#include <qpmg.hh>

Detailed Description

template<int d, class Prolongation, class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>
class Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >

Definition at line 465 of file qpmg.hh.

Inheritance diagram for Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >:

Public Types
using	Self = QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >

using	MatrixA = NumaBCRSMatrix< EntryA >

using	MatrixB = NumaBCRSMatrix< Dune::FieldMatrix< Real, 1, d > >

using	VectorX = Dune::BlockVector< Dune::FieldVector< Real, d > >

using	VectorB = Dune::BlockVector< Dune::FieldVector< Real, 1 > >

using	SmootherType = std::conditional_t< smoothersEqual, QPSmoother< d, double >, std::variant< QPSmoother< d, double >, QPSmoother< d, double > > >

Public Member Functions
	QPMultiGridStrict (MatrixA const &A, MatrixB const &B, std::vector< Prolongation > &&prolongations, Real smootherRegularization=0, bool blocks=true, bool directOnCoarse=true)
	Constructs the solver, providing the matrices \( A \) and \( B \). More...

	~QPMultiGridStrict ()
	Destructor. More...

std::tuple< VectorX, int >	solve (VectorX x, VectorX const &c, VectorB const &b, double tol, int vcycles) const
	Approximately solves the QP for the given right hand side vectors up to a given tolerance. More...

VectorX	step (VectorX const &x, VectorX c, VectorB b) const
	Computes a single V-cycle correction for approximately solving the QP for the given right hand side vectors. More...

std::tuple< VectorX, int >	solve (VectorX x, VectorX const &c, VectorB const &b, double tol, int vcycles) const
	Approximately solves the QP for the given right hand side vectors up to a given tolerance. More...

Self &	setCoarseLevel (int coarselevel)
	Defines the grid level to be used as coarse grid. More...

Self &	setSmoothings (int pre, int post)

Self &	setCoarseCorrections (int n)
	Sets the number of coarse corrections to compute and apply. More...

Self &	setBulkMode (ParallelMode m)
	Defines the smoothing strategy to use for unconstrained degrees of freedom. More...

Self &	setLogger (MGSolverStatistics< d, double > *logger)
	Sets the logging facility for reporting solver statistics. More...

Static Public Attributes
static constexpr bool	smoothersEqual

Protected Member Functions
virtual double	computeEnergy (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x) const

virtual std::tuple< VectorX, VectorB, int >	gradient (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x) const
	Computes the gradient of the (non-augmented) Lagrangian. More...

virtual std::tuple< VectorX, VectorX, VectorX, VectorB, int >	gradient_extended (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x) const
	Computes the gradient of the (non-augmented) Lagrangian. More...

virtual double	qpLinesearch (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &dx) const

virtual double	computeEnergy (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x) const=0
	Compute the problem energy of current iterate for logging purposes. More...

virtual std::tuple< VectorX, VectorB, int >	gradient (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x) const=0
	Compute the problem gradient of current iterate. More...

virtual std::tuple< VectorX, VectorX, VectorX, VectorB, int >	gradient_extended (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &x) const=0
	Computes the gradient of current iterate, giving more information on the components of the gradient. (It might be split in several terms grad0 and grad1). More...

virtual double	qpLinesearch (MatrixA const &A, MatrixB const &B, VectorX const &c, VectorB const &b, VectorX const &dx) const=0
	Compute the optimal step size in direction of dx. More...

MatrixB const &	B () const
	Provides a reference to the fine grid constraints. More...

Protected Attributes
std::vector< SmootherType >	smoothers

Member Typedef Documentation

◆ MatrixA

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

using Kaskade::QPMultiGridBase< d, Prolongation, Smoother, CoarseSmoother, Real >::MatrixA = NumaBCRSMatrix<EntryA>

Definition at line 98 of file qpmg.hh.

◆ MatrixB

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

using Kaskade::QPMultiGridBase< d, Prolongation, Smoother, CoarseSmoother, Real >::MatrixB = NumaBCRSMatrix<Dune::FieldMatrix<Real,1,d> >

Definition at line 99 of file qpmg.hh.

◆ Self

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

using Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::Self = QPMultiGridStrict<d,Prolongation,Real,Smoother,CoarseSmoother>

Definition at line 471 of file qpmg.hh.

◆ SmootherType

using Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::SmootherType = std::conditional_t<smoothersEqual, QPSmoother< d, double > , std::variant<QPSmoother< d, double > ,QPSmoother< d, double > > >

inherited

Definition at line 105 of file qpmg.hh.

