#include <algorithm>
#include <cmath>
#include <cstddef>
#include <functional>
#include <limits>
#include <map>
#include <memory>
#include <ostream>
#include <random>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <utility>
#include <vector>
#include <Eigen/Core>
#include <Eigen/Sparse>
#include "drake/common/cond.h"
#include "drake/common/drake_assert.h"
#include "drake/common/drake_copyable.h"
#include "drake/common/drake_throw.h"
#include "drake/common/dummy_value.h"
#include "drake/common/eigen_types.h"
#include "drake/common/extract_double.h"
#include "drake/common/fmt.h"
#include "drake/common/hash.h"
#include "drake/common/random.h"

Include dependency graph for expression.h:

This graph shows which files directly or indirectly include this file:

Classes
class	Expression
	Represents a symbolic form of an expression. More...

struct	hash< drake::symbolic::Expression >

struct	less< drake::symbolic::Expression >

struct	equal_to< drake::symbolic::Expression >

struct	numeric_limits< drake::symbolic::Expression >

class	uniform_real_distribution< drake::symbolic::Expression >
	Provides std::uniform_real_distribution, U(a, b), for symbolic expressions. More...

class	normal_distribution< drake::symbolic::Expression >
	Provides std::normal_distribution, N(μ, σ), for symbolic expressions. More...

class	exponential_distribution< drake::symbolic::Expression >
	Provides std::exponential_distribution, Exp(λ), for symbolic expressions. More...

struct	dummy_value< symbolic::Expression >
	Specializes common/dummy_value.h. More...

struct	is_eigen_nonvector_expression_double_pair< DerivedV, DerivedB >

struct	is_eigen_vector_expression_double_pair< DerivedV, DerivedB >

Namespaces
	drake

	drake::symbolic

Typedefs
using	Substitution = std::unordered_map< Variable, Expression >

Functions
Expression	operator+ (Expression lhs, const Expression &rhs)

Expression &	operator+= (Expression &lhs, const Expression &rhs)

Expression	operator+ (const Expression &e)

Expression	operator- (Expression lhs, const Expression &rhs)

Expression &	operator-= (Expression &lhs, const Expression &rhs)

Expression	operator- (const Expression &e)

Expression	operator * (Expression lhs, const Expression &rhs)

Expression &	operator *= (Expression &lhs, const Expression &rhs)

Expression	operator/ (Expression lhs, const Expression &rhs)

Expression &	operator/= (Expression &lhs, const Expression &rhs)

Expression	log (const Expression &e)

Expression	abs (const Expression &e)

Expression	exp (const Expression &e)

Expression	sqrt (const Expression &e)

Expression	pow (const Expression &e1, const Expression &e2)

Expression	sin (const Expression &e)

Expression	cos (const Expression &e)

Expression	tan (const Expression &e)

Expression	asin (const Expression &e)

Expression	acos (const Expression &e)

Expression	atan (const Expression &e)

Expression	atan2 (const Expression &e1, const Expression &e2)

Expression	sinh (const Expression &e)

Expression	cosh (const Expression &e)

Expression	tanh (const Expression &e)

Expression	min (const Expression &e1, const Expression &e2)

Expression	max (const Expression &e1, const Expression &e2)

Expression	clamp (const Expression &v, const Expression &lo, const Expression &hi)

Expression	ceil (const Expression &e)

Expression	floor (const Expression &e)

Expression	if_then_else (const Formula &f_cond, const Expression &e_then, const Expression &e_else)

Expression	uninterpreted_function (std::string name, std::vector< Expression > arguments)
	Constructs an uninterpreted-function expression with `name` and `arguments`. More...

void	swap (Expression &a, Expression &b)

std::ostream &	operator<< (std::ostream &os, const Expression &e)

bool	is_constant (const Expression &e)
	Checks if `e` is a constant expression. More...

bool	is_constant (const Expression &e, double v)
	Checks if `e` is a constant expression representing `v`. More...

