Namespaces
namespace	detail
namespace	slicing

Classes
class	scope_exit
	scope_exit is a general-purpose scope guard intended to call its exit function when a scope is exited. More...
class	IntrusiveSharedPtr
	A custom intrusive shared pointer implementation without thread synchronization overhead. More...
class	OCP
	This class allows the user to pose and solve a constrained optimal control problem (OCP) in a variety of ways. More...
class	VariableBlock
	A submatrix of autodiff variables with reference semantics. More...
class	VariableMatrix
	A matrix of autodiff variables. More...
class	Gradient
	This class calculates the gradient of a variable with respect to a vector of variables. More...
struct	InteriorPointMatrixCallbacks
	Matrix callbacks for the interior-point method solver. More...
struct	FilterEntry
	Filter entry consisting of cost and constraint violation. More...
class	Filter
	Step filter. More...
class	Jacobian
	This class calculates the Jacobian of a vector of variables with respect to a vector of variables. More...
class	RegularizedLDLT
	Solves systems of linear equations using a regularized LDLT factorization. More...
class	SetupProfiler
	Records the number of profiler measurements (start/stop pairs) and the average duration between each start and stop call. More...
class	Problem
	This class allows the user to pose a constrained nonlinear optimization problem in natural mathematical notation and solve it. More...
class	Inertia
	Represents the inertia of a matrix (the number of positive, negative, and zero eigenvalues). More...
struct	Options
	Solver options. More...
class	function_ref
class	function_ref< R(Args...)>
	An implementation of std::function_ref, a lightweight non-owning reference to a callable. More...
struct	IterationInfo
	Solver iteration information exposed to an iteration callback. More...
class	Hessian
	This class calculates the Hessian of a variable with respect to a vector of variables. More...
class	Variable
	An autodiff variable pointing to an expression node. More...
struct	EqualityConstraints
	A vector of equality constraints of the form cₑ(x) = 0. More...
struct	InequalityConstraints
	A vector of inequality constraints of the form cᵢ(x) ≥ 0. More...
class	Slice
	Represents a sequence of elements in an iterable object. More...
class	Spy
	Writes the sparsity pattern of a sparse matrix to a file. More...
struct	Bounds
	Bound constraint metadata. More...
class	PoolResource
	This class implements a pool memory resource. More...
class	PoolAllocator
	This class is an allocator for the pool resource. More...
class	SleipnirBase
	Marker interface for concepts to determine whether a given scalar or matrix type belongs to Sleipnir. More...
struct	NewtonMatrixCallbacks
	Matrix callbacks for the Newton's method solver. More...
struct	SQPMatrixCallbacks
	Matrix callbacks for the Sequential Quadratic Programming (SQP) solver. More...
class	ScopedProfiler
	Starts a profiler in the constructor and stops it in the destructor. More...
struct	MultistartResult
	The result of a multistart solve. More...
class	SolveProfiler
	Records the number of profiler measurements (start/stop pairs) and the average duration between each start and stop call. More...

Concepts
concept	SleipnirType
concept	MatrixLike
concept	ScalarLike
concept	EigenMatrixLike
concept	SleipnirMatrixLike
concept	SleipnirScalarLike

Enumerations
enum class	TimestepMethod : uint8_t { FIXED , VARIABLE , VARIABLE_SINGLE }
	Enum describing the type of system timestep. More...
enum class	TranscriptionMethod : uint8_t { DIRECT_TRANSCRIPTION , DIRECT_COLLOCATION , SINGLE_SHOOTING }
	Enum describing an OCP transcription method. More...
enum class	DynamicsType : uint8_t { EXPLICIT_ODE , DISCRETE }
	Enum describing a type of system dynamics constraints. More...
enum class	ExitStatus : int8_t { SUCCESS = 0 , CALLBACK_REQUESTED_STOP = 1 , TOO_FEW_DOFS = -1 , LOCALLY_INFEASIBLE = -2 , GLOBALLY_INFEASIBLE = -3 , FACTORIZATION_FAILED = -4 , LINE_SEARCH_FAILED = -5 , NONFINITE_INITIAL_COST_OR_CONSTRAINTS = -6 , DIVERGING_ITERATES = -7 , MAX_ITERATIONS_EXCEEDED = -8 , TIMEOUT = -9 }
	Solver exit status. Negative values indicate failure. More...
enum class	ExpressionType : uint8_t { NONE , CONSTANT , LINEAR , QUADRATIC , NONLINEAR }
	Expression type. More...
enum class	IterationType : uint8_t { NORMAL , ACCEPTED_SOC , REJECTED_SOC }
	Iteration type. More...

