Namespaces
namespace	helpers

Classes
struct	DenseKernel
	A dense Bunch-Kaufman based kernel. More...

struct	LqrKnotTpl
	Struct describing a stage of a constrained LQ problem. More...

struct	LqrProblemTpl

class	ParallelRiccatiSolver
	A parallel-condensing LQ solver. More...

struct	ProximalRiccatiKernel
	Kernel for use in Riccati-like algorithms for the proximal LQ subproblem. More...

class	ProximalRiccatiSolver
	A Riccati-like solver for the proximal LQ subproblem in ProxDDP. More...

class	RiccatiSolverBase

class	RiccatiSolverDense
	A stagewise-dense Riccati solver. This algorithm uses a dense Bunch-Kaufman factorization at every stage. More...

struct	StageFactor
	Per-node struct for all computations in the factorization. More...

Functions
template<typename MatrixType, class A>
MatrixType::PlainObject	blockTridiagToDenseMatrix (const std::vector< MatrixType, A > &subdiagonal, const std::vector< MatrixType, A > &diagonal, const std::vector< MatrixType, A > &superdiagonal)

template<typename MatrixType, class A, typename InputType, typename OutType, typename Scalar = typename MatrixType::Scalar>
bool	blockTridiagMatMul (const std::vector< MatrixType, A > &Asub, const std::vector< MatrixType, A > &Adiag, const std::vector< MatrixType, A > &Asuper, const BlkMatrix< InputType, -1, 1 > &b, BlkMatrix< OutType, -1, 1 > &c, const Scalar beta)
	Evaluate c <- beta * c + A * b, where `A` is the block-tridiagonal matrix described by the first three inputs.

template<typename MatrixType, class A, class A2, typename RhsType, typename DecType>
bool	symmetricBlockTridiagSolve (std::vector< MatrixType, A > &subdiagonal, std::vector< MatrixType, A > &diagonal, const std::vector< MatrixType, A > &superdiagonal, BlkMatrix< RhsType, -1, 1 > &rhs, std::vector< DecType, A2 > &facs)
	Solve a symmetric block-tridiagonal \(Ax=b\) problem by in-place factorization. The subdiagonal will be used to store factorization coefficients.

template<typename MatrixType, class A, class A2, typename RhsType, typename DecType>
bool	blockTridiagRefinementStep (const std::vector< MatrixType, A > &transposedUfacs, const std::vector< MatrixType, A > &superdiagonal, const std::vector< DecType, A2 > &diagonalFacs, BlkMatrix< RhsType, -1, 1 > &rhs)
	Given the decomposed matrix data, just perform the backward-forward step of the algorithm.

template<typename MatrixType, class A, class A2, typename RhsType, typename DecType>
bool	symmetricBlockTridiagSolveDownLooking (std::vector< MatrixType, A > &subdiagonal, std::vector< MatrixType, A > &diagonal, std::vector< MatrixType, A > &superdiagonal, BlkMatrix< RhsType, -1, 1 > &rhs, std::vector< DecType, A2 > &facs)
	Solve a symmetric block-tridiagonal \(Ax=b\) problem by in-place factorization. The subdiagonal will be used to store factorization coefficients. This version starts by looking down from the top-left corner of the matrix.

template<typename Scalar>
bool	lqrKnotsSameDim (const LqrKnotTpl< Scalar > &lhs, const LqrKnotTpl< Scalar > &rhs)

template<typename Scalar>
std::ostream &	operator<< (std::ostream &oss, const LqrKnotTpl< Scalar > &self)

template<typename Scalar>
	ParallelRiccatiSolver (LqrProblemTpl< Scalar > &, const uint) -> ParallelRiccatiSolver< Scalar >

template<typename Scalar>
	ProximalRiccatiSolver (const LqrProblemTpl< Scalar > &) -> ProximalRiccatiSolver< Scalar >

template<class T, class A>
boost::span< T >	make_span_from_indices (std::vector< T, A > &vec, size_t i0, size_t i1)
	Create a boost::span object from a vector and two indices.

template<class T, class A>
boost::span< const T >	make_span_from_indices (const std::vector< T, A > &vec, size_t i0, size_t i1)
	Create a boost::span object from a vector and two indices.

