/*
    * Copyright (C) 2015 Alberto Irurueta Carro (alberto@irurueta.com)
    *
    * Licensed 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 com.irurueta.ar.calibration.estimators;
  
  import com.irurueta.algebra.AlgebraException;
  import com.irurueta.algebra.ArrayUtils;
  import com.irurueta.algebra.Matrix;
  import com.irurueta.ar.calibration.ImageOfAbsoluteConic;
  import com.irurueta.geometry.ProjectiveTransformation2D;
  import com.irurueta.geometry.Transformation2D;
  import com.irurueta.geometry.estimators.LockedException;
  import com.irurueta.geometry.estimators.NotReadyException;
  import com.irurueta.numerical.robust.RobustEstimatorException;
  import com.irurueta.numerical.robust.RobustEstimatorMethod;
  
  import java.util.List;
  
  /**
   * This is an abstract class for algorithms to robustly find the best
   * ImageOfAbsoluteConic (IAC) for provided collection of 2D homographies.
   * Implementions of this class should be able to detect and discard outliers
   * in order to find the best solution.
   */
  public abstract class ImageOfAbsoluteConicRobustEstimator {
      /**
       * Default robust estimator method when none is provided.
       * In general for IAC estimation is best to use PROSAC or RANSAC than
       * any other method, as it provides more robust results.
       */
      public static final RobustEstimatorMethod DEFAULT_ROBUST_METHOD = RobustEstimatorMethod.PROSAC;
  
      /**
       * Default amount of progress variation before notifying a change in
       * estimation progress. By default, this is set to 5%.
       */
      public static final float DEFAULT_PROGRESS_DELTA = 0.05f;
  
      /**
       * Minimum allowed value for progress delta.
       */
      public static final float MIN_PROGRESS_DELTA = 0.0f;
  
      /**
       * Maximum allowed value for progress delta.
       */
      public static final float MAX_PROGRESS_DELTA = 1.0f;
  
      /**
       * Constant defining default confidence of the estimated result, which is
       * 99%. This means that with a probability of 99% estimation will be
       * accurate because chosen sub-samples will be inliers.
       */
      public static final double DEFAULT_CONFIDENCE = 0.99;
  
      /**
       * Default maximum allowed number of iterations.
       */
      public static final int DEFAULT_MAX_ITERATIONS = 5000;
  
      /**
       * Minimum allowed confidence value.
       */
      public static final double MIN_CONFIDENCE = 0.0;
  
      /**
       * Maximum allowed confidence value.
       */
      public static final double MAX_CONFIDENCE = 1.0;
  
      /**
       * Minimum allowed number of iterations.
       */
      public static final int MIN_ITERATIONS = 1;
  
      /**
       * Homographies to estimate image of absolute conic (IAC).
       */
      protected List<Transformation2D> homographies;
  
      /**
       * Internal non-robust estimator of IAC.
       */
      protected final LMSEImageOfAbsoluteConicEstimator iacEstimator;
  
      /**
       * Listener to be notified of events such as when estimation starts, ends or
      * its progress significantly changes.
      */
     protected ImageOfAbsoluteConicRobustEstimatorListener listener;
 
     /**
      * Indicates if this estimator is locked because an estimation is being
      * computed.
      */
     protected boolean locked;
 
     /**
      * Amount of progress variation before notifying a progress change during
      * estimation.
      */
     protected float progressDelta;
 
     /**
      * Amount of confidence expressed as a value between 0.0 and 1.0 (which is
      * equivalent to 100%). The amount of confidence indicates the probability
      * that the estimated result is correct. Usually this value will be close
      * to 1.0, but not exactly 1.0.
      */
     protected double confidence;
 
     /**
      * Maximum allowed number of iterations. When the maximum number of
      * iterations is exceeded, result will not be available, however an
      * approximate result will be available for retrieval.
      */
     protected int maxIterations;
 
     // internal members to compute residuals
 
     /**
      * IAC matrix for one iteration of the robust estimator.
      * This is used during residuals estimation.
      * This instance is reused for performance reasons.
      */
     private Matrix iacMatrix;
 
