/*
    * 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.vector.leastsquares;
  
  import org.hipparchus.analysis.MultivariateMatrixFunction;
  import org.hipparchus.analysis.MultivariateVectorFunction;
  import org.hipparchus.exception.MathIllegalStateException;
  import org.hipparchus.linear.Array2DRowRealMatrix;
  import org.hipparchus.linear.ArrayRealVector;
  import org.hipparchus.linear.DiagonalMatrix;
  import org.hipparchus.linear.EigenDecompositionSymmetric;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.linear.RealVector;
  import org.hipparchus.optim.AbstractOptimizationProblem;
  import org.hipparchus.optim.ConvergenceChecker;
  import org.hipparchus.optim.LocalizedOptimFormats;
  import org.hipparchus.optim.PointVectorValuePair;
  import org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem.Evaluation;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.Incrementor;
  import org.hipparchus.util.Pair;
  
  /**
   * A Factory for creating {@link LeastSquaresProblem}s.
   *
   */
  public class LeastSquaresFactory {
  
      /** Prevent instantiation. */
      private LeastSquaresFactory() {}
  
      /**
       * Create a {@link org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem}
       * from the given elements. There will be no weights applied (unit weights).
       *
       * @param model          the model function. Produces the computed values.
       * @param observed       the observed (target) values
       * @param start          the initial guess.
       * @param weight         the weight matrix
       * @param checker        convergence checker
       * @param maxEvaluations the maximum number of times to evaluate the model
       * @param maxIterations  the maximum number to times to iterate in the algorithm
       * @param lazyEvaluation Whether the call to {@link Evaluation#evaluate(RealVector)}
       * will defer the evaluation until access to the value is requested.
       * @param paramValidator Model parameters validator.
       * @return the specified General Least Squares problem.
       *
       */
      public static LeastSquaresProblem create(final MultivariateJacobianFunction model,
                                               final RealVector observed,
                                               final RealVector start,
                                               final RealMatrix weight,
                                               final ConvergenceChecker<Evaluation> checker,
                                               final int maxEvaluations,
                                               final int maxIterations,
                                               final boolean lazyEvaluation,
                                               final ParameterValidator paramValidator) {
          final LeastSquaresProblem p = new LocalLeastSquaresProblem(model,
                                                                     observed,
                                                                     start,
                                                                     checker,
                                                                     maxEvaluations,
                                                                     maxIterations,
                                                                     lazyEvaluation,
                                                                     paramValidator);
          if (weight != null) {
              return weightMatrix(p, weight);
          } else {
              return p;
          }
      }
  
      /**
       * Create a {@link org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem}
       * from the given elements. There will be no weights applied (unit weights).
       *
       * @param model          the model function. Produces the computed values.
       * @param observed       the observed (target) values
       * @param start          the initial guess.
       * @param checker        convergence checker
      * @param maxEvaluations the maximum number of times to evaluate the model
      * @param maxIterations  the maximum number to times to iterate in the algorithm
      * @return the specified General Least Squares problem.
      */
     public static LeastSquaresProblem create(final MultivariateJacobianFunction model,
                                              final RealVector observed,
                                              final RealVector start,
                                              final ConvergenceChecker<Evaluation> checker,
                                              final int maxEvaluations,
                                              final int maxIterations) {
         return create(model,
                       observed,
                       start,
                       null,
                       checker,
                       maxEvaluations,
                       maxIterations,
                       false,
                       null);
     }
 
     /**
      * Create a {@link org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem}
      * from the given elements.
      *
      * @param model          the model function. Produces the computed values.
      * @param observed       the observed (target) values
      * @param start          the initial guess.
      * @param weight         the weight matrix
      * @param checker        convergence checker
      * @param maxEvaluations the maximum number of times to evaluate the model
      * @param maxIterations  the maximum number to times to iterate in the algorithm
      * @return the specified General Least Squares problem.
      */
     public static LeastSquaresProblem create(final MultivariateJacobianFunction model,
                                              final RealVector observed,
                                              final RealVector start,
                                              final RealMatrix weight,
                                              final ConvergenceChecker<Evaluation> checker,
                                              final int maxEvaluations,
                                              final int maxIterations) {
         return weightMatrix(create(model,
                                    observed,
                                    start,
                                    checker,
                                    maxEvaluations,
                                    maxIterations),
                             weight);
     }
 
