/*
    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.optim.nonlinear.scalar.noderiv;
  
  import java.util.Arrays;
  import java.util.Random;
  
  import org.hipparchus.analysis.MultivariateFunction;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.MathIllegalStateException;
  import org.hipparchus.optim.InitialGuess;
  import org.hipparchus.optim.MaxEval;
  import org.hipparchus.optim.PointValuePair;
  import org.hipparchus.optim.SimpleBounds;
  import org.hipparchus.optim.nonlinear.scalar.GoalType;
  import org.hipparchus.optim.nonlinear.scalar.ObjectiveFunction;
  import org.hipparchus.util.FastMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test for {@link BOBYQAOptimizer}.
   */
  public class BOBYQAOptimizerTest {
  
      static final int DIM = 13;
  
      @Test(expected=MathIllegalArgumentException.class)
      public void testInitOutOfBounds() {
          double[] startPoint = point(DIM, 3);
          double[][] boundaries = boundaries(DIM, -1, 2);
          doTest(new Rosen(), startPoint, boundaries,
                  GoalType.MINIMIZE,
                  1e-13, 1e-6, 2000, null);
      }
  
      @Test(expected=MathIllegalArgumentException.class)
      public void testBoundariesDimensionMismatch() {
          double[] startPoint = point(DIM, 0.5);
          double[][] boundaries = boundaries(DIM + 1, -1, 2);
          doTest(new Rosen(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 2000, null);
      }
  
      @Test(expected=MathIllegalArgumentException.class)
      public void testProblemDimensionTooSmall() {
          double[] startPoint = point(1, 0.5);
          doTest(new Rosen(), startPoint, null,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 2000, null);
      }
  
      @Test(expected=MathIllegalStateException.class)
      public void testMaxEvaluations() {
          final int lowMaxEval = 2;
          double[] startPoint = point(DIM, 0.1);
          double[][] boundaries = null;
          doTest(new Rosen(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, lowMaxEval, null);
       }
  
      @Test
      public void testRosen() {
          double[] startPoint = point(DIM,0.1);
          double[][] boundaries = null;
          PointValuePair expected = new PointValuePair(point(DIM,1.0),0.0);
          doTest(new Rosen(), startPoint, boundaries,
                  GoalType.MINIMIZE,
                  1e-13, 1e-6, 2000, expected);
       }
  
      @Test
      public void testMaximize() {
          double[] startPoint = point(DIM,1.0);
          double[][] boundaries = null;
          PointValuePair expected = new PointValuePair(point(DIM,0.0),1.0);
          doTest(new MinusElli(), startPoint, boundaries,
                  GoalType.MAXIMIZE,
                 2e-10, 5e-6, 1000, expected);
         boundaries = boundaries(DIM,-0.3,0.3);
         startPoint = point(DIM,0.1);
         doTest(new MinusElli(), startPoint, boundaries,
                 GoalType.MAXIMIZE,
                 2e-10, 5e-6, 1000, expected);
     }
 
     @Test
     public void testEllipse() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new Elli(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 1000, expected);
      }
 
     @Test
     public void testElliRotated() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new ElliRotated(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-12, 1e-6, 10000, expected);
     }
 
     @Test
     public void testCigar() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new Cigar(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 100, expected);
     }
 
     @Test
     public void testTwoAxes() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new TwoAxes(), startPoint, boundaries,
                 GoalType.MINIMIZE, 2*
                 1e-13, 1e-6, 100, expected);
      }
 
     @Test
     public void testCigTab() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new CigTab(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 5e-5, 100, expected);
      }
 
     @Test
     public void testSphere() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new Sphere(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 100, expected);
     }
 
     @Test
     public void testTablet() {
         double[] startPoint = point(DIM,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new Tablet(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 100, expected);
     }
 
     @Test
     public void testDiffPow() {
         double[] startPoint = point(DIM/2,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM/2,0.0),0.0);
         doTest(new DiffPow(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-8, 1e-1, 21000, expected);
     }
 
