FormulaPositiveSemidefinite Class Reference

Detailed Description

Symbolic formula representing positive-semidefinite (PSD) constraint.

#include <drake/common/symbolic/expression/formula_cell.h>

Public Member Functions
	FormulaPositiveSemidefinite (const Eigen::Ref< const MatrixX< Expression > > &m)
	Constructs a positive-semidefinite formula from a symmetric matrix m.
template<typename Derived>
	FormulaPositiveSemidefinite (const Eigen::TriangularView< Derived, Eigen::Lower > &l)
	Constructs a symbolic positive-semidefinite formula from a lower triangular-view l.
template<typename Derived>
	FormulaPositiveSemidefinite (const Eigen::TriangularView< Derived, Eigen::Upper > &u)
	Constructs a symbolic positive-semidefinite formula from an upper triangular-view u.
	~FormulaPositiveSemidefinite () override
void	HashAppendDetail (DelegatingHasher *) const override
	Sends all hash-relevant bytes for this FormulaCell type into the given hasher, per the hash_append generic hashing concept – except for get_kind(), because Formula already sends that.
Variables	GetFreeVariables () const override
	Returns set of free variables in formula.
bool	EqualTo (const FormulaCell &f) const override
	Checks structural equality.
bool	Less (const FormulaCell &f) const override
	Checks ordering between this PSD formula and f.
bool	Evaluate (const Environment &env) const override
	Evaluates under a given environment.
Formula	Substitute (const Substitution &s) const override
	Returns a Formula obtained by replacing all occurrences of the variables in s in the current formula cell with the corresponding expressions in s.
std::ostream &	Display (std::ostream &os) const override
	Outputs string representation of formula into output stream os.
const MatrixX< symbolic::Expression > &	get_matrix () const
	Returns the corresponding matrix in this PSD formula.
Public Member Functions inherited from FormulaCell
FormulaKind	get_kind () const
	Returns kind of formula.
	FormulaCell ()=delete
	Default constructor (deleted).
FormulaCell &	operator= (FormulaCell &&f)=delete
	Move-assign (deleted).
FormulaCell &	operator= (const FormulaCell &f)=delete
	Copy-assign (deleted).

Additional Inherited Members
Protected Member Functions inherited from FormulaCell
	FormulaCell (FormulaCell &&f)=default
	Move-construct a formula from an rvalue.
	FormulaCell (const FormulaCell &f)=default
	Copy-construct a formula from an lvalue.
	FormulaCell (FormulaKind k)
	Construct FormulaCell of kind k.
virtual	~FormulaCell ()
	Default destructor.

Constructor & Destructor Documentation

FormulaPositiveSemidefinite() [1/3]

FormulaPositiveSemidefinite ( const Eigen::Ref< const MatrixX< Expression > > & m )

explicit

Constructs a positive-semidefinite formula from a symmetric matrix m.

Exceptions

std::exception

if m is not symmetric.

Note

This constructor checks if m is symmetric, which can be costly.

FormulaPositiveSemidefinite() [2/3]

template<typename Derived>

FormulaPositiveSemidefinite ( const Eigen::TriangularView< Derived, Eigen::Lower > & l )

explicit

Constructs a symbolic positive-semidefinite formula from a lower triangular-view l.

FormulaPositiveSemidefinite() [3/3]

template<typename Derived>

FormulaPositiveSemidefinite ( const Eigen::TriangularView< Derived, Eigen::Upper > & u )

explicit

Constructs a symbolic positive-semidefinite formula from an upper triangular-view u.

~FormulaPositiveSemidefinite()

~FormulaPositiveSemidefinite ( )

override

Member Function Documentation

Display()

std::ostream & Display ( std::ostream & os ) const

overridevirtual

Outputs string representation of formula into output stream os.

Implements FormulaCell.

EqualTo()

bool EqualTo ( const FormulaCell & c ) const

nodiscardoverridevirtual

Checks structural equality.

Implements FormulaCell.

Evaluate()

bool Evaluate ( const Environment & env ) const

nodiscardoverridevirtual

Evaluates under a given environment.

Implements FormulaCell.

get_matrix()

const MatrixX< symbolic::Expression > & get_matrix ( ) const

nodiscard

Returns the corresponding matrix in this PSD formula.

GetFreeVariables()

Variables GetFreeVariables ( ) const

nodiscardoverridevirtual

Returns set of free variables in formula.

Implements FormulaCell.

HashAppendDetail()

void HashAppendDetail ( DelegatingHasher * ) const

overridevirtual

Sends all hash-relevant bytes for this FormulaCell type into the given hasher, per the hash_append generic hashing concept – except for get_kind(), because Formula already sends that.

Implements FormulaCell.

Less()

bool Less ( const FormulaCell & f ) const

nodiscardoverridevirtual

Checks ordering between this PSD formula and f.

The ordering between two PSD formulas psd1 and psd2 are determined by the ordering between the two matrices m1 in psd1 and m2 in psd2.

First, we compare the size of m1 and m2:

• If m1 is smaller than m2, psd1.Less(psd2) is true.
• If m2 is smaller than m1, psd1.Less(psd2) is false.

If m1 and m2 are of the same size, we perform element-wise comparison by following column-major order. See the following example:

m1 << x + y, -3.14,
      -3.14,     y;
m2 << x + y,  3.14,
       3.14,     y;
const Formula psd1{positive_semidefinite(m1)};
const Formula psd2{positive_semidefinite(m2)};
 
EXPECT_TRUE(psd1.Less(psd2));

Note

In the code above, psd1.Less(psd2) holds because we have

• m1 in column-major ordering : (x + y) -3.14 -3.14 y_
• m2 in column-major ordering : (x + y) 3.14 3.14 y_.

Implements FormulaCell.

Substitute()

Formula Substitute ( const Substitution & s ) const

nodiscardoverridevirtual

Returns a Formula obtained by replacing all occurrences of the variables in s in the current formula cell with the corresponding expressions in s.

Implements FormulaCell.

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

• drake/common/symbolic/expression/formula_cell.h