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-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN2_LEASTSQUARES_H
-#define EIGEN2_LEASTSQUARES_H
-
-namespace Eigen { 
-
-/** \ingroup LeastSquares_Module
-  *
-  * \leastsquares_module
-  *
-  * For a set of points, this function tries to express
-  * one of the coords as a linear (affine) function of the other coords.
-  *
-  * This is best explained by an example. This function works in full
-  * generality, for points in a space of arbitrary dimension, and also over
-  * the complex numbers, but for this example we will work in dimension 3
-  * over the real numbers (doubles).
-  *
-  * So let us work with the following set of 5 points given by their
-  * \f$(x,y,z)\f$ coordinates:
-  * @code
-    Vector3d points[5];
-    points[0] = Vector3d( 3.02, 6.89, -4.32 );
-    points[1] = Vector3d( 2.01, 5.39, -3.79 );
-    points[2] = Vector3d( 2.41, 6.01, -4.01 );
-    points[3] = Vector3d( 2.09, 5.55, -3.86 );
-    points[4] = Vector3d( 2.58, 6.32, -4.10 );
-  * @endcode
-  * Suppose that we want to express the second coordinate (\f$y\f$) as a linear
-  * expression in \f$x\f$ and \f$z\f$, that is,
-  * \f[ y=ax+bz+c \f]
-  * for some constants \f$a,b,c\f$. Thus, we want to find the best possible
-  * constants \f$a,b,c\f$ so that the plane of equation \f$y=ax+bz+c\f$ fits
-  * best the five above points. To do that, call this function as follows:
-  * @code
-    Vector3d coeffs; // will store the coefficients a, b, c
-    linearRegression(
-      5,
-      &points,
-      &coeffs,
-      1 // the coord to express as a function of
-        // the other ones. 0 means x, 1 means y, 2 means z.
-    );
-  * @endcode
-  * Now the vector \a coeffs is approximately
-  * \f$( 0.495 ,  -1.927 ,  -2.906 )\f$.
-  * Thus, we get \f$a=0.495, b = -1.927, c = -2.906\f$. Let us check for
-  * instance how near points[0] is from the plane of equation \f$y=ax+bz+c\f$.
-  * Looking at the coords of points[0], we see that:
-  * \f[ax+bz+c = 0.495 * 3.02 + (-1.927) * (-4.32) + (-2.906) = 6.91.\f]
-  * On the other hand, we have \f$y=6.89\f$. We see that the values
-  * \f$6.91\f$ and \f$6.89\f$
-  * are near, so points[0] is very near the plane of equation \f$y=ax+bz+c\f$.
-  *
-  * Let's now describe precisely the parameters:
-  * @param numPoints the number of points
-  * @param points the array of pointers to the points on which to perform the linear regression
-  * @param result pointer to the vector in which to store the result.
-                  This vector must be of the same type and size as the
-                  data points. The meaning of its coords is as follows.
-                  For brevity, let \f$n=Size\f$,
-                  \f$r_i=result[i]\f$,
-                  and \f$f=funcOfOthers\f$. Denote by
-                  \f$x_0,\ldots,x_{n-1}\f$
-                  the n coordinates in the n-dimensional space.
-                  Then the resulting equation is:
-                  \f[ x_f = r_0 x_0 + \cdots + r_{f-1}x_{f-1}
-                   + r_{f+1}x_{f+1} + \cdots + r_{n-1}x_{n-1} + r_n. \f]
-  * @param funcOfOthers Determines which coord to express as a function of the
-                        others. Coords are numbered starting from 0, so that a
-                        value of 0 means \f$x\f$, 1 means \f$y\f$,
-                        2 means \f$z\f$, ...
-  *
-  * \sa fitHyperplane()
-  */
-template<typename VectorType>
-void linearRegression(int numPoints,
-                      VectorType **points,
-                      VectorType *result,
-                      int funcOfOthers )
-{
-  typedef typename VectorType::Scalar Scalar;
-  typedef Hyperplane<Scalar, VectorType::SizeAtCompileTime> HyperplaneType;
-  const int size = points[0]->size();
-  result->resize(size);
-  HyperplaneType h(size);
-  fitHyperplane(numPoints, points, &h);
-  for(int i = 0; i < funcOfOthers; i++)
-    result->coeffRef(i) = - h.coeffs()[i] / h.coeffs()[funcOfOthers];
-  for(int i = funcOfOthers; i < size; i++)
-    result->coeffRef(i) = - h.coeffs()[i+1] / h.coeffs()[funcOfOthers];
-}
-
-/** \ingroup LeastSquares_Module
-  *
-  * \leastsquares_module
-  *
-  * This function is quite similar to linearRegression(), so we refer to the
-  * documentation of this function and only list here the differences.
-  *
-  * The main difference from linearRegression() is that this function doesn't
-  * take a \a funcOfOthers argument. Instead, it finds a general equation
-  * of the form
-  * \f[ r_0 x_0 + \cdots + r_{n-1}x_{n-1} + r_n = 0, \f]
-  * where \f$n=Size\f$, \f$r_i=retCoefficients[i]\f$, and we denote by
-  * \f$x_0,\ldots,x_{n-1}\f$ the n coordinates in the n-dimensional space.
-  *
-  * Thus, the vector \a retCoefficients has size \f$n+1\f$, which is another
-  * difference from linearRegression().
-  *
-  * In practice, this function performs an hyper-plane fit in a total least square sense
-  * via the following steps:
-  *  1 - center the data to the mean
-  *  2 - compute the covariance matrix
-  *  3 - pick the eigenvector corresponding to the smallest eigenvalue of the covariance matrix
-  * The ratio of the smallest eigenvalue and the second one gives us a hint about the relevance
-  * of the solution. This value is optionally returned in \a soundness.
-  *
-  * \sa linearRegression()
-  */
-template<typename VectorType, typename HyperplaneType>
-void fitHyperplane(int numPoints,
-                   VectorType **points,
-                   HyperplaneType *result,
-                   typename NumTraits<typename VectorType::Scalar>::Real* soundness = 0)
-{
-  typedef typename VectorType::Scalar Scalar;
-  typedef Matrix<Scalar,VectorType::SizeAtCompileTime,VectorType::SizeAtCompileTime> CovMatrixType;
-  EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType)
-  ei_assert(numPoints >= 1);
-  int size = points[0]->size();
-  ei_assert(size+1 == result->coeffs().size());
-
-  // compute the mean of the data
-  VectorType mean = VectorType::Zero(size);
-  for(int i = 0; i < numPoints; ++i)
-    mean += *(points[i]);
-  mean /= numPoints;
-
-  // compute the covariance matrix
-  CovMatrixType covMat = CovMatrixType::Zero(size, size);
-  for(int i = 0; i < numPoints; ++i)
-  {
-    VectorType diff = (*(points[i]) - mean).conjugate();
-    covMat += diff * diff.adjoint();
-  }
-
-  // now we just have to pick the eigen vector with smallest eigen value
-  SelfAdjointEigenSolver<CovMatrixType> eig(covMat);
-  result->normal() = eig.eigenvectors().col(0);
-  if (soundness)
-    *soundness = eig.eigenvalues().coeff(0)/eig.eigenvalues().coeff(1);
-
-  // let's compute the constant coefficient such that the
-  // plane pass trough the mean point:
-  result->offset() = - (result->normal().cwise()* mean).sum();
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN2_LEASTSQUARES_H