     /**
      * Matrix representation of an homography.
      * This is used during residuals estimation.
      * This instance is reused for performance reasons.
      */
     private Matrix homMatrix;
 
     /**
      * Sub-matrix of homography used as the left term on a matrix multiplication.
      * This is used during residuals estimation.
      * This instance is reused for performance reasons.
      */
     private double[] subMatrixLeft;
 
     /**
      * Sub-matrix of homography used as the right term on a matrix
      * multiplication.
      * This is used during residuals estimation.
      * This instance is reused for performance reasons.
      */
     private Matrix subMatrixRight;
 
     /**
      * Product multiplication of IAC by the right term.
      * This is used during residuals estimation.
      * This instance is reused for performance reasons.
      */
     private Matrix mult1;
 
     /**
      * Constructor.
      */
     protected ImageOfAbsoluteConicRobustEstimator() {
         progressDelta = DEFAULT_PROGRESS_DELTA;
         confidence = DEFAULT_CONFIDENCE;
         maxIterations = DEFAULT_MAX_ITERATIONS;
         iacEstimator = new LMSEImageOfAbsoluteConicEstimator();
     }
 
     /**
      * Constructor.
      *
      * @param listener listener to be notified of events such as when
      *                 estimation starts, ends or its progress significantly changes.
      */
     protected ImageOfAbsoluteConicRobustEstimator(final ImageOfAbsoluteConicRobustEstimatorListener listener) {
         this();
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param homographies list of homographies (2D transformations) used to
      *                     estimate the image of absolute conic (IAC), which can be used to obtain
      *                     pinhole camera intrinsic parameters.
      * @throws IllegalArgumentException if not enough homographies are provided
      *                                  for default settings. Hence, at least 1 homography must be provided.
      */
     protected ImageOfAbsoluteConicRobustEstimator(final List<Transformation2D> homographies) {
         this();
         internalSetHomographies(homographies);
     }
 
     /**
      * Constructor.
      *
      * @param homographies list of homographies (2D transformations) used to
      *                     estimate the image of absolute conic (IAC), which can be used to obtain
      *                     pinhole camera intrinsic parameters.
      * @param listener     listener to be notified of events such as when estimation
      *                     starts, ends or estimation progress changes.
      * @throws IllegalArgumentException if not enough homographies are provided
      *                                  for default settings. Hence, at least 1 homography must be provided.
      */
     protected ImageOfAbsoluteConicRobustEstimator(
             final List<Transformation2D> homographies, final ImageOfAbsoluteConicRobustEstimatorListener listener) {
         this(listener);
         internalSetHomographies(homographies);
     }
 
     /**
      * Returns boolean indicating whether camera skewness is assumed to be zero
      * or not.
      * Skewness determines whether LCD sensor cells are properly aligned or not,
      * where zero indicates perfect alignment.
      * Typically, skewness is a value equal or very close to zero.
      *
      * @return true if camera skewness is assumed to be zero, otherwise camera
      * skewness is estimated.
      */
     public boolean isZeroSkewness() {
         return iacEstimator.isZeroSkewness();
     }
 
     /**
      * Sets boolean indicating whether camera skewness is assumed to be zero or
      * not.
      * Skewness determines whether LCD sensor cells are properly aligned or not,
      * where zero indicates perfect alignment.
      * Typically, skewness is a value equal or very close to zero.
      *
      * @param zeroSkewness true if camera skewness is assumed to be zero,
      *                     otherwise camera skewness is estimated.
      * @throws LockedException if estimator is locked.
      */
     public void setZeroSkewness(final boolean zeroSkewness) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
 
         iacEstimator.setZeroSkewness(zeroSkewness);
     }
 
     /**
      * Returns boolean indicating whether principal point is assumed to be at
      * origin of coordinates or not.
      * Typically principal point is located at image center (origin of
      * coordinates), and usually matches the center of radial distortion if
      * it is taken into account.
      *
      * @return true if principal point is assumed to be at origin of
      * coordinates, false if principal point must be estimated.
      */
     public boolean isPrincipalPointAtOrigin() {
         return iacEstimator.isPrincipalPointAtOrigin();
     }
 
