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Assignment operators are used to assign values to variables:

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Python Numerical Methods

This notebook contains an excerpt from the Python Programming and Numerical Methods - A Guide for Engineers and Scientists , the content is also available at Berkeley Python Numerical Methods .

The copyright of the book belongs to Elsevier. We also have this interactive book online for a better learning experience. The code is released under the MIT license . If you find this content useful, please consider supporting the work on Elsevier or Amazon !

< 2.0 Variables and Basic Data Structures | Contents | 2.2 Data Structure - Strings >

Variables and Assignment ¶

When programming, it is useful to be able to store information in variables. A variable is a string of characters and numbers associated with a piece of information. The assignment operator , denoted by the “=” symbol, is the operator that is used to assign values to variables in Python. The line x=1 takes the known value, 1, and assigns that value to the variable with name “x”. After executing this line, this number will be stored into this variable. Until the value is changed or the variable deleted, the character x behaves like the value 1.

TRY IT! Assign the value 2 to the variable y. Multiply y by 3 to show that it behaves like the value 2.

A variable is more like a container to store the data in the computer’s memory, the name of the variable tells the computer where to find this value in the memory. For now, it is sufficient to know that the notebook has its own memory space to store all the variables in the notebook. As a result of the previous example, you will see the variable “x” and “y” in the memory. You can view a list of all the variables in the notebook using the magic command %whos .

TRY IT! List all the variables in this notebook

Note that the equal sign in programming is not the same as a truth statement in mathematics. In math, the statement x = 2 declares the universal truth within the given framework, x is 2 . In programming, the statement x=2 means a known value is being associated with a variable name, store 2 in x. Although it is perfectly valid to say 1 = x in mathematics, assignments in Python always go left : meaning the value to the right of the equal sign is assigned to the variable on the left of the equal sign. Therefore, 1=x will generate an error in Python. The assignment operator is always last in the order of operations relative to mathematical, logical, and comparison operators.

TRY IT! The mathematical statement x=x+1 has no solution for any value of x . In programming, if we initialize the value of x to be 1, then the statement makes perfect sense. It means, “Add x and 1, which is 2, then assign that value to the variable x”. Note that this operation overwrites the previous value stored in x .

There are some restrictions on the names variables can take. Variables can only contain alphanumeric characters (letters and numbers) as well as underscores. However, the first character of a variable name must be a letter or underscores. Spaces within a variable name are not permitted, and the variable names are case-sensitive (e.g., x and X will be considered different variables).

TIP! Unlike in pure mathematics, variables in programming almost always represent something tangible. It may be the distance between two points in space or the number of rabbits in a population. Therefore, as your code becomes increasingly complicated, it is very important that your variables carry a name that can easily be associated with what they represent. For example, the distance between two points in space is better represented by the variable dist than x , and the number of rabbits in a population is better represented by nRabbits than y .

Note that when a variable is assigned, it has no memory of how it was assigned. That is, if the value of a variable, y , is constructed from other variables, like x , reassigning the value of x will not change the value of y .

EXAMPLE: What value will y have after the following lines of code are executed?

WARNING! You can overwrite variables or functions that have been stored in Python. For example, the command help = 2 will store the value 2 in the variable with name help . After this assignment help will behave like the value 2 instead of the function help . Therefore, you should always be careful not to give your variables the same name as built-in functions or values.

TIP! Now that you know how to assign variables, it is important that you learn to never leave unassigned commands. An unassigned command is an operation that has a result, but that result is not assigned to a variable. For example, you should never use 2+2 . You should instead assign it to some variable x=2+2 . This allows you to “hold on” to the results of previous commands and will make your interaction with Python must less confusing.

You can clear a variable from the notebook using the del function. Typing del x will clear the variable x from the workspace. If you want to remove all the variables in the notebook, you can use the magic command %reset .

In mathematics, variables are usually associated with unknown numbers; in programming, variables are associated with a value of a certain type. There are many data types that can be assigned to variables. A data type is a classification of the type of information that is being stored in a variable. The basic data types that you will utilize throughout this book are boolean, int, float, string, list, tuple, dictionary, set. A formal description of these data types is given in the following sections.

