          // Initial is minimum.
          for (int i = 0; i < dim; i++) {
              init[i] = minPoint[i];
         }
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);
 
         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i] - 20;
         }
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);
     }
 
     @Test
     public void testMaximizeQuadratic() {
         final MultivariateFunction func = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     final double a = x[0] - 1;
                     final double b = x[1] - 1;
                     return -a * a - b * b + 1;
                 }
             };
 
         int dim = 2;
         final double[] maxPoint = new double[dim];
         for (int i = 0; i < dim; i++) {
             maxPoint[i] = 1;
         }
 
         double[] init = new double[dim];
 
         // Initial is minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = maxPoint[i];
         }
         doTest(func, maxPoint, init,  GoalType.MAXIMIZE, 1e-9, 1e-8);
 
         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = maxPoint[i] - 20;
         }
         doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);
     }
 
     /**
      * Ensure that we do not increase the number of function evaluations when
      * the function values are scaled up.
      * Note that the tolerances parameters passed to the constructor must
      * still hold sensible values because they are used to set the line search
      * tolerances.
      */
     @Test
     public void testRelativeToleranceOnScaledValues() {
         final MultivariateFunction func = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     final double a = x[0] - 1;
                     final double b = x[1] - 1;
                     return a * a * JdkMath.sqrt(JdkMath.abs(a)) + b * b + 1;
                 }
             };
 
         int dim = 2;
         final double[] minPoint = new double[dim];
         for (int i = 0; i < dim; i++) {
             minPoint[i] = 1;
         }
 
         double[] init = new double[dim];
         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i] - 20;
         }
 
         final double relTol = 1e-10;
 
         final int maxEval = 1000;
         // Very small absolute tolerance to rely solely on the relative
         // tolerance as a stopping criterion
         final PowellOptimizer optim = new PowellOptimizer(relTol, 1e-100);
 
         final PointValuePair funcResult = optim.optimize(new MaxEval(maxEval),
                                                          new ObjectiveFunction(func),
                                                          GoalType.MINIMIZE,
                                                          new InitialGuess(init));
         final double funcValue = func.value(funcResult.getPoint());
         final int funcEvaluations = optim.getEvaluations();
 
         final double scale = 1e10;
         final MultivariateFunction funcScaled = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     return scale * func.value(x);
                 }
             };
 
         final PointValuePair funcScaledResult = optim.optimize(new MaxEval(maxEval),
                                                                new ObjectiveFunction(funcScaled),
                                                                GoalType.MINIMIZE,
                                                                new InitialGuess(init));
         final double funcScaledValue = funcScaled.value(funcScaledResult.getPoint());
         final int funcScaledEvaluations = optim.getEvaluations();
 
         // Check that both minima provide the same objective funciton values,
         // within the relative function tolerance.
         Assert.assertEquals(1, funcScaledValue / (scale * funcValue), relTol);
 
         // Check that the numbers of evaluations are the same.
         Assert.assertEquals(funcEvaluations, funcScaledEvaluations);
     }
 
     /**
      * @param func Function to optimize.
      * @param optimum Expected optimum.
      * @param init Starting point.
      * @param goal Minimization or maximization.
      * @param fTol Tolerance (relative error on the objective function) for
      * "Powell" algorithm.
      * @param pointTol Tolerance for checking that the optimum is correct.
      */
     private void doTest(MultivariateFunction func,
                         double[] optimum,
                         double[] init,
                         GoalType goal,
                         double fTol,
                         double pointTol) {
         final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));
 
         final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                      new ObjectiveFunction(func),
                                                      goal,
                                                      new InitialGuess(init));
         final double[] point = result.getPoint();
 
         for (int i = 0, dim = optimum.length; i < dim; i++) {
             Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                                 optimum[i], point[i], pointTol);
         }
     }
 
     /**
      * @param func Function to optimize.
      * @param optimum Expected optimum.
      * @param init Starting point.
      * @param goal Minimization or maximization.
      * @param fTol Tolerance (relative error on the objective function) for
      * "Powell" algorithm.
      * @param fLineTol Tolerance (relative error on the objective function)
      * for the internal line search algorithm.
      * @param pointTol Tolerance for checking that the optimum is correct.
      */
     private void doTest(MultivariateFunction func,
                         double[] optimum,
                         double[] init,
                         GoalType goal,
                         double fTol,
                         double fLineTol,
                         double pointTol) {
         final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
                                                           fLineTol, Math.ulp(1d));
 
         final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                      new ObjectiveFunction(func),
                                                      goal,
                                                      new InitialGuess(init));
         final double[] point = result.getPoint();
 
         for (int i = 0, dim = optimum.length; i < dim; i++) {
             Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                                 optimum[i], point[i], pointTol);
         }
 
         Assert.assertTrue(optim.getIterations() > 0);
     }
 }