     /**
      * Sets boolean indicating whether principal point is assumed to be at
      * origin of coordinates or not.
      * Typically principal point is located at image center (origin of
      * coordinates), and usually matches the center of radial distortion if it
      * is taken into account.
      *
      * @param principalPointAtOrigin true if principal point is assumed to bet
      *                               at origin of coordinates, false if principal point must be estimated
      * @throws LockedException if estimator is locked.
      */
     public void setPrincipalPointAtOrigin(final boolean principalPointAtOrigin) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
 
         iacEstimator.setPrincipalPointAtOrigin(principalPointAtOrigin);
     }
 
     /**
      * Returns boolean indicating whether aspect ratio of focal distances (i.e.
      * vertical focal distance divided by horizontal focal distance) is known or
      * not.
      * Notice that focal distance aspect ratio is not related to image size
      * aspect ratio. Typically, LCD sensor cells are square and hence aspect
      * ratio of focal distances is known and equal to 1.
      * This value is only taken into account if skewness is assumed to be zero,
      * otherwise it is ignored.
      *
      * @return true if focal distance aspect ratio is known, false otherwise.
      */
     public boolean isFocalDistanceAspectRatioKnown() {
         return iacEstimator.isFocalDistanceAspectRatioKnown();
     }
 
     /**
      * Sets boolean indicating whether aspect ratio of focal distances (i.e.
      * vertical focal distance divided by horizontal focal distance) is known or
      * not.
      * Notice that focal distance aspect ratio is not related to image size
      * aspect ratio. Typically, LCD sensor cells are square and hence aspect
      * ratio of focal distances is known and equal to 1.
      * This value is only taken into account if skewness is assumed to be zero,
      * otherwise it is ignored.
      *
      * @param focalDistanceAspectRatioKnown true if focal distance aspect ratio
      *                                      is known, false otherwise.
      * @throws LockedException if estimator is locked.
      */
     public void setFocalDistanceAspectRatioKnown(final boolean focalDistanceAspectRatioKnown) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
 
         iacEstimator.setFocalDistanceAspectRatioKnown(focalDistanceAspectRatioKnown);
     }
 
     /**
      * Returns aspect ratio of focal distances (i.e. vertical focal distance
      * divided by horizontal focal distance).
      * This value is only taken into account if skewness is assumed to be zero
      * and focal distance aspect ratio is marked as known, otherwise it is
      * ignored.
      * By default, this is 1.0, since it is taken into account that typically
      * LCD sensor cells are square and hence aspect ratio focal distances is
      * known and equal to 1.
      * Notice that focal distance aspect ratio is not related to image size
      * aspect ratio.
      * Notice that a negative aspect ratio indicates that vertical axis is
      * reversed. This can be useful in some situations where image vertical
      * coordinates are reversed respect to the physical world (i.e. in computer
      * graphics typically image vertical coordinates go downwards, while in
      * physical world they go upwards).
      *
      * @return aspect ratio of focal distances.
      */
     public double getFocalDistanceAspectRatio() {
         return iacEstimator.getFocalDistanceAspectRatio();
     }
 
     /**
      * Sets aspect ratio of focal distances (i.e. vertical focal distance
      * divided by horizontal focal distance).
      * This value is only taken into account if skewness is assumed to be zero
      * and focal distance aspect ratio is marked as known, otherwise it is
      * ignored.
      * By default, this is 1.0, since it is taken into account that typically
      * LCD sensor cells are square and hence aspect ratio focal distances is
      * known and equal to 1.
      * Notice that focal distance aspect ratio is not related to image size
      * aspect ratio.
      * Notice that a negative aspect ratio indicates that vertical axis is
      * reversed. This can be useful in some situations where image vertical
      * coordinates are reversed respect to the physical world (i.e. in computer
      * graphics typically image vertical coordinates go downwards, while in
      * physical world they go upwards).
      *
      * @param focalDistanceAspectRatio aspect ratio of focal distances to be set
      * @throws LockedException          if estimator is locked.
      * @throws IllegalArgumentException if focal distance aspect ratio is too
      *                                  close to zero, as it might produce numerical instabilities.
      */
     public void setFocalDistanceAspectRatio(final double focalDistanceAspectRatio) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
 
