Ginkgo  Generated from pipelines/164546034 branch based on develop. Ginkgo version 1.2.0
A numerical linear algebra library targeting many-core architectures
Modules | Classes | Macros | Typedefs
Linear Operators

A module dedicated to the implementation and usage of the Linear operators in Ginkgo. More...

Collaboration diagram for Linear Operators:

Modules

 Factorizations
 A module dedicated to the implementation and usage of the Factorizations in Ginkgo.
 
 SpMV employing different Matrix formats
 A module dedicated to the implementation and usage of the various Matrix Formats in Ginkgo.
 
 Preconditioners
 A module dedicated to the implementation and usage of the Preconditioners in Ginkgo.
 
 Solvers
 A module dedicated to the implementation and usage of the Solvers in Ginkgo.
 

Classes

class  gko::Combination< ValueType >
 The Combination class can be used to construct a linear combination of multiple linear operators c1 * op1 + c2 * op2 + ... More...
 
class  gko::Composition< ValueType >
 The Composition class can be used to compose linear operators op1, op2, ..., opn and obtain the operator op1 * op2 * ... More...
 
class  gko::LinOpFactory
 A LinOpFactory represents a higher order mapping which transforms one linear operator into another. More...
 
class  gko::ReadableFromMatrixData< ValueType, IndexType >
 A LinOp implementing this interface can read its data from a matrix_data structure. More...
 
class  gko::WritableToMatrixData< ValueType, IndexType >
 A LinOp implementing this interface can write its data to a matrix_data structure. More...
 
class  gko::Preconditionable
 A LinOp implementing this interface can be preconditioned. More...
 
class  gko::EnableLinOp< ConcreteLinOp, PolymorphicBase >
 The EnableLinOp mixin can be used to provide sensible default implementations of the majority of the LinOp and PolymorphicObject interface. More...
 
class  gko::Perturbation< ValueType >
 The Perturbation class can be used to construct a LinOp to represent the operation (identity + scalar * basis * projector). More...
 
class  gko::factorization::Ilu< ValueType, IndexType >
 Represents an incomplete LU factorization – ILU(0) – of a sparse matrix. More...
 
class  gko::factorization::ParIct< ValueType, IndexType >
 ParICT is an incomplete threshold-based Cholesky factorization which is computed in parallel. More...
 
class  gko::factorization::ParIlu< ValueType, IndexType >
 ParILU is an incomplete LU factorization which is computed in parallel. More...
 
class  gko::factorization::ParIlut< ValueType, IndexType >
 ParILUT is an incomplete threshold-based LU factorization which is computed in parallel. More...
 
class  gko::matrix::Coo< ValueType, IndexType >
 COO stores a matrix in the coordinate matrix format. More...
 
class  gko::matrix::Csr< ValueType, IndexType >
 CSR is a matrix format which stores only the nonzero coefficients by compressing each row of the matrix (compressed sparse row format). More...
 
class  gko::matrix::Dense< ValueType >
 Dense is a matrix format which explicitly stores all values of the matrix. More...
 
class  gko::matrix::Ell< ValueType, IndexType >
 ELL is a matrix format where stride with explicit zeros is used such that all rows have the same number of stored elements. More...
 
class  gko::matrix::Hybrid< ValueType, IndexType >
 HYBRID is a matrix format which splits the matrix into ELLPACK and COO format. More...
 
class  gko::matrix::Identity< ValueType >
 This class is a utility which efficiently implements the identity matrix (a linear operator which maps each vector to itself). More...
 
class  gko::matrix::IdentityFactory< ValueType >
 This factory is a utility which can be used to generate Identity operators. More...
 
class  gko::matrix::Permutation< IndexType >
 Permutation is a matrix "format" which stores the row and column permutation arrays which can be used for re-ordering the rows and columns a matrix. More...
 
class  gko::matrix::Sellp< ValueType, IndexType >
 SELL-P is a matrix format similar to ELL format. More...
 
class  gko::matrix::SparsityCsr< ValueType, IndexType >
 SparsityCsr is a matrix format which stores only the sparsity pattern of a sparse matrix by compressing each row of the matrix (compressed sparse row format). More...
 
class  gko::preconditioner::Ilu< LSolverType, USolverType, ReverseApply, IndexType >
 The Incomplete LU (ILU) preconditioner solves the equation $LUx = b$ for a given lower triangular matrix L, an upper triangular matrix U and the right hand side b (can contain multiple right hand sides). More...
 