Functions
template<typename T, typename... Args>
IntrusiveSharedPtr< T >	make_intrusive_shared (Args &&... args)
	Constructs an object of type T and wraps it in an intrusive shared pointer using args as the parameter list for the constructor of T.
template<typename T, typename Alloc, typename... Args>
IntrusiveSharedPtr< T >	allocate_intrusive_shared (Alloc alloc, Args &&... args)
	Constructs an object of type T and wraps it in an intrusive shared pointer using alloc as the storage allocator of T and args as the parameter list for the constructor of T.
template class	EXPORT_TEMPLATE_DECLARE (SLEIPNIR_DLLEXPORT) OCP< double >
template<typename Derived>
	VariableMatrix (const Eigen::MatrixBase< Derived > &) -> VariableMatrix< typename Derived::Scalar >
template<typename Derived>
	VariableMatrix (const Eigen::DiagonalBase< Derived > &) -> VariableMatrix< typename Derived::Scalar >
template<typename Scalar>
VariableMatrix< Scalar >	cwise_reduce (const VariableMatrix< Scalar > &lhs, const VariableMatrix< Scalar > &rhs, function_ref< Variable< Scalar >(const Variable< Scalar > &x, const Variable< Scalar > &y)> binary_op)
	Applies a coefficient-wise reduce operation to two matrices.
template<typename Scalar>
VariableMatrix< Scalar >	block (std::initializer_list< std::initializer_list< VariableMatrix< Scalar > > > list)
	Assemble a VariableMatrix from a nested list of blocks.
template<typename Scalar>
VariableMatrix< Scalar >	block (const std::vector< std::vector< VariableMatrix< Scalar > > > &list)
	Assemble a VariableMatrix from a nested list of blocks.
template<typename Scalar>
VariableMatrix< Scalar >	solve (const VariableMatrix< Scalar > &A, const VariableMatrix< Scalar > &B)
	Solves the VariableMatrix equation AX = B for X.
template SLEIPNIR_DLLEXPORT VariableMatrix< double >	solve (const VariableMatrix< double > &A, const VariableMatrix< double > &B)
template<typename Scalar>
Scalar	fraction_to_the_boundary_rule (const Eigen::Vector< Scalar, Eigen::Dynamic > &x, const Eigen::Vector< Scalar, Eigen::Dynamic > &p, Scalar τ)
	Applies fraction-to-the-boundary rule to a variable and its iterate, then returns a fraction of the iterate step size within (0, 1].
template<typename R, typename... Args>
constexpr void	swap (function_ref< R(Args...)> &lhs, function_ref< R(Args...)> &rhs) noexcept
	Swaps the referred callables of lhs and rhs.
template<typename R, typename... Args>
	function_ref (R(*)(Args...)) -> function_ref< R(Args...)>
template<template< typename > typename T, typename Scalar> requires SleipnirMatrixLike<T<Scalar>, Scalar>
	Variable (T< Scalar >) -> Variable< Scalar >
template<std::floating_point T>
	Variable (T) -> Variable< T >
template<std::integral T>
	Variable (T) -> Variable< T >
template<typename Scalar>
Variable< Scalar >	abs (const Variable< Scalar > &x)
	abs() for Variables.
template<typename Scalar>
Variable< Scalar >	acos (const Variable< Scalar > &x)
	acos() for Variables.
template<typename Scalar>
Variable< Scalar >	asin (const Variable< Scalar > &x)
	asin() for Variables.
template<typename Scalar>
Variable< Scalar >	atan (const Variable< Scalar > &x)
	atan() for Variables.
template<typename Scalar>
Variable< Scalar >	atan2 (const ScalarLike auto &y, const Variable< Scalar > &x)
	atan2() for Variables.
template<typename Scalar>
Variable< Scalar >	atan2 (const Variable< Scalar > &y, const ScalarLike auto &x)
	atan2() for Variables.
template<typename Scalar>
Variable< Scalar >	atan2 (const Variable< Scalar > &y, const Variable< Scalar > &x)
	atan2() for Variables.
template<typename Scalar>
Variable< Scalar >	cbrt (const Variable< Scalar > &x)
	cbrt() for Variables.
template<typename Scalar>
Variable< Scalar >	cos (const Variable< Scalar > &x)
	cos() for Variables.
template<typename Scalar>
Variable< Scalar >	cosh (const Variable< Scalar > &x)
	cosh() for Variables.
template<typename Scalar>
Variable< Scalar >	erf (const Variable< Scalar > &x)
	erf() for Variables.
template<typename Scalar>
Variable< Scalar >	exp (const Variable< Scalar > &x)
	exp() for Variables.
template<typename Scalar>
Variable< Scalar >	hypot (const ScalarLike auto &x, const Variable< Scalar > &y)
	hypot() for Variables.
template<typename Scalar>
Variable< Scalar >	hypot (const Variable< Scalar > &x, const ScalarLike auto &y)
	hypot() for Variables.
template<typename Scalar>
Variable< Scalar >	hypot (const Variable< Scalar > &x, const Variable< Scalar > &y)
	hypot() for Variables.
template<typename Scalar>
Variable< Scalar >	log (const Variable< Scalar > &x)
	log() for Variables.
template<typename Scalar>
Variable< Scalar >	log10 (const Variable< Scalar > &x)
	log10() for Variables.
template<typename Scalar>
Variable< Scalar >	pow (const ScalarLike auto &base, const Variable< Scalar > &power)
	pow() for Variables.
template<typename Scalar>
Variable< Scalar >	pow (const Variable< Scalar > &base, const ScalarLike auto &power)
	pow() for Variables.
template<typename Scalar>
Variable< Scalar >	pow (const Variable< Scalar > &base, const Variable< Scalar > &power)
	pow() for Variables.
template<typename Scalar>
Variable< Scalar >	sign (const Variable< Scalar > &x)
	sign() for Variables.
template<typename Scalar>
Variable< Scalar >	sin (const Variable< Scalar > &x)
	sin() for Variables.
template<typename Scalar>
Variable< Scalar >	sinh (const Variable< Scalar > &x)
	sinh() for Variables.
template<typename Scalar>
Variable< Scalar >	sqrt (const Variable< Scalar > &x)
	sqrt() for Variables.
template<typename Scalar>
Variable< Scalar >	tan (const Variable< Scalar > &x)
	tan() for Variables.
template<typename Scalar>
Variable< Scalar >	tanh (const Variable< Scalar > &x)
	tanh() for Variables.
template<typename Scalar>
Variable< Scalar >	hypot (const Variable< Scalar > &x, const Variable< Scalar > &y, const Variable< Scalar > &z)
	hypot() for Variables.
template<typename Scalar, ScalarLike LHS, ScalarLike RHS> requires SleipnirScalarLike<LHS, Scalar> \|\| SleipnirScalarLike<RHS, Scalar>
auto	make_constraints (LHS &&lhs, RHS &&rhs)
template<typename Scalar, ScalarLike LHS, MatrixLike RHS> requires SleipnirScalarLike<LHS, Scalar> \|\| SleipnirMatrixLike<RHS, Scalar>
auto	make_constraints (LHS &&lhs, RHS &&rhs)
template<typename Scalar, MatrixLike LHS, ScalarLike RHS> requires SleipnirMatrixLike<LHS, Scalar> \|\| SleipnirScalarLike<RHS, Scalar>
auto	make_constraints (LHS &&lhs, RHS &&rhs)
template<typename Scalar, MatrixLike LHS, MatrixLike RHS> requires SleipnirMatrixLike<LHS, Scalar> \|\| SleipnirMatrixLike<RHS, Scalar>
auto	make_constraints (LHS &&lhs, RHS &&rhs)
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && (!SleipnirType<RHS>)
auto	operator== (LHS &&lhs, RHS &&rhs)
	Equality operator that returns an equality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && (!SleipnirType<LHS>) && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && SleipnirType<RHS>
auto	operator== (LHS &&lhs, RHS &&rhs)
	Equality operator that returns an equality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && SleipnirType<RHS>
auto	operator== (LHS &&lhs, RHS &&rhs)
	Equality operator that returns an equality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && (SleipnirType<LHS> \|\| SleipnirType<RHS>)
auto	operator< (LHS &&lhs, RHS &&rhs)
	Less-than comparison operator that returns an inequality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && (SleipnirType<LHS> \|\| SleipnirType<RHS>)
auto	operator<= (LHS &&lhs, RHS &&rhs)