     @Test
     public void testSsDiffPow() {
         double[] startPoint = point(DIM/2,1.0);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM/2,0.0),0.0);
         doTest(new SsDiffPow(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-2, 1.3e-1, 50000, expected);
     }
 
     @Test
     public void testAckley() {
         double[] startPoint = point(DIM,0.1);
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new Ackley(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-7, 1e-5, 1000, expected);
     }
 
     @Test
     public void testRastrigin() {
         double[] startPoint = point(DIM,1.0);
 
         double[][] boundaries = null;
         PointValuePair expected =
             new PointValuePair(point(DIM,0.0),0.0);
         doTest(new Rastrigin(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 1000, expected);
     }
 
     @Test
     public void testConstrainedRosen() {
         double[] startPoint = point(DIM,0.1);
 
         double[][] boundaries = boundaries(DIM,-1,2);
         PointValuePair expected =
             new PointValuePair(point(DIM,1.0),0.0);
         doTest(new Rosen(), startPoint, boundaries,
                 GoalType.MINIMIZE,
                 1e-13, 1e-6, 2000, expected);
     }
 
     /**
      * @param func Function to optimize.
      * @param startPoint Starting point.
      * @param boundaries Upper / lower point limit.
      * @param goal Minimization or maximization.
      * @param fTol Tolerance relative error on the objective function.
      * @param pointTol Tolerance for checking that the optimum is correct.
      * @param maxEvaluations Maximum number of evaluations.
      * @param expected Expected point / value.
      */
     private void doTest(MultivariateFunction func,
                         double[] startPoint,
                         double[][] boundaries,
                         GoalType goal,
                         double fTol,
                         double pointTol,
                         int maxEvaluations,
                         PointValuePair expected) {
         doTest(func,
                startPoint,
                boundaries,
                goal,
                fTol,
                pointTol,
                maxEvaluations,
                0,
                expected,
                "");
     }
 
     /**
      * @param func Function to optimize.
      * @param startPoint Starting point.
      * @param boundaries Upper / lower point limit.
      * @param goal Minimization or maximization.
      * @param fTol Tolerance relative error on the objective function.
      * @param pointTol Tolerance for checking that the optimum is correct.
      * @param maxEvaluations Maximum number of evaluations.
      * @param additionalInterpolationPoints Number of interpolation to used
      * in addition to the default (2 * dim + 1).
      * @param expected Expected point / value.
      */
     private void doTest(MultivariateFunction func,
                         double[] startPoint,
                         double[][] boundaries,
                         GoalType goal,
                         double fTol,
                         double pointTol,
                         int maxEvaluations,
                         int additionalInterpolationPoints,
                         PointValuePair expected,
                         String assertMsg) {
 
 //         System.out.println(func.getClass().getName() + " BEGIN"); // XXX
 
         int dim = startPoint.length;
         final int numIterpolationPoints = 2 * dim + 1 + additionalInterpolationPoints;
         BOBYQAOptimizer optim = new BOBYQAOptimizer(numIterpolationPoints);
         PointValuePair result = boundaries == null ?
             optim.optimize(new MaxEval(maxEvaluations),
                            new ObjectiveFunction(func),
                            goal,
                            SimpleBounds.unbounded(dim),
                            new InitialGuess(startPoint)) :
             optim.optimize(new MaxEval(maxEvaluations),
                            new ObjectiveFunction(func),
                            goal,
                            new InitialGuess(startPoint),
                            new SimpleBounds(boundaries[0],
                                             boundaries[1]));
 //        System.out.println(func.getClass().getName() + " = "
 //              + optim.getEvaluations() + " f(");
 //        for (double x: result.getPoint())  System.out.print(x + " ");
 //        System.out.println(") = " +  result.getValue());
         Assert.assertEquals(assertMsg, expected.getValue(), result.getValue(), fTol);
         for (int i = 0; i < dim; i++) {
             Assert.assertEquals(expected.getPoint()[i],
                                 result.getPoint()[i], pointTol);
         }
 