bool	is_zero (const Expression &e)
	Checks if `e` is 0.0. More...

bool	is_one (const Expression &e)
	Checks if `e` is 1.0. More...

bool	is_neg_one (const Expression &e)
	Checks if `e` is -1.0. More...

bool	is_two (const Expression &e)
	Checks if `e` is 2.0. More...

bool	is_nan (const Expression &e)
	Checks if `e` is NaN. More...

bool	is_variable (const Expression &e)
	Checks if `e` is a variable expression. More...

bool	is_addition (const Expression &e)
	Checks if `e` is an addition expression. More...

bool	is_multiplication (const Expression &e)
	Checks if `e` is a multiplication expression. More...

bool	is_division (const Expression &e)
	Checks if `e` is a division expression. More...

bool	is_log (const Expression &e)
	Checks if `e` is a log expression. More...

bool	is_abs (const Expression &e)
	Checks if `e` is an abs expression. More...

bool	is_exp (const Expression &e)
	Checks if `e` is an exp expression. More...

bool	is_sqrt (const Expression &e)
	Checks if `e` is a square-root expression. More...

bool	is_pow (const Expression &e)
	Checks if `e` is a power-function expression. More...

bool	is_sin (const Expression &e)
	Checks if `e` is a sine expression. More...

bool	is_cos (const Expression &e)
	Checks if `e` is a cosine expression. More...

bool	is_tan (const Expression &e)
	Checks if `e` is a tangent expression. More...

bool	is_asin (const Expression &e)
	Checks if `e` is an arcsine expression. More...

bool	is_acos (const Expression &e)
	Checks if `e` is an arccosine expression. More...

bool	is_atan (const Expression &e)
	Checks if `e` is an arctangent expression. More...

bool	is_atan2 (const Expression &e)
	Checks if `e` is an arctangent2 expression. More...

bool	is_sinh (const Expression &e)
	Checks if `e` is a hyperbolic-sine expression. More...

bool	is_cosh (const Expression &e)
	Checks if `e` is a hyperbolic-cosine expression. More...

bool	is_tanh (const Expression &e)
	Checks if `e` is a hyperbolic-tangent expression. More...

bool	is_min (const Expression &e)
	Checks if `e` is a min expression. More...

bool	is_max (const Expression &e)
	Checks if `e` is a max expression. More...

bool	is_ceil (const Expression &e)
	Checks if `e` is a ceil expression. More...

bool	is_floor (const Expression &e)
	Checks if `e` is a floor expression. More...

bool	is_if_then_else (const Expression &e)
	Checks if `e` is an if-then-else expression. More...

bool	is_uninterpreted_function (const Expression &e)
	Checks if `e` is an uninterpreted-function expression. More...

double	get_constant_value (const Expression &e)
	Returns the constant value of the constant expression `e`. More...

const Variable &	get_variable (const Expression &e)
	Returns the embedded variable in the variable expression `e`. More...

const Expression &	get_argument (const Expression &e)
	Returns the argument in the unary expression `e`. More...

const Expression &	get_first_argument (const Expression &e)
	Returns the first argument of the binary expression `e`. More...

const Expression &	get_second_argument (const Expression &e)
	Returns the second argument of the binary expression `e`. More...

double	get_constant_in_addition (const Expression &e)
	Returns the constant part of the addition expression `e`. More...

const std::map< Expression, double > &	get_expr_to_coeff_map_in_addition (const Expression &e)
	Returns the map from an expression to its coefficient in the addition expression `e`. More...

double	get_constant_in_multiplication (const Expression &e)
	Returns the constant part of the multiplication expression `e`. More...

const std::map< Expression, Expression > &	get_base_to_exponent_map_in_multiplication (const Expression &e)
	Returns the map from a base expression to its exponent expression in the multiplication expression `e`. More...