	Less-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && (SleipnirType<LHS> \|\| SleipnirType<RHS>)
auto	operator> (LHS &&lhs, RHS &&rhs)
	Greater-than comparison operator that returns an inequality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && (!SleipnirType<RHS>)
auto	operator>= (LHS &&lhs, RHS &&rhs)
	Greater-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && (!SleipnirType<LHS>) && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && SleipnirType<RHS>
auto	operator>= (LHS &&lhs, RHS &&rhs)
	Greater-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.
template<typename LHS, typename RHS> requires (ScalarLike<LHS> \|\| MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> \|\| MatrixLike<RHS>) && SleipnirType<RHS>
auto	operator>= (LHS &&lhs, RHS &&rhs)
	Greater-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.
template<typename L, typename X, typename U> requires (ScalarLike<L> \|\| MatrixLike<L>) && SleipnirType<X> && (ScalarLike<U> \|\| MatrixLike<U>)
auto	bounds (L &&l, X &&x, U &&u)
	Helper function for creating bound constraints.
template<typename Scalar>
Bounds< Scalar >	get_bounds (std::span< Variable< Scalar > > decision_variables, std::span< Variable< Scalar > > inequality_constraints, const Eigen::SparseMatrix< Scalar, Eigen::RowMajor > &A_i)
	A "bound constraint" is any linear constraint in one scalar variable.
template<typename Derived> requires (static_cast<bool>(Eigen::DenseBase<Derived>::IsVectorAtCompileTime))
void	project_onto_bounds (Eigen::DenseBase< Derived > &x, std::span< const std::pair< typename Eigen::DenseBase< Derived >::Scalar, typename Eigen::DenseBase< Derived >::Scalar > > decision_variable_indices_to_bounds, const typename Eigen::DenseBase< Derived >::Scalar κ_1=typename Eigen::DenseBase< Derived >::Scalar(1e-2), const typename Eigen::DenseBase< Derived >::Scalar κ_2=typename Eigen::DenseBase< Derived >::Scalar(1e-2))
	Projects the decision variables onto the given bounds, while ensuring some configurable distance from the boundary if possible.
SLEIPNIR_DLLEXPORT PoolResource &	global_pool_resource ()
	Returns a global pool memory resource.
template<typename T>
PoolAllocator< T >	global_pool_allocator ()
	Returns an allocator for a global pool memory resource.
template<typename Scalar>
Scalar	error_estimate (const Eigen::Vector< Scalar, Eigen::Dynamic > &g)
	Returns the error estimate using the KKT conditions for Newton's method.
template<typename Scalar>
Scalar	error_estimate (const Eigen::Vector< Scalar, Eigen::Dynamic > &g, const Eigen::SparseMatrix< Scalar > &A_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &y)
	Returns the error estimate using the KKT conditions for SQP.
template<typename Scalar>
Scalar	error_estimate (const Eigen::Vector< Scalar, Eigen::Dynamic > &g, const Eigen::SparseMatrix< Scalar > &A_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e, const Eigen::SparseMatrix< Scalar > &A_i, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_i, const Eigen::Vector< Scalar, Eigen::Dynamic > &s, const Eigen::Vector< Scalar, Eigen::Dynamic > &y, const Eigen::Vector< Scalar, Eigen::Dynamic > &z, Scalar μ)
	Returns the error estimate using the KKT conditions for the interior-point method.
void	unreachable ()
template<typename... T>
void	print (fmt::format_string< T... > fmt, T &&... args)
	Wrapper around fmt::print() that squelches write failure exceptions.
template<typename... T>
void	print (std::FILE *f, fmt::format_string< T... > fmt, T &&... args)
	Wrapper around fmt::print() that squelches write failure exceptions.
template<typename... T>
void	println (fmt::format_string< T... > fmt, T &&... args)
	Wrapper around fmt::println() that squelches write failure exceptions.
template<typename... T>
void	println (std::FILE *f, fmt::format_string< T... > fmt, T &&... args)
	Wrapper around fmt::println() that squelches write failure exceptions.
template<typename Scalar>
bool	is_equality_locally_infeasible (const Eigen::SparseMatrix< Scalar > &A_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e)
	Returns true if the problem's equality constraints are locally infeasible.
template<typename Scalar>
bool	is_inequality_locally_infeasible (const Eigen::SparseMatrix< Scalar > &A_i, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_i)
	Returns true if the problem's inequality constraints are locally infeasible.
template<typename Scalar, typename DecisionVariables>
MultistartResult< Scalar, DecisionVariables >	multistart (function_ref< MultistartResult< Scalar, DecisionVariables >(const DecisionVariables &initial_guess)> solve, std::span< const DecisionVariables > initial_guesses)
	Solves an optimization problem from different starting points in parallel, then returns the solution with the lowest cost.
template<typename Scalar>
Scalar	kkt_error (const Eigen::Vector< Scalar, Eigen::Dynamic > &g)
	Returns the KKT error for Newton's method.
template<typename Scalar>
Scalar	kkt_error (const Eigen::Vector< Scalar, Eigen::Dynamic > &g, const Eigen::SparseMatrix< Scalar > &A_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &y)
	Returns the KKT error for Sequential Quadratic Programming.
template<typename Scalar>
Scalar	kkt_error (const Eigen::Vector< Scalar, Eigen::Dynamic > &g, const Eigen::SparseMatrix< Scalar > &A_e, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e, const Eigen::SparseMatrix< Scalar > &A_i, const Eigen::Vector< Scalar, Eigen::Dynamic > &c_i, const Eigen::Vector< Scalar, Eigen::Dynamic > &s, const Eigen::Vector< Scalar, Eigen::Dynamic > &y, const Eigen::Vector< Scalar, Eigen::Dynamic > &z, Scalar μ)
	Returns the KKT error for the interior-point method.
template<typename Rep, typename Period = std::ratio<1>>
constexpr double	to_ms (const std::chrono::duration< Rep, Period > &duration)
	Converts std::chrono::duration to a number of milliseconds rounded to three decimals.
template<typename Scalar>
std::string	power_of_10 (Scalar value)
	Renders value as power of 10.
template<typename Scalar>
void	print_too_few_dofs_error (const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e)
	Prints error for too few degrees of freedom.
template<typename Scalar>
void	print_c_e_local_infeasibility_error (const Eigen::Vector< Scalar, Eigen::Dynamic > &c_e)
	Prints equality constraint local infeasibility error.
template<typename Scalar>
void	print_c_i_local_infeasibility_error (const Eigen::Vector< Scalar, Eigen::Dynamic > &c_i)
	Prints inequality constraint local infeasibility error.
void	print_bound_constraint_global_infeasibility_error (const std::span< const std::pair< Eigen::Index, Eigen::Index > > conflicting_lower_upper_bound_indices)
template<typename Scalar, typename Rep, typename Period = std::ratio<1>>
void	print_iteration_diagnostics (int iterations, IterationType type, const std::chrono::duration< Rep, Period > &time, Scalar error, Scalar cost, Scalar infeasibility, Scalar complementarity, Scalar μ, Scalar δ, Scalar primal_α, Scalar primal_α_max, Scalar α_reduction_factor, Scalar dual_α)
	Prints diagnostics for the current iteration.
void	print_bottom_iteration_diagnostics ()
	Prints bottom of iteration diagnostics table.
template<int Width> requires (Width > 0)
std::string	histogram (double value)
	Renders histogram of the given normalized value.
void	print_solver_diagnostics (const gch::small_vector< SolveProfiler > &solve_profilers)
	Prints solver diagnostics.
void	print_autodiff_diagnostics (const gch::small_vector< SetupProfiler > &setup_profilers)
	Prints autodiff diagnostics.

