A parallel-condensing LQ solver. More...

#include <aligator/gar/parallel-solver.hpp>

Inheritance diagram for aligator::gar::ParallelRiccatiSolver< _Scalar >:

Collaboration diagram for aligator::gar::ParallelRiccatiSolver< _Scalar >:

Classes
struct	CondensedKkt

Public Types
using	Scalar = _Scalar

using	Base = RiccatiSolverBase<Scalar>

using	Kernel = ProximalRiccatiKernel<Scalar>

using	KnotType = LqrKnotTpl<Scalar>

using	BlkView = BlkMatrix<VectorRef, -1, 1>

using	allocator_type = ::aligator::polymorphic_allocator

Public Types inherited from aligator::gar::RiccatiSolverBase< _Scalar >
using	Scalar = _Scalar

using	LqrKnot = LqrKnotTpl<Scalar>

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS_WITH_ROW_TYPES (Scalar)

	ParallelRiccatiSolver (LqrProblemTpl< Scalar > &problem, const uint num_threads)

bool	backward (const Scalar mueq) override

void	collapseFeedback () override

void	assembleCondensedSystem (const Scalar mudyn)
	Create the sparse representation of the reduced KKT system.

bool	forward (VectorOfVectors &xs, VectorOfVectors &us, VectorOfVectors &vs, VectorOfVectors &lbdas, const std::optional< ConstVectorRef > &=std::nullopt) const override

void	cycleAppend (const KnotType &knot) override
	Cycle the solver data, given the specs from a given new knot.

VectorRef	getFeedforward (size_t i) override

RowMatrixRef	getFeedback (size_t i) override

allocator_type	get_allocator () const

uint	getNumThreads () const noexcept
	Number of parallel divisions in the problem: \(J+1\) in the math.

void	initializeTridiagSystem ()
	Initialize the buffers for the block-tridiagonal system.

Public Member Functions inherited from aligator::gar::RiccatiSolverBase< _Scalar >
	ALIGATOR_DYNAMIC_TYPEDEFS_WITH_ROW_TYPES (Scalar)

virtual bool	forward (std::vector< VectorXs > &xs, std::vector< VectorXs > &us, std::vector< VectorXs > &vs, std::vector< VectorXs > &lbdas, const std::optional< ConstVectorRef > &theta_=std::nullopt) const =0

virtual	~RiccatiSolverBase ()=default

Public Attributes
std::pmr::vector< StageFactor< Scalar > >	datas

CondensedKkt	condensedKktSystem
	Block-sparse condensed KKT system.

ArenaMatrix< VectorXs >	condensedKktRhs
	Contains the right-hand side and solution of the condensed KKT system.

ArenaMatrix< VectorXs >	condensedKktSolution

ArenaMatrix< VectorXs >	condensedErr

Scalar	condensedThreshold = 1e-10
	Tolerance on condensed KKT system.

uint	maxRefinementSteps = 5u
	Max number of refinement steps (condensed solver)

Protected Member Functions
void	initialize ()

Protected Attributes
uint	numThreads

LqrProblemTpl< Scalar > *	problem_

std::vector< long >	rhsDims_

Detailed Description

template<typename _Scalar>
class aligator::gar::ParallelRiccatiSolver< _Scalar >

A parallel-condensing LQ solver.

This solver condenses the problem into a reduced saddle-point problem in a subset of the states and costates, corresponding to the time indices where the problem was split up. These splitting variables are used to exploit the problem's partially-separable structure: each "leg" is then condensed into its value function with respect to both its initial state and last costate (linking to the next leg). The saddle-point is cast into a linear system which is solved by dense LDL factorization. This allows parallel resolution of a (long) linear subproblem on multiple CPU cores.

Definition at line 26 of file parallel-solver.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar>

using aligator::gar::ParallelRiccatiSolver< _Scalar >::Scalar = _Scalar

Definition at line 28 of file parallel-solver.hpp.

◆ Base

template<typename _Scalar>

using aligator::gar::ParallelRiccatiSolver< _Scalar >::Base = RiccatiSolverBase<Scalar>

Definition at line 30 of file parallel-solver.hpp.