◆ VectorB

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

using Kaskade::QPMultiGridBase< d, Prolongation, Smoother, CoarseSmoother, Real >::VectorB = Dune::BlockVector<Dune::FieldVector<Real,1> >

Definition at line 97 of file qpmg.hh.

◆ VectorX

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

using Kaskade::QPMultiGridBase< d, Prolongation, Smoother, CoarseSmoother, Real >::VectorX = Dune::BlockVector<Dune::FieldVector<Real,d> >

Definition at line 96 of file qpmg.hh.

Constructor & Destructor Documentation

◆ QPMultiGridStrict()

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::QPMultiGridStrict	(	MatrixA const &	A,
		MatrixB const &	B,
		std::vector< Prolongation > &&	prolongations,
		Real	smootherRegularization = `0`,
		bool	blocks = `true`,
		bool	directOnCoarse = `true`
	)

Constructs the solver, providing the matrices \( A \) and \( B \).

Parameters

A	the Hessian. The matrix is copied internally and need not exist after solver construction.
B	the constraints. The matrix is referenced internally and has to exist during the lifetime of the solver.
blocks	block=true: treat blocks of dof coupled by constraints jointly (default) block=false: treat all dofs individually (only for testing and comparison purposes)

Warning: This is intended for testing purposes only and may be removed in future.

Parameters

directOnCoarse

directOnCoarse=true use direct solver for problem on coarse grid
directOnCoarse=false use a few iterative (smoothing) steps on coarse grid (block Jacobi/Gauss Seidel)

◆ ~QPMultiGridStrict()

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::~QPMultiGridStrict ( )

Destructor.

Member Function Documentation

◆ B()

MatrixB const & Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::B ( ) const

protectedinherited

Provides a reference to the fine grid constraints.

◆ computeEnergy() [1/2]

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

virtual double Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::computeEnergy	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	x
	)		const

protectedvirtual

◆ computeEnergy() [2/2]

virtual double Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::computeEnergy	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	x
	)		const

protectedpure virtualinherited

Compute the problem energy of current iterate for logging purposes.

◆ gradient() [1/2]

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

virtual std::tuple< VectorX, VectorB, int > Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::gradient	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	x
	)		const

protectedvirtual

Computes the gradient of the (non-augmented) Lagrangian.

\[ g = Ax + c \]

Returns: a tuple ( \( g \),con,nActive) with the gradient, the constraint violation con = \( (Bx-b)_+ \) and the number of active constraints nActive

◆ gradient() [2/2]

virtual std::tuple< VectorX, VectorB, int > Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::gradient	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	x
	)		const

protectedpure virtualinherited

Compute the problem gradient of current iterate.

◆ gradient_extended() [1/2]

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

virtual std::tuple< VectorX, VectorX, VectorX, VectorB, int > Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::gradient_extended	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	x
	)		const

protectedvirtual

Computes the gradient of the (non-augmented) Lagrangian.

\[ g = Ax + c \]

Returns

a tuple (grad, grad0, grad1, cons, nActive) consisting of:

grad: full gradient given by
\[ Ax + c + \gamma*B^T(Bx-b)_+ \]
grad0: linear term give by
\[ Ax \]
grad1: constant term given by
\[ \gamma*B^T(Bx-b)_+ \]
cons: vector of constraint violation give by
\[ (Bx-b)_+ \]
nActive: number of active constraints, i.e.
\[ | \{ i \colon (Bx-b)_i >= 0 \} | \]

◆ gradient_extended() [2/2]

virtual std::tuple< VectorX, VectorX, VectorX, VectorB, int > Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::gradient_extended	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	x
	)		const

protectedpure virtualinherited

Computes the gradient of current iterate, giving more information on the components of the gradient. (It might be split in several terms grad0 and grad1).

◆ qpLinesearch() [1/2]

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

virtual double Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::qpLinesearch	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	dx
	)		const

protectedvirtual

◆ qpLinesearch() [2/2]

virtual double Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::qpLinesearch	(	MatrixA const &	A,
		MatrixB const &	B,
		VectorX const &	c,
		VectorB const &	b,
		VectorX const &	dx
	)		const

protectedpure virtualinherited

Compute the optimal step size in direction of dx.

◆ setBulkMode()

Self & Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::setBulkMode ( ParallelMode m )

inherited

Defines the smoothing strategy to use for unconstrained degrees of freedom.

