Detailed Description

Implements a constraint of the form \( lb <= Ax <= ub \).

#include <drake/solvers/constraint.h>

Public Member Functions
	LinearConstraint (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &lb, const Eigen::Ref< const Eigen::VectorXd > &ub)
	Construct the linear constraint lb <= A*x <= ub.
	LinearConstraint (const Eigen::SparseMatrix< double > &A, const Eigen::Ref< const Eigen::VectorXd > &lb, const Eigen::Ref< const Eigen::VectorXd > &ub)
	Overloads constructor with a sparse A matrix.
	~LinearConstraint () override
const Eigen::SparseMatrix< double > &	get_sparse_A () const
const Eigen::MatrixXd &	GetDenseA () const
	Get the matrix A as a dense matrix.
void	UpdateCoefficients (const Eigen::Ref< const Eigen::MatrixXd > &new_A, const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the linear term, upper and lower bounds in the linear constraint.
void	UpdateCoefficients (const Eigen::SparseMatrix< double > &new_A, const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Overloads UpdateCoefficients but with a sparse A matrix.
void	RemoveTinyCoefficient (double tol)
	Sets A(i, j) to zero if abs(A(i, j)) <= tol.
bool	is_dense_A_constructed () const
	Returns true iff this constraint already has a dense representation, i.e, if GetDenseA() will be cheap.
void	set_bounds (const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Set the upper and lower bounds of the constraint.
void	UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)
	Updates the lower bound.
void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound.
Does not allow copy, move, or assignment
	LinearConstraint (const LinearConstraint &)=delete
	LinearConstraint (LinearConstraint &&)=delete
LinearConstraint &	operator= (const LinearConstraint &)=delete
LinearConstraint &	operator= (LinearConstraint &&)=delete
Public Member Functions inherited from Constraint
template<typename DerivedLB, typename DerivedUB>
	Constraint (int num_constraints, int num_vars, const Eigen::MatrixBase< DerivedLB > &lb, const Eigen::MatrixBase< DerivedUB > &ub, const std::string &description="")
	Constructs a constraint which has num_constraints rows, with an input num_vars x 1 vector.
	Constraint (int num_constraints, int num_vars)
	Constructs a constraint which has num_constraints rows, with an input num_vars x 1 vector, with no bounds.
bool	CheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=1E-6) const
	Return whether this constraint is satisfied by the given value, x.
bool	CheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, double tol=1E-6) const
symbolic::Formula	CheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable > > &x) const
const Eigen::VectorXd &	lower_bound () const
const Eigen::VectorXd &	upper_bound () const
int	num_constraints () const
	Number of rows in the output constraint.
	Constraint (const Constraint &)=delete
Constraint &	operator= (const Constraint &)=delete
	Constraint (Constraint &&)=delete
Constraint &	operator= (Constraint &&)=delete
Public Member Functions inherited from EvaluatorBase
virtual	~EvaluatorBase ()
void	Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const
	Evaluates the expression.
void	Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const
	Evaluates the expression.
void	Eval (const Eigen::Ref< const VectorX< symbolic::Variable > > &x, VectorX< symbolic::Expression > *y) const
	Evaluates the expression.
void	set_description (const std::string &description)
	Set a human-friendly description for the evaluator.
const std::string &	get_description () const
	Getter for a human-friendly description for the evaluator.
std::ostream &	Display (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	Formats this evaluator into the given stream using vars for the bound decision variable names.
std::ostream &	Display (std::ostream &os) const
	Formats this evaluator into the given stream, without displaying the decision variables it is bound to.
std::string	ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const
	Returns a LaTeX string describing this evaluator.
int	num_vars () const
	Getter for the number of variables, namely the number of rows in x, as used in Eval(x, y).
int	num_outputs () const
	Getter for the number of outputs, namely the number of rows in y, as used in Eval(x, y).
void	SetGradientSparsityPattern (const std::vector< std::pair< int, int > > &gradient_sparsity_pattern)
	Set the sparsity pattern of the gradient matrix ∂y/∂x (the gradient of y value in Eval, w.r.t x in Eval) .
const std::optional< std::vector< std::pair< int, int > > > &	gradient_sparsity_pattern () const
	Returns the vector of (row_index, col_index) that contains all the entries in the gradient of Eval function (∂y/∂x) whose value could be non-zero, namely if ∂yᵢ/∂xⱼ could be non-zero, then the pair (i, j) is in gradient_sparsity_pattern.
bool	is_thread_safe () const
	Returns whether it is safe to call Eval in parallel.
	EvaluatorBase (const EvaluatorBase &)=delete
EvaluatorBase &	operator= (const EvaluatorBase &)=delete
	EvaluatorBase (EvaluatorBase &&)=delete
EvaluatorBase &	operator= (EvaluatorBase &&)=delete