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Python Assignment Operator

• Introduction

Chained Assignment

Shorthand assignment, shorthand assignment operators, playground: assignment operator practice, assignment methods.

All assignment operators are used to assign values to variables. Wait, is there more than one assignment operator? Yes, but they're all quite similar to the ones you've seen. You've used the most common assignment operator, and its symbol is a single equals sign ( = ).

For example, to assign x the value of 10 you type the following:

Different Assignment Methods

You have used this assignment statement before to assign values to variables. Apart from this very common way of using it, a few other situations use the same symbol for slightly different assignments.

You can assign the same value to multiple variables in one swoop by using an assignment chain:

This construct assigns 10 to x , y , and z . Using the chained assignment statement in Python is rare, but if you see it around, now you know what that's about.

Shorthand assignments, on the other hand, are a common occurrence in Python code. This is where the other assignment operators come into play. Shorthand assignments make writing code more efficient and can improve readability---at least once you know about them!

For example, think of a situation where you have a variable x and you want to add 1 to that variable:

This works well and is perfectly fine Python code. However, there is a more concise way of writing the same code using shorthand assignment :

Check out how the second line in these two code snippets is different. You don't need to write the name of the variable x a second time using the shorthand operator += like in the example above.

Both code examples shown achieve the exact same result and are equivalent. The shorthand assignment allows you to use less code to complete the task.

Python comes with a couple of shorthand assignment operators. Some of the most common ones include the following:

These operators are combinations of familiar arithmetic operators with the assignment operator ( = ). You have already used some of Python's arithmetic operators, and you'll learn more about them in the upcoming lesson.

Play around and combine different operators you can think of with the assignment operator below.

• Which ones work and do what you expect them to?
• Which ones don't?

Summary: Python Assignment Operator

• Assignment operators are used to assign values to variables
• Shorthand assignment is the most commonly used in Python
• The table summarizing the assignment operators is provided in the lesson
• Chain Assignment : A method used to assign multiple variables at one
• Shorthand Assignment : A series of short forms for manipulating data

Python Operators: Arithmetic, Assignment, Comparison, Logical, Identity, Membership, Bitwise

Operators are special symbols that perform some operation on operands and returns the result. For example, 5 + 6 is an expression where + is an operator that performs arithmetic add operation on numeric left operand 5 and the right side operand 6 and returns a sum of two operands as a result.

Python includes the operator module that includes underlying methods for each operator. For example, the + operator calls the operator.add(a,b) method.

Above, expression 5 + 6 is equivalent to the expression operator.add(5, 6) and operator.__add__(5, 6) . Many function names are those used for special methods, without the double underscores (dunder methods). For backward compatibility, many of these have functions with the double underscores kept.

Python includes the following categories of operators:

Arithmetic Operators

Assignment operators, comparison operators, logical operators, identity operators, membership test operators, bitwise operators.

Arithmetic operators perform the common mathematical operation on the numeric operands.

The arithmetic operators return the type of result depends on the type of operands, as below.

• If either operand is a complex number, the result is converted to complex;
• If either operand is a floating point number, the result is converted to floating point;
• If both operands are integers, then the result is an integer and no conversion is needed.

The following table lists all the arithmetic operators in Python:

The assignment operators are used to assign values to variables. The following table lists all the arithmetic operators in Python:

The comparison operators compare two operands and return a boolean either True or False. The following table lists comparison operators in Python.

The logical operators are used to combine two boolean expressions. The logical operations are generally applicable to all objects, and support truth tests, identity tests, and boolean operations.

The identity operators check whether the two objects have the same id value e.i. both the objects point to the same memory location.

The membership test operators in and not in test whether the sequence has a given item or not. For the string and bytes types, x in y is True if and only if x is a substring of y .

Bitwise operators perform operations on binary operands.

• Compare strings in Python
• Convert file data to list
• Convert User Input to a Number
• Convert String to Datetime in Python
• How to call external commands in Python?
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• How to pass value by reference in Python?
• Remove duplicate items from list in Python
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9. Classes ¶

Classes provide a means of bundling data and functionality together. Creating a new class creates a new type of object, allowing new instances of that type to be made. Each class instance can have attributes attached to it for maintaining its state. Class instances can also have methods (defined by its class) for modifying its state.

