Namespaces
namespace	helpers

Classes
struct	LQRKnotTpl
	Struct describing a stage of a constrained LQ problem. More...

struct	LQRProblemTpl

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...

struct	workrange_t

Typedefs
using	uint = unsigned int

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

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

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

template<typename MatrixType , typename RhsType , typename DecType >
bool	symmetricBlockTridiagSolveDownLooking (std::vector< MatrixType > &subdiagonal, std::vector< MatrixType > &diagonal, std::vector< MatrixType > &superdiagonal, BlkMatrix< RhsType, -1, 1 > &rhs, std::vector< DecType > &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 >
std::ostream &	operator<< (std::ostream &oss, const LQRKnotTpl< Scalar > &self)

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 mudyn, 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 mudyn, const Scalar mueq, const std::optional< typename math_types< Scalar >::ConstVectorRef > &theta_, bool verbose=false)

template<typename Scalar >
bool	lqrDenseMatrix (const LQRProblemTpl< Scalar > &problem, Scalar mudyn, Scalar mueq, typename math_types< Scalar >::MatrixXs &mat, typename math_types< Scalar >::VectorXs &rhs)
	Fill in a KKT constraint matrix and vector for the given LQ problem with the given dual-regularization parameters `mudyn` and `mueq`.

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

template<typename Scalar >
auto	lqrDenseMatrix (const LQRProblemTpl< Scalar > &problem, Scalar mudyn, Scalar mueq)
	Fill in a KKT constraint matrix and vector for the given LQ problem with the given dual-regularization parameters `mudyn` and `mueq`.

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)

workrange_t	get_work (uint horz, uint tid, uint num_threads)

template void	lqrCreateSparseMatrix< context::Scalar > (const LQRProblemTpl< context::Scalar > &problem, const context::Scalar mudyn, const context::Scalar mueq, Eigen::SparseMatrix< context::Scalar > &mat, context::VectorXs &rhs, bool update)

template std::array< context::Scalar, 3 >	lqrComputeKktError< context::Scalar > (const LQRProblemTpl< context::Scalar > &, boost::span< const context::VectorXs >, boost::span< const context::VectorXs >, boost::span< const context::VectorXs >, boost::span< const context::VectorXs >, const context::Scalar, const context::Scalar, const std::optional< context::ConstVectorRef > &, bool)

template auto	lqrDenseMatrix< context::Scalar > (const LQRProblemTpl< context::Scalar > &, context::Scalar, context::Scalar)

Detailed Description

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

Author: Wilson Jallet

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

Typedef Documentation

◆ uint

using aligator::gar::uint = unsigned int

Definition at line 7 of file work.hpp.

Function Documentation

◆ blockTridiagToDenseMatrix()

template<typename MatrixType >

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

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

◆ blockTridiagMatMul()

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

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

Definition at line 50 of file block-tridiagonal.hpp.

◆ symmetricBlockTridiagSolve()

template<typename MatrixType , typename RhsType , typename DecType >

bool aligator::gar::symmetricBlockTridiagSolve	(	std::vector< MatrixType > &	subdiagonal,
		std::vector< MatrixType > &	diagonal,
		const std::vector< MatrixType > &	superdiagonal,
		BlkMatrix< RhsType, -1, 1 > &	rhs,
		std::vector< DecType > &	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 79 of file block-tridiagonal.hpp.

◆ blockTridiagRefinementStep()

template<typename MatrixType , typename RhsType , typename DecType >

bool aligator::gar::blockTridiagRefinementStep	(	const std::vector< MatrixType > &	transposedUfacs,
		const std::vector< MatrixType > &	superdiagonal,
		const std::vector< DecType > &	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 143 of file block-tridiagonal.hpp.

◆ symmetricBlockTridiagSolveDownLooking()

template<typename MatrixType , typename RhsType , typename DecType >

bool aligator::gar::symmetricBlockTridiagSolveDownLooking	(	std::vector< MatrixType > &	subdiagonal,
		std::vector< MatrixType > &	diagonal,
		std::vector< MatrixType > &	superdiagonal,
		BlkMatrix< RhsType, -1, 1 > &	rhs,
		std::vector< DecType > &	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 182 of file block-tridiagonal.hpp.

