Linear constraints over integer variables
Functionality by programming task » Programming models » Using integer variables and constraints

## Functions

void | Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, int c, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, IntVar y, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, int c, Reify r, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, IntVar y, Reify r, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, int c, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, IntVar y, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, int c, Reify r, IntPropLevel ipl=IPL_DEF)
| Post propagator for .
void | Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, IntVar y, Reify r, IntPropLevel ipl=IPL_DEF)
| Post propagator for .

## Detailed Description

All variants for linear constraints over integer variables share the following properties:

- Bounds consistency (over the real numbers) is supported for all constraints (actually, for disequlities always domain consistency is used as it is cheaper). Domain consistency is supported for all non-reified constraint. As bounds consistency for inequalities coincides with domain consistency, the only real variation is for linear equations. Domain consistent linear equations have exponential complexity, so use with care!
- If the integer propagation level IPL_DEF is used as argument (hence, default propagation) and the linear constraint is sufficiently simple (two variables with unit coefficients), the domain consistent propagation is used.
- Variables occurring multiply in the argument arrays are replaced by a single occurrence: for example, becomes .
- If in the above simplification the value for (or for and ) exceeds the limits for integers as defined in Int::Limits, an exception of type Int::OutOfLimits is thrown.
- Assume the constraint . If exceeds the maximal available precision (at least ), an exception of type Int::OutOfLimits is thrown.
- In all other cases, the created propagators are accurate (that is, they will not silently overflow during propagation).

## Function Documentation

## linear() [1/8]

void Gecode::linear | ( | Home | home,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | int | c,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Definition at line 41 of file linear-int.cpp.

## linear() [2/8]

void Gecode::linear | ( | Home | home,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | IntVar | y,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Definition at line 97 of file linear-int.cpp.

## linear() [3/8]

void Gecode::linear | ( | Home | home,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | int | c,
|  | Reify | r,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Definition at line 54 of file linear-int.cpp.

## linear() [4/8]

void Gecode::linear | ( | Home | home,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | IntVar | y,
|  | Reify | r,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Definition at line 127 of file linear-int.cpp.

## linear() [5/8]

void Gecode::linear | ( | Home | home,
|  | const IntArgs & | a,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | int | c,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 67 of file linear-int.cpp.

## linear() [6/8]

void Gecode::linear | ( | Home | home,
|  | const IntArgs & | a,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | IntVar | y,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 141 of file linear-int.cpp.

## linear() [7/8]

void Gecode::linear | ( | Home | home,
|  | const IntArgs & | a,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | int | c,
|  | Reify | r,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 82 of file linear-int.cpp.

## linear() [8/8]

void Gecode::linear | ( | Home | home,
|  | const IntArgs & | a,
|  | const IntVarArgs & | x,
|  | IntRelType | irt,
|  | IntVar | y,
|  | Reify | r,
|  | IntPropLevel | ipl = IPL_DEF )

Post propagator for .

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 173 of file linear-int.cpp.