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Reference documentation for deal.II version 9.6.0
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Classes | |
struct | Inverse |
struct | Inverse< 4, 3, adouble > |
struct | SortEigenValuesVectors |
Functions | |
template<int dim, typename Number > | |
void | tridiagonalize (const ::SymmetricTensor< 2, dim, Number > &A, ::Tensor< 2, dim, Number > &Q, std::array< Number, dim > &d, std::array< Number, dim - 1 > &e) |
template<int dim, typename Number > | |
std::array< std::pair< Number, Tensor< 1, dim, Number > >, dim > | ql_implicit_shifts (const ::SymmetricTensor< 2, dim, Number > &A) |
template<int dim, typename Number > | |
std::array< std::pair< Number, Tensor< 1, dim, Number > >, dim > | jacobi (::SymmetricTensor< 2, dim, Number > A) |
template<typename Number > | |
std::array< std::pair< Number, Tensor< 1, 2, Number > >, 2 > | hybrid (const ::SymmetricTensor< 2, 2, Number > &A) |
template<typename Number > | |
std::array< std::pair< Number, Tensor< 1, 3, Number > >, 3 > | hybrid (const ::SymmetricTensor< 2, 3, Number > &A) |
A namespace for functions and classes that are internal to how the SymmetricTensor class (and its associate functions) works.
void internal::SymmetricTensorImplementation::tridiagonalize | ( | const ::SymmetricTensor< 2, dim, Number > & | A, |
::Tensor< 2, dim, Number > & | Q, | ||
std::array< Number, dim > & | d, | ||
std::array< Number, dim - 1 > & | e ) |
Tridiagonalize a rank-2 symmetric tensor using the Householder method. The specialized algorithm implemented here is given in [131] and is based off of the generic algorithm presented in section 11.3.2 of [178].
[in] | A | This tensor to be tridiagonalized |
[out] | Q | The orthogonal matrix effecting the transformation |
[out] | d | The diagonal elements of the tridiagonal matrix |
[out] | e | The off-diagonal elements of the tridiagonal matrix |
std::array< std::pair< Number, Tensor< 1, dim, Number > >, dim > internal::SymmetricTensorImplementation::ql_implicit_shifts | ( | const ::SymmetricTensor< 2, dim, Number > & | A | ) |
Compute the eigenvalues and eigenvectors of a real-valued rank-2 symmetric tensor using the QL algorithm with implicit shifts. The specialized algorithm implemented here is given in [131] and is based off of the generic algorithm presented in section 11.4.3 of [178].
[in] | A | The tensor of which the eigenvectors and eigenvalues are to be computed. |
std::array< std::pair< Number, Tensor< 1, dim, Number > >, dim > internal::SymmetricTensorImplementation::jacobi | ( | ::SymmetricTensor< 2, dim, Number > | A | ) |
Compute the eigenvalues and eigenvectors of a real-valued rank-2 symmetric tensor using the Jacobi algorithm. The specialized algorithm implemented here is given in [131] and is based off of the generic algorithm presented in section 11.4.3 of [178].
[in] | A | The tensor of which the eigenvectors and eigenvalues are to be computed. |
std::array< std::pair< Number, Tensor< 1, 2, Number > >, 2 > internal::SymmetricTensorImplementation::hybrid | ( | const ::SymmetricTensor< 2, 2, Number > & | A | ) |
Compute the eigenvalues and eigenvectors of a real-valued rank-2 symmetric 2x2 tensor using the characteristic equation to compute eigenvalues and an analytical approach based on the cross-product for the eigenvectors. If the computations are deemed too inaccurate then the method falls back to ql_implicit_shifts.
[in] | A | The tensor of which the eigenvectors and eigenvalues are to be computed. |
std::array< std::pair< Number, Tensor< 1, 3, Number > >, 3 > internal::SymmetricTensorImplementation::hybrid | ( | const ::SymmetricTensor< 2, 3, Number > & | A | ) |
Compute the eigenvalues and eigenvectors of a real-valued rank-2 symmetric 3x3 tensor using the characteristic equation to compute eigenvalues and an analytical approach based on the cross-product for the eigenvectors. If the computations are deemed too inaccurate then the method falls back to ql_implicit_shifts. The specialized algorithm implemented here is given in [131].
[in] | A | The tensor of which the eigenvectors and eigenvalues are to be computed. |