gko::solver::Idr#

Induced dimension reduction. A short-recurrence Krylov method that maintains a fixed-dimensional shadow space (the subspace_dim factory parameter, default 2; 4 or 8 are common larger choices) and exposes the kappa, deterministic and complex_subspace factory parameters. Often outperforms Bicgstab on hard non-symmetric problems while keeping memory bounded.

template<typename ValueType = default_precision>
class Idr #

Inherits from

  • public gko::EnableLinOp<Idr<default_precision>>

  • public gko::solver::EnablePreconditionedIterativeSolver<default_precision, Idr<default_precision>>

  • public gko::Transposable

IDR(s) is an efficient method for solving large nonsymmetric systems of linear equations. The implemented version is the one presented in the paper “Algorithm 913: An elegant IDR(s) variant that efficiently exploits

biorthogonality properties” by M. B. Van Gijzen and P. Sonneveld.

The method is based on the induced dimension reduction theorem which provides a way to construct subsequent residuals that lie in a sequence of shrinking subspaces. These subspaces are spanned by s vectors which are first generated randomly and then orthonormalized. They are stored in a dense matrix.

Template Parameters:

ValueType – precision of the elements of the system matrix.

Public Functions

virtual std::unique_ptr<LinOp> transpose() const override#

Returns a LinOp representing the transpose of the Transposable object.

Returns:

a pointer to the new transposed object

virtual std::unique_ptr<LinOp> conj_transpose() const override#

Returns a LinOp representing the conjugate transpose of the Transposable object.

Returns:

a pointer to the new conjugate transposed object

inline bool apply_uses_initial_guess() const override#

Return true as iterative solvers use the data in x as an initial guess.

Returns:

true as iterative solvers use the data in x as an initial guess.

inline size_type get_subspace_dim() const#

Gets the subspace dimension of the solver.

Returns:

the subspace Dimension

inline void set_subspace_dim(const size_type other)#

Sets the subspace dimension of the solver.

Parameters:

other – the new subspace Dimension

inline remove_complex<ValueType> get_kappa() const#

Gets the kappa parameter of the solver.

Returns:

the kappa parameter

inline void set_kappa(const remove_complex<ValueType> other)#

Sets the kappa parameter of the solver.

Parameters:

other – the new kappa parameter

inline bool get_deterministic() const#

Gets the deterministic parameter of the solver.

Returns:

the deterministic parameter

inline void set_deterministic(const bool other)#

Sets the deterministic parameter of the solver.

Parameters:

other – the new deterministic parameter

inline bool get_complex_subspace() const#

Gets the complex_subspace parameter of the solver.

Returns:

the complex_subspace parameter

inline void set_complex_subpsace(const bool other)#

Sets the complex_subspace parameter of the solver.

Deprecated:

Please use set_complex_subspace instead

Parameters:

other – the new complex_subspace parameter

inline void set_complex_subspace(const bool other)#

Sets the complex_subspace parameter of the solver.

Parameters:

other – the new complex_subspace parameter

Public Static Functions

static parameters_type parse(
const config::pnode &config,
const config::registry &context,
const config::type_descriptor &td_for_child = config::make_type_descriptor<ValueType>(),
)#

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.

Parameters:

  • config – the property tree for setting

  • context – the registry

  • td_for_child – the type descriptor for children configs. The default uses the value type of this class.

Returns:

parameters

struct parameters_type #

Inherits from

  • public gko::solver::enable_preconditioned_iterative_solver_factory_parameters<parameters_type, Factory>

Public Members

size_type subspace_dim#

Dimension of the subspace S. Determines how many intermediate residuals are computed in each iteration.

remove_complex<ValueType> kappa#

Threshold to determine if Av_n and v_n are too close to being perpendicular. This is considered to be the case if $|(Av_n)^H * v_n / (norm(Av_n) * norm(v_n))| < kappa$

bool deterministic#

If set to true, the vectors spanning the subspace S are chosen deterministically. This is mostly needed for testing purposes.

Note: If ‘deterministic’ is set to true, the subspace vectors are generated in serial on the CPU, which can be very slow.

The default behaviour is to choose the subspace vectors randomly.

bool complex_subspace#

If set to true, IDR will use a complex subspace S also for real problems, allowing for faster convergence and better results by acknowledging the influence of complex eigenvectors.

The default is false.