/*
    * 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.
   */
  package org.apache.commons.math4.legacy.fitting.leastsquares;
  
  import org.apache.commons.geometry.euclidean.twod.Vector2D;
  import org.apache.commons.math4.legacy.analysis.MultivariateMatrixFunction;
  import org.apache.commons.math4.legacy.analysis.MultivariateVectorFunction;
  import org.apache.commons.math4.legacy.exception.ConvergenceException;
  import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
  import org.apache.commons.math4.legacy.fitting.leastsquares.LeastSquaresOptimizer.Optimum;
  import org.apache.commons.math4.legacy.fitting.leastsquares.LeastSquaresProblem.Evaluation;
  import org.apache.commons.math4.legacy.linear.Array2DRowRealMatrix;
  import org.apache.commons.math4.legacy.linear.ArrayRealVector;
  import org.apache.commons.math4.legacy.linear.BlockRealMatrix;
  import org.apache.commons.math4.legacy.linear.DiagonalMatrix;
  import org.apache.commons.math4.legacy.linear.RealMatrix;
  import org.apache.commons.math4.legacy.linear.RealVector;
  import org.apache.commons.math4.legacy.optim.ConvergenceChecker;
  import org.apache.commons.math4.legacy.optim.SimpleVectorValueChecker;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.apache.commons.math4.legacy.core.Pair;
  import org.junit.Assert;
  import org.junit.Test;
  
  import java.io.IOException;
  import java.util.Arrays;
  
  /**
   * Some of the unit tests are re-implementations of the MINPACK <a
   * href="http://www.netlib.org/minpack/ex/file17">file17</a> and <a
   * href="http://www.netlib.org/minpack/ex/file22">file22</a> test files. The
   * redistribution policy for MINPACK is available <a href="http://www.netlib.org/minpack/disclaimer">here</a>.
   * <p>
   * <T> Concrete implementation of an optimizer.
   *
   */
  public abstract class AbstractLeastSquaresOptimizerAbstractTest {
  
      /** default absolute tolerance of comparisons */
      public static final double TOL = 1e-10;
  
      public LeastSquaresBuilder base() {
          return new LeastSquaresBuilder()
                  .checkerPair(new SimpleVectorValueChecker(1e-6, 1e-6))
                  .maxEvaluations(100)
                  .maxIterations(getMaxIterations());
      }
  
      public LeastSquaresBuilder builder(CircleVectorial c) {
          final double[] weights = new double[c.getN()];
          Arrays.fill(weights, 1.0);
          return base()
                  .model(c.getModelFunction(), c.getModelFunctionJacobian())
                  .target(new double[c.getN()])
                  .weight(new DiagonalMatrix(weights));
      }
  
      public LeastSquaresBuilder builder(StatisticalReferenceDataset dataset) {
          StatisticalReferenceDataset.LeastSquaresProblem problem
                  = dataset.getLeastSquaresProblem();
          final double[] weights = new double[dataset.getNumObservations()];
          Arrays.fill(weights, 1.0);
          return base()
                  .model(problem.getModelFunction(), problem.getModelFunctionJacobian())
                  .target(dataset.getData()[1])
                  .weight(new DiagonalMatrix(weights))
                  .start(dataset.getStartingPoint(0));
      }
  
      public void fail(LeastSquaresOptimizer optimizer) {
          Assert.fail("Expected Exception from: " + optimizer.toString());
      }
  
      /**
       * Check the value of a vector.
       * @param tolerance the absolute tolerance of comparisons
       * @param actual the vector to test
       * @param expected the expected values
       */
      public void assertEquals(double tolerance, RealVector actual, double... expected){
          for (int i = 0; i < expected.length; i++) {
              Assert.assertEquals(expected[i], actual.getEntry(i), tolerance);
          }
          Assert.assertEquals(expected.length, actual.getDimension());
      }
 
