Drake
Drake C++ Documentation
PerspectiveQuadraticCost Class Reference

Detailed Description

If \( z = Ax + b,\) implements a cost of the form:

\[ (z_1^2 + z_2^2 + ... + z_{n-1}^2) / z_0. \]

Note that this cost is convex when we additionally constrain z_0 > 0.

It is treated as a generic nonlinear objective by most solvers.

Costs of this form are sometimes referred to as "quadratic over linear".

#include <drake/solvers/cost.h>

Public Member Functions

 PerspectiveQuadraticCost (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b)
 Construct a cost of the form (z_1^2 + z_2^2 + ... More...
 
 ~PerspectiveQuadraticCost () override
 
const Eigen::MatrixXd & A () const
 
const Eigen::VectorXd & b () const
 
void UpdateCoefficients (const Eigen::Ref< const Eigen::MatrixXd > &new_A, const Eigen::Ref< const Eigen::VectorXd > &new_b)
 Updates the coefficients of the cost. More...
 
Does not allow copy, move, or assignment
 PerspectiveQuadraticCost (const PerspectiveQuadraticCost &)=delete
 
PerspectiveQuadraticCostoperator= (const PerspectiveQuadraticCost &)=delete
 
 PerspectiveQuadraticCost (PerspectiveQuadraticCost &&)=delete
 
PerspectiveQuadraticCostoperator= (PerspectiveQuadraticCost &&)=delete
 
- Public Member Functions inherited from Cost
 Cost (const Cost &)=delete
 
Costoperator= (const Cost &)=delete
 
 Cost (Cost &&)=delete
 
Costoperator= (Cost &&)=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...
 
 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 Cost
 Cost (int num_vars, const std::string &description="")
 Constructs a cost evaluator. More...
 
- 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)
 

Constructor & Destructor Documentation

◆ PerspectiveQuadraticCost() [1/3]

◆ PerspectiveQuadraticCost() [2/3]

◆ PerspectiveQuadraticCost() [3/3]

PerspectiveQuadraticCost ( const Eigen::Ref< const Eigen::MatrixXd > &  A,
const Eigen::Ref< const Eigen::VectorXd > &  b 
)

Construct a cost of the form (z_1^2 + z_2^2 + ...

  • z_{n-1}^2) / z_0 where z = Ax + b.
    Parameters
    ALinear term.
    bConstant term.

◆ ~PerspectiveQuadraticCost()

~PerspectiveQuadraticCost ( )
override

Member Function Documentation

◆ A()

const Eigen::MatrixXd& A ( ) const

◆ b()

const Eigen::VectorXd& b ( ) const

◆ 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
xInput vector.
yOutput 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
xInput vector.
yOutput 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]xInput vector.
[out]yOutput 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.

◆ operator=() [1/2]

◆ operator=() [2/2]

PerspectiveQuadraticCost& operator= ( const PerspectiveQuadraticCost )
delete

◆ UpdateCoefficients()

void UpdateCoefficients ( const Eigen::Ref< const Eigen::MatrixXd > &  new_A,
const Eigen::Ref< const Eigen::VectorXd > &  new_b 
)

Updates the coefficients of the cost.

Note that the number of variables (columns of A) cannot change.

Parameters
new_ANew linear term.
new_bNew constant term.

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