Lines Matching full:matrix
36 * \brief Tridiagonal decomposition of a selfadjoint matrix
38 * \tparam _MatrixType the type of the matrix of which we are computing the
40 * Matrix class template.
42 * This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that:
43 …* \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real symmetric tridiagonal matrix.
45 * A tridiagonal matrix is a matrix which has nonzero elements only on the
47 * decomposition of a selfadjoint matrix is in fact a tridiagonal
49 * eigenvalues and eigenvectors of a selfadjoint matrix.
52 * given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&)
82 … typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
84 …typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> SubDiagonalTy…
103 * \param [in] size Positive integer, size of the matrix whose tridiagonal
119 /** \brief Constructor; computes tridiagonal decomposition of given matrix.
121 * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
130 explicit Tridiagonalization(const EigenBase<InputType>& matrix)
131 : m_matrix(matrix.derived()),
132 m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),
139 /** \brief Computes tridiagonal decomposition of given matrix.
141 * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
146 * the matrix successively in the required form using Householder
148 * the size of the given matrix.
151 * object, if the size of the matrix does not change.
157 Tridiagonalization& compute(const EigenBase<InputType>& matrix)
159 m_matrix = matrix.derived();
160 m_hCoeffs.resize(matrix.rows()-1, 1);
172 * to compute the tridiagonal decomposition of a matrix.
174 * The Householder coefficients allow the reconstruction of the matrix
190 * \returns a const reference to a matrix with the internal representation
195 * to compute the tridiagonal decomposition of a matrix.
197 * The returned matrix contains the following information:
198 * - the strict upper triangular part is equal to the input matrix A.
200 * symmetric matrix T.
203 * householderCoefficients(), allows to reconstruct the matrix Q as
210 * with M the matrix returned by this function.
225 /** \brief Returns the unitary matrix Q in the decomposition
227 * \returns object representing the matrix Q
231 * to compute the tridiagonal decomposition of a matrix.
234 * HouseholderSequence. You can either apply it directly to a matrix or
235 * you can convert it to a matrix of type #MatrixType.
248 /** \brief Returns an expression of the tridiagonal matrix T in the decomposition
250 * \returns expression object representing the matrix T
254 * to compute the tridiagonal decomposition of a matrix.
256 * Currently, this function can be used to extract the matrix T from internal
257 * data and copy it to a dense matrix object. In most cases, it may be
258 * sufficient to directly use the packed matrix or the vector expressions
260 * dense copy matrix with this function.
271 /** \brief Returns the diagonal of the tridiagonal matrix T in the decomposition.
277 * to compute the tridiagonal decomposition of a matrix.
286 /** \brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
292 * to compute the tridiagonal decomposition of a matrix.
324 * Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place.
326 …* \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is refere…
331 * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal
332 * and lower sub-diagonal of the matrix \a matA.
333 * The unitary matrix Q is represented in a compact way as a product of
342 * Implemented from Golub's "Matrix Computations", algorithm 8.3.1.
388 * \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal
390 * The rest is left unchanged. On output, the orthogonal matrix Q
392 * \param[out] diag The diagonal of the tridiagonal matrix T in the
394 * \param[out] subdiag The subdiagonal of the tridiagonal matrix T in
396 * \param[in] extractQ If true, the orthogonal matrix Q in the
399 * Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place
401 * symmetric tridiagonal matrix.
403 * The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If
404 * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower
405 * part of the matrix \p mat is destroyed.
416 * Householder coefficients, and to reconstruct the matrix Q from the Householder
419 * Example (this uses the same matrix as the example in
524 * \tparam MatrixType type of underlying dense matrix
532 * \param[in] mat The underlying dense matrix