     /**
      * @return the default number of allowed iterations (which will be used when not
      *         specified otherwise).
      */
     public abstract int getMaxIterations();
 
     /**
      * Get an instance of the optimizer under test.
      *
      * @return the subject under test.
      */
     public abstract LeastSquaresOptimizer getOptimizer();
 
     /**
      * The subject under test.
      */
     protected final LeastSquaresOptimizer optimizer = this.getOptimizer();
 
     @Test
     public void testGetIterations() {
         LeastSquaresProblem lsp = base()
                 .target(new double[]{1})
                 .weight(new DiagonalMatrix(new double[]{1}))
                 .start(new double[]{3})
                 .model(new MultivariateJacobianFunction() {
                     @Override
                     public Pair<RealVector, RealMatrix> value(final RealVector point) {
                         return new Pair<>(
                                 new ArrayRealVector(
                                         new double[]{
                                                 JdkMath.pow(point.getEntry(0), 4)
                                         },
                                         false),
                                 new Array2DRowRealMatrix(
                                         new double[][]{
                                                 {0.25 * JdkMath.pow(point.getEntry(0), 3)}
                                         },
                                         false)
                         );
                     }
                 })
                 .build();
 
         Optimum optimum = optimizer.optimize(lsp);
 
         //TODO more specific test? could pass with 'return 1;'
         Assert.assertTrue(optimum.getIterations() > 0);
     }
 
     @Test
     public void testTrivial() {
         LinearProblem problem
                 = new LinearProblem(new double[][]{{2}},
                 new double[]{3});
         LeastSquaresProblem ls = problem.getBuilder().build();
 
         Optimum optimum = optimizer.optimize(ls);
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(TOL, optimum.getPoint(), 1.5);
         Assert.assertEquals(0.0, optimum.getResiduals().getEntry(0), TOL);
     }
 
     @Test
     public void testQRColumnsPermutation() {
         LinearProblem problem
                 = new LinearProblem(new double[][]{{1, -1}, {0, 2}, {1, -2}},
                 new double[]{4, 6, 1});
 
         Optimum optimum = optimizer.optimize(problem.getBuilder().build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(TOL, optimum.getPoint(), 7, 3);
         assertEquals(TOL, optimum.getResiduals(), 0, 0, 0);
     }
 
     @Test
     public void testNoDependency() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {2, 0, 0, 0, 0, 0},
                 {0, 2, 0, 0, 0, 0},
                 {0, 0, 2, 0, 0, 0},
                 {0, 0, 0, 2, 0, 0},
                 {0, 0, 0, 0, 2, 0},
                 {0, 0, 0, 0, 0, 2}
         }, new double[]{0, 1.1, 2.2, 3.3, 4.4, 5.5});
 
         Optimum optimum = optimizer.optimize(problem.getBuilder().build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         for (int i = 0; i < problem.target.length; ++i) {
             Assert.assertEquals(0.55 * i, optimum.getPoint().getEntry(i), TOL);
         }
     }
 
     @Test
     public void testOneSet() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {1, 0, 0},
                 {-1, 1, 0},
                 {0, -1, 1}
         }, new double[]{1, 1, 1});
 
         Optimum optimum = optimizer.optimize(problem.getBuilder().build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(TOL, optimum.getPoint(), 1, 2, 3);
     }
 
     @Test
     public void testTwoSets() {
         double epsilon = 1e-7;
         LinearProblem problem = new LinearProblem(new double[][]{
                 {2, 1, 0, 4, 0, 0},
                 {-4, -2, 3, -7, 0, 0},
                 {4, 1, -2, 8, 0, 0},
                 {0, -3, -12, -1, 0, 0},
                 {0, 0, 0, 0, epsilon, 1},
                 {0, 0, 0, 0, 1, 1}
         }, new double[]{2, -9, 2, 2, 1 + epsilon * epsilon, 2});
 
