dg::BICGSTABl< ContainerType > Class Template Reference

Preconditioned BICGSTAB(l) method to solve \( Ax=b\). More...

Public Types
using	container_type = ContainerType
using	value_type = dg::get_value_type< ContainerType >

Public Member Functions
	BICGSTABl ()=default
	Allocate nothing, Call construct method before usage. More...
	BICGSTABl (const ContainerType &copyable, unsigned max_iterations, unsigned l_input)
	Allocate memory for the preconditioned BICGSTABl method. More...
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...
void	set_max (unsigned new_max)
	Set the maximum number of iterations. More...
unsigned	get_max () const
	Get the current maximum number of iterations. More...
const ContainerType &	copyable () const
	Return an object of same size as the object used for construction. More...
void	set_verbose (bool verbose)
	Set or unset debugging output during iterations. More...
void	set_throw_on_fail (bool throw_on_fail)
	Set or unset a throw on failure-to-converge. More...
template<class MatrixType0 , class ContainerType0 , class ContainerType1 , class MatrixType1 , class ContainerType2 >
unsigned	solve (MatrixType0 &&A, ContainerType0 &x, const ContainerType1 &b, MatrixType1 &&P, const ContainerType2 &W, value_type eps=1e-12, value_type nrmb_correction=1)
	Solve \( Ax = b\) using a preconditioned BICGSTABl method. More...

Detailed Description

template<class ContainerType>
class dg::BICGSTABl< ContainerType >

Preconditioned BICGSTAB(l) method to solve \( Ax=b\).

Note

BICGSTAB(l) is a method for solving non-symmetrical linear systems. BICGSTAB(l) is a modification of BICGSTAB that aims to improve convergence. See a paper here https://pdfs.semanticscholar.org/c185/7ceab3c9ab4dbcb6a52fb62916f5757c0b38.pdf

Member Typedef Documentation

container_type

template<class ContainerType >

using dg::BICGSTABl< ContainerType >::container_type = ContainerType

value_type

template<class ContainerType >

using dg::BICGSTABl< ContainerType >::value_type = dg::get_value_type<ContainerType>

value type of the ContainerType class

Constructor & Destructor Documentation

BICGSTABl() [1/2]

template<class ContainerType >

dg::BICGSTABl< ContainerType >::BICGSTABl ( )

default

Allocate nothing, Call construct method before usage.

BICGSTABl() [2/2]

template<class ContainerType >

dg::BICGSTABl< ContainerType >::BICGSTABl ( const ContainerType &  copyable, unsigned  max_iterations, unsigned  l_input  )

inline

Allocate memory for the preconditioned BICGSTABl method.

Parameters

copyable	A ContainerType must be copy-constructible from this
max_iterations	Maximum number of iterations (there is 2 matrix-vector products plus 2 Preconditioner-vector products per iteration)
l_input	Size of polynomial used for stabilisation. Usually 2 or 4 is a good number (makes l_input Bi-CG iterations before computing the minimal residual)

Note

l_input=1 computes exactly the same as Bi-CGstab does

Member Function Documentation

construct()

template<class ContainerType >

template<class ... Params>

void dg::BICGSTABl< ContainerType >::construct ( Params &&...  ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params

deduced by the compiler

Parameters

ps	parameters forwarded to constructors

copyable()

template<class ContainerType >

const ContainerType & dg::BICGSTABl< ContainerType >::copyable ( ) const

inline

Return an object of same size as the object used for construction.

Returns

A copyable object; what it contains is undefined, its size is important

get_max()

template<class ContainerType >

unsigned dg::BICGSTABl< ContainerType >::get_max ( ) const

inline

Get the current maximum number of iterations.

Returns

the current maximum

set_max()

template<class ContainerType >

void dg::BICGSTABl< ContainerType >::set_max ( unsigned  new_max )

inline

Set the maximum number of iterations.

Parameters

new_max

New maximum number

set_throw_on_fail()

template<class ContainerType >

void dg::BICGSTABl< ContainerType >::set_throw_on_fail ( bool  throw_on_fail )

inline

Set or unset a throw on failure-to-converge.

Parameters

throw_on_fail

If true, the solve method will thow a dg::Fail if it is unable to converge

Note

the default value is true

set_verbose()

template<class ContainerType >

void dg::BICGSTABl< ContainerType >::set_verbose ( bool  verbose )

inline

Set or unset debugging output during iterations.

Parameters

verbose

If true, additional output will be written to std::cout during solution

solve()

template<class ContainerType >

template<class MatrixType0 , class ContainerType0 , class ContainerType1 , class MatrixType1 , class ContainerType2 >

unsigned dg::BICGSTABl< ContainerType >::solve	(	MatrixType0 &&	A,
		ContainerType0 &	x,
		const ContainerType1 &	b,
		MatrixType1 &&	P,
		const ContainerType2 &	W,
		value_type	eps = 1e-12,
		value_type	nrmb_correction = 1
	)

Solve \( Ax = b\) using a preconditioned BICGSTABl method.

The iteration stops if \( ||P(Ax-b)||_W < \epsilon( ||Pb||_S + C) \) where \(C\) is the absolute error in units of \( \epsilon\) and \( W \) defines a square norm

Attention

The stopping criterion differs from that of CG or LGMRES by the preconditioner. It is unfortunately cumbersome to obtain the real residual in this algorithm. If P is diagonal there is the opportunity to use W to offset its effect.

Parameters

A	A matrix
x	Contains an initial value on input and the solution on output.
b	The right hand side vector. x and b may not be the same vector.
P	The preconditioner to be used
W	Weights used to define the scalar product and the norm for the error condition
eps	The relative error to be respected
nrmb_correction	the absolute error C in units of eps to be respected

Returns

Number of iterations used to achieve desired precision (in each iteration the matrix has to be applied twice)

Note

The method will throw dg::Fail if the desired accuracy is not reached within max_iterations You can unset this behaviour with the set_throw_on_fail member

Template Parameters

MatrixType

Any class for which a specialization of TensorTraits exists and defines a tensor_category derived from AnyMatrixTag. Furthermore, any functor/lambda type with signature void operator()( const ContainerType0&, ContainerType1&) . For example scalar or Container: Scalars and containers act as diagonal matrices. std::function<void( const ContainerType0&, ContainerType1&)> dg::HMatrix and dg::IHMatrix with dg::HVec or std::vector<dg::HVec> dg::DMatrix and dg::IDMatrix with dg::DVec or std::vector<dg::DVec> dg::MHMatrix with dg::MHVec or std::vector<dg::MHVec> dg::MDMatrix with dg::MDVec or std::vector<dg::MDVec> In case of SelfMadeMatrixTag only those blas2 functions that have a corresponding member function in the Matrix class (e.g. symv( const ContainerType0&, ContainerType1&); ) can be called. If a Container has the RecursiveVectorTag, then the matrix is applied to each of the elements unless the type has the SelfMadeMatrixTag or is a Functor type.

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

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The documentation for this class was generated from the following file:

• bicgstabl.h