     /**
      * Create a {@link org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem}
      * from the given elements.
      * <p>
      * This factory method is provided for continuity with previous interfaces. Newer
      * applications should use {@link #create(MultivariateJacobianFunction, RealVector,
      * RealVector, ConvergenceChecker, int, int)}, or {@link #create(MultivariateJacobianFunction,
      * RealVector, RealVector, RealMatrix, ConvergenceChecker, int, int)}.
      *
      * @param model          the model function. Produces the computed values.
      * @param jacobian       the jacobian of the model with respect to the parameters
      * @param observed       the observed (target) values
      * @param start          the initial guess.
      * @param weight         the weight matrix
      * @param checker        convergence checker
      * @param maxEvaluations the maximum number of times to evaluate the model
      * @param maxIterations  the maximum number to times to iterate in the algorithm
      * @return the specified General Least Squares problem.
      */
     public static LeastSquaresProblem create(final MultivariateVectorFunction model,
                                              final MultivariateMatrixFunction jacobian,
                                              final double[] observed,
                                              final double[] start,
                                              final RealMatrix weight,
                                              final ConvergenceChecker<Evaluation> checker,
                                              final int maxEvaluations,
                                              final int maxIterations) {
         return create(model(model, jacobian),
                       new ArrayRealVector(observed, false),
                       new ArrayRealVector(start, false),
                       weight,
                       checker,
                       maxEvaluations,
                       maxIterations);
     }
 
     /**
      * Apply a dense weight matrix to the {@link LeastSquaresProblem}.
      *
      * @param problem the unweighted problem
      * @param weights the matrix of weights
      * @return a new {@link LeastSquaresProblem} with the weights applied. The original
      *         {@code problem} is not modified.
      */
     public static LeastSquaresProblem weightMatrix(final LeastSquaresProblem problem,
                                                    final RealMatrix weights) {
         final RealMatrix weightSquareRoot = squareRoot(weights);
         return new LeastSquaresAdapter(problem) {
             /** {@inheritDoc} */
             @Override
             public Evaluation evaluate(final RealVector point) {
                 return new DenseWeightedEvaluation(super.evaluate(point), weightSquareRoot);
             }
         };
     }
 
     /**
      * Apply a diagonal weight matrix to the {@link LeastSquaresProblem}.
      *
      * @param problem the unweighted problem
      * @param weights the diagonal of the weight matrix
      * @return a new {@link LeastSquaresProblem} with the weights applied. The original
      *         {@code problem} is not modified.
      */
     public static LeastSquaresProblem weightDiagonal(final LeastSquaresProblem problem,
                                                      final RealVector weights) {
         // TODO more efficient implementation
         return weightMatrix(problem, new DiagonalMatrix(weights.toArray()));
     }
 
     /**
      * Count the evaluations of a particular problem. The {@code counter} will be
      * incremented every time {@link LeastSquaresProblem#evaluate(RealVector)} is called on
      * the <em>returned</em> problem.
      *
      * @param problem the problem to track.
      * @param counter the counter to increment.
      * @return a least squares problem that tracks evaluations
      */
     public static LeastSquaresProblem countEvaluations(final LeastSquaresProblem problem,
                                                        final Incrementor counter) {
         return new LeastSquaresAdapter(problem) {
 
             /** {@inheritDoc} */
             @Override
             public Evaluation evaluate(final RealVector point) {
                 counter.increment();
                 return super.evaluate(point);
             }
 
             // Delegate the rest.
         };
     }
 
     /**
      * View a convergence checker specified for a {@link PointVectorValuePair} as one
      * specified for an {@link Evaluation}.
      *
      * @param checker the convergence checker to adapt.
      * @return a convergence checker that delegates to {@code checker}.
      */
     public static ConvergenceChecker<Evaluation> evaluationChecker(final ConvergenceChecker<PointVectorValuePair> checker) {
         return new ConvergenceChecker<Evaluation>() {
             /** {@inheritDoc} */
             @Override
             public boolean converged(final int iteration,
                                      final Evaluation previous,
                                      final Evaluation current) {
                 return checker.converged(
                         iteration,
                         new PointVectorValuePair(
                                 previous.getPoint().toArray(),
                                 previous.getResiduals().toArray(),
                                 false),
                         new PointVectorValuePair(
                                 current.getPoint().toArray(),
                                 current.getResiduals().toArray(),
                                 false)
                 );
             }
         };
     }
 
