#include <variable_and_expressions.h>

Public Member Functions
	LinearExpression ()=default

	LinearExpression (const LinearExpression &other)=default

	LinearExpression (LinearExpression &&other) noexcept

	LinearExpression (std::initializer_list< LinearTerm > terms, double offset)

	LinearExpression (double offset)

	LinearExpression (Variable variable)

	LinearExpression (const LinearTerm &term)

LinearExpression &	operator= (const LinearExpression &other)=default

LinearExpression &	operator= (LinearExpression &&other) noexcept

LinearExpression &	operator+= (const LinearExpression &other)

LinearExpression &	operator+= (const LinearTerm &term)

LinearExpression &	operator+= (Variable variable)

LinearExpression &	operator+= (double value)

LinearExpression &	operator-= (const LinearExpression &other)

LinearExpression &	operator-= (const LinearTerm &term)

LinearExpression &	operator-= (Variable variable)

LinearExpression &	operator-= (double value)

LinearExpression &	operator*= (double value)

LinearExpression &	operator/= (double value)

template<typename Iterable >
void	AddSum (const Iterable &items)
	}

template<typename LeftIterable , typename RightIterable >
void	AddInnerProduct (const LeftIterable &left, const RightIterable &right)

const VariableMap< double > &	terms () const
	Returns the terms in this expression.

double	offset () const

double	Evaluate (const VariableMap< double > &variable_values) const

double	EvaluateWithDefaultZero (const VariableMap< double > &variable_values) const

const ModelStorage *	storage () const

Static Public Member Functions
template<typename Iterable >
static LinearExpression	Sum (const Iterable &items)

template<typename LeftIterable , typename RightIterable >
static LinearExpression	InnerProduct (const LeftIterable &left, const RightIterable &right)

Public Attributes
*	this = item

Friends
LinearExpression	operator- (LinearExpression expr)

std::ostream &	operator<< (std::ostream &ostr, const LinearExpression &expression)

Detailed Description

This class represents a sum of variables multiplied by coefficient and an optional offset constant. For example: "3*x + 2*y + 5".

All operations, including constructor, will raise an assertion if the operands involve variables from different Model objects.

Contrary to Variable type, expressions owns the linear expression their represent. Hence they are usually passed by reference to prevent unnecessary copies.

Todo

(b/169415098): add a function to remove zero terms.

(b/169415834): study if exact zeros should be automatically removed.

(b/169415103): add tests that some expressions don't compile.

Definition at line 229 of file variable_and_expressions.h.

Constructor & Destructor Documentation

◆ LinearExpression() [1/7]

operations_research::math_opt::LinearExpression::LinearExpression ( )

default

For unit testing purpose, we define optional counters. We have to explicitly define the default constructor, copy constructor and assignment operators in that case. Else we use the defaults.

◆ LinearExpression() [2/7]

operations_research::math_opt::LinearExpression::LinearExpression ( const LinearExpression & other )

default

◆ LinearExpression() [3/7]

operations_research::math_opt::LinearExpression::LinearExpression ( LinearExpression && other )

inlinenoexcept

We have to define a custom move constructor as we need to reset storage_ to nullptr.

Definition at line 1390 of file variable_and_expressions.h.

◆ LinearExpression() [4/7]

operations_research::math_opt::LinearExpression::LinearExpression	(	std::initializer_list< LinearTerm >	terms,
		double	offset )

inline

Usually users should use the overloads of operators to build linear expressions. For example, assuming x and y are Variable, then x + 2*y / + 5 will build a LinearExpression automatically.

The same variable may appear multiple times in the input list; we must accumulate the coefficients.

Definition at line 1409 of file variable_and_expressions.h.

◆ LinearExpression() [5/7]

operations_research::math_opt::LinearExpression::LinearExpression ( double offset )

inline

Definition at line 1423 of file variable_and_expressions.h.

◆ LinearExpression() [6/7]

operations_research::math_opt::LinearExpression::LinearExpression ( Variable variable )

inline

Definition at line 1426 of file variable_and_expressions.h.