Enumeration Type Documentation

◆ DynamicsType

enum class slp::DynamicsType : uint8_t

strong

Enum describing a type of system dynamics constraints.

Enumerator
EXPLICIT_ODE	The dynamics are a function in the form dx/dt = f(t, x, u).
DISCRETE	The dynamics are a function in the form xₖ₊₁ = f(t, xₖ, uₖ).

◆ ExitStatus

enum class slp::ExitStatus : int8_t

strong

Solver exit status. Negative values indicate failure.

Enumerator
SUCCESS	Solved the problem to the desired tolerance.
CALLBACK_REQUESTED_STOP	The solver returned its solution so far after the user requested a stop.
TOO_FEW_DOFS	The solver determined the problem to be overconstrained and gave up.
LOCALLY_INFEASIBLE	The solver determined the problem to be locally infeasible and gave up.
GLOBALLY_INFEASIBLE	The problem setup frontend determined the problem to have an empty feasible region.
FACTORIZATION_FAILED	The linear system factorization failed.
LINE_SEARCH_FAILED	The backtracking line search failed, and the problem isn't locally infeasible.
NONFINITE_INITIAL_COST_OR_CONSTRAINTS	The solver encountered nonfinite initial cost or constraints and gave up.
DIVERGING_ITERATES	The solver encountered diverging primal iterates xₖ and/or sₖ and gave up.
MAX_ITERATIONS_EXCEEDED	The solver returned its solution so far after exceeding the maximum number of iterations.
TIMEOUT	The solver returned its solution so far after exceeding the maximum elapsed wall clock time.

◆ ExpressionType

enum class slp::ExpressionType : uint8_t

strong

Expression type.

Used for autodiff caching.

Enumerator
NONE	There is no expression.
CONSTANT	The expression is a constant.
LINEAR	The expression is composed of linear and lower-order operators.
QUADRATIC	The expression is composed of quadratic and lower-order operators.
NONLINEAR	The expression is composed of nonlinear and lower-order operators.

◆ IterationType

enum class slp::IterationType : uint8_t

strong

Iteration type.

Enumerator
NORMAL	Normal iteration.
ACCEPTED_SOC	Accepted second-order correction iteration.
REJECTED_SOC	Rejected second-order correction iteration.

◆ TimestepMethod

enum class slp::TimestepMethod : uint8_t

strong

Enum describing the type of system timestep.

Enumerator
FIXED	The timestep is a fixed constant.
VARIABLE	The timesteps are allowed to vary as independent decision variables.
VARIABLE_SINGLE	The timesteps are equal length but allowed to vary as a single decision variable.

◆ TranscriptionMethod

enum class slp::TranscriptionMethod : uint8_t

strong

Enum describing an OCP transcription method.

Enumerator
DIRECT_TRANSCRIPTION	Each state is a decision variable constrained to the integrated dynamics of the previous state.
DIRECT_COLLOCATION	The trajectory is modeled as a series of cubic polynomials where the centerpoint slope is constrained.
SINGLE_SHOOTING	States depend explicitly as a function of all previous states and all previous inputs.

Function Documentation

◆ abs()

template<typename Scalar>

Variable< Scalar > slp::abs ( const Variable< Scalar > & x )

abs() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ acos()

template<typename Scalar>

Variable< Scalar > slp::acos ( const Variable< Scalar > & x )

acos() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ allocate_intrusive_shared()

template<typename T, typename Alloc, typename... Args>

IntrusiveSharedPtr< T > slp::allocate_intrusive_shared	(	Alloc	alloc,
		Args &&...	args )

Constructs an object of type T and wraps it in an intrusive shared pointer using alloc as the storage allocator of T and args as the parameter list for the constructor of T.

Template Parameters

T	Type of object for intrusive shared pointer.
Alloc	Type of allocator for T.
Args	Types of constructor arguments.

Parameters

alloc	The allocator for T.
args	Constructor arguments for T.

◆ asin()

template<typename Scalar>

Variable< Scalar > slp::asin ( const Variable< Scalar > & x )

asin() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ atan()

template<typename Scalar>

Variable< Scalar > slp::atan ( const Variable< Scalar > & x )

atan() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ atan2() [1/3]

template<typename Scalar>

Variable< Scalar > slp::atan2	(	const ScalarLike auto &	y,
		const Variable< Scalar > &	x )

atan2() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

y	The y argument.
x	The x argument.

◆ atan2() [2/3]

template<typename Scalar>

Variable< Scalar > slp::atan2	(	const Variable< Scalar > &	y,
		const ScalarLike auto &	x )

atan2() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

y	The y argument.
x	The x argument.

◆ atan2() [3/3]

template<typename Scalar>

Variable< Scalar > slp::atan2	(	const Variable< Scalar > &	y,
		const Variable< Scalar > &	x )

atan2() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

y	The y argument.
x	The x argument.

◆ block() [1/2]

template<typename Scalar>

VariableMatrix< Scalar > slp::block ( const std::vector< std::vector< VariableMatrix< Scalar > > > & list )

Assemble a VariableMatrix from a nested list of blocks.

Each row's blocks must have the same height, and the assembled block rows must have the same width. For example, for the block matrix [[A, B], [C]] to be constructible, the number of rows in A and B must match, and the number of columns in [A, B] and [C] must match.

This overload is for Python bindings only.

Template Parameters

Scalar Scalar type.

Parameters

list	The nested list of blocks.

◆ block() [2/2]

template<typename Scalar>

VariableMatrix< Scalar > slp::block ( std::initializer_list< std::initializer_list< VariableMatrix< Scalar > > > list )

Assemble a VariableMatrix from a nested list of blocks.

