Drake
Drake C++ Documentation
PositiveSemidefiniteConstraint Class Reference

Detailed Description

Implements a positive semidefinite constraint on a symmetric matrix S

\[\text{ S is p.s.d }\]

namely, all eigen values of S are non-negative.

Note
if the matix S has 1 row, then it is better to impose a linear inequality constraints; if it has 2 rows, then it is better to impose a rotated Lorentz cone constraint, since a 2 x 2 matrix S being p.s.d is equivalent to the constraint [S(0, 0), S(1, 1), S(0, 1)] in the rotated Lorentz cone.

#include <drake/solvers/constraint.h>

Public Member Functions

 PositiveSemidefiniteConstraint (int rows)
 Impose the constraint that a symmetric matrix with size rows x rows is positive semidefinite. More...
 
 ~PositiveSemidefiniteConstraint () override
 
int matrix_rows () const
 
Does not allow copy, move, or assignment
 PositiveSemidefiniteConstraint (const PositiveSemidefiniteConstraint &)=delete
 
PositiveSemidefiniteConstraintoperator= (const PositiveSemidefiniteConstraint &)=delete
 
 PositiveSemidefiniteConstraint (PositiveSemidefiniteConstraint &&)=delete
 
PositiveSemidefiniteConstraintoperator= (PositiveSemidefiniteConstraint &&)=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 symmetric matrix. More...
 
void DoEval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const override
 
void DoEval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const override
 
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

◆ PositiveSemidefiniteConstraint() [1/3]

◆ PositiveSemidefiniteConstraint() [2/3]

◆ PositiveSemidefiniteConstraint() [3/3]

PositiveSemidefiniteConstraint ( int  rows)
explicit

Impose the constraint that a symmetric matrix with size rows x rows is positive semidefinite.

See also
MathematicalProgram::AddPositiveSemidefiniteConstraint() for how to use this constraint on some decision variables. We currently use this constraint as a place holder in MathematicalProgram, to indicate the positive semidefiniteness of some decision variables.
Parameters
rowsThe number of rows (and columns) of the symmetric matrix.
Note
rows should be a positive integer. If rows==1 or rows==2, then consider imposing a linear inequality or rotated Lorentz cone constraint respectively.

Example:

// Create a MathematicalProgram object.
auto prog = MathematicalProgram();
// Add a 3 x 3 symmetric matrix S to optimization program as new decision
// variables.
auto S = prog.NewSymmetricContinuousVariables<3>("S");
// Impose a positive semidefinite constraint on S.
std::shared_ptr<PositiveSemidefiniteConstraint> psd_constraint =
prog.AddPositiveSemidefiniteConstraint(S);
/////////////////////////////////////////////////////////////
// Add more constraints to make the program more interesting,
// but this is not needed.
// Add the constraint that S(1, 0) = 1.
prog.AddBoundingBoxConstraint(1, 1, S(1, 0));
// Minimize S(0, 0) + S(1, 1) + S(2, 2).
prog.AddLinearCost(Eigen::RowVector3d(1, 1, 1), {S.diagonal()});
/////////////////////////////////////////////////////////////
// Now solve the program.
auto result = Solve(prog);
// Retrieve the solution of matrix S.
auto S_value = GetSolution(S, result);
// Compute the eigen values of the solution, to see if they are
// all non-negative.
Vector6d S_stacked;
S_stacked << S_value.col(0), S_value.col(1), S_value.col(2);
Eigen::VectorXd S_eigen_values;
psd_constraint->Eval(S_stacked, S_eigen_values);
std::cout<<"S solution is: " << S << std::endl;
std::cout<<"The eigen value of S is " << S_eigen_values << std::endl;

◆ ~PositiveSemidefiniteConstraint()

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 symmetric matrix.

Parameters
xThe stacked columns of the symmetric matrix.

Implements EvaluatorBase.

◆ DoEval() [2/3]

void DoEval ( const Eigen::Ref< const AutoDiffVecXd > &  x,
AutoDiffVecXd y 
) const
overrideprotectedvirtual
Parameters
xThe stacked columns of the symmetric matrix. This function is not supported yet, 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
Parameters
xThe stacked columns of the symmetric matrix. This function is not supported, since Eigen's eigen value solver does not accept symbolic::Expression.

Implements EvaluatorBase.

◆ DoToLatex()

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

Reimplemented from EvaluatorBase.

◆ matrix_rows()

int matrix_rows ( ) const

◆ operator=() [1/2]

◆ operator=() [2/2]


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