const std::string &	get_uninterpreted_function_name (const Expression &e)
	Returns the name of an uninterpreted-function expression `e`. More...

const std::vector< Expression > &	get_uninterpreted_function_arguments (const Expression &e)
	Returns the arguments of an uninterpreted-function expression `e`. More...

const Formula &	get_conditional_formula (const Expression &e)
	Returns the conditional formula in the if-then-else expression `e`. More...

const Expression &	get_then_expression (const Expression &e)
	Returns the 'then' expression in the if-then-else expression `e`. More...

const Expression &	get_else_expression (const Expression &e)
	Returns the 'else' expression in the if-then-else expression `e`. More...

Expression	operator+ (const Variable &var)

Expression	operator- (const Variable &var)

Expression	TaylorExpand (const Expression &f, const Environment &a, int order)
	Returns the Taylor series expansion of `f` around `a` of order `order`. More...

bool	operator!= (const uniform_real_distribution< drake::symbolic::Expression > &lhs, const uniform_real_distribution< drake::symbolic::Expression > &rhs)

std::ostream &	operator<< (std::ostream &os, const uniform_real_distribution< drake::symbolic::Expression > &d)

bool	operator!= (const normal_distribution< drake::symbolic::Expression > &lhs, const normal_distribution< drake::symbolic::Expression > &rhs)

std::ostream &	operator<< (std::ostream &os, const normal_distribution< drake::symbolic::Expression > &d)

bool	operator!= (const exponential_distribution< drake::symbolic::Expression > &lhs, const exponential_distribution< drake::symbolic::Expression > &rhs)

std::ostream &	operator<< (std::ostream &os, const exponential_distribution< drake::symbolic::Expression > &d)

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, Expression > &&std::is_same_v< typename MatrixR::Scalar, double >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, double > &&std::is_same_v< typename MatrixR::Scalar, Expression >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, Expression > &&std::is_same_v< typename MatrixR::Scalar, Variable >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, Variable > &&std::is_same_v< typename MatrixR::Scalar, Expression >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, Variable > &&std::is_same_v< typename MatrixR::Scalar, double >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, double > &&std::is_same_v< typename MatrixR::Scalar, Variable >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, Variable > &&std::is_same_v< typename MatrixR::Scalar, Variable >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<typename MatrixL , typename MatrixR >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< MatrixL >, MatrixL > &&std::is_base_of_v< Eigen::MatrixBase< MatrixR >, MatrixR > &&std::is_same_v< typename MatrixL::Scalar, Expression > &&std::is_same_v< typename MatrixR::Scalar, Expression >, internal::ExpressionMatMulResult< MatrixL, MatrixR > >	operator * (const MatrixL &lhs, const MatrixR &rhs)
	Provides the following matrix operations: More...

template<int Dim, int LhsMode, int RhsMode, int LhsOptions, int RhsOptions>
auto	operator * (const Eigen::Transform< Expression, Dim, LhsMode, LhsOptions > &t1, const Eigen::Transform< double, Dim, RhsMode, RhsOptions > &t2)
	Transform<double> * Transform<Expression> => Transform<Expression> More...

template<int Dim, int LhsMode, int RhsMode, int LhsOptions, int RhsOptions>
auto	operator * (const Eigen::Transform< double, Dim, LhsMode, LhsOptions > &t1, const Eigen::Transform< Expression, Dim, RhsMode, RhsOptions > &t2)
	Transform<Expression> * Transform<double> => Transform<Expression> More...

template<typename Derived >
std::enable_if_t< std::is_same_v< typename Derived::Scalar, Expression >, MatrixLikewise< double, Derived > >	Evaluate (const Eigen::MatrixBase< Derived > &m, const Environment &env=Environment{}, RandomGenerator *random_generator=nullptr)
	Evaluates a symbolic matrix `m` using `env` and `random_generator`. More...