◆ LinearExpression() [7/7]

operations_research::math_opt::LinearExpression::LinearExpression ( const LinearTerm & term )

inline

Definition at line 1429 of file variable_and_expressions.h.

Member Function Documentation

◆ AddInnerProduct()

template<typename LeftIterable , typename RightIterable >

void operations_research::math_opt::LinearExpression::AddInnerProduct	(	const LeftIterable &	left,
		const RightIterable &	right )

inline

} In particular, the multiplication will be performed on the types of the elements in left and right (take care with low precision types), but the addition will always use double precision.

Definition at line 1703 of file variable_and_expressions.h.

◆ AddSum()

template<typename Iterable >

void operations_research::math_opt::LinearExpression::AddSum ( const Iterable & items )

inline

}

Definition at line 1662 of file variable_and_expressions.h.

◆ Evaluate()

double operations_research::math_opt::LinearExpression::Evaluate ( const VariableMap< double > & variable_values ) const

Compute the numeric value of this expression when variables are substituted by their values in variable_values.

Will CHECK fail if a variable in terms() is missing from variables_values.

Definition at line 59 of file variable_and_expressions.cc.

◆ EvaluateWithDefaultZero()

double operations_research::math_opt::LinearExpression::EvaluateWithDefaultZero ( const VariableMap< double > & variable_values ) const

Compute the numeric value of this expression when variables are substituted by their values in variable_values, or zero if missing from the map.

This function won't check that the variables in the input map are indeed in the same model as the ones of the expression.

Definition at line 71 of file variable_and_expressions.cc.

◆ InnerProduct()

template<typename LeftIterable , typename RightIterable >

LinearExpression operations_research::math_opt::LinearExpression::InnerProduct	(	const LeftIterable &	left,
		const RightIterable &	right )

inlinestatic

Creates a new LinearExpression object equal to the inner product. The implementation is equivalent to: LinearExpression expr; expr.AddInnerProduct(left, right);

Definition at line 1709 of file variable_and_expressions.h.

◆ offset()

double operations_research::math_opt::LinearExpression::offset ( ) const

inline

Definition at line 1724 of file variable_and_expressions.h.

◆ operator*=()

LinearExpression & operations_research::math_opt::LinearExpression::operator*= ( double value )

inline

Definition at line 1645 of file variable_and_expressions.h.

◆ operator+=() [1/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator+= ( const LinearExpression & other )

inline

Here we know that each key in other.terms_ has already been checked and thus we don't need to compare in the loop. Of course this only applies if the other has terms.

Definition at line 1587 of file variable_and_expressions.h.

◆ operator+=() [2/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator+= ( const LinearTerm & term )

inline

Definition at line 1601 of file variable_and_expressions.h.

◆ operator+=() [3/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator+= ( double value )

inline

Definition at line 1612 of file variable_and_expressions.h.

◆ operator+=() [4/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator+= ( Variable variable )

inline

Definition at line 1607 of file variable_and_expressions.h.

◆ operator-=() [1/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator-= ( const LinearExpression & other )

inline

See operator+=.

Definition at line 1617 of file variable_and_expressions.h.

◆ operator-=() [2/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator-= ( const LinearTerm & term )

inline

Definition at line 1629 of file variable_and_expressions.h.

◆ operator-=() [3/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator-= ( double value )

inline

Definition at line 1640 of file variable_and_expressions.h.

◆ operator-=() [4/4]

LinearExpression & operations_research::math_opt::LinearExpression::operator-= ( Variable variable )

inline

Definition at line 1635 of file variable_and_expressions.h.

◆ operator/=()

LinearExpression & operations_research::math_opt::LinearExpression::operator/= ( double value )

inline

Definition at line 1653 of file variable_and_expressions.h.

◆ operator=() [1/2]

LinearExpression & operations_research::math_opt::LinearExpression::operator= ( const LinearExpression & other )

default

◆ operator=() [2/2]

LinearExpression & operations_research::math_opt::LinearExpression::operator= ( LinearExpression && other )

inlinenoexcept

We have to define a custom move assignment operator as we need to reset storage_ to nullptr.

Definition at line 1400 of file variable_and_expressions.h.