         Optimum optimum = optimizer.optimize(problem.getBuilder().build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(TOL, optimum.getPoint(), 3, 4, -1, -2, 1 + epsilon, 1 - epsilon);
     }
 
     @Test
     public void testNonInvertible() throws Exception {
         try {
             LinearProblem problem = new LinearProblem(new double[][]{
                     {1, 2, -3},
                     {2, 1, 3},
                     {-3, 0, -9}
             }, new double[]{1, 1, 1});
 
             optimizer.optimize(problem.getBuilder().build());
 
             fail(optimizer);
         } catch (ConvergenceException e) {
             //expected
         }
     }
 
     @Test
     public void testIllConditioned() {
         LinearProblem problem1 = new LinearProblem(new double[][]{
                 {10, 7, 8, 7},
                 {7, 5, 6, 5},
                 {8, 6, 10, 9},
                 {7, 5, 9, 10}
         }, new double[]{32, 23, 33, 31});
         final double[] start = {0, 1, 2, 3};
 
         Optimum optimum = optimizer
                 .optimize(problem1.getBuilder().start(start).build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(TOL, optimum.getPoint(), 1, 1, 1, 1);
 
         LinearProblem problem2 = new LinearProblem(new double[][]{
                 {10.00, 7.00, 8.10, 7.20},
                 {7.08, 5.04, 6.00, 5.00},
                 {8.00, 5.98, 9.89, 9.00},
                 {6.99, 4.99, 9.00, 9.98}
         }, new double[]{32, 23, 33, 31});
 
         optimum = optimizer.optimize(problem2.getBuilder().start(start).build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(1e-8, optimum.getPoint(), -81, 137, -34, 22);
     }
 
     @Test
     public void testMoreEstimatedParametersSimple() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {3, 2, 0, 0},
                 {0, 1, -1, 1},
                 {2, 0, 1, 0}
         }, new double[]{7, 3, 5});
 
         Optimum optimum = optimizer
                 .optimize(problem.getBuilder().start(new double[]{7, 6, 5, 4}).build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
     }
 
     @Test
     public void testMoreEstimatedParametersUnsorted() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {1, 1, 0, 0, 0, 0},
                 {0, 0, 1, 1, 1, 0},
                 {0, 0, 0, 0, 1, -1},
                 {0, 0, -1, 1, 0, 1},
                 {0, 0, 0, -1, 1, 0}
         }, new double[]{3, 12, -1, 7, 1});
 
         Optimum optimum = optimizer.optimize(
                 problem.getBuilder().start(new double[]{2, 2, 2, 2, 2, 2}).build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         RealVector point = optimum.getPoint();
         //the first two elements are under constrained
         //check first two elements obey the constraint: sum to 3
         Assert.assertEquals(3, point.getEntry(0) + point.getEntry(1), TOL);
         //#constrains = #states fro the last 4 elements
         assertEquals(TOL, point.getSubVector(2, 4), 3, 4, 5, 6);
     }
 
     @Test
     public void testRedundantEquations() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {1, 1},
                 {1, -1},
                 {1, 3}
         }, new double[]{3, 1, 5});
 
         Optimum optimum = optimizer
                 .optimize(problem.getBuilder().start(new double[]{1, 1}).build());
 
         Assert.assertEquals(0, optimum.getRMS(), TOL);
         assertEquals(TOL, optimum.getPoint(), 2, 1);
     }
 
     @Test
     public void testInconsistentEquations() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {1, 1},
                 {1, -1},
                 {1, 3}
         }, new double[]{3, 1, 4});
 
         Optimum optimum = optimizer
                 .optimize(problem.getBuilder().start(new double[]{1, 1}).build());
 
         //TODO what is this actually testing?
         Assert.assertTrue(optimum.getRMS() > 0.1);
     }
 
     @Test
     public void testInconsistentSizes1() {
         try {
             LinearProblem problem
                     = new LinearProblem(new double[][]{{1, 0},
                     {0, 1}},
                     new double[]{-1, 1});
 