◆ Kernel

template<typename _Scalar>

using aligator::gar::ParallelRiccatiSolver< _Scalar >::Kernel = ProximalRiccatiKernel<Scalar>

Definition at line 31 of file parallel-solver.hpp.

◆ KnotType

template<typename _Scalar>

using aligator::gar::ParallelRiccatiSolver< _Scalar >::KnotType = LqrKnotTpl<Scalar>

Definition at line 32 of file parallel-solver.hpp.

◆ BlkView

template<typename _Scalar>

using aligator::gar::ParallelRiccatiSolver< _Scalar >::BlkView = BlkMatrix<VectorRef, -1, 1>

Definition at line 33 of file parallel-solver.hpp.

◆ allocator_type

template<typename _Scalar>

using aligator::gar::ParallelRiccatiSolver< _Scalar >::allocator_type = ::aligator::polymorphic_allocator

Definition at line 34 of file parallel-solver.hpp.

Constructor & Destructor Documentation

◆ ParallelRiccatiSolver()

template<typename _Scalar>

aligator::gar::ParallelRiccatiSolver< _Scalar >::ParallelRiccatiSolver	(	LqrProblemTpl< Scalar > &	problem,
		const uint	num_threads )

explicit

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS_WITH_ROW_TYPES()

template<typename _Scalar>

aligator::gar::ParallelRiccatiSolver< _Scalar >::ALIGATOR_DYNAMIC_TYPEDEFS_WITH_ROW_TYPES ( Scalar )

◆ backward()

template<typename _Scalar>

bool aligator::gar::ParallelRiccatiSolver< _Scalar >::backward ( const Scalar mueq )

overridevirtual

Implements aligator::gar::RiccatiSolverBase< _Scalar >.

◆ collapseFeedback()

template<typename _Scalar>

void aligator::gar::ParallelRiccatiSolver< _Scalar >::collapseFeedback ( )

inlineoverridevirtual

For applicable solvers, updates the first feedback gain in-place to correspond to the first Riccati gain.

See also: aligator::gar::ParallelRiccatiSolver for a non-trivial implementation.

Reimplemented from aligator::gar::RiccatiSolverBase< _Scalar >.

Definition at line 41 of file parallel-solver.hpp.

◆ assembleCondensedSystem()

template<typename _Scalar>

void aligator::gar::ParallelRiccatiSolver< _Scalar >::assembleCondensedSystem ( const Scalar mudyn )

Create the sparse representation of the reduced KKT system.

◆ forward()

template<typename _Scalar>

bool aligator::gar::ParallelRiccatiSolver< _Scalar >::forward	(	VectorOfVectors &	xs,
		VectorOfVectors &	us,
		VectorOfVectors &	vs,
		VectorOfVectors &	lbdas,
		const std::optional< ConstVectorRef > &	= std::nullopt ) const

override

◆ cycleAppend()

template<typename _Scalar>

void aligator::gar::ParallelRiccatiSolver< _Scalar >::cycleAppend ( const KnotType & knot )

overridevirtual

Cycle the solver data, given the specs from a given new knot.

Implements aligator::gar::RiccatiSolverBase< _Scalar >.

◆ getFeedforward()

template<typename _Scalar>

VectorRef aligator::gar::ParallelRiccatiSolver< _Scalar >::getFeedforward ( size_t i )

inlineoverridevirtual

Implements aligator::gar::RiccatiSolverBase< _Scalar >.

Definition at line 80 of file parallel-solver.hpp.

◆ getFeedback()

template<typename _Scalar>

RowMatrixRef aligator::gar::ParallelRiccatiSolver< _Scalar >::getFeedback ( size_t i )

inlineoverridevirtual

Implements aligator::gar::RiccatiSolverBase< _Scalar >.

Definition at line 81 of file parallel-solver.hpp.

◆ get_allocator()

template<typename _Scalar>

allocator_type aligator::gar::ParallelRiccatiSolver< _Scalar >::get_allocator ( ) const

inline

Definition at line 83 of file parallel-solver.hpp.

