Drake
Drake C++ Documentation
LinearConstraint Class Reference

## 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)

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

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

LinearConstraintoperator= (const LinearConstraint &)=delete

LinearConstraint (LinearConstraint &&)=delete

LinearConstraintoperator= (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

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...

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...

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
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)

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

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)

## Protected Attributes

internal::SparseAndDenseMatrix A_

## ◆ 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

## ◆ 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& 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

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

## ◆ UpdateUpperBound()

 void UpdateUpperBound