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. More...

	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. More...

	~LinearConstraint () override

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

const Eigen::MatrixXd &	GetDenseA () const
	Get the matrix A as a dense matrix. More...

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. More...

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. More...

void	RemoveTinyCoefficient (double tol)
	Sets A(i, j) to zero if abs(A(i, j)) <= tol. More...

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

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. More...

void	UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)
	Updates the lower bound. More...

void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound. More...

Does not allow copy, move, or assignment
	LinearConstraint (const LinearConstraint &)=delete

LinearConstraint &	operator= (const LinearConstraint &)=delete

	LinearConstraint (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. More...

	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. More...

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`. More...

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. More...

	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. More...

void	Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const
	Evaluates the expression. More...

void	Eval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const
	Evaluates the expression. More...

void	set_description (const std::string &description)
	Set a human-friendly description for the evaluator. More...

const std::string &	get_description () const
	Getter for a human-friendly description for the evaluator. More...

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. More...

std::ostream &	Display (std::ostream &os) const
	Formats this evaluator into the given stream, without displaying the decision variables it is bound to. More...

std::string	ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const
	Returns a LaTeX string describing this evaluator. More...

int	num_vars () const
	Getter for the number of variables, namely the number of rows in x, as used in Eval(x, y). More...

int	num_outputs () const
	Getter for the number of outputs, namely the number of rows in y, as used in Eval(x, y). More...

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) . More...

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. More...

bool	is_thread_safe () const
	Returns whether it is safe to call Eval in parallel. More...

	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. More...

void	DoEval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const override
	Implements expression evaluation for scalar type AutoDiffXd. More...

void	DoEval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const override
	Implements expression evaluation for scalar type symbolic::Expression. More...

std::ostream &	DoDisplay (std::ostream &, const VectorX< symbolic::Variable > &) const override
	NVI implementation of Display. More...

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. More...

void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound. More...

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. More...

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. More...

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 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() [2/3]

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() [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= ( LinearConstraint && )

delete

◆ operator=() [2/2]

LinearConstraint& operator= ( const 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

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_up	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

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

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_