◆ getNumThreads()

template<typename _Scalar>

uint aligator::gar::ParallelRiccatiSolver< _Scalar >::getNumThreads ( ) const

inlinenoexcept

Number of parallel divisions in the problem: \(J+1\) in the math.

Definition at line 97 of file parallel-solver.hpp.

◆ initializeTridiagSystem()

template<typename _Scalar>

void aligator::gar::ParallelRiccatiSolver< _Scalar >::initializeTridiagSystem ( )

Initialize the buffers for the block-tridiagonal system.

◆ initialize()

template<typename _Scalar>

void aligator::gar::ParallelRiccatiSolver< _Scalar >::initialize ( )

protected

Member Data Documentation

◆ datas

template<typename _Scalar>

std::pmr::vector<StageFactor<Scalar> > aligator::gar::ParallelRiccatiSolver< _Scalar >::datas

Definition at line 85 of file parallel-solver.hpp.

◆ condensedKktSystem

template<typename _Scalar>

CondensedKkt aligator::gar::ParallelRiccatiSolver< _Scalar >::condensedKktSystem

Block-sparse condensed KKT system.

Definition at line 88 of file parallel-solver.hpp.

◆ condensedKktRhs

template<typename _Scalar>

ArenaMatrix<VectorXs> aligator::gar::ParallelRiccatiSolver< _Scalar >::condensedKktRhs

Contains the right-hand side and solution of the condensed KKT system.

Definition at line 90 of file parallel-solver.hpp.

◆ condensedKktSolution

template<typename _Scalar>

ArenaMatrix<VectorXs> aligator::gar::ParallelRiccatiSolver< _Scalar >::condensedKktSolution

Definition at line 90 of file parallel-solver.hpp.

◆ condensedErr

template<typename _Scalar>

ArenaMatrix<VectorXs> aligator::gar::ParallelRiccatiSolver< _Scalar >::condensedErr

Definition at line 90 of file parallel-solver.hpp.

◆ condensedThreshold

template<typename _Scalar>

Scalar aligator::gar::ParallelRiccatiSolver< _Scalar >::condensedThreshold = 1e-10

Tolerance on condensed KKT system.

Definition at line 92 of file parallel-solver.hpp.

◆ maxRefinementSteps

template<typename _Scalar>

uint aligator::gar::ParallelRiccatiSolver< _Scalar >::maxRefinementSteps = 5u

Max number of refinement steps (condensed solver)

Definition at line 94 of file parallel-solver.hpp.

◆ numThreads

template<typename _Scalar>

uint aligator::gar::ParallelRiccatiSolver< _Scalar >::numThreads

protected

Definition at line 103 of file parallel-solver.hpp.

◆ problem_

template<typename _Scalar>

LqrProblemTpl<Scalar>* aligator::gar::ParallelRiccatiSolver< _Scalar >::problem_

protected

Definition at line 104 of file parallel-solver.hpp.

◆ rhsDims_

template<typename _Scalar>

std::vector<long> aligator::gar::ParallelRiccatiSolver< _Scalar >::rhsDims_

protected

Definition at line 105 of file parallel-solver.hpp.

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

include/aligator/gar/parallel-solver.hpp

Classes

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ Base

◆ Kernel

◆ KnotType

◆ BlkView

◆ allocator_type

Constructor & Destructor Documentation

◆ ParallelRiccatiSolver()

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS_WITH_ROW_TYPES()

◆ backward()

◆ collapseFeedback()

◆ assembleCondensedSystem()

◆ forward()

◆ cycleAppend()

◆ getFeedforward()

◆ getFeedback()

◆ get_allocator()

◆ getNumThreads()

◆ initializeTridiagSystem()

◆ initialize()

Member Data Documentation

◆ datas

◆ condensedKktSystem

◆ condensedKktRhs

◆ condensedKktSolution

◆ condensedErr

◆ condensedThreshold

◆ maxRefinementSteps

◆ numThreads

◆ problem_

◆ rhsDims_