         iacEstimator.setFocalDistanceAspectRatio(focalDistanceAspectRatio);
     }
 
     /**
      * Returns reference to listener to be notified of events such as when
      * estimation starts, ends or its progress significantly changes.
      *
      * @return listener to be notified of events.
      */
     public ImageOfAbsoluteConicRobustEstimatorListener getListener() {
         return listener;
     }
 
     /**
      * Sets listener to be notified of events such as when estimation starts,
      * ends or its progress significantly changes.
      *
      * @param listener listener to be notified of events.
      * @throws LockedException if robust estimator is locked.
      */
     public void setListener(final ImageOfAbsoluteConicRobustEstimatorListener listener) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
         this.listener = listener;
     }
 
     /**
      * Indicates whether listener has been provided and is available for
      * retrieval.
      *
      * @return true if available, false otherwise.
      */
     public boolean isListenerAvailable() {
         return listener != null;
     }
 
     /**
      * Indicates if this instance is locked because estimation is being
      * computed.
      *
      * @return true if locked, false otherwise.
      */
     public boolean isLocked() {
         return locked;
     }
 
     /**
      * Returns amount of progress variation before notifying a progress change
      * during estimation.
      *
      * @return amount of progress variation before notifying a progress change
      * during estimation.
      */
     public float getProgressDelta() {
         return progressDelta;
     }
 
     /**
      * Sets amount of progress variation before notifying a progress change
      * during estimation.
      *
      * @param progressDelta amount of progress variation before notifying a
      *                      progress change during estimation.
      * @throws IllegalArgumentException if progress delta is less than zero or
      *                                  greater than 1.
      * @throws LockedException          if this estimator is locked because an estimation
      *                                  is being computed.
      */
     public void setProgressDelta(final float progressDelta) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
         if (progressDelta < MIN_PROGRESS_DELTA || progressDelta > MAX_PROGRESS_DELTA) {
             throw new IllegalArgumentException();
         }
         this.progressDelta = progressDelta;
     }
 
     /**
      * Returns amount of confidence expressed as a value between 0.0 and 1.0
      * (which is equivalent to 100%). The amount of confidence indicates the
      * probability that the estimated result is correct. Usually this value will
      * be close to 1.0, but not exactly 1.0.
      *
      * @return amount of confidence as a value between 0.0 and 1.0.
      */
     public double getConfidence() {
         return confidence;
     }
 
     /**
      * Sets amount of confidence expressed as a value between 0.0 and 1.0 (which
      * is equivalent to 100%). The amount of confidence indicates the
      * probability that the estimated result is correct. Usually this value will
      * be close to 1.0, but not exactly 1.0.
      *
      * @param confidence confidence to be set as a value between 0.0 and 1.0.
      * @throws IllegalArgumentException if provided value is not between 0.0 and
      *                                  1.0.
      * @throws LockedException          if this estimator is locked because an estimator
      *                                  is being computed.
      */
     public void setConfidence(final double confidence) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
         if (confidence < MIN_CONFIDENCE || confidence > MAX_CONFIDENCE) {
             throw new IllegalArgumentException();
         }
         this.confidence = confidence;
     }
 
     /**
      * Returns maximum allowed number of iterations. If maximum allowed number
      * of iterations is achieved without converging to a result when calling
      * estimate(), a RobustEstimatorException will be raised.
      *
      * @return maximum allowed number of iterations.
      */
     public int getMaxIterations() {
         return maxIterations;
     }
 
     /**
      * Sets maximum allowed number of iterations. When the maximum number of
      * iterations is exceeded, result will not be available, however an
      * approximate result will be available for retrieval.
      *
      * @param maxIterations maximum allowed number of iterations to be set.
      * @throws IllegalArgumentException if provided value is less than 1.
      * @throws LockedException          if this estimator is locked because an estimation
      *                                  is being computed.
      */
     public void setMaxIterations(final int maxIterations) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
         if (maxIterations < MIN_ITERATIONS) {
             throw new IllegalArgumentException();
         }
         this.maxIterations = maxIterations;
     }
 