             //TODO why is this part here? hasn't it been tested already?
             Optimum optimum = optimizer.optimize(problem.getBuilder().build());
 
             Assert.assertEquals(0, optimum.getRMS(), TOL);
             assertEquals(TOL, optimum.getPoint(), -1, 1);
 
             //TODO move to builder test
             optimizer.optimize(
                     problem.getBuilder().weight(new DiagonalMatrix(new double[]{1})).build());
 
             fail(optimizer);
         } catch (DimensionMismatchException e) {
             //expected
         }
     }
 
     @Test
     public void testInconsistentSizes2() {
         try {
             LinearProblem problem
                     = new LinearProblem(new double[][]{{1, 0}, {0, 1}},
                     new double[]{-1, 1});
 
             Optimum optimum = optimizer.optimize(problem.getBuilder().build());
 
             Assert.assertEquals(0, optimum.getRMS(), TOL);
             assertEquals(TOL, optimum.getPoint(), -1, 1);
 
             //TODO move to builder test
             optimizer.optimize(
                     problem.getBuilder()
                             .target(new double[]{1})
                             .weight(new DiagonalMatrix(new double[]{1}))
                             .build()
             );
 
             fail(optimizer);
         } catch (DimensionMismatchException e) {
             //expected
         }
     }
 
     @Test
     public void testCircleFitting() {
         CircleVectorial circle = new CircleVectorial();
         circle.addPoint(30, 68);
         circle.addPoint(50, -6);
         circle.addPoint(110, -20);
         circle.addPoint(35, 15);
         circle.addPoint(45, 97);
         final double[] start = {98.680, 47.345};
 
         Optimum optimum = optimizer.optimize(builder(circle).start(start).build());
 
         Assert.assertTrue(optimum.getEvaluations() < 10);
 
         double rms = optimum.getRMS();
         Assert.assertEquals(1.768262623567235, JdkMath.sqrt(circle.getN()) * rms, TOL);
 
         Vector2D center = Vector2D.of(optimum.getPoint().getEntry(0), optimum.getPoint().getEntry(1));
         Assert.assertEquals(69.96016176931406, circle.getRadius(center), 1e-6);
         Assert.assertEquals(96.07590211815305, center.getX(), 1e-6);
         Assert.assertEquals(48.13516790438953, center.getY(), 1e-6);
 
         double[][] cov = optimum.getCovariances(1e-14).getData();
         Assert.assertEquals(1.839, cov[0][0], 0.001);
         Assert.assertEquals(0.731, cov[0][1], 0.001);
         Assert.assertEquals(cov[0][1], cov[1][0], 1e-14);
         Assert.assertEquals(0.786, cov[1][1], 0.001);
 
         // add perfect measurements and check formal errors are reduced
         double r = circle.getRadius(center);
         for (double d = 0; d < 2 * JdkMath.PI; d += 0.01) {
             circle.addPoint(center.getX() + r * JdkMath.cos(d), center.getY() + r * JdkMath.sin(d));
         }
 
         double[] weights = new double[circle.getN()];
         Arrays.fill(weights, 2);
 
         optimum = optimizer.optimize(
                 builder(circle).weight(new DiagonalMatrix(weights)).start(start).build());
 
         cov = optimum.getCovariances(1e-14).getData();
         Assert.assertEquals(0.0016, cov[0][0], 0.001);
         Assert.assertEquals(3.2e-7, cov[0][1], 1e-9);
         Assert.assertEquals(cov[0][1], cov[1][0], 1e-14);
         Assert.assertEquals(0.0016, cov[1][1], 0.001);
     }
 
     @Test
     public void testCircleFittingBadInit() {
         CircleVectorial circle = new CircleVectorial();
         double[][] points = circlePoints;
         double[] weights = new double[points.length];
         final double[] start = {-12, -12};
         Arrays.fill(weights, 2);
         for (int i = 0; i < points.length; ++i) {
             circle.addPoint(points[i][0], points[i][1]);
         }
 
