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16   * \brief Class for computing matrix square roots of upper quasi-triangular matrices.
17 * \tparam MatrixType type of the argument of the matrix square root,
18 * expected to be an instantiation of the Matrix class template.
21 * matrix stored in the upper Hessenberg part of the matrix passed to
33 * \param[in] A upper quasi-triangular matrix whose square root
45 /** \brief Compute the matrix square root
96 // pre: T is quasi-upper-triangular and sqrtT is a zero matrix of the same size
150 Matrix<Scalar,2,2> block = T.template block<2,2>(i,i);
151 EigenSolver<Matrix<Scalar,2,2> > es(block);
174 Matrix<Scalar,1,2> rhs = T.template block<1,2>(i,j);
177 Matrix<Scalar,2,2> A = sqrtT.coeff(i,i) * Matrix<Scalar,2,2>::Identity();
188 Matrix<Scalar,2,1> rhs = T.template block<2,1>(i,j);
191 Matrix<Scalar,2,2> A = sqrtT.coeff(j,j) * Matrix<Scalar,2,2>::Identity();
202 Matrix<Scalar,2,2> A = sqrtT.template block<2,2>(i,i);
203 Matrix<Scalar,2,2> B = sqrtT.template block<2,2>(j,j);
204 Matrix<Scalar,2,2> C = T.template block<2,2>(i,j);
207 Matrix<Scalar,2,2> X;
219 EIGEN_STATIC_ASSERT((internal::is_same<SmallMatrixType, Matrix<Scalar,2,2> >::value),
222 Matrix<Scalar,4,4> coeffMatrix = Matrix<Scalar,4,4>::Zero();
236 Matrix<Scalar,4,1> rhs;
242 Matrix<Scalar,4,1> result;
253 * \brief Class for computing matrix square roots of upper triangular matrices.
254 * \tparam MatrixType type of the argument of the matrix square root,
255 * expected to be an instantiation of the Matrix class template.
257 * This class computes the square root of the upper triangular matrix
259 * the matrix passed to the constructor.
273 /** \brief Compute the matrix square root
309 // denominator may be zero if original matrix is singular
322 * \brief Class for computing matrix square roots of general matrices.
323 * \tparam MatrixType type of the argument of the matrix square root,
324 * expected to be an instantiation of the Matrix class template.
335 * \param[in] A matrix whose square root is to be computed.
342 /** \brief Compute the matrix square root
423 * \brief Proxy for the matrix square root of some matrix (expression).
425 * \tparam Derived Type of the argument to the matrix square root.
427 * This class holds the argument to the matrix square root until it
440 * \param[in] src %Matrix (expression) forming the argument of the
441 * matrix square root.
445 /** \brief Compute the matrix square root.
447 * \param[out] result the matrix