There are several ways that string representations can be created from an expression, but the :func:`expression_to_string <pyomo.core.expr.expression_to_string>` function provides the most flexible mechanism for generating a string representation. The options to this function control distinct aspects of the string representation.
The default string representation is an algebraic form, which closely mimics the Python operations used to construct an expression. The :data:`verbose` flag can be set to :const:`True` to generate a string representation that is a nested functional form. For example:
.. literalinclude:: ../../src/expr/managing_ex1.spy
The string representation used for variables in expression can be customized to define different label formats. If the :data:`labeler` option is specified, then this function (or class functor) is used to generate a string label used to represent the variable. Pyomo defines a variety of labelers in the pyomo.core.base.label module. For example, the :class:`NumericLabeler` defines a functor that can be used to sequentially generate simple labels with a prefix followed by the variable count:
.. literalinclude:: ../../src/expr/managing_ex2.spy
The :data:`smap` option is used to specify a symbol map object (:class:`SymbolMap <pyomo.core.expr.symbol_map.SymbolMap>`), which caches the variable label data. This option is normally specified in contexts where the string representations for many expressions are being generated. In that context, a symbol map ensures that variables in different expressions have a consistent label in their associated string representations.
There are two other standard ways to generate string representations:
- Call the :func:`__str__` magic method (e.g. using the Python :func:`str()` function. This calls :func:`expression_to_string <pyomo.core.expr.expression_to_string>`, using the default values for all arguments.
- Call the :func:`to_string` method on the :class:`ExpressionBase<pyomo.core.expr.ExpressionBase>` class. This calls :func:`expression_to_string <pyomo.core.expr.expression_to_string>` and accepts the same arguments.
Expressions can be evaluated when all variables and parameters in the expression have a value. The :func:`value <pyomo.core.expr.value>` function can be used to walk the expression tree and compute the value of an expression. For example:
.. literalinclude:: ../../src/expr/managing_ex5.spy
Additionally, expressions define the :func:`__call__` method, so the following is another way to compute the value of an expression:
.. literalinclude:: ../../src/expr/managing_ex6.spy
If a parameter or variable is undefined, then the :func:`value <pyomo.core.expr.value>` function and :func:`__call__` method will raise an exception. This exception can be suppressed using the :attr:`exception` option. For example:
.. literalinclude:: ../../src/expr/managing_ex7.spy
This option is useful in contexts where adding a try block is inconvenient in your modeling script.
Note
Both the :func:`value <pyomo.core.expr.value>` function and :func:`__call__` method call the :func:`evaluate_expression <pyomo.core.expr.evaluate_expression>` function. In practice, this function will be slightly faster, but the difference is only meaningful when expressions are evaluated many times.
Expression transformations sometimes need to find all nodes in an expression tree that are of a given type. Pyomo contains two utility functions that support this functionality. First, the :func:`identify_components <pyomo.core.expr.identify_components>` function is a generator function that walks the expression tree and yields all nodes whose type is in a specified set of node types. For example:
.. literalinclude:: ../../src/expr/managing_ex8.spy
The :func:`identify_variables <pyomo.core.expr.identify_variables>` function is a generator function that yields all nodes that are variables. Pyomo uses several different classes to represent variables, but this set of variable types does not need to be specified by the user. However, the :attr:`include_fixed` flag can be specified to omit fixed variables. For example:
.. literalinclude:: ../../src/expr/managing_ex9.spy
Many of the utility functions defined above are implemented by walking an expression tree and performing an operation at nodes in the tree. For example, evaluating an expression is performed using a post-order depth-first search process where the value of a node is computed using the values of its children.
Walking an expression tree can be tricky, and the code requires intimate knowledge of the design of the expression system. Pyomo includes several classes that define visitor patterns for walking expression tree:
- :class:`StreamBasedExpressionVisitor <pyomo.core.expr.StreamBasedExpressionVisitor>`
- The most general and extensible visitor class. This visitor
implements an event-based approach for walking the tree inspired by
the
expatlibrary for processing XML files. The visitor has seven event callbacks that users can hook into, providing very fine-grained control over the expression walker. - :class:`SimpleExpressionVisitor <pyomo.core.expr.SimpleExpressionVisitor>`
- A :func:`visitor` method is called for each node in the tree, and the visitor class collects information about the tree.