         Optimum optimum = optimizer.optimize(builder(circle).weight(new DiagonalMatrix(weights)).start(start).build());
 
         Vector2D center = Vector2D.of(optimum.getPoint().getEntry(0), optimum.getPoint().getEntry(1));
         Assert.assertTrue(optimum.getEvaluations() < 25);
         Assert.assertEquals(0.043, optimum.getRMS(), 1e-3);
         Assert.assertEquals(0.292235, circle.getRadius(center), 1e-6);
         Assert.assertEquals(-0.151738, center.getX(), 1e-6);
         Assert.assertEquals(0.2075001, center.getY(), 1e-6);
     }
 
     @Test
     public void testCircleFittingGoodInit() {
         CircleVectorial circle = new CircleVectorial();
         double[][] points = circlePoints;
         double[] weights = new double[points.length];
         Arrays.fill(weights, 2);
         for (int i = 0; i < points.length; ++i) {
             circle.addPoint(points[i][0], points[i][1]);
         }
         final double[] start = {0, 0};
 
         Optimum optimum = optimizer.optimize(
                 builder(circle).weight(new DiagonalMatrix(weights)).start(start).build());
 
         assertEquals(1e-6, optimum.getPoint(), -0.1517383071957963, 0.2074999736353867);
         Assert.assertEquals(0.04268731682389561, optimum.getRMS(), 1e-8);
     }
 
     private final double[][] circlePoints = new double[][]{
             {-0.312967, 0.072366}, {-0.339248, 0.132965}, {-0.379780, 0.202724},
             {-0.390426, 0.260487}, {-0.361212, 0.328325}, {-0.346039, 0.392619},
             {-0.280579, 0.444306}, {-0.216035, 0.470009}, {-0.149127, 0.493832},
             {-0.075133, 0.483271}, {-0.007759, 0.452680}, {0.060071, 0.410235},
             {0.103037, 0.341076}, {0.118438, 0.273884}, {0.131293, 0.192201},
             {0.115869, 0.129797}, {0.072223, 0.058396}, {0.022884, 0.000718},
             {-0.053355, -0.020405}, {-0.123584, -0.032451}, {-0.216248, -0.032862},
             {-0.278592, -0.005008}, {-0.337655, 0.056658}, {-0.385899, 0.112526},
             {-0.405517, 0.186957}, {-0.415374, 0.262071}, {-0.387482, 0.343398},
             {-0.347322, 0.397943}, {-0.287623, 0.458425}, {-0.223502, 0.475513},
             {-0.135352, 0.478186}, {-0.061221, 0.483371}, {0.003711, 0.422737},
             {0.065054, 0.375830}, {0.108108, 0.297099}, {0.123882, 0.222850},
             {0.117729, 0.134382}, {0.085195, 0.056820}, {0.029800, -0.019138},
             {-0.027520, -0.072374}, {-0.102268, -0.091555}, {-0.200299, -0.106578},
             {-0.292731, -0.091473}, {-0.356288, -0.051108}, {-0.420561, 0.014926},
             {-0.471036, 0.074716}, {-0.488638, 0.182508}, {-0.485990, 0.254068},
             {-0.463943, 0.338438}, {-0.406453, 0.404704}, {-0.334287, 0.466119},
             {-0.254244, 0.503188}, {-0.161548, 0.495769}, {-0.075733, 0.495560},
             {0.001375, 0.434937}, {0.082787, 0.385806}, {0.115490, 0.323807},
             {0.141089, 0.223450}, {0.138693, 0.131703}, {0.126415, 0.049174},
             {0.066518, -0.010217}, {-0.005184, -0.070647}, {-0.080985, -0.103635},
             {-0.177377, -0.116887}, {-0.260628, -0.100258}, {-0.335756, -0.056251},
             {-0.405195, -0.000895}, {-0.444937, 0.085456}, {-0.484357, 0.175597},
             {-0.472453, 0.248681}, {-0.438580, 0.347463}, {-0.402304, 0.422428},
             {-0.326777, 0.479438}, {-0.247797, 0.505581}, {-0.152676, 0.519380},
             {-0.071754, 0.516264}, {0.015942, 0.472802}, {0.076608, 0.419077},
             {0.127673, 0.330264}, {0.159951, 0.262150}, {0.153530, 0.172681},
             {0.140653, 0.089229}, {0.078666, 0.024981}, {0.023807, -0.037022},
             {-0.048837, -0.077056}, {-0.127729, -0.075338}, {-0.221271, -0.067526}
     };
 