     /**
      * Gets list of homographies to estimate IAC.
      *
      * @return list of homographies to estimate IAC.
      */
     public List<Transformation2D> getHomographies() {
         return homographies;
     }
 
     /**
      * Sets list of homographies to estimate IAC.
      *
      * @param homographies list of homographies to estimate IAC.
      * @throws LockedException          if estimator is locked.
      * @throws IllegalArgumentException if provided list of homographies does
      *                                  not contain enough elements to estimate the DIAC using current
      *                                  settings.
      */
     public void setHomographies(final List<Transformation2D> homographies) throws LockedException {
         if (isLocked()) {
             throw new LockedException();
         }
         internalSetHomographies(homographies);
     }
 
     /**
      * Returns minimum number of required homographies needed to estimate the
      * Imag eof Absolute Conic (IAC).
      * If no constraints are imposed, then at least 3 homographies are required.
      * For each constraint imposed, one less equation will be required, hence
      * if skewness is assumed to be known (by using its typical value of zero),
      * then only 4 equations will be needed.
      * If also the horizontal and vertical coordinates of the principal point
      * are assumed to be known (by being placed at the 2D origin of coordinates,
      * which is a typical value), then only 2 equations will be needed
      * (1 homography).
      *
      * @return minimum number of required homographies required to estimate the
      * IAC.
      */
     public int getMinNumberOfRequiredHomographies() {
         return iacEstimator.getMinNumberOfRequiredHomographies();
     }
 
     /**
      * Returns value indicating whether required data has been provided so that
      * IAC estimation can start.
      * If true, estimator is ready to compute the IAC, otherwise more data needs
      * to be provided.
      *
      * @return true if estimator is ready, false otherwise.
      */
     public boolean isReady() {
         return homographies != null && homographies.size() >= getMinNumberOfRequiredHomographies();
     }
 
     /**
      * Returns quality scores corresponding to each homography.
      * The larger the score value the better the quality of the homography.
      * This implementation always returns null.
      * Subclasses using quality scores must implement proper behaviour.
      *
      * @return quality scores corresponding to each homography.
      */
     public double[] getQualityScores() {
         return null;
     }
 
     /**
      * Sets quality scores corresponding to each homography.
      * The larger the score value the better the quality of the homography.
      * This implementation makes no action.
      * Subclasses using quality scores must implement proper behaviour.
      *
      * @param qualityScores quality scores corresponding to each homography.
      * @throws LockedException          if robust estimator is locked because an
      *                                  estimation is already in progress.
      * @throws IllegalArgumentException if provided quality scores length is
      *                                  smaller than minimum required number of homographies.
      */
     public void setQualityScores(final double[] qualityScores) throws LockedException {
     }
 
     /**
      * Estimates Image of Absolute Conic (IAC).
      *
      * @return estimated IAC.
      * @throws LockedException          if robust estimator is locked because an
      *                                  estimation is already in progress.
      * @throws NotReadyException        if provided input data is not enough to start
      *                                  the estimation.
      * @throws RobustEstimatorException if estimation fails for any reason
      *                                  (i.e. numerical instability, no solution available, etc).
      */
     public abstract ImageOfAbsoluteConic estimate() throws LockedException, NotReadyException,
             RobustEstimatorException;
 
     /**
      * Returns method being used for robust estimation.
      *
      * @return method being used for robust estimation.
      */
     public abstract RobustEstimatorMethod getMethod();
 
     /**
      * Creates an image of absolute conic robust estimator using provided
      * method.
      *
      * @param method method of a robust estimator algorithm to estimate best
      *               IAC.
      * @return an instance of an image of absolute conic robust estimator.
      */
     public static ImageOfAbsoluteConicRobustEstimator create(final RobustEstimatorMethod method) {
         return switch (method) {
             case LMEDS -> new LMedSImageOfAbsoluteConicRobustEstimator();
             case MSAC -> new MSACImageOfAbsoluteConicRobustEstimator();
             case PROSAC -> new PROSACImageOfAbsoluteConicRobustEstimator();
             case PROMEDS -> new PROMedSImageOfAbsoluteConicRobustEstimator();
             default -> new RANSACImageOfAbsoluteConicRobustEstimator();
         };
     }
 