 //         System.out.println(func.getClass().getName() + " END"); // XXX
     }
 
     private static double[] point(int n, double value) {
         double[] ds = new double[n];
         Arrays.fill(ds, value);
         return ds;
     }
 
     private static double[][] boundaries(int dim,
             double lower, double upper) {
         double[][] boundaries = new double[2][dim];
         for (int i = 0; i < dim; i++)
             boundaries[0][i] = lower;
         for (int i = 0; i < dim; i++)
             boundaries[1][i] = upper;
         return boundaries;
     }
 
     private static class Sphere implements MultivariateFunction {
 
         public double value(double[] x) {
             double f = 0;
             for (int i = 0; i < x.length; ++i)
                 f += x[i] * x[i];
             return f;
         }
     }
 
     private static class Cigar implements MultivariateFunction {
         private double factor;
 
         Cigar() {
             this(1e3);
         }
 
         Cigar(double axisratio) {
             factor = axisratio * axisratio;
         }
 
         public double value(double[] x) {
             double f = x[0] * x[0];
             for (int i = 1; i < x.length; ++i)
                 f += factor * x[i] * x[i];
             return f;
         }
     }
 
     private static class Tablet implements MultivariateFunction {
         private double factor;
 
         Tablet() {
             this(1e3);
         }
 
         Tablet(double axisratio) {
             factor = axisratio * axisratio;
         }
 
         public double value(double[] x) {
             double f = factor * x[0] * x[0];
             for (int i = 1; i < x.length; ++i)
                 f += x[i] * x[i];
             return f;
         }
     }
 
     private static class CigTab implements MultivariateFunction {
         private double factor;
 
         CigTab() {
             this(1e4);
         }
 
         CigTab(double axisratio) {
             factor = axisratio;
         }
 
         public double value(double[] x) {
             int end = x.length - 1;
             double f = x[0] * x[0] / factor + factor * x[end] * x[end];
             for (int i = 1; i < end; ++i)
                 f += x[i] * x[i];
             return f;
         }
     }
 
     private static class TwoAxes implements MultivariateFunction {
 
         private double factor;
 
         TwoAxes() {
             this(1e6);
         }
 
         TwoAxes(double axisratio) {
             factor = axisratio * axisratio;
         }
 
         public double value(double[] x) {
             double f = 0;
             for (int i = 0; i < x.length; ++i)
                 f += (i < x.length / 2 ? factor : 1) * x[i] * x[i];
             return f;
         }
     }
 
     private static class ElliRotated implements MultivariateFunction {
         private Basis B = new Basis();
         private double factor;
 
         ElliRotated() {
             this(1e3);
         }
 
         ElliRotated(double axisratio) {
             factor = axisratio * axisratio;
         }
 
         public double value(double[] x) {
             double f = 0;
             x = B.Rotate(x);
             for (int i = 0; i < x.length; ++i)
                 f += FastMath.pow(factor, i / (x.length - 1.)) * x[i] * x[i];
             return f;
         }
     }
 
     private static class Elli implements MultivariateFunction {
 
         private double factor;
 
         Elli() {
             this(1e3);
         }
 
         Elli(double axisratio) {
             factor = axisratio * axisratio;
         }
 
         public double value(double[] x) {
             double f = 0;
             for (int i = 0; i < x.length; ++i)
                 f += FastMath.pow(factor, i / (x.length - 1.)) * x[i] * x[i];
             return f;
         }
     }
 
     private static class MinusElli implements MultivariateFunction {
         private final Elli elli = new Elli();
         public double value(double[] x) {
             return 1.0 - elli.value(x);
         }
     }
 