Compared with other programming languages, Python’s class mechanism adds classes with a minimum of new syntax and semantics. It is a mixture of the class mechanisms found in C++ and Modula-3. Python classes provide all the standard features of Object Oriented Programming: the class inheritance mechanism allows multiple base classes, a derived class can override any methods of its base class or classes, and a method can call the method of a base class with the same name. Objects can contain arbitrary amounts and kinds of data. As is true for modules, classes partake of the dynamic nature of Python: they are created at runtime, and can be modified further after creation.

In C++ terminology, normally class members (including the data members) are public (except see below Private Variables ), and all member functions are virtual . As in Modula-3, there are no shorthands for referencing the object’s members from its methods: the method function is declared with an explicit first argument representing the object, which is provided implicitly by the call. As in Smalltalk, classes themselves are objects. This provides semantics for importing and renaming. Unlike C++ and Modula-3, built-in types can be used as base classes for extension by the user. Also, like in C++, most built-in operators with special syntax (arithmetic operators, subscripting etc.) can be redefined for class instances.

(Lacking universally accepted terminology to talk about classes, I will make occasional use of Smalltalk and C++ terms. I would use Modula-3 terms, since its object-oriented semantics are closer to those of Python than C++, but I expect that few readers have heard of it.)

9.1. A Word About Names and Objects ¶

Objects have individuality, and multiple names (in multiple scopes) can be bound to the same object. This is known as aliasing in other languages. This is usually not appreciated on a first glance at Python, and can be safely ignored when dealing with immutable basic types (numbers, strings, tuples). However, aliasing has a possibly surprising effect on the semantics of Python code involving mutable objects such as lists, dictionaries, and most other types. This is usually used to the benefit of the program, since aliases behave like pointers in some respects. For example, passing an object is cheap since only a pointer is passed by the implementation; and if a function modifies an object passed as an argument, the caller will see the change — this eliminates the need for two different argument passing mechanisms as in Pascal.

9.2. Python Scopes and Namespaces ¶

Before introducing classes, I first have to tell you something about Python’s scope rules. Class definitions play some neat tricks with namespaces, and you need to know how scopes and namespaces work to fully understand what’s going on. Incidentally, knowledge about this subject is useful for any advanced Python programmer.

Let’s begin with some definitions.

A namespace is a mapping from names to objects. Most namespaces are currently implemented as Python dictionaries, but that’s normally not noticeable in any way (except for performance), and it may change in the future. Examples of namespaces are: the set of built-in names (containing functions such as abs() , and built-in exception names); the global names in a module; and the local names in a function invocation. In a sense the set of attributes of an object also form a namespace. The important thing to know about namespaces is that there is absolutely no relation between names in different namespaces; for instance, two different modules may both define a function maximize without confusion — users of the modules must prefix it with the module name.

By the way, I use the word attribute for any name following a dot — for example, in the expression z.real , real is an attribute of the object z . Strictly speaking, references to names in modules are attribute references: in the expression modname.funcname , modname is a module object and funcname is an attribute of it. In this case there happens to be a straightforward mapping between the module’s attributes and the global names defined in the module: they share the same namespace! [ 1 ]

Attributes may be read-only or writable. In the latter case, assignment to attributes is possible. Module attributes are writable: you can write modname.the_answer = 42 . Writable attributes may also be deleted with the del statement. For example, del modname.the_answer will remove the attribute the_answer from the object named by modname .

Namespaces are created at different moments and have different lifetimes. The namespace containing the built-in names is created when the Python interpreter starts up, and is never deleted. The global namespace for a module is created when the module definition is read in; normally, module namespaces also last until the interpreter quits. The statements executed by the top-level invocation of the interpreter, either read from a script file or interactively, are considered part of a module called __main__ , so they have their own global namespace. (The built-in names actually also live in a module; this is called builtins .)

The local namespace for a function is created when the function is called, and deleted when the function returns or raises an exception that is not handled within the function. (Actually, forgetting would be a better way to describe what actually happens.) Of course, recursive invocations each have their own local namespace.