◆ storage()

const ModelStorage * operations_research::math_opt::LinearExpression::storage ( ) const

inline

Definition at line 1726 of file variable_and_expressions.h.

◆ Sum()

template<typename Iterable >

LinearExpression operations_research::math_opt::LinearExpression::Sum ( const Iterable & items )

inlinestatic

Creates a new LinearExpression object equal to the sum. The implementation is equivalent to: LinearExpression expr; expr.AddSum(items);

Definition at line 1669 of file variable_and_expressions.h.

◆ terms()

const VariableMap< double > & operations_research::math_opt::LinearExpression::terms ( ) const

inline

Returns the terms in this expression.

Definition at line 1722 of file variable_and_expressions.h.

Friends And Related Symbol Documentation

◆ operator-

LinearExpression operator- ( LinearExpression expr )

friend

We intentionally pass one of the LinearExpression argument by value so that we don't make unnecessary copies of temporary objects by using the move constructor and the returned values optimization (RVO).

Definition at line 1432 of file variable_and_expressions.h.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	ostr,
		const LinearExpression &	expression )

friend

Todo

(b/169415597): improve linear expression format:

make sure to quote the variable name so that we support:

Definition at line 81 of file variable_and_expressions.cc.

Member Data Documentation

◆ this

* operations_research::math_opt::LinearExpression::this = item

Adds each element of items to this.

Specifically, letting (i_1, i_2, ..., i_n) = items adds i_1 + i_2 + ... + i_n to this.

Example: const Variable a = ...; const Variable b = ...; const std::vector<Variable> vars = {a, b}; LinearExpression expr(8.0); expr.AddSum(vars); Results in expr having the value a + b + 8.0.

Compile time requirements:

Iterable is a sequence (an array or object with begin() and end()).
The type of an element of items is one of double, Variable, LinearTerm or LinearExpression (or is implicitly convertible to one of these types, e.g. int).

Note: The implementation is equivalent to: for(const auto item : items) {

Adds the inner product of left and right to this.

Specifically, letting (l_1, l_2 ..., l_n) = left, (r_1, r_2, ..., r_n) = right, adds l_1 * r_1 + l_2 * r_2 + ... + l_n * r_n to this.

Example: const Variable a = ...; const Variable b = ...; const std::vector<Variable> left = {a, b}; const std::vector<double> right = {10.0, 2.0}; LinearExpression expr(3.0); expr.AddInnerProduct(left, right) Results in expr having the value 10.0 * a + 2.0 * b + 3.0.

Compile time requirements:

LeftIterable and RightIterable are both sequences (arrays or objects with begin() and end())
For both left and right, their elements a type of either double, Variable, LinearTerm or LinearExpression (or type implicitly convertible to one of these types, e.g. int).
At least one of left or right has elements with type double (or a type implicitly convertible, e.g. int). Runtime requirements (or CHECK fails):
left and right have an equal number of elements.

Note: The implementation is equivalent to the following pseudocode: for(const auto& [l, r] : zip(left, right)) {

Definition at line 292 of file variable_and_expressions.h.

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

ortools/math_opt/cpp/variable_and_expressions.h
ortools/math_opt/cpp/variable_and_expressions.cc

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ LinearExpression() [1/7]

◆ LinearExpression() [2/7]

◆ LinearExpression() [3/7]

◆ LinearExpression() [4/7]

◆ LinearExpression() [5/7]

◆ LinearExpression() [6/7]

◆ LinearExpression() [7/7]

Member Function Documentation

◆ AddInnerProduct()

◆ AddSum()

◆ Evaluate()

◆ EvaluateWithDefaultZero()

◆ InnerProduct()

◆ offset()

◆ operator*=()

◆ operator+=() [1/4]

◆ operator+=() [2/4]

◆ operator+=() [3/4]

◆ operator+=() [4/4]

◆ operator-=() [1/4]

◆ operator-=() [2/4]

◆ operator-=() [3/4]

◆ operator-=() [4/4]

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ storage()

◆ Sum()

◆ terms()

Friends And Related Symbol Documentation

◆ operator-

◆ operator<<

Member Data Documentation

◆ this