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20 * \brief Class for computing matrix functions.
41 /** \brief Constructor.
51 /** \brief Compute the matrix function.
65 * \brief Partial specialization of MatrixFunction for real matrices
85 /** \brief Constructor.
92 /** \brief Compute the matrix function.
112 typename internal::nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
113 AtomicType& m_atomic; /**< \brief Class for computing matrix function of atomic blocks. */
120 * \brief Partial specialization of MatrixFunction for complex matrices
161 typename internal::nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
162 AtomicType& m_atomic; /**< \brief Class for computing matrix function of atomic blocks. */
163 MatrixType m_T; /**< \brief Triangular part of Schur decomposition */
164 MatrixType m_U; /**< \brief Unitary part of Schur decomposition */
165 MatrixType m_fT; /**< \brief %Matrix function applied to #m_T */
166 ListOfClusters m_clusters; /**< \brief Partition of eigenvalues into clusters of ei'vals "close" to each other */
167 DynamicIntVectorType m_eivalToCluster; /**< \brief m_eivalToCluster[i] = j means i-th ei'val is in j-th cluster */
168 DynamicIntVectorType m_clusterSize; /**< \brief Number of eigenvalues in each clusters */
169 DynamicIntVectorType m_blockStart; /**< \brief Row index at which block corresponding to i-th cluster starts */
170 IntVectorType m_permutation; /**< \brief Permutation which groups ei'vals in the same cluster together */
172 /** \brief Maximum distance allowed between eigenvalues to be considered "close".
183 /** \brief Constructor.
195 /** \brief Compute the matrix function.
215 /** \brief Store the Schur decomposition of #m_A in #m_T and #m_U */
224 /** \brief Partition eigenvalues in clusters of ei'vals close to each other
267 /** \brief Find cluster in #m_clusters containing some value
284 /** \brief Compute #m_clusterSize and #m_eivalToCluster using #m_clusters */
306 /** \brief Compute #m_blockStart using #m_clusterSize */
317 /** \brief Compute #m_permutation using #m_eivalToCluster and #m_blockStart */
330 /** \brief Permute Schur decomposition in #m_U and #m_T according to #m_permutation */
348 /** \brief Swap rows \a index and \a index+1 in Schur decomposition in #m_U and #m_T */
359 /** \brief Compute block diagonal part of #m_fT.
375 /** \brief Return block of matrix according to blocking given by #m_blockStart */
382 /** \brief Compute part of #m_fT above block diagonal.
408 /** \brief Solve a triangular Sylvester equation AX + XB = C
477 * \brief Proxy for the matrix function of some matrix (expression).
496 /** \brief Constructor.
504 /** \brief Compute the matrix function.