A scope is a textual region of a Python program where a namespace is directly accessible. “Directly accessible” here means that an unqualified reference to a name attempts to find the name in the namespace.

Although scopes are determined statically, they are used dynamically. At any time during execution, there are 3 or 4 nested scopes whose namespaces are directly accessible:

the innermost scope, which is searched first, contains the local names

the scopes of any enclosing functions, which are searched starting with the nearest enclosing scope, contain non-local, but also non-global names

the next-to-last scope contains the current module’s global names

the outermost scope (searched last) is the namespace containing built-in names

If a name is declared global, then all references and assignments go directly to the next-to-last scope containing the module’s global names. To rebind variables found outside of the innermost scope, the nonlocal statement can be used; if not declared nonlocal, those variables are read-only (an attempt to write to such a variable will simply create a new local variable in the innermost scope, leaving the identically named outer variable unchanged).

Usually, the local scope references the local names of the (textually) current function. Outside functions, the local scope references the same namespace as the global scope: the module’s namespace. Class definitions place yet another namespace in the local scope.

It is important to realize that scopes are determined textually: the global scope of a function defined in a module is that module’s namespace, no matter from where or by what alias the function is called. On the other hand, the actual search for names is done dynamically, at run time — however, the language definition is evolving towards static name resolution, at “compile” time, so don’t rely on dynamic name resolution! (In fact, local variables are already determined statically.)

A special quirk of Python is that – if no global or nonlocal statement is in effect – assignments to names always go into the innermost scope. Assignments do not copy data — they just bind names to objects. The same is true for deletions: the statement del x removes the binding of x from the namespace referenced by the local scope. In fact, all operations that introduce new names use the local scope: in particular, import statements and function definitions bind the module or function name in the local scope.

The global statement can be used to indicate that particular variables live in the global scope and should be rebound there; the nonlocal statement indicates that particular variables live in an enclosing scope and should be rebound there.

9.2.1. Scopes and Namespaces Example ¶

This is an example demonstrating how to reference the different scopes and namespaces, and how global and nonlocal affect variable binding:

The output of the example code is:

Note how the local assignment (which is default) didn’t change scope_test 's binding of spam . The nonlocal assignment changed scope_test 's binding of spam , and the global assignment changed the module-level binding.

You can also see that there was no previous binding for spam before the global assignment.

9.3. A First Look at Classes ¶

Classes introduce a little bit of new syntax, three new object types, and some new semantics.

9.3.1. Class Definition Syntax ¶

The simplest form of class definition looks like this:

Class definitions, like function definitions ( def statements) must be executed before they have any effect. (You could conceivably place a class definition in a branch of an if statement, or inside a function.)

In practice, the statements inside a class definition will usually be function definitions, but other statements are allowed, and sometimes useful — we’ll come back to this later. The function definitions inside a class normally have a peculiar form of argument list, dictated by the calling conventions for methods — again, this is explained later.

When a class definition is entered, a new namespace is created, and used as the local scope — thus, all assignments to local variables go into this new namespace. In particular, function definitions bind the name of the new function here.

When a class definition is left normally (via the end), a class object is created. This is basically a wrapper around the contents of the namespace created by the class definition; we’ll learn more about class objects in the next section. The original local scope (the one in effect just before the class definition was entered) is reinstated, and the class object is bound here to the class name given in the class definition header ( ClassName in the example).

9.3.2. Class Objects ¶

Class objects support two kinds of operations: attribute references and instantiation.

Attribute references use the standard syntax used for all attribute references in Python: obj.name . Valid attribute names are all the names that were in the class’s namespace when the class object was created. So, if the class definition looked like this:

then MyClass.i and MyClass.f are valid attribute references, returning an integer and a function object, respectively. Class attributes can also be assigned to, so you can change the value of MyClass.i by assignment. __doc__ is also a valid attribute, returning the docstring belonging to the class: "A simple example class" .

Class instantiation uses function notation. Just pretend that the class object is a parameterless function that returns a new instance of the class. For example (assuming the above class):

creates a new instance of the class and assigns this object to the local variable x .

