Drake
Drake C++ Documentation
LinearMatrixInequalityConstraint Class Reference

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...
 
Does not allow copy, move, or assignment
 LinearMatrixInequalityConstraint (const LinearMatrixInequalityConstraint &)=delete
 
LinearMatrixInequalityConstraintoperator= (const LinearMatrixInequalityConstraint &)=delete
 
 LinearMatrixInequalityConstraint (LinearMatrixInequalityConstraint &&)=delete
 
LinearMatrixInequalityConstraintoperator= (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
 
Constraintoperator= (const Constraint &)=delete
 
 Constraint (Constraint &&)=delete
 
Constraintoperator= (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
 
EvaluatorBaseoperator= (const EvaluatorBase &)=delete
 
 EvaluatorBase (EvaluatorBase &&)=delete
 
EvaluatorBaseoperator= (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() [2/3]

◆ LinearMatrixInequalityConstraint() [3/3]

LinearMatrixInequalityConstraint ( std::vector< Eigen::MatrixXd >  F,
double  symmetry_tolerance = 1E-10 
)
Parameters
FEach symmetric matrix F[i] should be of the same size.
symmetry_toleranceThe precision to determine if the input matrices Fi are all symmetric.
See also
math::IsSymmetric().

◆ ~LinearMatrixInequalityConstraint()

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]

◆ operator=() [2/2]


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