PIPE_CG or the pipelined conjugate gradient method is an iterative type Krylov subspace method which is suitable for symmetric positive definite methods.
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std::unique_ptr< LinOp > | transpose () const override |
| Returns a LinOp representing the transpose of the Transposable object.
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std::unique_ptr< LinOp > | conj_transpose () const override |
| Returns a LinOp representing the conjugate transpose of the Transposable object.
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bool | apply_uses_initial_guess () const override |
| Return true as iterative solvers use the data in x as an initial guess.
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const parameters_type & | get_parameters () const |
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const PipeCg< default_precision > * | apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const |
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PipeCg< default_precision > * | apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) |
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const PipeCg< default_precision > * | apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const |
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PipeCg< default_precision > * | apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) |
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std::unique_ptr< PipeCg< default_precision > > | create_default (std::shared_ptr< const Executor > exec) const |
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std::unique_ptr< PipeCg< default_precision > > | create_default () const |
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std::unique_ptr< PipeCg< default_precision > > | clone (std::shared_ptr< const Executor > exec) const |
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std::unique_ptr< PipeCg< default_precision > > | clone () const |
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PipeCg< default_precision > * | copy_from (const PolymorphicObject *other) |
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std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PipeCg< default_precision > > * | copy_from (std::unique_ptr< Derived > &&other) |
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std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PipeCg< default_precision > > * | copy_from (const std::unique_ptr< Derived > &other) |
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PipeCg< default_precision > * | copy_from (const std::shared_ptr< const PolymorphicObject > &other) |
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PipeCg< default_precision > * | move_from (ptr_param< PolymorphicObject > other) |
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PipeCg< default_precision > * | clear () |
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LinOp * | apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) |
| Applies a linear operator to a vector (or a sequence of vectors).
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const LinOp * | apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const |
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LinOp * | apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) |
| Performs the operation x = alpha * op(b) + beta * x.
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const LinOp * | apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const |
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const dim< 2 > & | get_size () const noexcept |
| Returns the size of the operator.
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LinOp & | operator= (const LinOp &)=default |
| Copy-assigns a LinOp.
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LinOp & | operator= (LinOp &&other) |
| Move-assigns a LinOp.
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| LinOp (const LinOp &)=default |
| Copy-constructs a LinOp.
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| LinOp (LinOp &&other) |
| Move-constructs a LinOp.
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std::unique_ptr< LinOp > | create_default (std::shared_ptr< const Executor > exec) const |
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std::unique_ptr< LinOp > | create_default () const |
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std::unique_ptr< LinOp > | clone (std::shared_ptr< const Executor > exec) const |
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std::unique_ptr< LinOp > | clone () const |
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LinOp * | copy_from (const PolymorphicObject *other) |
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std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, LinOp > * | copy_from (std::unique_ptr< Derived > &&other) |
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std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, LinOp > * | copy_from (const std::unique_ptr< Derived > &other) |
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LinOp * | copy_from (const std::shared_ptr< const PolymorphicObject > &other) |
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LinOp * | move_from (ptr_param< PolymorphicObject > other) |
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LinOp * | clear () |
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PolymorphicObject & | operator= (const PolymorphicObject &) |
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std::unique_ptr< PolymorphicObject > | create_default (std::shared_ptr< const Executor > exec) const |
| Creates a new "default" object of the same dynamic type as this object.
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std::unique_ptr< PolymorphicObject > | create_default () const |
| Creates a new "default" object of the same dynamic type as this object.
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std::unique_ptr< PolymorphicObject > | clone (std::shared_ptr< const Executor > exec) const |
| Creates a clone of the object.
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std::unique_ptr< PolymorphicObject > | clone () const |
| Creates a clone of the object.
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PolymorphicObject * | copy_from (const PolymorphicObject *other) |
| Copies another object into this object.
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template<typename Derived, typename Deleter> |
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PolymorphicObject > * | copy_from (std::unique_ptr< Derived, Deleter > &&other) |
| Moves another object into this object.
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template<typename Derived, typename Deleter> |
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PolymorphicObject > * | copy_from (const std::unique_ptr< Derived, Deleter > &other) |
| Copies another object into this object.
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PolymorphicObject * | copy_from (const std::shared_ptr< const PolymorphicObject > &other) |
| Copies another object into this object.
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PolymorphicObject * | move_from (ptr_param< PolymorphicObject > other) |
| Moves another object into this object.
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PolymorphicObject * | clear () |
| Transforms the object into its default state.
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std::shared_ptr< const Executor > | get_executor () const noexcept |
| Returns the Executor of the object.
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void | add_logger (std::shared_ptr< const Logger > logger) override |
| Adds a new logger to the list of subscribed loggers.
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void | remove_logger (const Logger *logger) override |
| Removes a logger from the list of subscribed loggers.
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void | remove_logger (ptr_param< const Logger > logger) |
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const std::vector< std::shared_ptr< const Logger > > & | get_loggers () const override |
| Returns the vector containing all loggers registered at this object.
