# Entities¶

## `Constr`¶

The constraint class.

Constraints are created by adding linear equations to a model using the addConstr method.

### ``` idx: int ``` `property` `readonly` ¶

The unique id of the constraint in the model.

## `Graph`¶

The graph class.

Graphs are created by adding them to a model using the the addGraph method.

### ``` idx ``` `property` `readonly` ¶

The unique id of the graph in the model.

### ``` m ``` `property` `readonly` ¶

The number of edges.

### ``` n ``` `property` `readonly` ¶

The number of vertices.

### ``` sink ``` `property` `readonly` ¶

The sink vertex of the graph.

### ``` source ``` `property` `readonly` ¶

The source vertex of the graph.

### ``` vars ``` `property` `readonly` ¶

The edge variables associated to the graph

## `LinEqua`¶

Class to represent linear equations.

Equations are primarily used as temporary objects when adding linear expressions to models. It should not be necessary to use them by themselves.

The equation consists of an LinExpr and a ConstrSense such that

``````expr = 2 * x + 3 * y + 6
equa = LinEqua(expr, 'L') # 2 * x + 3 * y <= 6
equa = expr <= 0 # 2 * x + 3 * y <= 6
``````

The LinEqua derives from LinExpr and can be manipulated in the same fashion.

### ``` __init__(self, expr, sense='E', rhs=0) ``` `special` ¶

Initialize linear equation

Parameters:

Name Type Description Default
`expr` `Union[flowty.entities.LinExpr, LinEqua]`

An expression or copy from another equation

required
`sense` `str`

The constraints sense as either Equal, LessOrEqual, or GreaterOrEqual.

`'E'`

## `LinExpr`¶

Class to represent linear expressions.

Expressions are operator overloaded so it is possible to do

``````expr = 2 * x - y + 4
expr += 3 * z
expr *= 2
expr += otherExpr
``````

### ``` coefs: List[float] ``` `property` `readonly` ¶

A list of the coefficients.

### ``` constant: float ``` `property` `readonly` ¶

The constant term.

### ``` vars: List[Var] ``` `property` `readonly` ¶

A list of the variables.

### ``` __init__(self, coefs=[], vars=[], constant=0.0) ``` `special` ¶

Initialize linear expression

Parameters:

Name Type Description Default
`coefs` `List[float]`

List of coefficients.

`[]`
`vars` `List[Var]`

List of variables.

`[]`
`constant` `float`

A constant term

`0.0`

Exceptions:

Type Description
`ValueError`

If `coefs` and `vars` do not have the same length.

### ``` addConstant(self, constant) ```¶

Adds a constant to the linear expression.

Parameters:

Name Type Description Default
`constant` `float`

required

### ``` addExpr(self, expr) ```¶

Adds another expression to the linear expression.

Parameters:

Name Type Description Default
`expr` `LinExpr`

required

### ``` addTerm(self, coef, var) ```¶

Adds a term to the linear expression.

Parameters:

Name Type Description Default
`coef` `float`

The coefficients.

required
`var` `Var`

The variable.

required

## `Var`¶

The variable class.

Variables are created by adding variables to a model using the either the addVar method to create a single variable or the addGraph method to add a graph with corresponding edge variables stored in the Graph.vars property.

For an edge variable this class offers the possibility to query for source and target vertices or the edge in the graph.

### ``` edge: Tuple[int, int] ``` `property` `readonly` ¶

The edge of a edge variable.

Exceptions:

Type Description
`ValueError`

If the variable is not associated with a graph.

### ``` idx: int ``` `property` `readonly` ¶

The unique id of the variable in the model.

The lower bound.

### ``` name: str ``` `property` `readonly` ¶

The variable name.

### ``` source: int ``` `property` `readonly` ¶

The source vertex of a edge variable.

Exceptions:

Type Description
`ValueError`

If the variable is not associated with a graph.

### ``` target: int ``` `property` `readonly` ¶

The target vertex of a edge variable.

Exceptions:

Type Description
`ValueError`

If the variable is not associated with a graph.

### ``` type: str ``` `property` `readonly` ¶

The type given with VarType.

The upper bound.

### ``` x: float ``` `property` `readonly` ¶

The value in the current solution