class  gko::preconditioner::Isai< IsaiType, ValueType, IndexType >
 The Incomplete Sparse Approximate Inverse (ISAI) Preconditioner generates an approximate inverse matrix for a given lower triangular matrix L or upper triangular matrix U. More...
 
class  gko::preconditioner::Jacobi< ValueType, IndexType >
 A block-Jacobi preconditioner is a block-diagonal linear operator, obtained by inverting the diagonal blocks of the source operator. More...
 
class  gko::solver::Bicg< ValueType >
 BICG or the Biconjugate gradient method is a Krylov subspace solver. More...
 
class  gko::solver::Bicgstab< ValueType >
 BiCGSTAB or the Bi-Conjugate Gradient-Stabilized is a Krylov subspace solver. More...
 
class  gko::solver::Cg< ValueType >
 CG or the conjugate gradient method is an iterative type Krylov subspace method which is suitable for symmetric positive definite methods. More...
 
class  gko::solver::Cgs< ValueType >
 CGS or the conjugate gradient square method is an iterative type Krylov subspace method which is suitable for general systems. More...
 
class  gko::solver::Fcg< ValueType >
 FCG or the flexible conjugate gradient method is an iterative type Krylov subspace method which is suitable for symmetric positive definite methods. More...
 
class  gko::solver::Gmres< ValueType >
 GMRES or the generalized minimal residual method is an iterative type Krylov subspace method which is suitable for nonsymmetric linear systems. More...
 
class  gko::solver::Ir< ValueType >
 Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the error of the current solution via the current residual. More...
 
class  gko::solver::LowerTrs< ValueType, IndexType >
 LowerTrs is the triangular solver which solves the system L x = b, when L is a lower triangular matrix. More...
 
class  gko::solver::UpperTrs< ValueType, IndexType >
 UpperTrs is the triangular solver which solves the system U x = b, when U is an upper triangular matrix. More...
 

Macros

#define GKO_CREATE_FACTORY_PARAMETERS(_parameters_name, _factory_name)
 This Macro will generate a new type containing the parameters for the factory _factory_name. More...
 
#define GKO_ENABLE_LIN_OP_FACTORY(_lin_op, _parameters_name, _factory_name)
 This macro will generate a default implementation of a LinOpFactory for the LinOp subclass it is defined in. More...
 
#define GKO_ENABLE_BUILD_METHOD(_factory_name)
 Defines a build method for the factory, simplifying its construction by removing the repetitive typing of factory's name. More...
 
#define GKO_FACTORY_PARAMETER(_name, ...)
 Creates a factory parameter in the factory parameters structure. More...
 

Typedefs

template<typename ConcreteFactory , typename ConcreteLinOp , typename ParametersType , typename PolymorphicBase = LinOpFactory>
using gko::EnableDefaultLinOpFactory = EnableDefaultFactory< ConcreteFactory, ConcreteLinOp, ParametersType, PolymorphicBase >
 This is an alias for the EnableDefaultFactory mixin, which correctly sets the template parameters to enable a subclass of LinOpFactory. More...
 

Detailed Description

A module dedicated to the implementation and usage of the Linear operators in Ginkgo.

Below we elaborate on one of the most important concepts of Ginkgo, the linear operator. The linear operator (LinOp) is a base class for all linear algebra objects in Ginkgo. The main benefit of having a single base class for the entire collection of linear algebra objects (as opposed to having separate hierarchies for matrices, solvers and preconditioners) is the generality it provides.

Advantages of this approach and usage

A common interface often allows for writing more generic code. If a user's routine requires only operations provided by the LinOp interface, the same code can be used for any kind of linear operators, independent of whether these are matrices, solvers or preconditioners. This feature is also extensively used in Ginkgo itself. For example, a preconditioner used inside a Krylov solver is a LinOp. This allows the user to supply a wide variety of preconditioners: either the ones which were designed to be used in this scenario (like ILU or block-Jacobi), a user-supplied matrix which is known to be a good preconditioner for the specific problem, or even another solver (e.g., if constructing a flexible GMRES solver).

For example, a matrix free implementation would require the user to provide an apply implementation and instead of passing the generated matrix to the solver, they would have to provide their apply implementation for all the executors needed and no other code needs to be changed. See The custom-matrix-format program example for more details.

Linear operator as a concept

The linear operator (LinOp) is a base class for all linear algebra objects in Ginkgo. The main benefit of having a single base class for the entire collection of linear algebra objects (as opposed to having separate hierarchies for matrices, solvers and preconditioners) is the generality it provides.