The instantiation operation (“calling” a class object) creates an empty object. Many classes like to create objects with instances customized to a specific initial state. Therefore a class may define a special method named __init__() , like this:

When a class defines an __init__() method, class instantiation automatically invokes __init__() for the newly created class instance. So in this example, a new, initialized instance can be obtained by:

Of course, the __init__() method may have arguments for greater flexibility. In that case, arguments given to the class instantiation operator are passed on to __init__() . For example,

9.3.3. Instance Objects ¶

Now what can we do with instance objects? The only operations understood by instance objects are attribute references. There are two kinds of valid attribute names: data attributes and methods.

data attributes correspond to “instance variables” in Smalltalk, and to “data members” in C++. Data attributes need not be declared; like local variables, they spring into existence when they are first assigned to. For example, if x is the instance of MyClass created above, the following piece of code will print the value 16 , without leaving a trace:

The other kind of instance attribute reference is a method . A method is a function that “belongs to” an object.

Valid method names of an instance object depend on its class. By definition, all attributes of a class that are function objects define corresponding methods of its instances. So in our example, x.f is a valid method reference, since MyClass.f is a function, but x.i is not, since MyClass.i is not. But x.f is not the same thing as MyClass.f — it is a method object , not a function object.

9.3.4. Method Objects ¶

Usually, a method is called right after it is bound:

In the MyClass example, this will return the string 'hello world' . However, it is not necessary to call a method right away: x.f is a method object, and can be stored away and called at a later time. For example:

will continue to print hello world until the end of time.

What exactly happens when a method is called? You may have noticed that x.f() was called without an argument above, even though the function definition for f() specified an argument. What happened to the argument? Surely Python raises an exception when a function that requires an argument is called without any — even if the argument isn’t actually used…

Actually, you may have guessed the answer: the special thing about methods is that the instance object is passed as the first argument of the function. In our example, the call x.f() is exactly equivalent to MyClass.f(x) . In general, calling a method with a list of n arguments is equivalent to calling the corresponding function with an argument list that is created by inserting the method’s instance object before the first argument.

In general, methods work as follows. When a non-data attribute of an instance is referenced, the instance’s class is searched. If the name denotes a valid class attribute that is a function object, references to both the instance object and the function object are packed into a method object. When the method object is called with an argument list, a new argument list is constructed from the instance object and the argument list, and the function object is called with this new argument list.

9.3.5. Class and Instance Variables ¶

Generally speaking, instance variables are for data unique to each instance and class variables are for attributes and methods shared by all instances of the class:

As discussed in A Word About Names and Objects , shared data can have possibly surprising effects with involving mutable objects such as lists and dictionaries. For example, the tricks list in the following code should not be used as a class variable because just a single list would be shared by all Dog instances:

Correct design of the class should use an instance variable instead:

9.4. Random Remarks ¶

If the same attribute name occurs in both an instance and in a class, then attribute lookup prioritizes the instance:

Data attributes may be referenced by methods as well as by ordinary users (“clients”) of an object. In other words, classes are not usable to implement pure abstract data types. In fact, nothing in Python makes it possible to enforce data hiding — it is all based upon convention. (On the other hand, the Python implementation, written in C, can completely hide implementation details and control access to an object if necessary; this can be used by extensions to Python written in C.)

Clients should use data attributes with care — clients may mess up invariants maintained by the methods by stamping on their data attributes. Note that clients may add data attributes of their own to an instance object without affecting the validity of the methods, as long as name conflicts are avoided — again, a naming convention can save a lot of headaches here.

There is no shorthand for referencing data attributes (or other methods!) from within methods. I find that this actually increases the readability of methods: there is no chance of confusing local variables and instance variables when glancing through a method.

Often, the first argument of a method is called self . This is nothing more than a convention: the name self has absolutely no special meaning to Python. Note, however, that by not following the convention your code may be less readable to other Python programmers, and it is also conceivable that a class browser program might be written that relies upon such a convention.

Any function object that is a class attribute defines a method for instances of that class. It is not necessary that the function definition is textually enclosed in the class definition: assigning a function object to a local variable in the class is also ok. For example:

Now f , g and h are all attributes of class C that refer to function objects, and consequently they are all methods of instances of C — h being exactly equivalent to g . Note that this practice usually only serves to confuse the reader of a program.

