operations_research::math_opt::QuadraticExpression Class Reference

#include <variable_and_expressions.h>

Public Member Functions
	QuadraticExpression ()=default
	QuadraticExpression (const QuadraticExpression &other)=default
	QuadraticExpression (QuadraticExpression &&other) noexcept
	QuadraticExpression (std::initializer_list< QuadraticTerm > quadratic_terms, std::initializer_list< LinearTerm > linear_terms, double offset)
	QuadraticExpression (double offset)
	QuadraticExpression (Variable variable)
	QuadraticExpression (const LinearTerm &term)
	QuadraticExpression (LinearExpression expr)
	QuadraticExpression (const QuadraticTerm &term)
QuadraticExpression &	operator= (const QuadraticExpression &other)=default
QuadraticExpression &	operator= (QuadraticExpression &&other) noexcept
double	offset () const
const VariableMap< double > &	linear_terms () const
const QuadraticTermMap< double > &	quadratic_terms () const
QuadraticExpression &	operator+= (double value)
QuadraticExpression &	operator+= (Variable variable)
QuadraticExpression &	operator+= (const LinearTerm &term)
QuadraticExpression &	operator+= (const LinearExpression &expr)
QuadraticExpression &	operator+= (const QuadraticTerm &term)
QuadraticExpression &	operator+= (const QuadraticExpression &expr)
QuadraticExpression &	operator-= (double value)
QuadraticExpression &	operator-= (Variable variable)
QuadraticExpression &	operator-= (const LinearTerm &term)
QuadraticExpression &	operator-= (const LinearExpression &expr)
QuadraticExpression &	operator-= (const QuadraticTerm &term)
QuadraticExpression &	operator-= (const QuadraticExpression &expr)
QuadraticExpression &	operator*= (double value)
QuadraticExpression &	operator/= (double value)
template<typename Iterable>
void	AddSum (const Iterable &items)
	}
template<typename LeftIterable, typename RightIterable>
void	AddInnerProduct (const LeftIterable &left, const RightIterable &right)
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 QuadraticExpression	Sum (const Iterable &items)
static RightIterable QuadraticExpression	InnerProduct (const LeftIterable &left, const RightIterable &right)

Public Attributes
*	this = item

Friends
QuadraticExpression	operator- (QuadraticExpression expr)
std::ostream &	operator<< (std::ostream &ostr, const QuadraticExpression &expr)

Detailed Description

This class represents a sum of quadratic terms, linear terms, and constant offset. For example: "3*x*y + 2*x + 1".

Mixing terms involving variables from different ModelStorage objects will lead to CHECK fails, including from the constructors.

The type owns the associated data representing the terms, and so should usually be passed by (const) reference to avoid unnecessary copies.

Note for implementers: Care must be taken to ensure that linear_terms_.storage() and quadratic_terms_.storage() do not disagree. That is, it is forbidden that both are non-null and not equal. Use CheckModelsAgree() and the initializer_list constructor to enforce this invariant in any class or friend method.

Definition at line 747 of file variable_and_expressions.h.

Constructor & Destructor Documentation

QuadraticExpression() [1/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( )

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.

QuadraticExpression() [2/9]

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

default

QuadraticExpression() [3/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( QuadraticExpression && other )

inlinenoexcept

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

Definition at line 2156 of file variable_and_expressions.h.

QuadraticExpression() [4/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( std::initializer_list< QuadraticTerm > quadratic_terms, std::initializer_list< LinearTerm > linear_terms, double offset )

inline

Users should prefer the default constructor and operator overloads to build expressions.

Definition at line 2179 of file variable_and_expressions.h.

QuadraticExpression() [5/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( double offset )

inline

Definition at line 2197 of file variable_and_expressions.h.

QuadraticExpression() [6/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( Variable variable )

inline

Definition at line 2200 of file variable_and_expressions.h.

QuadraticExpression() [7/9]

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

inline

Definition at line 2203 of file variable_and_expressions.h.

QuadraticExpression() [8/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( LinearExpression expr )

inline

Definition at line 2206 of file variable_and_expressions.h.

QuadraticExpression() [9/9]

operations_research::math_opt::QuadraticExpression::QuadraticExpression ( const QuadraticTerm & term )

inline

Definition at line 2215 of file variable_and_expressions.h.

Member Function Documentation

AddInnerProduct()

template<typename LeftIterable, typename RightIterable>

void operations_research::math_opt::QuadraticExpression::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 2767 of file variable_and_expressions.h.

AddSum()

template<typename Iterable>

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

inline

}

Definition at line 2753 of file variable_and_expressions.h.

Evaluate()

double operations_research::math_opt::QuadraticExpression::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 linear_terms() or quadratic_terms() is missing from variables_values.

Definition at line 118 of file variable_and_expressions.cc.

EvaluateWithDefaultZero()

double operations_research::math_opt::QuadraticExpression::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 140 of file variable_and_expressions.cc.

InnerProduct()

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

inlinestatic

Definition at line 2773 of file variable_and_expressions.h.

linear_terms()

const VariableMap< double > & operations_research::math_opt::QuadraticExpression::linear_terms ( ) const

inline

Definition at line 2222 of file variable_and_expressions.h.

offset()

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

inline

Definition at line 2220 of file variable_and_expressions.h.

operator*=()

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

inline

Note

Not adding/removing/altering variables in expression, just modifying coefficients, so no need to check that models agree.

