Detailed Description

Impose the matrix inequality constraint on variable x

\[ F_0 + x_1 F_1 + ... + x_n F_n \text{ is p.s.d} \]

where p.s.d stands for positive semidefinite.

\( F_0, F_1, ..., F_n \) are all given symmetric matrices of the same size.

Note: if the matrices Fᵢ all have 1 row, then it is better to impose a linear inequality constraints; if they all have 2 rows, then it is better to impose a rotated Lorentz cone constraint, since a 2 x 2 matrix X being p.s.d is equivalent to the constraint [X(0, 0), X(1, 1), X(0, 1)] in the rotated Lorentz cone.

#include <drake/solvers/constraint.h>

Public Member Functions
	LinearMatrixInequalityConstraint (std::vector< Eigen::MatrixXd > F, double symmetry_tolerance=1E-10)

	~LinearMatrixInequalityConstraint () override

const std::vector< Eigen::MatrixXd > &	F () const

int	matrix_rows () const
	Gets the number of rows in the matrix inequality constraint. More...

void	WarnOnSmallMatrixSize () const
	Warn if the matrix size is 1x1 or 2x2. More...

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

LinearMatrixInequalityConstraint &	operator= (const LinearMatrixInequalityConstraint &)=delete

	LinearMatrixInequalityConstraint (LinearMatrixInequalityConstraint &&)=delete

LinearMatrixInequalityConstraint &	operator= (LinearMatrixInequalityConstraint &&)=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
	Evaluate the eigen values of the linear matrix. More...

void	DoEval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const override
	This function is not supported, since Eigen's eigen value solver does not accept AutoDiffXd. More...

void	DoEval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const override
	This function is not supported, since Eigen's eigen value solver does not accept symbolic::Expression type. 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...

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

void	set_num_outputs (int num_outputs)

void	set_is_thread_safe (bool is_thread_safe)

Constructor & Destructor Documentation

◆ LinearMatrixInequalityConstraint() [1/3]

LinearMatrixInequalityConstraint ( const LinearMatrixInequalityConstraint & )

delete

◆ LinearMatrixInequalityConstraint() [2/3]

LinearMatrixInequalityConstraint ( LinearMatrixInequalityConstraint && )

delete

◆ LinearMatrixInequalityConstraint() [3/3]

LinearMatrixInequalityConstraint	(	std::vector< Eigen::MatrixXd >	F,
		double	symmetry_tolerance = `1E-10`
	)

Parameters

F	Each symmetric matrix F[i] should be of the same size.
symmetry_tolerance	The precision to determine if the input matrices Fi are all symmetric.

See also: math::IsSymmetric().

◆ ~LinearMatrixInequalityConstraint()

~LinearMatrixInequalityConstraint ( )

override

Member Function Documentation

◆ DoEval() [1/3]

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

overrideprotectedvirtual

Evaluate the eigen values of the linear matrix.

Implements EvaluatorBase.

◆ DoEval() [2/3]

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

overrideprotectedvirtual

This function is not supported, since Eigen's eigen value solver does not accept AutoDiffXd.

Implements EvaluatorBase.

◆ DoEval() [3/3]

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

overrideprotectedvirtual

This function is not supported, since Eigen's eigen value solver does not accept symbolic::Expression type.

Implements EvaluatorBase.

◆ DoToLatex()

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

overrideprotectedvirtual

Reimplemented from EvaluatorBase.

◆ F()

const std::vector<Eigen::MatrixXd>& F ( ) const

◆ matrix_rows()

int matrix_rows ( ) const

Gets the number of rows in the matrix inequality constraint.

Namely Fi are all matrix_rows() x matrix_rows() matrices.

◆ operator=() [1/2]

LinearMatrixInequalityConstraint& operator= ( LinearMatrixInequalityConstraint && )

delete

◆ operator=() [2/2]

LinearMatrixInequalityConstraint& operator= ( const LinearMatrixInequalityConstraint & )

delete

◆ WarnOnSmallMatrixSize()

void WarnOnSmallMatrixSize ( ) const

Warn if the matrix size is 1x1 or 2x2.

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

drake/solvers/constraint.h

Detailed Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ LinearMatrixInequalityConstraint() [1/3]

◆ LinearMatrixInequalityConstraint() [2/3]

◆ LinearMatrixInequalityConstraint() [3/3]

◆ ~LinearMatrixInequalityConstraint()

Member Function Documentation

◆ DoEval() [1/3]

◆ DoEval() [2/3]

◆ DoEval() [3/3]

◆ DoToLatex()

◆ F()

◆ matrix_rows()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ WarnOnSmallMatrixSize()