Methods may call other methods by using method attributes of the self argument:

Methods may reference global names in the same way as ordinary functions. The global scope associated with a method is the module containing its definition. (A class is never used as a global scope.) While one rarely encounters a good reason for using global data in a method, there are many legitimate uses of the global scope: for one thing, functions and modules imported into the global scope can be used by methods, as well as functions and classes defined in it. Usually, the class containing the method is itself defined in this global scope, and in the next section we’ll find some good reasons why a method would want to reference its own class.

Each value is an object, and therefore has a class (also called its type ). It is stored as object.__class__ .

9.5. Inheritance ¶

Of course, a language feature would not be worthy of the name “class” without supporting inheritance. The syntax for a derived class definition looks like this:

The name BaseClassName must be defined in a namespace accessible from the scope containing the derived class definition. In place of a base class name, other arbitrary expressions are also allowed. This can be useful, for example, when the base class is defined in another module:

Execution of a derived class definition proceeds the same as for a base class. When the class object is constructed, the base class is remembered. This is used for resolving attribute references: if a requested attribute is not found in the class, the search proceeds to look in the base class. This rule is applied recursively if the base class itself is derived from some other class.

There’s nothing special about instantiation of derived classes: DerivedClassName() creates a new instance of the class. Method references are resolved as follows: the corresponding class attribute is searched, descending down the chain of base classes if necessary, and the method reference is valid if this yields a function object.

Derived classes may override methods of their base classes. Because methods have no special privileges when calling other methods of the same object, a method of a base class that calls another method defined in the same base class may end up calling a method of a derived class that overrides it. (For C++ programmers: all methods in Python are effectively virtual .)

An overriding method in a derived class may in fact want to extend rather than simply replace the base class method of the same name. There is a simple way to call the base class method directly: just call BaseClassName.methodname(self, arguments) . This is occasionally useful to clients as well. (Note that this only works if the base class is accessible as BaseClassName in the global scope.)

Python has two built-in functions that work with inheritance:

Use isinstance() to check an instance’s type: isinstance(obj, int) will be True only if obj.__class__ is int or some class derived from int .

Use issubclass() to check class inheritance: issubclass(bool, int) is True since bool is a subclass of int . However, issubclass(float, int) is False since float is not a subclass of int .

9.5.1. Multiple Inheritance ¶

Python supports a form of multiple inheritance as well. A class definition with multiple base classes looks like this:

For most purposes, in the simplest cases, you can think of the search for attributes inherited from a parent class as depth-first, left-to-right, not searching twice in the same class where there is an overlap in the hierarchy. Thus, if an attribute is not found in DerivedClassName , it is searched for in Base1 , then (recursively) in the base classes of Base1 , and if it was not found there, it was searched for in Base2 , and so on.

In fact, it is slightly more complex than that; the method resolution order changes dynamically to support cooperative calls to super() . This approach is known in some other multiple-inheritance languages as call-next-method and is more powerful than the super call found in single-inheritance languages.

Dynamic ordering is necessary because all cases of multiple inheritance exhibit one or more diamond relationships (where at least one of the parent classes can be accessed through multiple paths from the bottommost class). For example, all classes inherit from object , so any case of multiple inheritance provides more than one path to reach object . To keep the base classes from being accessed more than once, the dynamic algorithm linearizes the search order in a way that preserves the left-to-right ordering specified in each class, that calls each parent only once, and that is monotonic (meaning that a class can be subclassed without affecting the precedence order of its parents). Taken together, these properties make it possible to design reliable and extensible classes with multiple inheritance. For more detail, see The Python 2.3 Method Resolution Order .

9.6. Private Variables ¶

“Private” instance variables that cannot be accessed except from inside an object don’t exist in Python. However, there is a convention that is followed by most Python code: a name prefixed with an underscore (e.g. _spam ) should be treated as a non-public part of the API (whether it is a function, a method or a data member). It should be considered an implementation detail and subject to change without notice.

Since there is a valid use-case for class-private members (namely to avoid name clashes of names with names defined by subclasses), there is limited support for such a mechanism, called name mangling . Any identifier of the form __spam (at least two leading underscores, at most one trailing underscore) is textually replaced with _classname__spam , where classname is the current class name with leading underscore(s) stripped. This mangling is done without regard to the syntactic position of the identifier, as long as it occurs within the definition of a class.