Each row's blocks must have the same height, and the assembled block rows must have the same width. For example, for the block matrix [[A, B], [C]] to be constructible, the number of rows in A and B must match, and the number of columns in [A, B] and [C] must match.

Template Parameters

Scalar Scalar type.

Parameters

list	The nested list of blocks.

◆ bounds()

template<typename L, typename X, typename U>
requires (ScalarLike<L> || MatrixLike<L>) && SleipnirType<X> && (ScalarLike<U> || MatrixLike<U>)

auto slp::bounds	(	L &&	l,
		X &&	x,
		U &&	u )

Helper function for creating bound constraints.

Parameters

l	Lower bound.
x	Variable to bound.
u	Upper bound.

◆ cbrt()

template<typename Scalar>

Variable< Scalar > slp::cbrt ( const Variable< Scalar > & x )

cbrt() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ cos()

template<typename Scalar>

Variable< Scalar > slp::cos ( const Variable< Scalar > & x )

cos() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ cosh()

template<typename Scalar>

Variable< Scalar > slp::cosh ( const Variable< Scalar > & x )

cosh() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ cwise_reduce()

template<typename Scalar>

VariableMatrix< Scalar > slp::cwise_reduce	(	const VariableMatrix< Scalar > &	lhs,
		const VariableMatrix< Scalar > &	rhs,
		function_ref< Variable< Scalar >(const Variable< Scalar > &x, const Variable< Scalar > &y)>	binary_op )

Applies a coefficient-wise reduce operation to two matrices.

Template Parameters

Scalar Scalar type.

Parameters

lhs	The left-hand side of the binary operator.
rhs	The right-hand side of the binary operator.
binary_op	The binary operator to use for the reduce operation.

◆ erf()

template<typename Scalar>

Variable< Scalar > slp::erf ( const Variable< Scalar > & x )

erf() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ error_estimate() [1/3]

template<typename Scalar>

Scalar slp::error_estimate ( const Eigen::Vector< Scalar, Eigen::Dynamic > & g )

Returns the error estimate using the KKT conditions for Newton's method.

Template Parameters

Scalar Scalar type.

Parameters

g	Gradient of the cost function ∇f.

◆ error_estimate() [2/3]

template<typename Scalar>

Scalar slp::error_estimate	(	const Eigen::Vector< Scalar, Eigen::Dynamic > &	g,
		const Eigen::SparseMatrix< Scalar > &	A_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_e,
		const Eigen::SparseMatrix< Scalar > &	A_i,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_i,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	s,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	y,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	z,
		Scalar	μ )

Returns the error estimate using the KKT conditions for the interior-point method.

Template Parameters

Scalar Scalar type.

Parameters

g	Gradient of the cost function ∇f.
A_e	The problem's equality constraint Jacobian Aₑ(x) evaluated at the current iterate.
c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.
A_i	The problem's inequality constraint Jacobian Aᵢ(x) evaluated at the current iterate.
c_i	The problem's inequality constraints cᵢ(x) evaluated at the current iterate.
s	Inequality constraint slack variables.
y	Equality constraint dual variables.
z	Inequality constraint dual variables.
μ	Barrier parameter.

◆ error_estimate() [3/3]

template<typename Scalar>

Scalar slp::error_estimate	(	const Eigen::Vector< Scalar, Eigen::Dynamic > &	g,
		const Eigen::SparseMatrix< Scalar > &	A_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	y )

Returns the error estimate using the KKT conditions for SQP.

Template Parameters

Scalar Scalar type.

Parameters

g	Gradient of the cost function ∇f.
A_e	The problem's equality constraint Jacobian Aₑ(x) evaluated at the current iterate.
c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.
y	Equality constraint dual variables.

◆ exp()

template<typename Scalar>

Variable< Scalar > slp::exp ( const Variable< Scalar > & x )

exp() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ EXPORT_TEMPLATE_DECLARE()

template class slp::EXPORT_TEMPLATE_DECLARE ( SLEIPNIR_DLLEXPORT )

extern

◆ fraction_to_the_boundary_rule()

template<typename Scalar>

Scalar slp::fraction_to_the_boundary_rule	(	const Eigen::Vector< Scalar, Eigen::Dynamic > &	x,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	p,
		Scalar	τ )

Applies fraction-to-the-boundary rule to a variable and its iterate, then returns a fraction of the iterate step size within (0, 1].

Template Parameters

Scalar Scalar type.

Parameters

x	The variable.
p	The iterate on the variable.
τ	Fraction-to-the-boundary rule scaling factor within (0, 1].

Returns: Fraction of the iterate step size within (0, 1].

◆ function_ref()

template<typename R, typename... Args>

slp::function_ref ( R(* )(Args...) ) ->function_ref< R(Args...)>

◆ get_bounds()

template<typename Scalar>

Bounds< Scalar > slp::get_bounds	(	std::span< Variable< Scalar > >	decision_variables,
		std::span< Variable< Scalar > >	inequality_constraints,
		const Eigen::SparseMatrix< Scalar, Eigen::RowMajor > &	A_i )

A "bound constraint" is any linear constraint in one scalar variable.

Computes which constraints, if any, are bound constraints, the tightest bounds on each decision variable, and whether or not they're feasible (given previously encountered bounds),

Template Parameters

Scalar Scalar type.

Parameters

decision_variables	Decision variables corresponding to each column of A_i.
inequality_constraints	Variables representing the left-hand side of cᵢ(decision_variables) ≥ 0.
A_i	The Jacobian of inequality_constraints wrt decision_variables, evaluated anywhere, in row-major storage; in practice, since we typically store Jacobians column-major, the user of this function must perform a transpose.

◆ global_pool_allocator()

template<typename T>

PoolAllocator< T > slp::global_pool_allocator ( )

Returns an allocator for a global pool memory resource.

Template Parameters

T	The type of object in the pool.

◆ global_pool_resource()

SLEIPNIR_DLLEXPORT PoolResource & slp::global_pool_resource ( )

Returns a global pool memory resource.

◆ histogram()

template<int Width>
requires (Width > 0)

std::string slp::histogram ( double value )

Renders histogram of the given normalized value.

Template Parameters

Width Width of the histogram in characters.

Parameters

value Normalized value from 0 to 1.

◆ hypot() [1/4]

template<typename Scalar>

Variable< Scalar > slp::hypot	(	const ScalarLike auto &	x,
		const Variable< Scalar > &	y )

hypot() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The x argument.
y	The y argument.

