Drake
Drake C++ Documentation

Detailed Description

lb ≤ .5 xᵀQx + bᵀx ≤ ub Without loss of generality, the class stores a symmetric matrix Q.

For a non-symmetric matrix Q₀, we can define Q = (Q₀ + Q₀ᵀ) / 2, since xᵀQ₀x = xᵀQ₀ᵀx = xᵀ*(Q₀+Q₀ᵀ)/2 *x. The first equality holds because the transpose of a scalar is the scalar itself. Hence we can always convert a non-symmetric matrix Q₀ to a symmetric matrix Q.

#include <drake/solvers/constraint.h>

Public Types

enum  HessianType { kPositiveSemidefinite, kNegativeSemidefinite, kIndefinite }
 Whether the Hessian matrix is positive semidefinite, negative semidefinite, or indefinite. More...
 

Public Member Functions

template<typename DerivedQ , typename Derivedb >
 QuadraticConstraint (const Eigen::MatrixBase< DerivedQ > &Q0, const Eigen::MatrixBase< Derivedb > &b, double lb, double ub, std::optional< HessianType > hessian_type=std::nullopt)
 Construct a quadratic constraint. More...
 
 ~QuadraticConstraint () override
 
virtual const Eigen::MatrixXd & Q () const
 The symmetric matrix Q, being the Hessian of this constraint. More...
 
virtual const Eigen::VectorXd & b () const
 
HessianType hessian_type () const
 
bool is_convex () const
 Returns if this quadratic constraint is convex. More...
 
template<typename DerivedQ , typename DerivedB >
void UpdateCoefficients (const Eigen::MatrixBase< DerivedQ > &new_Q, const Eigen::MatrixBase< DerivedB > &new_b, std::optional< HessianType > hessian_type=std::nullopt)
 Updates the quadratic and linear term of the constraint. More...
 
Does not allow copy, move, or assignment
 QuadraticConstraint (const QuadraticConstraint &)=delete
 
QuadraticConstraintoperator= (const QuadraticConstraint &)=delete
 
 QuadraticConstraint (QuadraticConstraint &&)=delete
 
QuadraticConstraintoperator= (QuadraticConstraint &&)=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
 

Static Public Attributes

static const int kNumConstraints = 1
 

Additional Inherited Members

- 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...
 
void set_num_outputs (int num_outputs)
 
void set_is_thread_safe (bool is_thread_safe)
 

Member Enumeration Documentation

◆ HessianType

enum HessianType
strong

Whether the Hessian matrix is positive semidefinite, negative semidefinite, or indefinite.

Enumerator
kPositiveSemidefinite 
kNegativeSemidefinite 
kIndefinite 

Constructor & Destructor Documentation

◆ QuadraticConstraint() [1/3]

◆ QuadraticConstraint() [2/3]

◆ QuadraticConstraint() [3/3]

QuadraticConstraint ( const Eigen::MatrixBase< DerivedQ > &  Q0,
const Eigen::MatrixBase< Derivedb > &  b,
double  lb,
double  ub,
std::optional< HessianType hessian_type = std::nullopt 
)

Construct a quadratic constraint.

Template Parameters
DerivedQThe type for Q.
DerivedbThe type for b.
Parameters
Q0The square matrix. Notice that Q₀ does not have to be symmetric.
bThe linear coefficient.
lbThe lower bound.
ubThe upper bound.
hessian_type(optional) Indicates the type of Hessian matrix Q0. If hessian_type is not std::nullopt, then the user guarantees the type of Q0. If hessian_type=std::nullopt, then QuadraticConstraint will check the type of Q0. To speed up the constructor, set hessian_type != std::nullopt if you can. If this type is set incorrectly, then the downstream code (for example the solver) will malfunction.
Exceptions
std::exceptionif Q0 isn't a square matrix, or b.rows() != Q0.rows().

◆ ~QuadraticConstraint()

~QuadraticConstraint ( )
override

Member Function Documentation

◆ b()

virtual const Eigen::VectorXd& b ( ) const
virtual

◆ hessian_type()

HessianType hessian_type ( ) const

◆ is_convex()

bool is_convex ( ) const

Returns if this quadratic constraint is convex.

◆ operator=() [1/2]

QuadraticConstraint& operator= ( const QuadraticConstraint )
delete

◆ operator=() [2/2]

QuadraticConstraint& operator= ( QuadraticConstraint &&  )
delete

◆ Q()

virtual const Eigen::MatrixXd& Q ( ) const
virtual

The symmetric matrix Q, being the Hessian of this constraint.

◆ UpdateCoefficients()

void UpdateCoefficients ( const Eigen::MatrixBase< DerivedQ > &  new_Q,
const Eigen::MatrixBase< DerivedB > &  new_b,
std::optional< HessianType hessian_type = std::nullopt 
)

Updates the quadratic and linear term of the constraint.

The new matrices need to have the same dimension as before.

Parameters
new_Qnew quadratic term
new_bnew linear term
hessian_type(optional) Indicates the type of Hessian matrix Q0. If hessian_type is not std::nullopt, then the user guarantees the type of Q0. If hessian_type=std::nullopt, then QuadraticConstraint will check the type of Q0. To speed up the constructor, set hessian_type != std::nullopt if you can.

Member Data Documentation

◆ kNumConstraints

const int kNumConstraints = 1
static

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