Lines Matching full:matrix

32   * \brief Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation
34 …* \tparam _MatrixType the type of the matrix of which we are computing the Hessenberg decomposition
36   * This class performs an Hessenberg decomposition of a matrix \f$ A \f$. In
38   * matrix \f$ Q \f$ and a Hessenberg matrix \f$ H \f$ such that \f$ A = Q H
39   * Q^T \f$. An orthogonal matrix is a matrix whose inverse equals its
40   * transpose (\f$ Q^{-1} = Q^T \f$). A Hessenberg matrix has zeros below the
42   * of a complex matrix is \f$ A = Q H Q^* \f$ with \f$ Q \f$ unitary (that is,
46   * given matrix. Alternatively, you can use the
82 …  typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
91       * \param [in] size  The size of the matrix whose Hessenberg decomposition will be computed.
109     /** \brief Constructor; computes Hessenberg decomposition of given matrix.
111       * \param[in]  matrix  Square matrix whose Hessenberg decomposition is to be computed.
119     explicit HessenbergDecomposition(const EigenBase<InputType>& matrix)
120       : m_matrix(matrix.derived()),
121         m_temp(matrix.rows()),
124       if(matrix.rows()<2)
129       m_hCoeffs.resize(matrix.rows()-1,1);
134     /** \brief Computes Hessenberg decomposition of given matrix.
136       * \param[in]  matrix  Square matrix whose Hessenberg decomposition is to be computed.
140       * matrix successively in the required form using Householder reflections
141       * (see, e.g., Algorithm 7.4.2 in Golub \& Van Loan, <i>%Matrix
143       * denotes the size of the given matrix.
152     HessenbergDecomposition& compute(const EigenBase<InputType>& matrix)
154       m_matrix = matrix.derived();
155       if(matrix.rows()<2)
160       m_hCoeffs.resize(matrix.rows()-1,1);
172       * before to compute the Hessenberg decomposition of a matrix.
174       * The Householder coefficients allow the reconstruction of the matrix
187       *	\returns a const reference to a matrix with the internal representation
192       * before to compute the Hessenberg decomposition of a matrix.
194       * The returned matrix contains the following information:
195       *  - the upper part and lower sub-diagonal represent the Hessenberg matrix H
198       *    allows to reconstruct the matrix Q as
205       *    with M the matrix returned by this function.
220     /** \brief Reconstructs the orthogonal matrix Q in the decomposition
222       * \returns object representing the matrix Q
226       * before to compute the Hessenberg decomposition of a matrix.
229       * HouseholderSequence. You can either apply it directly to a matrix or
230       * you can convert it to a matrix of type #MatrixType.
242     /** \brief Constructs the Hessenberg matrix H in the decomposition
244       * \returns expression object representing the matrix H
248       * before to compute the Hessenberg decomposition of a matrix.
250       * The object returned by this function constructs the Hessenberg matrix H
251       * when it is assigned to a matrix or otherwise evaluated. The matrix H is
252       * constructed from the packed matrix as returned by packedMatrix(): The
253       * upper part (including the subdiagonal) of the packed matrix contains
254       * the matrix H. It may sometimes be better to directly use the packed
255       * matrix instead of constructing the matrix H.
270     typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> VectorType;
284   * \param matA the input selfadjoint matrix
289   * Implemented from Golub's "%Matrix Computations", algorithm 8.3.1.
329   * \tparam MatrixType type of matrix in the Hessenberg decomposition
331   * Objects of this type represent the Hessenberg matrix in the Hessenberg
332   * decomposition of some matrix. The object holds a reference to the
349     /** \brief Hessenberg matrix in decomposition.
351       * \param[out] result  Hessenberg matrix in decomposition \p hess which