First, since all subclasses provide a common interface, the library users are exposed to a smaller set of routines. For example, a matrix-vector product, a preconditioner application, or even a system solve are just different terms given to the operation of applying a certain linear operator to a vector. As such, Ginkgo uses the same routine name, LinOp::apply() for each of these operations, where the actual operation performed depends on the type of linear operator involved in the operation.

Second, a common interface often allows for writing more generic code. If a user's routine requires only operations provided by the LinOp interface, the same code can be used for any kind of linear operators, independent of whether these are matrices, solvers or preconditioners. This feature is also extensively used in Ginkgo itself. For example, a preconditioner used inside a Krylov solver is a LinOp. This allows the user to supply a wide variety of preconditioners: either the ones which were designed to be used in this scenario (like ILU or block-Jacobi), a user-supplied matrix which is known to be a good preconditioner for the specific problem, or even another solver (e.g., if constructing a flexible GMRES solver).

A key observation for providing a unified interface for matrices, solvers, and preconditioners is that the most common operation performed on all of them can be expressed as an application of a linear operator to a vector:

Finally, direct manipulation of LinOp objects is rarely required in simple scenarios. As an illustrative example, one could construct a fixed-point iteration routine $x_{k+1} = Lx_k + b$ as follows:

std::unique_ptr<matrix::Dense<>> calculate_fixed_point(
int iters, const LinOp *L, const matrix::Dense<> *x0
const matrix::Dense<> *b)
{
auto x = gko::clone(x0);
auto tmp = gko::clone(x0);
auto one = Dense<>::create(L->get_executor(), {1.0,});
for (int i = 0; i < iters; ++i) {
L->apply(gko::lend(tmp), gko::lend(x));
x->add_scaled(gko::lend(one), gko::lend(b));
tmp->copy_from(gko::lend(x));
}
return x;
}

Here, if $L$ is a matrix, LinOp::apply() refers to the matrix vector product, and L->apply(a, b) computes $b = L \cdot a$. x->add_scaled(one.get(), b.get()) is the axpy vector update $x:=x+b$.

The interesting part of this example is the apply() routine at line 4 of the function body. Since this routine is part of the LinOp base class, the fixed-point iteration routine can calculate a fixed point not only for matrices, but for any type of linear operator.

Linear Operators

Macro Definition Documentation

◆ GKO_CREATE_FACTORY_PARAMETERS

#define GKO_CREATE_FACTORY_PARAMETERS (   _parameters_name,
  _factory_name 
)
Value:
public: \
class _factory_name; \
struct _parameters_name##_type \
: ::gko::enable_parameters_type<_parameters_name##_type, \
_factory_name>

This Macro will generate a new type containing the parameters for the factory _factory_name.

For more details, see GKO_ENABLE_LIN_OP_FACTORY(). It is required to use this macro before calling the macro GKO_ENABLE_LIN_OP_FACTORY(). It is also required to use the same names for all parameters between both macros.

Parameters
_parameters_namename of the parameters member in the class
_factory_namename of the generated factory type

◆ GKO_ENABLE_BUILD_METHOD

#define GKO_ENABLE_BUILD_METHOD (   _factory_name)
Value:
static auto build()->decltype(_factory_name::create()) \
{ \
return _factory_name::create(); \
} \
static_assert(true, \
"This assert is used to counter the false positive extra " \
"semi-colon warnings")

Defines a build method for the factory, simplifying its construction by removing the repetitive typing of factory's name.

Parameters
_factory_namethe factory for which to define the method

◆ GKO_ENABLE_LIN_OP_FACTORY

#define GKO_ENABLE_LIN_OP_FACTORY (   _lin_op,
  _parameters_name,
  _factory_name 
)

This macro will generate a default implementation of a LinOpFactory for the LinOp subclass it is defined in.

It is required to first call the macro GKO_CREATE_FACTORY_PARAMETERS() before this one in order to instantiate the parameters type first.

The list of parameters for the factory should be defined in a code block after the macro definition, and should contain a list of GKO_FACTORY_PARAMETER declarations. The class should provide a constructor with signature _lin_op(const _factory_name *, std::shared_ptr<const LinOp>) which the factory will use a callback to construct the object.