◆ hypot() [2/4]

template<typename Scalar>

Variable< Scalar > slp::hypot	(	const Variable< Scalar > &	x,
		const ScalarLike auto &	y )

hypot() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The x argument.
y	The y argument.

◆ hypot() [3/4]

template<typename Scalar>

Variable< Scalar > slp::hypot	(	const Variable< Scalar > &	x,
		const Variable< Scalar > &	y )

hypot() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The x argument.
y	The y argument.

◆ hypot() [4/4]

template<typename Scalar>

Variable< Scalar > slp::hypot	(	const Variable< Scalar > &	x,
		const Variable< Scalar > &	y,
		const Variable< Scalar > &	z )

hypot() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The x argument.
y	The y argument.
z	The z argument.

◆ is_equality_locally_infeasible()

template<typename Scalar>

bool slp::is_equality_locally_infeasible	(	const Eigen::SparseMatrix< Scalar > &	A_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_e )

Returns true if the problem's equality constraints are locally infeasible.

Template Parameters

Scalar Scalar type.

Parameters

A_e	The problem's equality constraint Jacobian Aₑ(x) evaluated at the current iterate.
c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.

◆ is_inequality_locally_infeasible()

template<typename Scalar>

bool slp::is_inequality_locally_infeasible	(	const Eigen::SparseMatrix< Scalar > &	A_i,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_i )

Returns true if the problem's inequality constraints are locally infeasible.

Template Parameters

Scalar Scalar type.

Parameters

A_i	The problem's inequality constraint Jacobian Aᵢ(x) evaluated at the current iterate.
c_i	The problem's inequality constraints cᵢ(x) evaluated at the current iterate.

◆ kkt_error() [1/3]

template<typename Scalar>

Scalar slp::kkt_error ( const Eigen::Vector< Scalar, Eigen::Dynamic > & g )

Returns the KKT error for Newton's method.

Template Parameters

Scalar Scalar type.

Parameters

g	Gradient of the cost function ∇f.

◆ kkt_error() [2/3]

template<typename Scalar>

Scalar slp::kkt_error	(	const Eigen::Vector< Scalar, Eigen::Dynamic > &	g,
		const Eigen::SparseMatrix< Scalar > &	A_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_e,
		const Eigen::SparseMatrix< Scalar > &	A_i,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_i,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	s,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	y,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	z,
		Scalar	μ )

Returns the KKT error for the interior-point method.

Template Parameters

Scalar Scalar type.

Parameters

g	Gradient of the cost function ∇f.
A_e	The problem's equality constraint Jacobian Aₑ(x) evaluated at the current iterate.
c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.
A_i	The problem's inequality constraint Jacobian Aᵢ(x) evaluated at the current iterate.
c_i	The problem's inequality constraints cᵢ(x) evaluated at the current iterate.
s	Inequality constraint slack variables.
y	Equality constraint dual variables.
z	Inequality constraint dual variables.
μ	Barrier parameter.

◆ kkt_error() [3/3]

template<typename Scalar>

Scalar slp::kkt_error	(	const Eigen::Vector< Scalar, Eigen::Dynamic > &	g,
		const Eigen::SparseMatrix< Scalar > &	A_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	c_e,
		const Eigen::Vector< Scalar, Eigen::Dynamic > &	y )

Returns the KKT error for Sequential Quadratic Programming.

Template Parameters

Scalar Scalar type.

Parameters

g	Gradient of the cost function ∇f.
A_e	The problem's equality constraint Jacobian Aₑ(x) evaluated at the current iterate.
c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.
y	Equality constraint dual variables.

◆ log()

template<typename Scalar>

Variable< Scalar > slp::log ( const Variable< Scalar > & x )

log() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ log10()

template<typename Scalar>

Variable< Scalar > slp::log10 ( const Variable< Scalar > & x )

log10() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ make_constraints() [1/4]

template<typename Scalar, MatrixLike LHS, MatrixLike RHS>
requires SleipnirMatrixLike<LHS, Scalar> || SleipnirMatrixLike<RHS, Scalar>

auto slp::make_constraints	(	LHS &&	lhs,
		RHS &&	rhs )

◆ make_constraints() [2/4]

template<typename Scalar, MatrixLike LHS, ScalarLike RHS>
requires SleipnirMatrixLike<LHS, Scalar> || SleipnirScalarLike<RHS, Scalar>

auto slp::make_constraints	(	LHS &&	lhs,
		RHS &&	rhs )

◆ make_constraints() [3/4]

template<typename Scalar, ScalarLike LHS, MatrixLike RHS>
requires SleipnirScalarLike<LHS, Scalar> || SleipnirMatrixLike<RHS, Scalar>

auto slp::make_constraints	(	LHS &&	lhs,
		RHS &&	rhs )

◆ make_constraints() [4/4]

template<typename Scalar, ScalarLike LHS, ScalarLike RHS>
requires SleipnirScalarLike<LHS, Scalar> || SleipnirScalarLike<RHS, Scalar>

auto slp::make_constraints	(	LHS &&	lhs,
		RHS &&	rhs )

◆ make_intrusive_shared()

template<typename T, typename... Args>

IntrusiveSharedPtr< T > slp::make_intrusive_shared ( Args &&... args )

Constructs an object of type T and wraps it in an intrusive shared pointer using args as the parameter list for the constructor of T.

Template Parameters

T	Type of object for intrusive shared pointer.
Args	Types of constructor arguments.

Parameters

args	Constructor arguments for T.

◆ multistart()

template<typename Scalar, typename DecisionVariables>

MultistartResult< Scalar, DecisionVariables > slp::multistart	(	function_ref< MultistartResult< Scalar, DecisionVariables >(const DecisionVariables &initial_guess)>	solve,
		std::span< const DecisionVariables >	initial_guesses )

Solves an optimization problem from different starting points in parallel, then returns the solution with the lowest cost.

Each solve is performed on a separate thread. Solutions from successful solves are always preferred over solutions from unsuccessful solves, and cost (lower is better) is the tiebreaker between successful solves.

Template Parameters

Scalar	Scalar type.
DecisionVariables	The type containing the decision variable initial guess.

Parameters

solve	A user-provided function that takes a decision variable initial guess and returns a MultistartResult.
initial_guesses	A list of decision variable initial guesses to try.