- :class:`ExpressionValueVisitor <pyomo.core.expr.ExpressionValueVisitor>`
- When the :func:`visitor` method is called on each node in the tree, the values of its children have been computed. The value of the node is returned from :func:`visitor`.
- :class:`ExpressionReplacementVisitor <pyomo.core.expr.ExpressionReplacementVisitor>`
- When the :func:`visitor` method is called on each node in the tree, it may clone or otherwise replace the node using objects for its children (which themselves may be clones or replacements from the original child objects). The new node object is returned from :func:`visitor`.
These classes define a variety of suitable tree search methods:
- :class:`StreamBasedExpressionVisitor <pyomo.core.expr.StreamBasedExpressionVisitor>`
walk_expression: depth-first traversal of the expression tree.
- :class:`ExpressionReplacementVisitor <pyomo.core.expr.ExpressionReplacementVisitor>`
walk_expression: depth-first traversal of the expression tree.
- :class:`SimpleExpressionVisitor <pyomo.core.expr.SimpleExpressionVisitor>`
xbfs: breadth-first search where leaf nodes are immediately visitedxbfs_yield_leaves: breadth-first search where leaf nodes are immediately visited, and the visit method yields a value
- :class:`ExpressionValueVisitor <pyomo.core.expr.ExpressionValueVisitor>`
dfs_postorder_stack: postorder depth-first search using a nonrecursive stack
To implement a visitor object, a user needs to provide specializations for specific events. For legacy visitors based on the PyUtilib visitor pattern (e.g., :class:`SimpleExpressionVisitor` and :class:`ExpressionValueVisitor`), one must create a subclass of one of these classes and override at least one of the following:
- :func:`visitor`
- Defines the operation that is performed when a node is visited. In the :class:`ExpressionValueVisitor <pyomo.core.expr.ExpressionValueVisitor>` and :class:`ExpressionReplacementVisitor <pyomo.core.expr.ExpressionReplacementVisitor>` visitor classes, this method returns a value that is used by its parent node.
- :func:`visiting_potential_leaf`
- Checks if the search should terminate with this node. If no,
then this method returns the tuple
(False, None). If yes, then this method returns(False, value), where value is computed by this method. This method is not used in the :class:`SimpleExpressionVisitor <pyomo.core.expr.SimpleExpressionVisitor>` visitor class. - :func:`finalize`
- This method defines the final value that is returned from the visitor. This is not normally redefined.
For modern visitors based on the :class:`StreamBasedExpressionVisitor <pyomo.core.expr.StreamBasedExpressionVisitor>`, one can either define a subclass, pass the callbacks to an instance of the base class, or assign the callbacks as attributes on an instance of the base class. The :class:`StreamBasedExpressionVisitor <pyomo.core.expr.StreamBasedExpressionVisitor>` provides seven callbacks, which are documented in the class documentation.
Detailed documentation of the APIs for these methods is provided with the class documentation for these visitors.
In this example, we describe an visitor class that counts the number of nodes in an expression (including leaf nodes). Consider the following class:
.. literalinclude:: ../../src/expr/managing_visitor1.spy
The class constructor creates a counter, and the :func:`visit` method increments this counter for every node that is visited. The :func:`finalize` method returns the value of this counter after the tree has been walked. The following function illustrates this use of this visitor class:
.. literalinclude:: ../../src/expr/managing_visitor2.spy
In this example, we describe an visitor class that clones the expression tree (including leaf nodes). Consider the following class:
.. literalinclude:: ../../src/expr/managing_visitor3.spy
The :func:`visit` method creates a new expression node with children specified by :attr:`values`. The :func:`visiting_potential_leaf` method performs a :func:`deepcopy` on leaf nodes, which are native Python types or non-expression objects.
.. literalinclude:: ../../src/expr/managing_visitor4.spy
In this example, we describe an visitor class that replaces variables with scaled variables, using a mutable parameter that can be modified later. the following class:
.. literalinclude:: ../../src/expr/managing_visitor5.spy
No other method need to be defined. The :func:`beforeChild` method identifies variable nodes and returns a product expression that contains a mutable parameter.
.. literalinclude:: ../../src/expr/managing_visitor6.spy
The :func:`scale_expression` function is called with an expression and a dictionary, :attr:`scale`, that maps variable ID to model parameter. For example:
.. literalinclude:: ../../src/expr/managing_visitor7.spy