◆ operator<<()

template<typename Scalar >

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

Definition at line 110 of file lqr-problem.hpp.

◆ 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 22 of file riccati-impl.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 29 of file riccati-impl.hpp.

◆ lqrCreateSparseMatrix()

template<typename Scalar >

void aligator::gar::lqrCreateSparseMatrix	(	const LQRProblemTpl< Scalar > &	problem,
		const Scalar	mudyn,
		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	mudyn,
		const Scalar	mueq,
		const std::optional< typename math_types< Scalar >::ConstVectorRef > &	theta_,
		bool	verbose = false )

◆ lqrDenseMatrix() [1/2]

template<typename Scalar >

bool aligator::gar::lqrDenseMatrix	(	const LQRProblemTpl< Scalar > &	problem,
		Scalar	mudyn,
		Scalar	mueq,
		typename math_types< Scalar >::MatrixXs &	mat,
		typename math_types< Scalar >::VectorXs &	rhs )

Fill in a KKT constraint matrix and vector for the given LQ problem with the given dual-regularization parameters mudyn and mueq.

Returns: Whether the matrices were successfully allocated.

◆ lqrNumRows()

template<typename Scalar >

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

Compute the number of rows in the problem matrix.

Definition at line 72 of file utils.hpp.

◆ lqrDenseMatrix() [2/2]

template<typename Scalar >

auto aligator::gar::lqrDenseMatrix	(	const LQRProblemTpl< Scalar > &	problem,
		Scalar	mudyn,
		Scalar	mueq )

Fill in a KKT constraint matrix and vector for the given LQ problem with the given dual-regularization parameters mudyn and mueq.

Definition at line 88 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 107 of file utils.hpp.

◆ lqrInitializeSolution()

template<typename Scalar >

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

Definition at line 140 of file utils.hpp.

◆ get_work()

workrange_t aligator::gar::get_work	(	uint	horz,
		uint	tid,
		uint	num_threads )

inline

Definition at line 14 of file work.hpp.

◆ lqrCreateSparseMatrix< context::Scalar >()

template void aligator::gar::lqrCreateSparseMatrix< context::Scalar >	(	const LQRProblemTpl< context::Scalar > &	problem,
		const context::Scalar	mudyn,
		const context::Scalar	mueq,
		Eigen::SparseMatrix< context::Scalar > &	mat,
		context::VectorXs &	rhs,
		bool	update )

◆ lqrComputeKktError< context::Scalar >()

template std::array< context::Scalar, 3 > aligator::gar::lqrComputeKktError< context::Scalar >	(	const LQRProblemTpl< context::Scalar > &	,
		boost::span< const context::VectorXs >	,
		boost::span< const context::VectorXs >	,
		boost::span< const context::VectorXs >	,
		boost::span< const context::VectorXs >	,
		const context::Scalar	,
		const context::Scalar	,
		const std::optional< context::ConstVectorRef > &	,
		bool	)

◆ lqrDenseMatrix< context::Scalar >()

template auto aligator::gar::lqrDenseMatrix< context::Scalar >	(	const LQRProblemTpl< context::Scalar > &	,
		context::Scalar	,
		context::Scalar	)

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ uint

Function Documentation

◆ blockTridiagToDenseMatrix()

◆ blockTridiagMatMul()

◆ symmetricBlockTridiagSolve()

◆ blockTridiagRefinementStep()

◆ symmetricBlockTridiagSolveDownLooking()

◆ operator<<()

◆ make_span_from_indices() [1/2]

◆ make_span_from_indices() [2/2]

◆ lqrCreateSparseMatrix()

◆ lqrComputeKktError()

◆ lqrDenseMatrix() [1/2]

◆ lqrNumRows()

◆ lqrDenseMatrix() [2/2]

◆ lqrDenseSolutionToTraj()

◆ lqrInitializeSolution()

◆ get_work()

◆ lqrCreateSparseMatrix< context::Scalar >()

◆ lqrComputeKktError< context::Scalar >()

◆ lqrDenseMatrix< context::Scalar >()