     /**
      * Computes the square-root of the weight matrix.
      *
      * @param m Symmetric, positive-definite (weight) matrix.
      * @return the square-root of the weight matrix.
      */
     private static RealMatrix squareRoot(final RealMatrix m) {
         if (m instanceof DiagonalMatrix) {
             final int dim = m.getRowDimension();
             final RealMatrix sqrtM = new DiagonalMatrix(dim);
             for (int i = 0; i < dim; i++) {
                 sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
             }
             return sqrtM;
         } else {
             final EigenDecompositionSymmetric dec = new EigenDecompositionSymmetric(m);
             return dec.getSquareRoot();
         }
     }
 
     /**
      * Combine a {@link MultivariateVectorFunction} with a {@link
      * MultivariateMatrixFunction} to produce a {@link MultivariateJacobianFunction}.
      *
      * @param value    the vector value function
      * @param jacobian the Jacobian function
      * @return a function that computes both at the same time
      */
     public static MultivariateJacobianFunction model(final MultivariateVectorFunction value,
                                                      final MultivariateMatrixFunction jacobian) {
         return new LocalValueAndJacobianFunction(value, jacobian);
     }
 
     /**
      * Combine a {@link MultivariateVectorFunction} with a {@link
      * MultivariateMatrixFunction} to produce a {@link MultivariateJacobianFunction}.
      */
     private static class LocalValueAndJacobianFunction
         implements ValueAndJacobianFunction {
         /** Model. */
         private final MultivariateVectorFunction value;
         /** Model's Jacobian. */
         private final MultivariateMatrixFunction jacobian;
 
         /**
          * @param value Model function.
          * @param jacobian Model's Jacobian function.
          */
         LocalValueAndJacobianFunction(final MultivariateVectorFunction value,
                                       final MultivariateMatrixFunction jacobian) {
             this.value = value;
             this.jacobian = jacobian;
         }
 
         /** {@inheritDoc} */
         @Override
         public Pair<RealVector, RealMatrix> value(final RealVector point) {
             //TODO get array from RealVector without copying?
             final double[] p = point.toArray();
 
             // Evaluate.
             return new Pair<>(computeValue(p),
                     computeJacobian(p));
         }
 
         /** {@inheritDoc} */
         @Override
         public RealVector computeValue(final double[] params) {
             return new ArrayRealVector(value.value(params), false);
         }
 
         /** {@inheritDoc} */
         @Override
         public RealMatrix computeJacobian(final double[] params) {
             return new Array2DRowRealMatrix(jacobian.value(params), false);
         }
     }
 
 
     /**
      * A private, "field" immutable (not "real" immutable) implementation of {@link
      * LeastSquaresProblem}.
      */
     private static class LocalLeastSquaresProblem
             extends AbstractOptimizationProblem<Evaluation>
             implements LeastSquaresProblem {
 
         /** Target values for the model function at optimum. */
         private final RealVector target;
         /** Model function. */
         private final MultivariateJacobianFunction model;
         /** Initial guess. */
         private final RealVector start;
         /** Whether to use lazy evaluation. */
         private final boolean lazyEvaluation;
         /** Model parameters validator. */
         private final ParameterValidator paramValidator;
 
         /**
          * Create a {@link LeastSquaresProblem} from the given data.
          *
          * @param model          the model function
          * @param target         the observed data
          * @param start          the initial guess
          * @param checker        the convergence checker
          * @param maxEvaluations the allowed evaluations
          * @param maxIterations  the allowed iterations
          * @param lazyEvaluation Whether the call to {@link Evaluation#evaluate(RealVector)}
          * will defer the evaluation until access to the value is requested.
          * @param paramValidator Model parameters validator.
          */
         LocalLeastSquaresProblem(final MultivariateJacobianFunction model,
                                  final RealVector target,
                                  final RealVector start,
                                  final ConvergenceChecker<Evaluation> checker,
                                  final int maxEvaluations,
                                  final int maxIterations,
                                  final boolean lazyEvaluation,
                                  final ParameterValidator paramValidator) {
             super(maxEvaluations, maxIterations, checker);
             this.target = target;
             this.model = model;
             this.start = start;
             this.lazyEvaluation = lazyEvaluation;
             this.paramValidator = paramValidator;
 
