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Ginkgo
Generated from pipelines/2837190956 branch based on develop. Ginkgo version 2.0.0
A numerical linear algebra library targeting many-core architectures
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Ginkgo
Generated from pipelines/2837190956 branch based on develop. Ginkgo version 2.0.0
A numerical linear algebra library targeting many-core architectures
|
ParILU is an incomplete LU factorization which is computed in parallel. More...
#include <ginkgo/core/factorization/par_ilu.hpp>
Classes | |
| class | Factory |
| struct | parameters_type |
Public Types | |
| using | value_type = ValueType |
| using | index_type = IndexType |
| using | matrix_type = matrix::Csr< ValueType, IndexType > |
| using | l_matrix_type = matrix_type |
| using | u_matrix_type = matrix_type |
 Public Types inherited from gko::Composition< ValueType > | |
| using | value_type = ValueType |
| using | transposed_type = Composition< ValueType > |
Public Member Functions | |
| std::shared_ptr< const matrix_type > | get_l_factor () const |
| std::shared_ptr< const matrix_type > | get_u_factor () const |
| const parameters_type & | get_parameters () const |
| Public Member Functions inherited from gko::Composition< ValueType > | |
| const std::vector< std::shared_ptr< const LinOp > > & | get_operators () const noexcept |
| Returns a list of operators of the composition. More... | |
| std::unique_ptr< LinOp > | transpose () const override |
| Returns a LinOp representing the transpose of the Transposable object. More... | |
| std::unique_ptr< LinOp > | conj_transpose () const override |
| Returns a LinOp representing the conjugate transpose of the Transposable object. More... | |
| Composition & | operator= (const Composition &) |
| Copy-assigns a Composition. More... | |
| Composition & | operator= (Composition &&) |
| Move-assigns a Composition. More... | |
| Composition (const Composition &) | |
| Copy-constructs a Composition. More... | |
| Composition (Composition &&) | |
| Move-constructs a Composition. More... | |
| Public Member Functions inherited from gko::LinOp | |
| void | apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const |
| Applies a linear operator to a vector (or a sequence of vectors). More... | |
| void | apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const |
| Performs the operation x = alpha * op(b) + beta * x. More... | |
| const dim< 2 > & | get_size () const noexcept |
| Returns the size of the operator. More... | |
| virtual bool | apply_uses_initial_guess () const |
| Returns true if the linear operator uses the data given in x as an initial guess. More... | |
| LinOp & | operator= (const LinOp &)=default |
| Copy-assigns a LinOp. More... | |
| LinOp & | operator= (LinOp &&other) |
| Move-assigns a LinOp. More... | |
| LinOp (const LinOp &)=default | |
| Copy-constructs a LinOp. More... | |
| LinOp (LinOp &&other) | |
| Move-constructs a LinOp. More... | |
| Public Member Functions inherited from gko::PolymorphicObject | |
| virtual void | validate_data () const |
| Throws gko::InvalidData exception if we found the data inside the object does not fulfill certain property up to our knowledge. | |
| PolymorphicObject & | operator= (const PolymorphicObject &) |
| std::shared_ptr< const Executor > | get_executor () const noexcept |
| Returns the Executor of the object. More... | |
| Public Member Functions inherited from gko::log::EnableLogging< PolymorphicObject > | |
| void | add_logger (std::shared_ptr< const Logger > logger) override |
| void | remove_logger (const Logger *logger) override |
| void | remove_logger (ptr_param< const Logger > logger) |
| const std::vector< std::shared_ptr< const Logger > > & | get_loggers () const override |
| void | clear_loggers () override |
| Public Member Functions inherited from gko::log::Loggable | |
| void | remove_logger (ptr_param< const Logger > logger) |
Static Public Member Functions | |
| template<typename... Args> | |
| static std::unique_ptr< Composition< ValueType > > | create (Args &&... args)=delete |
| static auto | build () -> decltype(Factory ::create()) |
| static parameters_type | parse (const config::pnode &config, const config::registry &context, const config::type_descriptor &td_for_child=config::make_type_descriptor< ValueType, IndexType >()) |
| Create the parameters from the property_tree. More... | |
| Static Public Member Functions inherited from gko::EnableCreateMethod< Composition< ValueType > > | |
| static std::unique_ptr< Composition< ValueType > > | create (Args &&... args) |
ParILU is an incomplete LU factorization which is computed in parallel.
\(L\) is a lower unitriangular, while \(U\) is an upper triangular matrix, which approximate a given matrix \(A\) with \(A \approx LU\). Here, \(L\) and \(U\) have the same sparsity pattern as \(A\), which is also called ILU(0).
The ParILU algorithm generates the incomplete factors iteratively, using a fixed-point iteration of the form
\[ F(L, U)_{ij} = \begin{cases} \frac{1}{u_{jj}} \left( a_{ij} - \sum_{k=1}^{j-1} l_{ik} u_{kj} \right), & i > j, \\ a_{ij} - \sum_{k=1}^{i-1} l_{ik} u_{kj}, & i \leq j. \end{cases} \]
In general, the entries of \(L\) and \(U\) can be iterated in parallel and in asynchronous fashion; the algorithm asymptotically converges to incomplete factors \(L\) and \(U\) fulfilling \( (R = A - L U)\vert_\mathcal{S} = 0\vert_\mathcal{S} \) where \(\mathcal{S}\) is the pre-defined sparsity pattern (in case of ILU(0), the sparsity pattern of the system matrix \(A\)). The number of ParILU sweeps needed for convergence depends on the parallelism level: For sequential execution, a single sweep is sufficient; for fine-grained parallelism, the number of sweeps necessary to get a good approximation of the incomplete factors depends heavily on the problem. On the OpenMP executor, 3 sweeps usually give a decent approximation in our experiments, while GPU executors can take 10 or more iterations.
| ValueType | Type of the values of all matrices used in this class |
| IndexType | Type of the indices of all matrices used in this class |
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static |
Create the parameters from the property_tree.
Because this is directly tied to the specific type, the value/index type settings within config are ignored and type_descriptor is only used for children configs.
| config | the property tree for setting |
| context | the registry |
| td_for_child | the type descriptor for children configs. The default uses the value/index type of this class. |
1.8.16