Protected Member Functions
void	DoEval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const override
	Implements expression evaluation for scalar type double.
void	DoEval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const override
	Implements expression evaluation for scalar type AutoDiffXd.
void	DoEval (const Eigen::Ref< const VectorX< symbolic::Variable > > &x, VectorX< symbolic::Expression > *y) const override
	Implements expression evaluation for scalar type symbolic::Expression.
std::ostream &	DoDisplay (std::ostream &, const VectorX< symbolic::Variable > &) const override
	NVI implementation of Display.
std::string	DoToLatex (const VectorX< symbolic::Variable > &, int) const override
Protected Member Functions inherited from Constraint
void	UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)
	Updates the lower bound.
void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound.
void	set_bounds (const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Set the upper and lower bounds of the constraint.
virtual bool	DoCheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, const double tol) const
virtual bool	DoCheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, const double tol) const
virtual symbolic::Formula	DoCheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable > > &x) const
Protected Member Functions inherited from EvaluatorBase
	EvaluatorBase (int num_outputs, int num_vars, const std::string &description="")
	Constructs a evaluator.
void	set_num_outputs (int num_outputs)
void	set_is_thread_safe (bool is_thread_safe)

Protected Attributes
internal::SparseAndDenseMatrix	A_

Constructor & Destructor Documentation

◆ LinearConstraint() [1/4]

LinearConstraint ( const LinearConstraint & )

delete

◆ LinearConstraint() [2/4]

LinearConstraint ( LinearConstraint && )

delete

◆ LinearConstraint() [3/4]

LinearConstraint	(	const Eigen::Ref< const Eigen::MatrixXd > &	A,
		const Eigen::Ref< const Eigen::VectorXd > &	lb,
		const Eigen::Ref< const Eigen::VectorXd > &	ub )

Construct the linear constraint lb <= A*x <= ub.

Throws if A has any entry which is not finite.

◆ LinearConstraint() [4/4]

LinearConstraint	(	const Eigen::SparseMatrix< double > &	A,
		const Eigen::Ref< const Eigen::VectorXd > &	lb,
		const Eigen::Ref< const Eigen::VectorXd > &	ub )

Overloads constructor with a sparse A matrix.

Throws if A has any entry which is not finite.

◆ ~LinearConstraint()

~LinearConstraint ( )

override

Member Function Documentation

◆ DoDisplay()

std::ostream & DoDisplay	(	std::ostream &	os,
		const VectorX< symbolic::Variable > &	vars ) const

overrideprotectedvirtual

NVI implementation of Display.

The default implementation will report the NiceTypeName, get_description, and list the bound variables. Subclasses may override to customize the message.

Precondition: vars size is consistent with num_vars".

Reimplemented from EvaluatorBase.

◆ DoEval() [1/3]

void DoEval	(	const Eigen::Ref< const AutoDiffVecXd > &	x,
		AutoDiffVecXd *	y ) const

overrideprotectedvirtual

Implements expression evaluation for scalar type AutoDiffXd.

Parameters

x	Input vector.
y	Output vector.

Precondition: x must be of size num_vars x 1.

Postcondition: y will be of size num_outputs x 1.

Implements EvaluatorBase.

◆ DoEval() [2/3]

void DoEval	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		Eigen::VectorXd *	y ) const

overrideprotectedvirtual

Implements expression evaluation for scalar type double.

Parameters

x	Input vector.
y	Output vector.

Precondition: x must be of size num_vars x 1.

Postcondition: y will be of size num_outputs x 1.

Implements EvaluatorBase.

◆ DoEval() [3/3]

void DoEval	(	const Eigen::Ref< const VectorX< symbolic::Variable > > &	x,
		VectorX< symbolic::Expression > *	y ) const

overrideprotectedvirtual

Implements expression evaluation for scalar type symbolic::Expression.

Parameters

[in]	x	Input vector.
[out]	y	Output vector.

Precondition: x must be of size num_vars x 1.

Postcondition: y will be of size num_outputs x 1.

Implements EvaluatorBase.