     private static class DiffPow implements MultivariateFunction {
 //        private int fcount = 0;
         public double value(double[] x) {
             double f = 0;
             for (int i = 0; i < x.length; ++i)
                 f += FastMath.pow(FastMath.abs(x[i]), 2. + 10 * (double) i
                         / (x.length - 1.));
 //            System.out.print("" + (fcount++) + ") ");
 //            for (int i = 0; i < x.length; i++)
 //                System.out.print(x[i] +  " ");
 //            System.out.println(" = " + f);
             return f;
         }
     }
 
     private static class SsDiffPow implements MultivariateFunction {
 
         public double value(double[] x) {
             double f = FastMath.pow(new DiffPow().value(x), 0.25);
             return f;
         }
     }
 
     private static class Rosen implements MultivariateFunction {
 
         public double value(double[] x) {
             double f = 0;
             for (int i = 0; i < x.length - 1; ++i)
                 f += 1e2 * (x[i] * x[i] - x[i + 1]) * (x[i] * x[i] - x[i + 1])
                 + (x[i] - 1.) * (x[i] - 1.);
             return f;
         }
     }
 
     private static class Ackley implements MultivariateFunction {
         private double axisratio;
 
         Ackley(double axra) {
             axisratio = axra;
         }
 
         public Ackley() {
             this(1);
         }
 
         public double value(double[] x) {
             double f = 0;
             double res2 = 0;
             double fac = 0;
             for (int i = 0; i < x.length; ++i) {
                 fac = FastMath.pow(axisratio, (i - 1.) / (x.length - 1.));
                 f += fac * fac * x[i] * x[i];
                 res2 += FastMath.cos(2. * FastMath.PI * fac * x[i]);
             }
             f = (20. - 20. * FastMath.exp(-0.2 * FastMath.sqrt(f / x.length))
                     + FastMath.exp(1.) - FastMath.exp(res2 / x.length));
             return f;
         }
     }
 
     private static class Rastrigin implements MultivariateFunction {
 
         private double axisratio;
         private double amplitude;
 
         Rastrigin() {
             this(1, 10);
         }
 
         Rastrigin(double axisratio, double amplitude) {
             this.axisratio = axisratio;
             this.amplitude = amplitude;
         }
 
         public double value(double[] x) {
             double f = 0;
             double fac;
             for (int i = 0; i < x.length; ++i) {
                 fac = FastMath.pow(axisratio, (i - 1.) / (x.length - 1.));
                 if (i == 0 && x[i] < 0)
                     fac *= 1.;
                 f += fac * fac * x[i] * x[i] + amplitude
                 * (1. - FastMath.cos(2. * FastMath.PI * fac * x[i]));
             }
             return f;
         }
     }
 
     private static class Basis {
         double[][] basis;
         Random rand = new Random(2); // use not always the same basis
 
         double[] Rotate(double[] x) {
             GenBasis(x.length);
             double[] y = new double[x.length];
             for (int i = 0; i < x.length; ++i) {
                 y[i] = 0;
                 for (int j = 0; j < x.length; ++j)
                     y[i] += basis[i][j] * x[j];
             }
             return y;
         }
 
         void GenBasis(int DIM) {
             if (basis != null ? basis.length == DIM : false)
                 return;
 
             double sp;
             int i, j, k;
 
             /* generate orthogonal basis */
             basis = new double[DIM][DIM];
             for (i = 0; i < DIM; ++i) {
                 /* sample components gaussian */
                 for (j = 0; j < DIM; ++j)
                     basis[i][j] = rand.nextGaussian();
                 /* substract projection of previous vectors */
                 for (j = i - 1; j >= 0; --j) {
                     for (sp = 0., k = 0; k < DIM; ++k)
                         sp += basis[i][k] * basis[j][k]; /* scalar product */
                     for (k = 0; k < DIM; ++k)
                         basis[i][k] -= sp * basis[j][k]; /* substract */
                 }
                 /* normalize */
                 for (sp = 0., k = 0; k < DIM; ++k)
                     sp += basis[i][k] * basis[i][k]; /* squared norm */
                 for (k = 0; k < DIM; ++k)
                     basis[i][k] /= FastMath.sqrt(sp);
             }
         }
     }
 }