Drake
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.

#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...

Set the sparsity pattern of the gradient matrix. More...

const 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 whose value could be non-zero. 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...

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...

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 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 > &lower_bound, const Eigen::Ref< const Eigen::VectorXd > &upper_bound)
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)

◆ PositiveSemidefiniteConstraint() [1/3]

 PositiveSemidefiniteConstraint ( const PositiveSemidefiniteConstraint & )
delete

◆ PositiveSemidefiniteConstraint() [2/3]

 PositiveSemidefiniteConstraint ( PositiveSemidefiniteConstraint && )
delete

◆ PositiveSemidefiniteConstraint() [3/3]

 PositiveSemidefiniteConstraint ( int rows )
explicit

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

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
 rows The number of rows (and columns) of the symmetric matrix.

Example:

// Create a MathematicalProgram object.
auto prog = MathematicalProgram();
// Add a 2 x 2 symmetric matrix S to optimization program as new decision
// variables.
auto S = prog.NewSymmetricContinuousVariables<2>("S");
// Impose a positive semidefinite constraint on S.
std::shared_ptr<PositiveSemidefiniteConstraint> psd_constraint =
/////////////////////////////////////////////////////////////
// Add more constraints to make the program more interesting,
// but this is not needed.
// Add the constraint that S(1, 0) = 1.
// Minimize S(0, 0) + S(1, 1).
/////////////////////////////////////////////////////////////
// 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.
Eigen::Vector4d S_stacked;
S_stacked << S_value.col(0), S_value.col(1);
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()

 ~PositiveSemidefiniteConstraint ( )
override

◆ 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
 x The stacked columns of the symmetric matrix.

Implements EvaluatorBase.

◆ DoEval() [2/3]

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

Implements EvaluatorBase.

◆ DoEval() [3/3]

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

Implements EvaluatorBase.

◆ matrix_rows()

 int matrix_rows ( ) const

◆ operator=() [1/2]

 PositiveSemidefiniteConstraint& operator= ( const PositiveSemidefiniteConstraint & )
delete

◆ operator=() [2/2]

 PositiveSemidefiniteConstraint& operator= ( PositiveSemidefiniteConstraint && )
delete

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