template<typename Scalar>
void	lqrCreateSparseMatrix (const LqrProblemTpl< Scalar > &problem, const Scalar mueq, Eigen::SparseMatrix< Scalar > &mat, Eigen::Matrix< Scalar, -1, 1 > &rhs, bool update)

template<typename Scalar>
std::array< Scalar, 3 >	lqrComputeKktError (const LqrProblemTpl< Scalar > &problem, boost::span< const typename math_types< Scalar >::VectorXs > xs, boost::span< const typename math_types< Scalar >::VectorXs > us, boost::span< const typename math_types< Scalar >::VectorXs > vs, boost::span< const typename math_types< Scalar >::VectorXs > lbdas, const Scalar mueq, const std::optional< typename math_types< Scalar >::ConstVectorRef > &theta=std::nullopt, bool verbose=false)

template<typename Scalar>
uint	lqrNumRows (const LqrProblemTpl< Scalar > &problem)
	Compute the number of rows in the problem matrix.

template<typename Scalar>
void	lqrDenseSolutionToTraj (const LqrProblemTpl< Scalar > &problem, const typename math_types< Scalar >::ConstVectorRef solution, std::vector< typename math_types< Scalar >::VectorXs > &xs, std::vector< typename math_types< Scalar >::VectorXs > &us, std::vector< typename math_types< Scalar >::VectorXs > &vs, std::vector< typename math_types< Scalar >::VectorXs > &lbdas)
	Convert dense RHS solution to its trajectory [x,u,v,lambda] solution.

template<typename Scalar>
auto	lqrInitializeSolution (const LqrProblemTpl< Scalar > &problem)

Detailed Description

Copyright: Copyright (C) 2023-2024 LAAS-CNRS, 2023-2025 INRIA

Function Documentation

◆ blockTridiagToDenseMatrix()

template<typename MatrixType, class A>

MatrixType::PlainObject aligator::gar::blockTridiagToDenseMatrix	(	const std::vector< MatrixType, A > &	subdiagonal,
		const std::vector< MatrixType, A > &	diagonal,
		const std::vector< MatrixType, A > &	superdiagonal )

Definition at line 14 of file block-tridiagonal.hpp.

◆ blockTridiagMatMul()

template<typename MatrixType, class A, typename InputType, typename OutType, typename Scalar = typename MatrixType::Scalar>

bool aligator::gar::blockTridiagMatMul	(	const std::vector< MatrixType, A > &	Asub,
		const std::vector< MatrixType, A > &	Adiag,
		const std::vector< MatrixType, A > &	Asuper,
		const BlkMatrix< InputType, -1, 1 > &	b,
		BlkMatrix< OutType, -1, 1 > &	c,
		const Scalar	beta )

Evaluate c <- beta * c + A * b, where A is the block-tridiagonal matrix described by the first three inputs.

Definition at line 52 of file block-tridiagonal.hpp.

◆ symmetricBlockTridiagSolve()

template<typename MatrixType, class A, class A2, typename RhsType, typename DecType>

bool aligator::gar::symmetricBlockTridiagSolve	(	std::vector< MatrixType, A > &	subdiagonal,
		std::vector< MatrixType, A > &	diagonal,
		const std::vector< MatrixType, A > &	superdiagonal,
		BlkMatrix< RhsType, -1, 1 > &	rhs,
		std::vector< DecType, A2 > &	facs )

Solve a symmetric block-tridiagonal \(Ax=b\) problem by in-place factorization. The subdiagonal will be used to store factorization coefficients.

Definition at line 82 of file block-tridiagonal.hpp.

◆ blockTridiagRefinementStep()

template<typename MatrixType, class A, class A2, typename RhsType, typename DecType>

bool aligator::gar::blockTridiagRefinementStep	(	const std::vector< MatrixType, A > &	transposedUfacs,
		const std::vector< MatrixType, A > &	superdiagonal,
		const std::vector< DecType, A2 > &	diagonalFacs,
		BlkMatrix< RhsType, -1, 1 > &	rhs )

Given the decomposed matrix data, just perform the backward-forward step of the algorithm.

Parameters

transposedUfacs	- transposed U factors in the decomposition
superdiagonal	- superdiagonal of the original matrix
diagonalFacs	- diagonal factor decompositions

Definition at line 147 of file block-tridiagonal.hpp.

◆ symmetricBlockTridiagSolveDownLooking()

template<typename MatrixType, class A, class A2, typename RhsType, typename DecType>

bool aligator::gar::symmetricBlockTridiagSolveDownLooking	(	std::vector< MatrixType, A > &	subdiagonal,
		std::vector< MatrixType, A > &	diagonal,
		std::vector< MatrixType, A > &	superdiagonal,
		BlkMatrix< RhsType, -1, 1 > &	rhs,
		std::vector< DecType, A2 > &	facs )

Solve a symmetric block-tridiagonal \(Ax=b\) problem by in-place factorization. The subdiagonal will be used to store factorization coefficients. This version starts by looking down from the top-left corner of the matrix.

Definition at line 188 of file block-tridiagonal.hpp.