◆ operator<()

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && (ScalarLike<RHS> || MatrixLike<RHS>) && (SleipnirType<LHS> || SleipnirType<RHS>)

auto slp::operator<	(	LHS &&	lhs,
		RHS &&	rhs )

Less-than comparison operator that returns an inequality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator<=()

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && (ScalarLike<RHS> || MatrixLike<RHS>) && (SleipnirType<LHS> || SleipnirType<RHS>)

auto slp::operator<=	(	LHS &&	lhs,
		RHS &&	rhs )

Less-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator==() [1/3]

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> || MatrixLike<RHS>) && SleipnirType<RHS>

auto slp::operator==	(	LHS &&	lhs,
		RHS &&	rhs )

Equality operator that returns an equality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator==() [2/3]

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && (!SleipnirType<LHS>) && (ScalarLike<RHS> || MatrixLike<RHS>) && SleipnirType<RHS>

auto slp::operator==	(	LHS &&	lhs,
		RHS &&	rhs )

Equality operator that returns an equality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator==() [3/3]

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> || MatrixLike<RHS>) && (!SleipnirType<RHS>)

auto slp::operator==	(	LHS &&	lhs,
		RHS &&	rhs )

Equality operator that returns an equality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator>()

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && (ScalarLike<RHS> || MatrixLike<RHS>) && (SleipnirType<LHS> || SleipnirType<RHS>)

auto slp::operator>	(	LHS &&	lhs,
		RHS &&	rhs )

Greater-than comparison operator that returns an inequality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator>=() [1/3]

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> || MatrixLike<RHS>) && SleipnirType<RHS>

auto slp::operator>=	(	LHS &&	lhs,
		RHS &&	rhs )

Greater-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator>=() [2/3]

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && (!SleipnirType<LHS>) && (ScalarLike<RHS> || MatrixLike<RHS>) && SleipnirType<RHS>

auto slp::operator>=	(	LHS &&	lhs,
		RHS &&	rhs )

Greater-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ operator>=() [3/3]

template<typename LHS, typename RHS>
requires (ScalarLike<LHS> || MatrixLike<LHS>) && SleipnirType<LHS> && (ScalarLike<RHS> || MatrixLike<RHS>) && (!SleipnirType<RHS>)

auto slp::operator>=	(	LHS &&	lhs,
		RHS &&	rhs )

Greater-than-or-equal-to comparison operator that returns an inequality constraint for two Variables.

Parameters

lhs	Left-hand side.
rhs	Left-hand side.

◆ pow() [1/3]

template<typename Scalar>

Variable< Scalar > slp::pow	(	const ScalarLike auto &	base,
		const Variable< Scalar > &	power )

pow() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

base	The base.
power	The power.

◆ pow() [2/3]

template<typename Scalar>

Variable< Scalar > slp::pow	(	const Variable< Scalar > &	base,
		const ScalarLike auto &	power )

pow() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

base	The base.
power	The power.

◆ pow() [3/3]

template<typename Scalar>

Variable< Scalar > slp::pow	(	const Variable< Scalar > &	base,
		const Variable< Scalar > &	power )

pow() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

base	The base.
power	The power.

◆ power_of_10()

template<typename Scalar>

std::string slp::power_of_10 ( Scalar value )

Renders value as power of 10.

Template Parameters

Scalar Scalar type.

Parameters

value Value.

◆ print() [1/2]

template<typename... T>

void slp::print	(	fmt::format_string< T... >	fmt,
		T &&...	args )

Wrapper around fmt::print() that squelches write failure exceptions.

◆ print() [2/2]

template<typename... T>

void slp::print	(	std::FILE *	f,
		fmt::format_string< T... >	fmt,
		T &&...	args )

Wrapper around fmt::print() that squelches write failure exceptions.

◆ print_autodiff_diagnostics()

void slp::print_autodiff_diagnostics ( const gch::small_vector< SetupProfiler > & setup_profilers )

inline

Prints autodiff diagnostics.

Parameters

setup_profilers Autodiff setup profilers.

◆ print_bottom_iteration_diagnostics()

void slp::print_bottom_iteration_diagnostics ( )

inline

Prints bottom of iteration diagnostics table.

◆ print_bound_constraint_global_infeasibility_error()

void slp::print_bound_constraint_global_infeasibility_error ( const std::span< const std::pair< Eigen::Index, Eigen::Index > > conflicting_lower_upper_bound_indices )

inline

◆ print_c_e_local_infeasibility_error()

template<typename Scalar>

void slp::print_c_e_local_infeasibility_error ( const Eigen::Vector< Scalar, Eigen::Dynamic > & c_e )

Prints equality constraint local infeasibility error.

Template Parameters

Scalar Scalar type.

Parameters

c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.

◆ print_c_i_local_infeasibility_error()

template<typename Scalar>

void slp::print_c_i_local_infeasibility_error ( const Eigen::Vector< Scalar, Eigen::Dynamic > & c_i )

Prints inequality constraint local infeasibility error.

Template Parameters

Scalar Scalar type.

Parameters

c_i	The problem's inequality constraints cᵢ(x) evaluated at the current iterate.

◆ print_iteration_diagnostics()

template<typename Scalar, typename Rep, typename Period = std::ratio<1>>

void slp::print_iteration_diagnostics	(	int	iterations,
		IterationType	type,
		const std::chrono::duration< Rep, Period > &	time,
		Scalar	error,
		Scalar	cost,
		Scalar	infeasibility,
		Scalar	complementarity,
		Scalar	μ,
		Scalar	δ,
		Scalar	primal_α,
		Scalar	primal_α_max,
		Scalar	α_reduction_factor,
		Scalar	dual_α )

Prints diagnostics for the current iteration.

Template Parameters

Scalar Scalar type.

Parameters

iterations	Number of iterations.
type	The iteration's type.
time	The iteration duration.
error	The error.
cost	The cost.
infeasibility	The infeasibility.
complementarity	The complementarity.
μ	The barrier parameter.
δ	The Hessian regularization factor.
primal_α	The primal step size.
primal_α_max	The max primal step size.
α_reduction_factor	Factor by which primal_α is reduced during backtracking.
dual_α	The dual step size.

◆ print_solver_diagnostics()

void slp::print_solver_diagnostics ( const gch::small_vector< SolveProfiler > & solve_profilers )

inline

Prints solver diagnostics.

Parameters

solve_profilers Solve profilers.

◆ print_too_few_dofs_error()

template<typename Scalar>

void slp::print_too_few_dofs_error ( const Eigen::Vector< Scalar, Eigen::Dynamic > & c_e )

Prints error for too few degrees of freedom.

Template Parameters

Scalar Scalar type.

Parameters

c_e	The problem's equality constraints cₑ(x) evaluated at the current iterate.

◆ println() [1/2]

template<typename... T>

void slp::println	(	fmt::format_string< T... >	fmt,
		T &&...	args )

Wrapper around fmt::println() that squelches write failure exceptions.