     /**
      * Creates an image of absolute conic robust estimator using provided
      * homographies.
      *
      * @param homographies  list of homographies.
      * @param qualityScores quality scores corresponding to each homography.
      * @param method        method of a robust estimator algorithm to estimate
      *                      best IAC.
      * @return an instance of an image of absolute conic robust estimator.
      * @throws IllegalArgumentException if provided list of homographies and
      *                                  quality scores don't have the same size or size is too short.
      */
     public static ImageOfAbsoluteConicRobustEstimator create(
             final List<Transformation2D> homographies, final double[] qualityScores,
             final RobustEstimatorMethod method) {
         return switch (method) {
             case LMEDS -> new LMedSImageOfAbsoluteConicRobustEstimator(homographies);
             case MSAC -> new MSACImageOfAbsoluteConicRobustEstimator(homographies);
             case PROSAC -> new PROSACImageOfAbsoluteConicRobustEstimator(homographies, qualityScores);
             case PROMEDS -> new PROMedSImageOfAbsoluteConicRobustEstimator(homographies, qualityScores);
             default -> new RANSACImageOfAbsoluteConicRobustEstimator(homographies);
         };
     }
 
     /**
      * Creates an image of absolute conic robust estimator using provided
      * homographies.
      *
      * @param homographies list of homographies.
      * @param method       method of a robust estimator algorithm to estimate
      *                     best IAC.
      * @return an instance of an image of absolute conic robust estimator.
      * @throws IllegalArgumentException if provided list of homographies is too
      *                                  short.
      */
     public static ImageOfAbsoluteConicRobustEstimator create(
             final List<Transformation2D> homographies, final RobustEstimatorMethod method) {
         return switch (method) {
             case LMEDS -> new LMedSImageOfAbsoluteConicRobustEstimator(homographies);
             case MSAC -> new MSACImageOfAbsoluteConicRobustEstimator(homographies);
             case PROSAC -> new PROSACImageOfAbsoluteConicRobustEstimator(homographies);
             case PROMEDS -> new PROMedSImageOfAbsoluteConicRobustEstimator(homographies);
             default -> new RANSACImageOfAbsoluteConicRobustEstimator(homographies);
         };
     }
 
     /**
      * Creates an image of absolute conic robust estimator using default
      * method.
      *
      * @return an instance of an image of absolute conic robust estimator.
      */
     public static ImageOfAbsoluteConicRobustEstimator create() {
         return create(DEFAULT_ROBUST_METHOD);
     }
 
     /**
      * Creates an image of absolute conic robust estimator using provided
      * homographies.
      *
      * @param homographies  list of homographies.
      * @param qualityScores quality scores corresponding to each point.
      * @return an instance of an image of absolute conic robust estimator.
      * @throws IllegalArgumentException if provided list of homographies and
      *                                  quality scores don't have the same size or size is too short.
      */
     public static ImageOfAbsoluteConicRobustEstimator create(
             final List<Transformation2D> homographies, final double[] qualityScores) {
         return create(homographies, qualityScores, DEFAULT_ROBUST_METHOD);
     }
 
     /**
      * Creates an image of absolute conic robust estimator using provided
      * homographies.
      *
      * @param homographies list of homographies.
      * @return an instance of an image of absolute conic robust estimator.
      * @throws IllegalArgumentException if provided list of homographies and
      *                                  is too short.
      */
     public static ImageOfAbsoluteConicRobustEstimator create(final List<Transformation2D> homographies) {
         return create(homographies, DEFAULT_ROBUST_METHOD);
     }
 