             if (lazyEvaluation &&
                 !(model instanceof ValueAndJacobianFunction)) {
                 // Lazy evaluation requires that value and Jacobian
                 // can be computed separately.
                 throw new MathIllegalStateException(LocalizedOptimFormats.INVALID_IMPLEMENTATION,
                                                     model.getClass().getName());
             }
         }
 
         /** {@inheritDoc} */
         @Override
         public int getObservationSize() {
             return target.getDimension();
         }
 
         /** {@inheritDoc} */
         @Override
         public int getParameterSize() {
             return start.getDimension();
         }
 
         /** {@inheritDoc} */
         @Override
         public RealVector getStart() {
             return start == null ? null : start.copy();
         }
 
         /** {@inheritDoc} */
         @Override
         public Evaluation evaluate(final RealVector point) {
             // Copy so optimizer can change point without changing our instance.
             final RealVector p = paramValidator == null ?
                 point.copy() :
                 paramValidator.validate(point.copy());
 
             if (lazyEvaluation) {
                 return new LazyUnweightedEvaluation((ValueAndJacobianFunction) model,
                                                     target,
                                                     p);
             } else {
                 // Evaluate value and jacobian in one function call.
                 final Pair<RealVector, RealMatrix> value = model.value(p);
                 return new UnweightedEvaluation(value.getFirst(),
                                                 value.getSecond(),
                                                 target,
                                                 p);
             }
         }
 
         /**
          * Container with the model evaluation at a particular point.
          */
         private static class UnweightedEvaluation extends AbstractEvaluation {
             /** Point of evaluation. */
             private final RealVector point;
             /** Derivative at point. */
             private final RealMatrix jacobian;
             /** Computed residuals. */
             private final RealVector residuals;
 
             /**
              * Create an {@link Evaluation} with no weights.
              *
              * @param values   the computed function values
              * @param jacobian the computed function Jacobian
              * @param target   the observed values
              * @param point    the abscissa
              */
             private UnweightedEvaluation(final RealVector values,
                                          final RealMatrix jacobian,
                                          final RealVector target,
                                          final RealVector point) {
                 super(target.getDimension());
                 this.jacobian = jacobian;
                 this.point = point;
                 this.residuals = target.subtract(values);
             }
 
             /** {@inheritDoc} */
             @Override
             public RealMatrix getJacobian() {
                 return jacobian;
             }
 
             /** {@inheritDoc} */
             @Override
             public RealVector getPoint() {
                 return point;
             }
 
             /** {@inheritDoc} */
             @Override
             public RealVector getResiduals() {
                 return residuals;
             }
         }
 
         /**
          * Container with the model <em>lazy</em> evaluation at a particular point.
          */
         private static class LazyUnweightedEvaluation extends AbstractEvaluation {
             /** Point of evaluation. */
             private final RealVector point;
             /** Model and Jacobian functions. */
             private final ValueAndJacobianFunction model;
             /** Target values for the model function at optimum. */
             private final RealVector target;
 
             /**
              * Create an {@link Evaluation} with no weights.
              *
              * @param model  the model function
              * @param target the observed values
              * @param point  the abscissa
              */
             private LazyUnweightedEvaluation(final ValueAndJacobianFunction model,
                                              final RealVector target,
                                              final RealVector point) {
                 super(target.getDimension());
                 // Safe to cast as long as we control usage of this class.
                 this.model = model;
                 this.point = point;
                 this.target = target;
             }
 
             /** {@inheritDoc} */
             @Override
             public RealMatrix getJacobian() {
                 return model.computeJacobian(point.toArray());
             }
 
             /** {@inheritDoc} */
             @Override
             public RealVector getPoint() {
                 return point;
             }
 
             /** {@inheritDoc} */
             @Override
             public RealVector getResiduals() {
                 return target.subtract(model.computeValue(point.toArray()));
             }
         }
     }
 }