In contact problems, those are usually the interior nodes, and the ones without potential contact partner. The smoother can operate in parallel (Jacobi) or sequentially (Gauss-Seidel). In the parallel way, an exact linesearch is performed after the smoothing in order to guarantee descent.

◆ setCoarseCorrections()

Self & Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::setCoarseCorrections ( int n )

inherited

Sets the number of coarse corrections to compute and apply.

Parameters

n	number of coarse corrections

n=0: just the smoother on the fine grid is performed, no multigrid at all (for testing purposes only).
n=1: V-cycle (default)
n=2: W-cycle

◆ setCoarseLevel()

Self & Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::setCoarseLevel ( int coarselevel )

inherited

Defines the grid level to be used as coarse grid.

Parameters

coarselevel the coarse grid level, between 0 and the max grid level

If coarselevel is outside its allowed range, it is projected onto that range.

◆ setLogger()

Self & Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::setLogger ( MGSolverStatistics< d, double > * logger )

inherited

Sets the logging facility for reporting solver statistics.

Parameters

logger a pointer to the logger object. This can be a nullpointer, in which case logging is stopped.

Ownership of the logger object remains with the caller. The logger object needs to exist for the lifetime of the QPMultiGrid class or until it is replaced by a different logger (or none).

◆ setSmoothings()

Self & Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::setSmoothings	(	int	pre,
		int	post
	)

inherited

◆ solve() [1/2]

std::tuple< VectorX, int > Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::solve	(	VectorX	x,
		VectorX const &	c,
		VectorB const &	b,
		double	tol,
		int	vcycles
	)		const

inherited

Approximately solves the QP for the given right hand side vectors up to a given tolerance.

Parameters

x	initial guess for the solution
c	linear objective term
b	constant constraint term
tol	tolerance

Returns: a tuple \( (x,\mathrm{iter}) \) of solution vector, multiplier update, and iteration count

◆ solve() [2/2]

template<int d, class Prolongation , class Real = double, class Smoother = QPSmoother<d,Real>, class CoarseSmoother = QPSmoother<d,Real>>

std::tuple< VectorX, int > Kaskade::QPMultiGridStrict< d, Prolongation, Real, Smoother, CoarseSmoother >::solve	(	VectorX	x,
		VectorX const &	c,
		VectorB const &	b,
		double	tol,
		int	vcycles
	)		const

Approximately solves the QP for the given right hand side vectors up to a given tolerance.

Parameters

x	initial guess for the solution
c	linear objective term
b	constant constraint term
lambda	approximate multiplier
tol	tolerance

Returns: a tuple \( (x,\delta\lambda,\mathrm{iter}) \) of solution vector, multiplier update, and iteration count

◆ step()

VectorX Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::step	(	VectorX const &	x,
		VectorX	c,
		VectorB	b
	)		const

inherited

Computes a single V-cycle correction for approximately solving the QP for the given right hand side vectors.

Parameters

x	initial guess for the solution
c	linear objective term
b	constant constraint term

Returns: the correction dx

Member Data Documentation

◆ smoothers

std::vector<SmootherType> Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::smoothers

protectedinherited

Definition at line 228 of file qpmg.hh.

◆ smoothersEqual

constexpr bool Kaskade::QPMultiGridBase< d, Prolongation, QPSmoother< d, double > , QPSmoother< d, double > , double >::smoothersEqual

staticconstexprinherited

Definition at line 104 of file qpmg.hh.

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

qpmg.hh

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ MatrixA

◆ MatrixB

◆ Self

◆ SmootherType

◆ VectorB

◆ VectorX

Constructor & Destructor Documentation

◆ QPMultiGridStrict()

◆ ~QPMultiGridStrict()

Member Function Documentation

◆ B()

◆ computeEnergy() [1/2]

◆ computeEnergy() [2/2]

◆ gradient() [1/2]

◆ gradient() [2/2]

◆ gradient_extended() [1/2]

◆ gradient_extended() [2/2]

◆ qpLinesearch() [1/2]

◆ qpLinesearch() [2/2]

◆ setBulkMode()

◆ setCoarseCorrections()

◆ setCoarseLevel()

◆ setLogger()

◆ setSmoothings()

◆ solve() [1/2]

◆ solve() [2/2]

◆ step()

Member Data Documentation

◆ smoothers

◆ smoothersEqual