Monomial Class Reference

Detailed Description

Represents a monomial, a product of powers of variables with non-negative integer exponents.

Note that it does not include the coefficient part of a monomial.

#include <drake/common/symbolic/monomial.h>

Public Member Functions
	Monomial ()=default
	Constructs a monomial equal to 1.
	Monomial (std::nullptr_t)
	Constructs a default value.
	Monomial (const std::map< Variable, int, Variable::CompareLess > &powers)
	Constructs a monomial from powers.
	Monomial (const Eigen::Ref< const VectorX< Variable > > &vars, const Eigen::Ref< const Eigen::VectorXi > &exponents)
	Constructs a monomial from a vector of variables vars and their corresponding integer exponents exponents.
	Monomial (const Expression &e)
	Converts an expression to a monomial if the expression is written as ∏ᵢpow(xᵢ, kᵢ), otherwise throws a runtime error.
	Monomial (const Variable &var)
	Constructs a monomial from var.
	Monomial (const Variable &var, int exponent)
	Constructs a monomial from var and exponent.
int	degree (const Variable &v) const
	Returns the degree of this monomial in a variable v.
int	total_degree () const
	Returns the total degree of this monomial.
Variables	GetVariables () const
	Returns the set of variables in this monomial.
const std::map< Variable, int, Variable::CompareLess > &	get_powers () const
	Returns the internal representation of Monomial, the map from a base (Variable) to its exponent (int).
double	Evaluate (const Environment &env) const
	Evaluates under a given environment env.
Eigen::VectorXd	Evaluate (const Eigen::Ref< const VectorX< symbolic::Variable > > &vars, const Eigen::Ref< const Eigen::MatrixXd > &vars_values) const
	Evaluates the monomial for a batch of data.
std::pair< double, Monomial >	EvaluatePartial (const Environment &env) const
	Partially evaluates using a given environment env.
Expression	ToExpression () const
	Returns a symbolic expression representing this monomial.
bool	operator== (const Monomial &m) const
	Checks if this monomial and m represent the same monomial.
bool	operator!= (const Monomial &m) const
	Checks if this monomial and m do not represent the same monomial.
Monomial &	operator*= (const Monomial &m)
	Returns this monomial multiplied by m.
Monomial &	pow_in_place (int p)
	Returns this monomial raised to p.
std::string	to_string () const
	Returns the string representation of this monomial.
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	Monomial (const Monomial &)=default
Monomial &	operator= (const Monomial &)=default
	Monomial (Monomial &&)=default
Monomial &	operator= (Monomial &&)=default

Friends
template<class HashAlgorithm>
void	hash_append (HashAlgorithm &hasher, const Monomial &item) noexcept
	Implements the hash_append generic hashing concept.

Constructor & Destructor Documentation

Monomial() [1/9]

Monomial ( const Monomial & )

default

Monomial() [2/9]

Monomial ( Monomial && )

default

Monomial() [3/9]

Monomial ( )

default

Constructs a monomial equal to 1.

Namely the total degree is zero.

Monomial() [4/9]

Monomial ( std::nullptr_t )

explicit

Constructs a default value.

This overload is used by Eigen when EIGEN_INITIALIZE_MATRICES_BY_ZERO is enabled.

Monomial() [5/9]

Monomial ( const std::map< Variable, int, Variable::CompareLess > & powers )

explicit

Constructs a monomial from powers.

Exceptions

std::exception

if powers includes a negative exponent.

Monomial() [6/9]

Monomial	(	const Eigen::Ref< const VectorX< Variable > > &	vars,
		const Eigen::Ref< const Eigen::VectorXi > &	exponents )

Constructs a monomial from a vector of variables vars and their corresponding integer exponents exponents.

For example, Monomial([x, y, z], [2, 0, 1]) constructs a monomial x²z.

Precondition

The size of vars should be the same as the size of exponents.

Exceptions

std::exception

if exponents includes a negative integer.

Monomial() [7/9]

Monomial ( const Expression & e )

explicit

Converts an expression to a monomial if the expression is written as ∏ᵢpow(xᵢ, kᵢ), otherwise throws a runtime error.

Precondition

is_polynomial(e) should be true.

Monomial() [8/9]

Monomial ( const Variable & var )

explicit

Constructs a monomial from var.

Monomial() [9/9]

Monomial	(	const Variable &	var,
		int	exponent )

Constructs a monomial from var and exponent.

Member Function Documentation

degree()

int degree

(

const Variable &

v

)

const

Returns the degree of this monomial in a variable v.

Evaluate() [1/2]

Eigen::VectorXd Evaluate	(	const Eigen::Ref< const VectorX< symbolic::Variable > > &	vars,
		const Eigen::Ref< const Eigen::MatrixXd > &	vars_values ) const

Evaluates the monomial for a batch of data.

We return monomial_vals such that monomial_vals(j) is obtained by substituting vars(i) with vars_values(i, j), note that vars_values.rows() == vars.rows() and vars_values.cols() == monomial_vals.rows().

Parameters

vars	The variables whose value will be substituted. vars must contain all variables in this->GetVariables(). Also vars cannot contain any duplicate variables, namely vars(i) != vars(j) if i != j.
vars_values	The i'th column of vars_values is the i'th data for vars.

Exceptions

std::exception

if vars doesn't contain all the variables in this->GetVariables().

Evaluate() [2/2]

double Evaluate

(

const Environment &

env

)

const

Evaluates under a given environment env.

Exceptions

std::exception

if there is a variable in this monomial whose assignment is not provided by env.

EvaluatePartial()

std::pair< double, Monomial > EvaluatePartial

(

const Environment &

env

)

const

Partially evaluates using a given environment env.

The evaluation result is of type pair<double, Monomial>. The first component (a double) represents the coefficient part while the second component represents the remaining parts of the monomial which was not evaluated.

Example 1. Evaluate with a fully-specified environment (x³*y²).EvaluatePartial({{x, 2}, {y, 3}}) = (2³ * 3² = 8 * 9 = 72, Monomial{} = 1).

Example 2. Evaluate with a partial environment (x³*y²).EvaluatePartial({{x, 2}}) = (2³ = 8, y²).

get_powers()

const std::map< Variable, int, Variable::CompareLess > & get_powers

(

)

const

Returns the internal representation of Monomial, the map from a base (Variable) to its exponent (int).

GetVariables()

Variables GetVariables

(

)

const

Returns the set of variables in this monomial.

operator!=()

bool operator!=

(

const Monomial &

m

)

const

Checks if this monomial and m do not represent the same monomial.

operator*=()

Monomial & operator*=

(

const Monomial &

m

)

Returns this monomial multiplied by m.

operator=() [1/2]

Monomial & operator= ( const Monomial & )

default

operator=() [2/2]

Monomial & operator= ( Monomial && )

default

operator==()

bool operator==

(

const Monomial &

m

)

const

Checks if this monomial and m represent the same monomial.

Two monomials are equal iff they contain the same variable raised to the same exponent.

pow_in_place()

Monomial & pow_in_place

(

int

p

)

Returns this monomial raised to p.

Exceptions

std::exception

if p is negative.

to_string()

std::string to_string

(

)

const

Returns the string representation of this monomial.

ToExpression()

Expression ToExpression

(

)

const

Returns a symbolic expression representing this monomial.

total_degree()

int total_degree

(

)

const

Returns the total degree of this monomial.

Friends And Related Symbol Documentation

hash_append

template<class HashAlgorithm>

void hash_append ( HashAlgorithm & hasher, const Monomial & item )

friend

Implements the hash_append generic hashing concept.

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

• drake/common/symbolic/monomial.h