Definition at line 2719 of file variable_and_expressions.h.

operator+=() [1/6]

QuadraticExpression & operations_research::math_opt::QuadraticExpression::operator+= ( const LinearExpression & expr )

inline

See comment in LinearExpression::operator+=.

Definition at line 2620 of file variable_and_expressions.h.

operator+=() [2/6]

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

inline

Definition at line 2614 of file variable_and_expressions.h.

operator+=() [3/6]

QuadraticExpression & operations_research::math_opt::QuadraticExpression::operator+= ( const QuadraticExpression & expr )

inline

See comment in LinearExpression::operator+=.

Definition at line 2641 of file variable_and_expressions.h.

operator+=() [4/6]

QuadraticExpression & operations_research::math_opt::QuadraticExpression::operator+= ( const QuadraticTerm & term )

inline

Definition at line 2633 of file variable_and_expressions.h.

operator+=() [5/6]

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

inline

In-place arithmetic operators.

These must guarantee that the underlying model storages for linear_terms_ and quadratic_terms_ agree upon exit of the function, using CheckModelsAgree(), the list initializer constructor for QuadraticExpression, or similar logic.

Note

Not touching terms, no need to check models

Definition at line 2602 of file variable_and_expressions.h.

operator+=() [6/6]

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

inline

Definition at line 2608 of file variable_and_expressions.h.

operator-=() [1/6]

QuadraticExpression & operations_research::math_opt::QuadraticExpression::operator-= ( const LinearExpression & expr )

inline

See comment in LinearExpression::operator+=.

Definition at line 2675 of file variable_and_expressions.h.

operator-=() [2/6]

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

inline

Definition at line 2669 of file variable_and_expressions.h.

operator-=() [3/6]

QuadraticExpression & operations_research::math_opt::QuadraticExpression::operator-= ( const QuadraticExpression & expr )

inline

See comment in LinearExpression::operator+=.

Definition at line 2696 of file variable_and_expressions.h.

operator-=() [4/6]

QuadraticExpression & operations_research::math_opt::QuadraticExpression::operator-= ( const QuadraticTerm & term )

inline

Definition at line 2688 of file variable_and_expressions.h.

operator-=() [5/6]

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

inline

Note

Not touching terms, no need to check models

Definition at line 2657 of file variable_and_expressions.h.

operator-=() [6/6]

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

inline

Definition at line 2663 of file variable_and_expressions.h.

operator/=()

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

inline

Note

Not adding/removing/altering variables in expression, just modifying coefficients, so no need to check that models agree.

Definition at line 2739 of file variable_and_expressions.h.

operator=() [1/2]

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

default

operator=() [2/2]

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

inlinenoexcept

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

Definition at line 2168 of file variable_and_expressions.h.

quadratic_terms()

const QuadraticTermMap< double > & operations_research::math_opt::QuadraticExpression::quadratic_terms ( ) const

inline

Definition at line 2226 of file variable_and_expressions.h.

storage()

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

inline

Definition at line 2218 of file variable_and_expressions.h.

Sum()

template<typename Iterable>

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

inlinestatic

Returns the sum of the elements of items.

Specifically, letting (i_1, i_2, ..., i_n) = items returns i_1 + i_2 + ... + i_n.

Example: const Variable a = ...; const Variable b = ...; const std::vector<QuadraticTerm> terms = {a * a, 2 * a * b, 3 * b * a}; QuadraticExpression::Sum(vars) => a^2 + 5 a * b Note, instead of: QuadraticExpression expr(3.0); expr += QuadraticExpression::Sum(items); Prefer: expr.AddSum(items);

See QuadraticExpression::AddSum() for a precise contract on the type Iterable.

Definition at line 2760 of file variable_and_expressions.h.

Friends And Related Symbol Documentation

operator-

QuadraticExpression operator- ( QuadraticExpression expr )

friend

We have 6 types that we must consider arithmetic among:

1. double (scalar value)
2. Variable (affine value)
3. LinearTerm (affine value)
4. LinearExpression (affine value)
5. QuadraticTerm (quadratic value)
6. QuadraticExpression (quadratic value) We care only about those methods that result in a QuadraticExpression. For example, multiplying a linear value with a linear value, or adding a scalar to a quadratic value. The single unary method is:

Note

A friend of QuadraticExpression, but does not touch variables

Definition at line 2353 of file variable_and_expressions.h.

operator<<

std::ostream & operator<< ( std::ostream & ostr, const QuadraticExpression & expr )

friend

Todo

(b/169415597): improve quadratic expression formatting. See b/170991498 for desired improvements for LinearExpression streaming which are also applicable here.

Definition at line 155 of file variable_and_expressions.cc.

Member Data Documentation

this

* operations_research::math_opt::QuadraticExpression::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}; const std::vector<QuadraticTerm> terms = {2 * a * b}; QuadraticExpression expr = 8; expr.AddSum(vars); expr.AddSum(terms); Results in expr having the value 2 * a * b + 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, LinearExpression, QuadraticTerm, or QuadraticExpression (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> vars = {a, b}; const std::vector<double> coeffs = {10.0, 2.0}; QuadraticExpression expr = 3.0; expr.AddInnerProduct(coeffs, vars); expr.AddInnerProduct(vars, vars); Results in expr having the value a^2 + b^2 + 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 are of type double, Variable, LinearTerm, LinearExpression, QuadraticTerm, or QuadraticExpression (or is implicitly convertible to one of these types, e.g. int). Runtime requirements (or CHECK fails):
• The inner product value, and its constitutive intermediate terms, can be represented as a QuadraticExpression (potentially through an implicit conversion).
• 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 822 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