◆ println() [2/2]

template<typename... T>

void slp::println	(	std::FILE *	f,
		fmt::format_string< T... >	fmt,
		T &&...	args )

Wrapper around fmt::println() that squelches write failure exceptions.

◆ project_onto_bounds()

template<typename Derived>
requires (static_cast<bool>(Eigen::DenseBase<Derived>::IsVectorAtCompileTime))

void slp::project_onto_bounds	(	Eigen::DenseBase< Derived > &	x,
		std::span< const std::pair< typename Eigen::DenseBase< Derived >::Scalar, typename Eigen::DenseBase< Derived >::Scalar > >	decision_variable_indices_to_bounds,
		const typename Eigen::DenseBase< Derived >::Scalar	κ_1 = typename Eigen::DenseBase<Derived>::Scalar(1e-2),
		const typename Eigen::DenseBase< Derived >::Scalar	κ_2 = typename Eigen::DenseBase<Derived>::Scalar(1e-2) )

Projects the decision variables onto the given bounds, while ensuring some configurable distance from the boundary if possible.

This is designed to match the algorithm given in section 3.6 of [2].

Parameters

x	A vector of decision variables.
decision_variable_indices_to_bounds	An array of bounds (stored [lower, upper]) for each decision variable in x.
κ_1	A constant controlling distance from the lower or upper bound when the difference between the upper and lower bound is small.
κ_2	A constant controlling distance from the lower or upper bound when the difference between the upper and lower bound is large (including when one of the bounds is ±∞).

◆ sign()

template<typename Scalar>

Variable< Scalar > slp::sign ( const Variable< Scalar > & x )

sign() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ sin()

template<typename Scalar>

Variable< Scalar > slp::sin ( const Variable< Scalar > & x )

sin() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ sinh()

template<typename Scalar>

Variable< Scalar > slp::sinh ( const Variable< Scalar > & x )

sinh() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ solve() [1/2]

template SLEIPNIR_DLLEXPORT VariableMatrix< double > slp::solve	(	const VariableMatrix< double > &	A,
		const VariableMatrix< double > &	B )

extern

◆ solve() [2/2]

template<typename Scalar>

VariableMatrix< Scalar > slp::solve	(	const VariableMatrix< Scalar > &	A,
		const VariableMatrix< Scalar > &	B )

Solves the VariableMatrix equation AX = B for X.

Template Parameters

Scalar Scalar type.

Parameters

A	The left-hand side.
B	The right-hand side.

Returns: The solution X.

◆ sqrt()

template<typename Scalar>

Variable< Scalar > slp::sqrt ( const Variable< Scalar > & x )

sqrt() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ swap()

template<typename R, typename... Args>

void slp::swap	(	function_ref< R(Args...)> &	lhs,
		function_ref< R(Args...)> &	rhs )

constexprnoexcept

Swaps the referred callables of lhs and rhs.

◆ tan()

template<typename Scalar>

Variable< Scalar > slp::tan ( const Variable< Scalar > & x )

tan() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ tanh()

template<typename Scalar>

Variable< Scalar > slp::tanh ( const Variable< Scalar > & x )

tanh() for Variables.

Template Parameters

Scalar Scalar type.

Parameters

x	The argument.

◆ to_ms()

template<typename Rep, typename Period = std::ratio<1>>

double slp::to_ms ( const std::chrono::duration< Rep, Period > & duration )

constexpr

Converts std::chrono::duration to a number of milliseconds rounded to three decimals.

◆ unreachable()

void slp::unreachable ( )

inline

◆ Variable() [1/3]

template<std::integral T>

slp::Variable ( T ) ->Variable< T >

◆ Variable() [2/3]

template<std::floating_point T>

slp::Variable ( T ) ->Variable< T >

◆ Variable() [3/3]

template<template< typename > typename T, typename Scalar>
requires SleipnirMatrixLike<T<Scalar>, Scalar>

slp::Variable ( T< Scalar > ) ->Variable< Scalar >

◆ VariableMatrix() [1/2]

template<typename Derived>

slp::VariableMatrix ( const Eigen::DiagonalBase< Derived > & ) ->VariableMatrix< typenameDerived::Scalar >

◆ VariableMatrix() [2/2]

template<typename Derived>

slp::VariableMatrix ( const Eigen::MatrixBase< Derived > & ) ->VariableMatrix< typenameDerived::Scalar >

Namespaces

Classes

Concepts

Enumerations

Functions

Enumeration Type Documentation

◆ DynamicsType

◆ ExitStatus

◆ ExpressionType

◆ IterationType

◆ TimestepMethod

◆ TranscriptionMethod

Function Documentation

◆ abs()

◆ acos()

◆ allocate_intrusive_shared()

◆ asin()

◆ atan()

◆ atan2() [1/3]

◆ atan2() [2/3]

◆ atan2() [3/3]

◆ block() [1/2]

◆ block() [2/2]

◆ bounds()

◆ cbrt()

◆ cos()

◆ cosh()

◆ cwise_reduce()

◆ erf()

◆ error_estimate() [1/3]

◆ error_estimate() [2/3]

◆ error_estimate() [3/3]

◆ exp()

◆ EXPORT_TEMPLATE_DECLARE()

◆ fraction_to_the_boundary_rule()

◆ function_ref()

◆ get_bounds()

◆ global_pool_allocator()

◆ global_pool_resource()

◆ histogram()

◆ hypot() [1/4]

◆ hypot() [2/4]

◆ hypot() [3/4]

◆ hypot() [4/4]

◆ is_equality_locally_infeasible()

◆ is_inequality_locally_infeasible()

◆ kkt_error() [1/3]

◆ kkt_error() [2/3]

◆ kkt_error() [3/3]

◆ log()

◆ log10()

◆ make_constraints() [1/4]

◆ make_constraints() [2/4]

◆ make_constraints() [3/4]

◆ make_constraints() [4/4]

◆ make_intrusive_shared()

◆ multistart()

◆ operator<()

◆ operator<=()

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

◆ operator>()

◆ operator>=() [1/3]

◆ operator>=() [2/3]

◆ operator>=() [3/3]

◆ pow() [1/3]

◆ pow() [2/3]

◆ pow() [3/3]

◆ power_of_10()

◆ print() [1/2]

◆ print() [2/2]

◆ print_autodiff_diagnostics()

◆ print_bottom_iteration_diagnostics()

◆ print_bound_constraint_global_infeasibility_error()

◆ print_c_e_local_infeasibility_error()

◆ print_c_i_local_infeasibility_error()

◆ print_iteration_diagnostics()

◆ print_solver_diagnostics()

◆ print_too_few_dofs_error()