     public void doTestStRD(final StatisticalReferenceDataset dataset,
                            final LeastSquaresOptimizer optimizer,
                            final double errParams,
                            final double errParamsSd) {
 
         final Optimum optimum = optimizer.optimize(builder(dataset).build());
 
         final RealVector actual = optimum.getPoint();
         for (int i = 0; i < actual.getDimension(); i++) {
             double expected = dataset.getParameter(i);
             double delta = JdkMath.abs(errParams * expected);
             Assert.assertEquals(dataset.getName() + ", param #" + i,
                     expected, actual.getEntry(i), delta);
         }
     }
 
     @Test
     public void testKirby2() throws IOException {
         doTestStRD(StatisticalReferenceDatasetFactory.createKirby2(), optimizer, 1E-7, 1E-7);
     }
 
     @Test
     public void testHahn1() throws IOException {
         doTestStRD(StatisticalReferenceDatasetFactory.createHahn1(), optimizer, 1E-7, 1E-4);
     }
 
     @Test
     public void testPointCopy() {
         LinearProblem problem = new LinearProblem(new double[][]{
                 {1, 0, 0},
                 {-1, 1, 0},
                 {0, -1, 1}
         }, new double[]{1, 1, 1});
         //mutable boolean
         final boolean[] checked = {false};
 
         final LeastSquaresBuilder builder = problem.getBuilder()
                 .checker(new ConvergenceChecker<Evaluation>() {
                     @Override
                     public boolean converged(int iteration, Evaluation previous, Evaluation current) {
                         Assert.assertFalse(previous.getPoint().equals(current.getPoint()));
                         Assert.assertArrayEquals(new double[3], previous.getPoint().toArray(), 0);
                         Assert.assertArrayEquals(new double[] {1, 2, 3}, current.getPoint().toArray(), TOL);
                         checked[0] = true;
                         return true;
                     }
                 });
         optimizer.optimize(builder.build());
 
         Assert.assertTrue(checked[0]);
     }
 
     class LinearProblem {
         private final RealMatrix factors;
         private final double[] target;
 
         LinearProblem(double[][] factors, double[] target) {
             this.factors = new BlockRealMatrix(factors);
             this.target = target;
         }
 
         public double[] getTarget() {
             return target;
         }
 
         public MultivariateVectorFunction getModelFunction() {
             return new MultivariateVectorFunction() {
                 @Override
                 public double[] value(double[] params) {
                     return factors.operate(params);
                 }
             };
         }
 
         public MultivariateMatrixFunction getModelFunctionJacobian() {
             return new MultivariateMatrixFunction() {
                 @Override
                 public double[][] value(double[] params) {
                     return factors.getData();
                 }
             };
         }
 
         public LeastSquaresBuilder getBuilder() {
             final double[] weights = new double[target.length];
             Arrays.fill(weights, 1.0);
             return base()
                     .model(getModelFunction(), getModelFunctionJacobian())
                     .target(target)
                     .weight(new DiagonalMatrix(weights))
                     .start(new double[factors.getColumnDimension()]);
         }
     }
 }