◆ lqrKnotsSameDim()

template<typename Scalar>

bool aligator::gar::lqrKnotsSameDim	(	const LqrKnotTpl< Scalar > &	lhs,
		const LqrKnotTpl< Scalar > &	rhs )

nodiscard

Definition at line 198 of file lqr-problem.hpp.

◆ operator<<()

template<typename Scalar>

std::ostream & aligator::gar::operator<<	(	std::ostream &	oss,
		const LqrKnotTpl< Scalar > &	self )

Definition at line 205 of file lqr-problem.hpp.

◆ ParallelRiccatiSolver()

template<typename Scalar>

aligator::gar::ParallelRiccatiSolver	(	LqrProblemTpl< Scalar > &	,
		const uint	) -> ParallelRiccatiSolver< Scalar >

◆ ProximalRiccatiSolver()

template<typename Scalar>

aligator::gar::ProximalRiccatiSolver ( const LqrProblemTpl< Scalar > & ) -> ProximalRiccatiSolver< Scalar >

◆ make_span_from_indices() [1/2]

template<class T, class A>

boost::span< T > aligator::gar::make_span_from_indices	(	std::vector< T, A > &	vec,
		size_t	i0,
		size_t	i1 )

inline

Create a boost::span object from a vector and two indices.

Definition at line 17 of file riccati-kernel.hpp.

◆ make_span_from_indices() [2/2]

template<class T, class A>

boost::span< const T > aligator::gar::make_span_from_indices	(	const std::vector< T, A > &	vec,
		size_t	i0,
		size_t	i1 )

inline

Create a boost::span object from a vector and two indices.

Definition at line 24 of file riccati-kernel.hpp.

◆ lqrCreateSparseMatrix()

template<typename Scalar>

void aligator::gar::lqrCreateSparseMatrix	(	const LqrProblemTpl< Scalar > &	problem,
		const Scalar	mueq,
		Eigen::SparseMatrix< Scalar > &	mat,
		Eigen::Matrix< Scalar, -1, 1 > &	rhs,
		bool	update )

◆ lqrComputeKktError()

template<typename Scalar>

std::array< Scalar, 3 > aligator::gar::lqrComputeKktError	(	const LqrProblemTpl< Scalar > &	problem,
		boost::span< const typename math_types< Scalar >::VectorXs >	xs,
		boost::span< const typename math_types< Scalar >::VectorXs >	us,
		boost::span< const typename math_types< Scalar >::VectorXs >	vs,
		boost::span< const typename math_types< Scalar >::VectorXs >	lbdas,
		const Scalar	mueq,
		const std::optional< typename math_types< Scalar >::ConstVectorRef > &	theta = std::nullopt,
		bool	verbose = false )

nodiscard

◆ lqrNumRows()

template<typename Scalar>

uint aligator::gar::lqrNumRows ( const LqrProblemTpl< Scalar > & problem )

Compute the number of rows in the problem matrix.

Definition at line 64 of file utils.hpp.

◆ lqrDenseSolutionToTraj()

template<typename Scalar>

void aligator::gar::lqrDenseSolutionToTraj	(	const LqrProblemTpl< Scalar > &	problem,
		const typename math_types< Scalar >::ConstVectorRef	solution,
		std::vector< typename math_types< Scalar >::VectorXs > &	xs,
		std::vector< typename math_types< Scalar >::VectorXs > &	us,
		std::vector< typename math_types< Scalar >::VectorXs > &	vs,
		std::vector< typename math_types< Scalar >::VectorXs > &	lbdas )

Convert dense RHS solution to its trajectory [x,u,v,lambda] solution.

Definition at line 80 of file utils.hpp.

◆ lqrInitializeSolution()

template<typename Scalar>

auto aligator::gar::lqrInitializeSolution ( const LqrProblemTpl< Scalar > & problem )

nodiscard

Definition at line 113 of file utils.hpp.

Namespaces

Classes

Functions

Detailed Description

Function Documentation

◆ blockTridiagToDenseMatrix()

◆ blockTridiagMatMul()

◆ symmetricBlockTridiagSolve()

◆ blockTridiagRefinementStep()

◆ symmetricBlockTridiagSolveDownLooking()

◆ lqrKnotsSameDim()

◆ operator<<()

◆ ParallelRiccatiSolver()

◆ ProximalRiccatiSolver()

◆ make_span_from_indices() [1/2]

◆ make_span_from_indices() [2/2]

◆ lqrCreateSparseMatrix()

◆ lqrComputeKktError()

◆ lqrNumRows()

◆ lqrDenseSolutionToTraj()

◆ lqrInitializeSolution()