Name mangling is helpful for letting subclasses override methods without breaking intraclass method calls. For example:

The above example would work even if MappingSubclass were to introduce a __update identifier since it is replaced with _Mapping__update in the Mapping class and _MappingSubclass__update in the MappingSubclass class respectively.

Note that the mangling rules are designed mostly to avoid accidents; it still is possible to access or modify a variable that is considered private. This can even be useful in special circumstances, such as in the debugger.

Notice that code passed to exec() or eval() does not consider the classname of the invoking class to be the current class; this is similar to the effect of the global statement, the effect of which is likewise restricted to code that is byte-compiled together. The same restriction applies to getattr() , setattr() and delattr() , as well as when referencing __dict__ directly.

9.7. Odds and Ends ¶

Sometimes it is useful to have a data type similar to the Pascal “record” or C “struct”, bundling together a few named data items. The idiomatic approach is to use dataclasses for this purpose:

A piece of Python code that expects a particular abstract data type can often be passed a class that emulates the methods of that data type instead. For instance, if you have a function that formats some data from a file object, you can define a class with methods read() and readline() that get the data from a string buffer instead, and pass it as an argument.

Instance method objects have attributes, too: m.__self__ is the instance object with the method m() , and m.__func__ is the function object corresponding to the method.

9.8. Iterators ¶

By now you have probably noticed that most container objects can be looped over using a for statement:

This style of access is clear, concise, and convenient. The use of iterators pervades and unifies Python. Behind the scenes, the for statement calls iter() on the container object. The function returns an iterator object that defines the method __next__() which accesses elements in the container one at a time. When there are no more elements, __next__() raises a StopIteration exception which tells the for loop to terminate. You can call the __next__() method using the next() built-in function; this example shows how it all works:

Having seen the mechanics behind the iterator protocol, it is easy to add iterator behavior to your classes. Define an __iter__() method which returns an object with a __next__() method. If the class defines __next__() , then __iter__() can just return self :

9.9. Generators ¶

Generators are a simple and powerful tool for creating iterators. They are written like regular functions but use the yield statement whenever they want to return data. Each time next() is called on it, the generator resumes where it left off (it remembers all the data values and which statement was last executed). An example shows that generators can be trivially easy to create:

Anything that can be done with generators can also be done with class-based iterators as described in the previous section. What makes generators so compact is that the __iter__() and __next__() methods are created automatically.

Another key feature is that the local variables and execution state are automatically saved between calls. This made the function easier to write and much more clear than an approach using instance variables like self.index and self.data .

In addition to automatic method creation and saving program state, when generators terminate, they automatically raise StopIteration . In combination, these features make it easy to create iterators with no more effort than writing a regular function.

9.10. Generator Expressions ¶

Some simple generators can be coded succinctly as expressions using a syntax similar to list comprehensions but with parentheses instead of square brackets. These expressions are designed for situations where the generator is used right away by an enclosing function. Generator expressions are more compact but less versatile than full generator definitions and tend to be more memory friendly than equivalent list comprehensions.

Table of Contents

• 9.1. A Word About Names and Objects
• 9.2.1. Scopes and Namespaces Example
• 9.3.1. Class Definition Syntax
• 9.3.2. Class Objects
• 9.3.3. Instance Objects
• 9.3.4. Method Objects
• 9.3.5. Class and Instance Variables
• 9.4. Random Remarks
• 9.5.1. Multiple Inheritance
• 9.6. Private Variables
• 9.7. Odds and Ends
• 9.8. Iterators
• 9.9. Generators
• 9.10. Generator Expressions

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Solving Assignment Problem using Linear Programming in Python

Learn how to use Python PuLP to solve Assignment problems using Linear Programming.

In earlier articles, we have seen various applications of Linear programming such as transportation, transshipment problem, Cargo Loading problem, and shift-scheduling problem. Now In this tutorial, we will focus on another model that comes under the class of linear programming model known as the Assignment problem. Its objective function is similar to transportation problems. Here we minimize the objective function time or cost of manufacturing the products by allocating one job to one machine.