A minimal example of a linear operator is the following:

{c++}
struct MyLinOp : public EnableLinOp<MyLinOp> {
GKO_ENABLE_LIN_OP_FACTORY(MyLinOp, my_parameters, Factory) {
// a factory parameter named "my_value", of type int and default
// value of 5
int GKO_FACTORY_PARAMETER(my_value, 5);
};
// constructor needed by EnableLinOp
explicit MyLinOp(std::shared_ptr<const Executor> exec) {
: EnableLinOp<MyLinOp>(exec) {}
// constructor needed by the factory
explicit MyLinOp(const Factory *factory,
std::shared_ptr<const LinOp> matrix)
: EnableLinOp<MyLinOp>(factory->get_executor()), matrix->get_size()),
// store factory's parameters locally
my_parameters_{factory->get_parameters()},
{
int value = my_parameters_.my_value;
// do something with value
}

MyLinOp can then be created as follows:

{c++}
auto exec = gko::ReferenceExecutor::create();
// create a factory with default `my_value` parameter
auto fact = MyLinOp::build().on(exec);
// create a operator using the factory:
auto my_op = fact->generate(gko::matrix::Identity::create(exec, 2));
std::cout << my_op->get_my_parameters().my_value; // prints 5
// create a factory with custom `my_value` parameter
auto fact = MyLinOp::build().with_my_value(0).on(exec);
// create a operator using the factory:
auto my_op = fact->generate(gko::matrix::Identity::create(exec, 2));
std::cout << my_op->get_my_parameters().my_value; // prints 0
Note
It is possible to combine both the #GKO_CREATE_FACTORY_PARAMETER() macro with this one in a unique macro for class templates (not with regular classes). Splitting this into two distinct macros allows to use them in all contexts. See https://stackoverflow.com/q/50202718/9385966 for more details.
Parameters
_lin_opconcrete operator for which the factory is to be created [CRTP parameter]
_parameters_namename of the parameters member in the class (its type is <_parameters_name>_type, the protected member's name is <_parameters_name>_, and the public getter's name is get_<_parameters_name>())
_factory_namename of the generated factory type

◆ GKO_FACTORY_PARAMETER

#define GKO_FACTORY_PARAMETER (   _name,
  ... 
)
Value:
mutable _name{__VA_ARGS__}; \
\
template <typename... Args> \
auto with_##_name(Args &&... _value) \
const->const ::gko::xstd::decay_t<decltype(*this)> & \
{ \
using type = decltype(this->_name); \
this->_name = type{std::forward<Args>(_value)...}; \
return *this; \
} \
static_assert(true, \
"This assert is used to counter the false positive extra " \
"semi-colon warnings")

Creates a factory parameter in the factory parameters structure.

Parameters
_namename of the parameter
<strong>VA_ARGS</strong>default value of the parameter
See also
GKO_ENABLE_LIN_OP_FACTORY for more details, and usage example

Typedef Documentation

◆ EnableDefaultLinOpFactory

template<typename ConcreteFactory , typename ConcreteLinOp , typename ParametersType , typename PolymorphicBase = LinOpFactory>
using gko::EnableDefaultLinOpFactory = typedef EnableDefaultFactory<ConcreteFactory, ConcreteLinOp, ParametersType, PolymorphicBase>

This is an alias for the EnableDefaultFactory mixin, which correctly sets the template parameters to enable a subclass of LinOpFactory.

Template Parameters
ConcreteFactorythe concrete factory which is being implemented [CRTP parmeter]
ConcreteLinOpthe concrete LinOp type which this factory produces, needs to have a constructor which takes a const ConcreteFactory *, and an std::shared_ptr<const LinOp> as parameters.
ParametersTypea subclass of enable_parameters_type template which defines all of the parameters of the factory
PolymorphicBaseparent of ConcreteFactory in the polymorphic hierarchy, has to be a subclass of LinOpFactory
GKO_FACTORY_PARAMETER
#define GKO_FACTORY_PARAMETER(_name,...)
Creates a factory parameter in the factory parameters structure.
Definition: lin_op.hpp:869
gko::clone
detail::cloned_type< Pointer > clone(const Pointer &p)
Creates a unique clone of the object pointed to by p.
Definition: utils.hpp:160
gko::lend
std::enable_if< detail::have_ownership_s< Pointer >::value, detail::pointee< Pointer > * >::type lend(const Pointer &p)
Returns a non-owning (plain) pointer to the object pointed to by p.
Definition: utils.hpp:253
GKO_ENABLE_LIN_OP_FACTORY
#define GKO_ENABLE_LIN_OP_FACTORY(_lin_op, _parameters_name, _factory_name)
This macro will generate a default implementation of a LinOpFactory for the LinOp subclass it is defi...
Definition: lin_op.hpp:801
gko::enable_parameters_type
The enable_parameters_type mixin is used to create a base implementation of the factory parameters st...
Definition: abstract_factory.hpp:269
gko::one
constexpr T one()
Returns the multiplicative identity for T.
Definition: math.hpp:570