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void | clear_loggers () override |
| Remove all loggers registered at this object.
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void | remove_logger (ptr_param< const Logger > logger) |
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void | convert_to (result_type *result) const override |
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void | move_to (result_type *result) override |
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void | convert_to (ptr_param< result_type > result) const |
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void | move_to (ptr_param< result_type > result) |
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| EnablePreconditionedIterativeSolver (std::shared_ptr< const LinOp > system_matrix, std::shared_ptr< const stop::CriterionFactory > stop_factory, std::shared_ptr< const LinOp > preconditioner) |
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| EnablePreconditionedIterativeSolver (std::shared_ptr< const LinOp > system_matrix, const FactoryParameters ¶ms) |
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EnableSolverBase & | operator= (const EnableSolverBase &other) |
| Creates a shallow copy of the provided system matrix, clones it onto this executor if executors don't match.
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EnableSolverBase & | operator= (EnableSolverBase &&other) |
| Moves the provided system matrix, clones it onto this executor if executors don't match.
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| EnableSolverBase (std::shared_ptr< const LinOp > system_matrix) |
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| EnableSolverBase (const EnableSolverBase &other) |
| Creates a shallow copy of the provided system matrix.
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| EnableSolverBase (EnableSolverBase &&other) |
| Moves the provided system matrix.
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int | get_num_workspace_ops () const override |
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std::vector< std::string > | get_workspace_op_names () const override |
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std::vector< int > | get_workspace_scalars () const override |
| Returns the IDs of all scalars (workspace vectors with system dimension-independent size, usually 1 x num_rhs).
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std::vector< int > | get_workspace_vectors () const override |
| Returns the IDs of all vectors (workspace vectors with system dimension-dependent size, usually system_matrix_size x num_rhs).
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std::shared_ptr< const LinOp > | get_system_matrix () const |
| Returns the system matrix, with its concrete type, used by the solver.
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EnableIterativeBase & | operator= (const EnableIterativeBase &other) |
| Creates a shallow copy of the provided stopping criterion, clones it onto this executor if executors don't match.
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EnableIterativeBase & | operator= (EnableIterativeBase &&other) |
| Moves the provided stopping criterion, clones it onto this executor if executors don't match.
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| EnableIterativeBase (std::shared_ptr< const stop::CriterionFactory > stop_factory) |
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| EnableIterativeBase (const EnableIterativeBase &other) |
| Creates a shallow copy of the provided stopping criterion.
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| EnableIterativeBase (EnableIterativeBase &&other) |
| Moves the provided stopping criterion.
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void | set_stop_criterion_factory (std::shared_ptr< const stop::CriterionFactory > new_stop_factory) override |
| Sets the stopping criterion of the solver.
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std::shared_ptr< const stop::CriterionFactory > | get_stop_criterion_factory () const |
| Gets the stopping criterion factory of the solver.
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void | set_preconditioner (std::shared_ptr< const LinOp > new_precond) override |
| Sets the preconditioner operator used by the Preconditionable.
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EnablePreconditionable & | operator= (const EnablePreconditionable &other) |
| Creates a shallow copy of the provided preconditioner, clones it onto this executor if executors don't match.
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EnablePreconditionable & | operator= (EnablePreconditionable &&other) |
| Moves the provided preconditioner, clones it onto this executor if executors don't match.
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| EnablePreconditionable (std::shared_ptr< const LinOp > preconditioner) |
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| EnablePreconditionable (const EnablePreconditionable &other) |
| Creates a shallow copy of the provided preconditioner.
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| EnablePreconditionable (EnablePreconditionable &&other) |
| Moves the provided preconditioner.
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virtual std::shared_ptr< const LinOp > | get_preconditioner () const |
| Returns the preconditioner operator used by the Preconditionable.
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template<typename ValueType = default_precision>
class gko::solver::PipeCg< ValueType >
PIPE_CG or the pipelined conjugate gradient method is an iterative type Krylov subspace method which is suitable for symmetric positive definite methods.
It improves upon the CG method by allowing computation of inner products and norms to be overlapped with operator and preconditioner application. The pipelined method scales up to the 10^6 nodes of the assumed exascale machine, while its standard counterpart level off about one order of magnitude earlier, as suggested in the referenced paper (see below).
Possible issues:
- Numerical instability: Due to the rearrangement of the operations, the method is known to be less stable than standard PCG.
- The method is suitable for cases where a large number of iterations need to be performed and when the solver is distributed over a large number of distributed nodes. The advantage of lesser number of reductions that need to be performed comes at the cost of increased vector operations, and the cost of increased storage of vectors.
- As the CG itself, this method performs very well for symmetric positive definite matrices but it is in general not suitable for general matrices.
The implementation in Ginkgo is based on the following paper: Pipelined, Flexible Krylov Subspace Methods, P. Sanan et. al, SISC, 2016, doi: 10.1137/15M1049130
- Template Parameters
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ValueType | precision of matrix elements |