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32   * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
36 * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
44 * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
134 * \returns the exact or least-square solution if the rank is greater or equal to the number of columns of A,
212 /** \returns the rank of the matrix of which *this is the QR decomposition.
218 inline Index rank() const
238 return cols() - rank();
251 return rank() == cols();
264 return rank() == rows();
301 /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
339 /** Returns the threshold that will be used by certain methods such as rank().
357 * \sa rank()
443 // if the corner is negligible, then we have less than full rank, and we can finish early
503 if(dec().rank()==0)
512 for (Index k = 0; k < dec().rank(); ++k)
522 .topLeftCorner(dec().rank(), dec().rank())
524 .solveInPlace(c.topRows(dec().rank()));
526 for(Index i = 0; i < dec().rank(); ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);
527 for(Index i = dec().rank(); i < cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();