     /**
      * Computes the residual between an image of absolute conic (IAC) and
      * a 2D transformation (homography).
      * Residual is derived from the fact that rotation matrices are
      * orthonormal (i.e. h1'*IAC*h2 = 0 and
      * h1'*IAC*h1 = h2'*IAC*h2 --&lt; h1'*IAC*h1 - h2'*IAC*h2 = 0).
      * The residual will be the average error of those two equations.
      *
      * @param iac        the matrix of an image of absolute conic (IAC)
      * @param homography 2D transformation (homography)
      * @return residual.
      */
     protected double residual(final ImageOfAbsoluteConic iac, final Transformation2D homography) {
 
         iac.normalize();
         if (homography instanceof ProjectiveTransformation2D projectiveTransformation2D) {
             projectiveTransformation2D.normalize();
         }
 
         try {
             if (iacMatrix == null) {
                 iacMatrix = iac.asMatrix();
             } else {
                 iac.asMatrix(iacMatrix);
             }
 
             if (homMatrix == null) {
                 homMatrix = homography.asMatrix();
             } else {
                 homography.asMatrix(homMatrix);
             }
 
             if (subMatrixLeft == null) {
                 subMatrixLeft = new double[ProjectiveTransformation2D.HOM_COORDS];
             }
             if (subMatrixRight == null) {
                 subMatrixRight = new Matrix(ProjectiveTransformation2D.HOM_COORDS, 1);
             }
             if (mult1 == null) {
                 mult1 = new Matrix(ProjectiveTransformation2D.HOM_COORDS, 1);
             }
 
             // 1st equation h1'*IAC*h2 = 0
 
             // 1st column of homography
             homMatrix.getSubmatrixAsArray(0, 0,
                     ProjectiveTransformation2D.HOM_COORDS - 1, 0, subMatrixLeft);
             // 2nd column of homography
             homMatrix.getSubmatrix(0, 1,
                     ProjectiveTransformation2D.HOM_COORDS - 1, 1, subMatrixRight);
 
             // IAC * h2
             iacMatrix.multiply(subMatrixRight, mult1);
 
             // h1' * (IAC * h2)
             final var error1 = Math.abs(ArrayUtils.dotProduct(subMatrixLeft, mult1.getBuffer()));
 
             // 2nd equation h1'*IAC*h1 - h2'*IAC*h2 = 0
 
             // 1st column of homography
             homMatrix.getSubmatrixAsArray(0, 0,
                     ProjectiveTransformation2D.HOM_COORDS - 1, 0, subMatrixLeft);
             homMatrix.getSubmatrix(0, 0,
                     ProjectiveTransformation2D.HOM_COORDS - 1, 0, subMatrixRight);
 
             // IAC * h1
             iacMatrix.multiply(subMatrixRight, mult1);
 
             // h1' * (IAC * h1)
             final var error2a = ArrayUtils.dotProduct(subMatrixLeft, mult1.getBuffer());
 
             // 2nd column of homography
             homMatrix.getSubmatrixAsArray(0, 1,
                     ProjectiveTransformation2D.HOM_COORDS - 1, 1, subMatrixLeft);
             homMatrix.getSubmatrix(0, 1,
                     ProjectiveTransformation2D.HOM_COORDS - 1, 1, subMatrixRight);
 
             // IAC * h2
             iacMatrix.multiply(subMatrixRight, mult1);
 
             // h2' * (IAC * h1)
             final var error2b = ArrayUtils.dotProduct(subMatrixLeft, mult1.getBuffer());
 
             final var error2 = Math.abs(error2a - error2b);
 
             return 0.5 * (error1 + error2);
         } catch (final AlgebraException e) {
             return Double.MAX_VALUE;
         }
     }
 
     /**
      * Sets list of homographies.
      * This method does not check whether estimator is locked.
      *
      * @param homographies list of homographies to estimate IAC.
      * @throws IllegalArgumentException if provided list of homographies is null
      *                                  or too small.
      */
     private void internalSetHomographies(final List<Transformation2D> homographies) {
         if (homographies == null || homographies.size() < getMinNumberOfRequiredHomographies()) {
             throw new IllegalArgumentException();
         }
 
         this.homographies = homographies;
     }
 }