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    * 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.math4.legacy.fitting.leastsquares.LeastSquaresProblem.Evaluation;
  import org.apache.commons.math4.legacy.linear.ArrayRealVector;
  import org.apache.commons.math4.legacy.linear.DecompositionSolver;
  import org.apache.commons.math4.legacy.linear.QRDecomposition;
  import org.apache.commons.math4.legacy.linear.RealMatrix;
  import org.apache.commons.math4.legacy.linear.RealVector;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  
  /**
   * An implementation of {@link Evaluation} that is designed for extension. All of the
   * methods implemented here use the methods that are left unimplemented.
   * <p>
   * TODO cache results?
   *
   * @since 3.3
   */
  public abstract class AbstractEvaluation implements Evaluation {
  
      /** number of observations. */
      private final int observationSize;
  
      /**
       * Constructor.
       *
       * @param observationSize the number of observations.
       * Needed for {@link #getRMS()} and {@link #getReducedChiSquare(int)}.
       */
      AbstractEvaluation(final int observationSize) {
          this.observationSize = observationSize;
      }
  
      /** {@inheritDoc} */
      @Override
      public RealMatrix getCovariances(double threshold) {
          // Set up the Jacobian.
          final RealMatrix j = this.getJacobian();
  
          // Compute transpose(J)J.
          final RealMatrix jTj = j.transpose().multiply(j);
  
          // Compute the covariances matrix.
          final DecompositionSolver solver
                  = new QRDecomposition(jTj, threshold).getSolver();
          return solver.getInverse();
      }
  
      /** {@inheritDoc} */
      @Override
      public RealVector getSigma(double covarianceSingularityThreshold) {
          final RealMatrix cov = this.getCovariances(covarianceSingularityThreshold);
          final int nC = cov.getColumnDimension();
          final RealVector sig = new ArrayRealVector(nC);
          for (int i = 0; i < nC; ++i) {
              sig.setEntry(i, JdkMath.sqrt(cov.getEntry(i,i)));
          }
          return sig;
      }
  
      /** {@inheritDoc} */
      @Override
      public double getRMS() {
          return JdkMath.sqrt(getReducedChiSquare(1));
      }
  
      /** {@inheritDoc} */
      @Override
      public double getCost() {
          return JdkMath.sqrt(getChiSquare());
      }
  
      /** {@inheritDoc} */
      @Override
      public double getChiSquare() {
          final ArrayRealVector r = new ArrayRealVector(getResiduals());
          return r.dotProduct(r);
      }
  
      /** {@inheritDoc} */
      @Override
      public double getReducedChiSquare(int numberOfFittedParameters) {
          return getChiSquare() / (observationSize - numberOfFittedParameters + 1);
     }
 }