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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * 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;
  
  import java.util.Arrays;
  import java.util.Collection;
  
  import org.apache.commons.math4.legacy.analysis.MultivariateMatrixFunction;
  import org.apache.commons.math4.legacy.analysis.MultivariateVectorFunction;
  import org.apache.commons.math4.legacy.analysis.ParametricUnivariateFunction;
  import org.apache.commons.math4.legacy.fitting.leastsquares.LeastSquaresOptimizer;
  import org.apache.commons.math4.legacy.fitting.leastsquares.LeastSquaresProblem;
  import org.apache.commons.math4.legacy.fitting.leastsquares.LevenbergMarquardtOptimizer;
  
  /**
   * Base class that contains common code for fitting parametric univariate
   * real functions <code>y = f(p<sub>i</sub>;x)</code>, where {@code x} is
   * the independent variable and the <code>p<sub>i</sub></code> are the
   * <em>parameters</em>.
   * <br>
   * A fitter will find the optimal values of the parameters by
   * <em>fitting</em> the curve so it remains very close to a set of
   * {@code N} observed points <code>(x<sub>k</sub>, y<sub>k</sub>)</code>,
   * {@code 0 <= k < N}.
   * <br>
   * An algorithm usually performs the fit by finding the parameter
   * values that minimizes the objective function
   * <pre><code>
   *  &sum;y<sub>k</sub> - f(x<sub>k</sub>)<sup>2</sup>,
   * </code></pre>
   * which is actually a least-squares problem.
   * This class contains boilerplate code for calling the
   * {@link #fit(Collection)} method for obtaining the parameters.
   * The problem setup, such as the choice of optimization algorithm
   * for fitting a specific function is delegated to subclasses.
   *
   * @since 3.3
   */
  public abstract class AbstractCurveFitter {
      /**
       * Fits a curve.
       * This method computes the coefficients of the curve that best
       * fit the sample of observed points.
       *
       * @param points Observations.
       * @return the fitted parameters.
       */
      public double[] fit(Collection<WeightedObservedPoint> points) {
          // Perform the fit.
          return getOptimizer().optimize(getProblem(points)).getPoint().toArray();
      }
  
      /**
       * Creates an optimizer set up to fit the appropriate curve.
       * <p>
       * The default implementation uses a {@link LevenbergMarquardtOptimizer
       * Levenberg-Marquardt} optimizer.
       * </p>
       * @return the optimizer to use for fitting the curve to the
       * given {@code points}.
       */
      protected LeastSquaresOptimizer getOptimizer() {
          return new LevenbergMarquardtOptimizer();
      }
  
      /**
       * Creates a least squares problem corresponding to the appropriate curve.
       *
       * @param points Sample points.
       * @return the least squares problem to use for fitting the curve to the
       * given {@code points}.
       */
      protected abstract LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points);
  
      /**
       * Vector function for computing function theoretical values.
       */
      protected static class TheoreticalValuesFunction {
          /** Function to fit. */
          private final ParametricUnivariateFunction f;
          /** Observations. */
          private final double[] points;
  
          /**
           * @param f function to fit.
          * @param observations Observations.
          */
         public TheoreticalValuesFunction(final ParametricUnivariateFunction f,
                                          final Collection<WeightedObservedPoint> observations) {
             this.f = f;
             this.points = observations.stream().mapToDouble(WeightedObservedPoint::getX).toArray();
         }
 
         /**
          * @return the model function values.
          */
         public MultivariateVectorFunction getModelFunction() {
             return new MultivariateVectorFunction() {
                 /** {@inheritDoc} */
                 @Override
                 public double[] value(double[] p) {
                     return Arrays.stream(points).map(point -> f.value(point, p)).toArray();
                 }
             };
         }
 
         /**
          * @return the model function Jacobian.
          */
         public MultivariateMatrixFunction getModelFunctionJacobian() {
             return new MultivariateMatrixFunction() {
                 /** {@inheritDoc} */
                 @Override
                 public double[][] value(double[] p) {
                     final int len = points.length;
                     final double[][] jacobian = new double[len][];
                     for (int i = 0; i < len; i++) {
                         jacobian[i] = f.gradient(points[i], p);
                     }
                     return jacobian;
                 }
             };
         }
     }
 }