Eigen::SparseMatrix< double >	Evaluate (const Eigen::Ref< const Eigen::SparseMatrix< Expression >> &m, const Environment &env=Environment{})
	Evaluates `m` using a given environment (by default, an empty environment). More...

template<typename Derived >
MatrixLikewise< Expression, Derived >	Substitute (const Eigen::MatrixBase< Derived > &m, const Substitution &subst)
	Substitutes a symbolic matrix `m` using a given substitution `subst`. More...

template<typename Derived >
MatrixLikewise< Expression, Derived >	Substitute (const Eigen::MatrixBase< Derived > &m, const Variable &var, const Expression &e)
	Substitutes `var` with `e` in a symbolic matrix `m`. More...

VectorX< Variable >	GetVariableVector (const Eigen::Ref< const VectorX< Expression >> &expressions)
	Constructs a vector of variables from the vector of variable expressions. More...

MatrixX< Expression >	Jacobian (const Eigen::Ref< const VectorX< Expression >> &f, const std::vector< Variable > &vars)
	Computes the Jacobian matrix J of the vector function `f` with respect to `vars`. More...

MatrixX< Expression >	Jacobian (const Eigen::Ref< const VectorX< Expression >> &f, const Eigen::Ref< const VectorX< Variable >> &vars)
	Computes the Jacobian matrix J of the vector function `f` with respect to `vars`. More...

Variables	GetDistinctVariables (const Eigen::Ref< const MatrixX< Expression >> &v)
	Returns the distinct variables in the matrix of expressions. More...

template<typename DerivedA , typename DerivedB >
std::enable_if_t< std::is_base_of_v< Eigen::MatrixBase< DerivedA >, DerivedA > &&std::is_base_of_v< Eigen::MatrixBase< DerivedB >, DerivedB > &&std::is_same_v< typename DerivedA::Scalar, Expression > &&std::is_same_v< typename DerivedB::Scalar, Expression >, bool >	CheckStructuralEquality (const DerivedA &m1, const DerivedB &m2)
	Checks if two Eigen::Matrix<Expression> `m1` and `m2` are structurally equal. More...

template<typename... Rest>
symbolic::Expression	cond (const symbolic::Formula &f_cond, double v_then, Rest... rest)
	Provides specialization of `cond` function defined in drake/common/cond.h file. More...

double	ExtractDoubleOrThrow (const symbolic::Expression &e)
	Returns the symbolic expression's value() as a double. More...

template<typename Derived >
std::enable_if_t< std::is_same_v< typename Derived::Scalar, symbolic::Expression >, MatrixLikewise< double, Derived > >	ExtractDoubleOrThrow (const Eigen::MatrixBase< Derived > &matrix)
	Returns `matrix` as an Eigen::Matrix<double, ...> with the same size allocation as `matrix`. More...

Function Documentation

◆ operator!=() [1/3]

bool std::operator!=	(	const uniform_real_distribution< drake::symbolic::Expression > &	lhs,
		const uniform_real_distribution< drake::symbolic::Expression > &	rhs
	)

◆ operator!=() [2/3]

bool std::operator!=	(	const normal_distribution< drake::symbolic::Expression > &	lhs,
		const normal_distribution< drake::symbolic::Expression > &	rhs
	)

◆ operator!=() [3/3]

bool std::operator!=	(	const exponential_distribution< drake::symbolic::Expression > &	lhs,
		const exponential_distribution< drake::symbolic::Expression > &	rhs
	)

◆ operator<<() [1/3]

std::ostream& std::operator<<	(	std::ostream &	os,
		const uniform_real_distribution< drake::symbolic::Expression > &	d
	)

◆ operator<<() [2/3]

std::ostream& std::operator<<	(	std::ostream &	os,
		const normal_distribution< drake::symbolic::Expression > &	d
	)

◆ operator<<() [3/3]

std::ostream& std::operator<<	(	std::ostream &	os,
		const exponential_distribution< drake::symbolic::Expression > &	d
	)

Classes

Namespaces

Typedefs