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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_QR_H
+#define EIGEN_QR_H
+
+/** \class QR
+  *
+  * \brief QR decomposition of a matrix
+  *
+  * \param MatrixType the type of the matrix of which we are computing the QR decomposition
+  *
+  * This class performs a QR decomposition using Householder transformations. The result is
+  * stored in a compact way.
+  *
+  * \todo add convenient method to direclty use the result in a compact way. First need to determine
+  * typical use cases though.
+  *
+  * \todo what about complex matrices ?
+  *
+  * \sa MatrixBase::qr()
+  */
+template<typename MatrixType> class QR
+{
+  public:
+
+    typedef typename MatrixType::Scalar Scalar;
+    typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> RMatrixType;
+    typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+    QR(const MatrixType& matrix)
+      : m_qr(matrix.rows(), matrix.cols()),
+        m_norms(matrix.cols())
+    {
+      _compute(matrix);
+    }
+
+    /** \returns whether or not the matrix is of full rank */
+    bool isFullRank() const { return ei_isMuchSmallerThan(m_norms.cwiseAbs().minCoeff(), Scalar(1)); }
+
+    RMatrixType matrixR(void) const;
+
+    MatrixType matrixQ(void) const;
+
+  private:
+
+    void _compute(const MatrixType& matrix);
+
+  protected:
+    MatrixType m_qr;
+    VectorType m_norms;
+};
+
+template<typename MatrixType>
+void QR<MatrixType>::_compute(const MatrixType& matrix)
+{
+  m_qr = matrix;
+  int rows = matrix.rows();
+  int cols = matrix.cols();
+
+  for (int k = 0; k < cols; k++)
+  {
+    int remainingSize = rows-k;
+
+    Scalar nrm = m_qr.col(k).end(remainingSize).norm();
+
+    if (nrm != Scalar(0))
+    {
+      // form k-th Householder vector
+      if (m_qr(k,k) < 0)
+        nrm = -nrm;
+
+      m_qr.col(k).end(rows-k) /= nrm;
+      m_qr(k,k) += 1.0;
+
+      // apply transformation to remaining columns
+      for (int j = k+1; j < cols; j++)
+      {
+        Scalar s = -(m_qr.col(k).end(remainingSize).transpose() * m_qr.col(j).end(remainingSize))(0,0) / m_qr(k,k);
+        m_qr.col(j).end(remainingSize) += s * m_qr.col(k).end(remainingSize);
+      }
+    }
+    m_norms[k] = -nrm;
+  }
+}
+
+/** \returns the matrix R */
+template<typename MatrixType>
+typename QR<MatrixType>::RMatrixType QR<MatrixType>::matrixR(void) const
+{
+  int cols = m_qr.cols();
+  RMatrixType res = m_qr.block(0,0,cols,cols).upperWithNullDiag();
+  res.diagonal() = m_norms;
+  return res;
+}
+
+/** \returns the matrix Q */
+template<typename MatrixType>
+MatrixType QR<MatrixType>::matrixQ(void) const
+{
+  int rows = m_qr.rows();
+  int cols = m_qr.cols();
+  MatrixType res = MatrixType::identity(rows, cols);
+  for (int k = cols-1; k >= 0; k--)
+  {
+    for (int j = k; j < cols; j++)
+    {
+      if (res(k,k) != Scalar(0))
+      {
+        int endLength = rows-k;
+        Scalar s = -(m_qr.col(k).end(endLength).transpose() * res.col(j).end(endLength))(0,0) / m_qr(k,k);
+
+        res.col(j).end(endLength) += s * m_qr.col(k).end(endLength);
+      }
+    }
+  }
+  return res;
+}
+
+/** \return the QR decomposition of \c *this.
+  *
+  * \sa class QR
+  */
+template<typename Derived>
+const QR<typename ei_eval<Derived>::type>
+MatrixBase<Derived>::qr() const
+{
+  return QR<typename ei_eval<Derived>::type>(derived());
+}
+
+
+#endif // EIGEN_QR_H