◆ DoToLatex()

std::string DoToLatex	(	const VectorX< symbolic::Variable > &	,
		int	) const

overrideprotectedvirtual

Reimplemented from EvaluatorBase.

◆ get_sparse_A()

const Eigen::SparseMatrix< double > & get_sparse_A ( ) const

◆ GetDenseA()

const Eigen::MatrixXd & GetDenseA ( ) const

Get the matrix A as a dense matrix.

Note: this might involve memory allocation to convert a sparse matrix to a dense one, for better performance you should call get_sparse_A() which returns a sparse matrix.

◆ is_dense_A_constructed()

bool is_dense_A_constructed ( ) const

Returns true iff this constraint already has a dense representation, i.e, if GetDenseA() will be cheap.

◆ operator=() [1/2]

LinearConstraint & operator= ( const LinearConstraint & )

delete

◆ operator=() [2/2]

LinearConstraint & operator= ( LinearConstraint && )

delete

◆ RemoveTinyCoefficient()

void RemoveTinyCoefficient ( double tol )

Sets A(i, j) to zero if abs(A(i, j)) <= tol.

Oftentimes the coefficient A is computed numerically with round-off errors. Such small round-off errors can cause numerical issues for certain optimization solvers. Hence it is recommended to remove the tiny coefficients to achieve numerical robustness.

Parameters

tol	The entries in A with absolute value <= tol will be set to 0.

Note: tol>= 0.

◆ set_bounds()

void set_bounds	(	const Eigen::Ref< const Eigen::VectorXd > &	new_lb,
		const Eigen::Ref< const Eigen::VectorXd > &	new_ub )

Set the upper and lower bounds of the constraint.

Parameters

new_lb	A num_constraints x 1 vector.
new_ub	A num_constraints x 1 vector.

Note: If the users want to expose this method in a sub-class, do using Constraint::set_bounds, as in LinearConstraint.

◆ UpdateCoefficients() [1/2]

void UpdateCoefficients	(	const Eigen::Ref< const Eigen::MatrixXd > &	new_A,
		const Eigen::Ref< const Eigen::VectorXd > &	new_lb,
		const Eigen::Ref< const Eigen::VectorXd > &	new_ub )

Updates the linear term, upper and lower bounds in the linear constraint.

The updated constraint is: new_lb <= new_A * x <= new_ub Note that the size of constraints (number of rows) can change, but the number of variables (number of cols) cannot.

Throws if new_A has any entry which is not finite or if new_A, new_lb, and new_ub don't all have the same number of rows.

Parameters

new_A	new linear term
new_lb	new lower bound
new_ub	new upper bound

◆ UpdateCoefficients() [2/2]

void UpdateCoefficients	(	const Eigen::SparseMatrix< double > &	new_A,
		const Eigen::Ref< const Eigen::VectorXd > &	new_lb,
		const Eigen::Ref< const Eigen::VectorXd > &	new_ub )

Overloads UpdateCoefficients but with a sparse A matrix.

Throws if new_A has any entry which is not finite or if new_A, new_lb, and new_ub don't all have the same number of rows.

◆ UpdateLowerBound()

void UpdateLowerBound ( const Eigen::Ref< const Eigen::VectorXd > & new_lb )

Updates the lower bound.

Note: if the users want to expose this method in a sub-class, do using Constraint::UpdateLowerBound, as in LinearConstraint.

◆ UpdateUpperBound()

void UpdateUpperBound ( const Eigen::Ref< const Eigen::VectorXd > & new_ub )

Updates the upper bound.

Note: if the users want to expose this method in a sub-class, do using Constraint::UpdateUpperBound, as in LinearConstraint.

Member Data Documentation

◆ A_

internal::SparseAndDenseMatrix A_

protected

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

drake/solvers/constraint.h

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ LinearConstraint() [1/4]

◆ LinearConstraint() [2/4]

◆ LinearConstraint() [3/4]

◆ LinearConstraint() [4/4]

◆ ~LinearConstraint()

Member Function Documentation

◆ DoDisplay()

◆ DoEval() [1/3]

◆ DoEval() [2/3]

◆ DoEval() [3/3]

◆ DoToLatex()

◆ get_sparse_A()

◆ GetDenseA()

◆ is_dense_A_constructed()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ RemoveTinyCoefficient()

◆ set_bounds()

◆ UpdateCoefficients() [1/2]

◆ UpdateCoefficients() [2/2]

◆ UpdateLowerBound()

◆ UpdateUpperBound()

Member Data Documentation

◆ A_