If we want to solve the maximization problem assignment problem then we subtract all the elements of the matrix from the highest element in the matrix or multiply the entire matrix by –1 and continue with the procedure. For solving the assignment problem, we use the Assignment technique or Hungarian method, or Flood’s technique.

The transportation problem is a special case of the linear programming model and the assignment problem is a special case of transportation problem, therefore it is also a special case of the linear programming problem.

In this tutorial, we are going to cover the following topics:

Assignment Problem

A problem that requires pairing two sets of items given a set of paired costs or profit in such a way that the total cost of the pairings is minimized or maximized. The assignment problem is a special case of linear programming.

For example, an operation manager needs to assign four jobs to four machines. The project manager needs to assign four projects to four staff members. Similarly, the marketing manager needs to assign the 4 salespersons to 4 territories. The manager’s goal is to minimize the total time or cost.

Problem Formulation

A manager has prepared a table that shows the cost of performing each of four jobs by each of four employees. The manager has stated his goal is to develop a set of job assignments that will minimize the total cost of getting all 4 jobs.  

Initialize LP Model

In this step, we will import all the classes and functions of pulp module and create a Minimization LP problem using LpProblem class.

Define Decision Variable

In this step, we will define the decision variables. In our problem, we have two variable lists: workers and jobs. Let’s create them using  LpVariable.dicts()  class.  LpVariable.dicts()  used with Python’s list comprehension.  LpVariable.dicts()  will take the following four values:

• First, prefix name of what this variable represents.
• Second is the list of all the variables.
• Third is the lower bound on this variable.
• Fourth variable is the upper bound.
• Fourth is essentially the type of data (discrete or continuous). The options for the fourth parameter are  LpContinuous  or  LpInteger .

Let’s first create a list route for the route between warehouse and project site and create the decision variables using LpVariable.dicts() the method.

Define Objective Function

In this step, we will define the minimum objective function by adding it to the LpProblem  object. lpSum(vector)is used here to define multiple linear expressions. It also used list comprehension to add multiple variables.

Define the Constraints

Here, we are adding two types of constraints: Each job can be assigned to only one employee constraint and Each employee can be assigned to only one job. We have added the 2 constraints defined in the problem by adding them to the LpProblem  object.

Solve Model

In this step, we will solve the LP problem by calling solve() method. We can print the final value by using the following for loop.

From the above results, we can infer that Worker-1 will be assigned to Job-1, Worker-2 will be assigned to job-3, Worker-3 will be assigned to Job-2, and Worker-4 will assign with job-4.

In this article, we have learned about Assignment problems, Problem Formulation, and implementation using the python PuLp library. We have solved the Assignment problem using a Linear programming problem in Python. Of course, this is just a simple case study, we can add more constraints to it and make it more complicated. You can also run other case studies on Cargo Loading problems , Staff scheduling problems . In upcoming articles, we will write more on different optimization problems such as transshipment problem, balanced diet problem. You can revise the basics of mathematical concepts in  this article  and learn about Linear Programming  in this article .

• Solving Blending Problem in Python using Gurobi
• Transshipment Problem in Python Using PuLP

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Solving an Assignment Problem

This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver.

In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview .

The costs of assigning workers to tasks are shown in the following table.

The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task.

MIP solution

The following sections describe how to solve the problem using the MPSolver wrapper .

Import the libraries

The following code imports the required libraries.

Create the data

The following code creates the data for the problem.

The costs array corresponds to the table of costs for assigning workers to tasks, shown above.

Declare the MIP solver

The following code declares the MIP solver.

Create the variables

The following code creates binary integer variables for the problem.

Create the constraints

Create the objective function.

The following code creates the objective function for the problem.

The value of the objective function is the total cost over all variables that are assigned the value 1 by the solver.

Invoke the solver

The following code invokes the solver.

Print the solution

The following code prints the solution to the problem.

Here is the output of the program.

Complete programs

Here are the complete programs for the MIP solution.

CP SAT solution

The following sections describe how to solve the problem using the CP-SAT solver.

Declare the model

The following code declares the CP-SAT model.

The following code sets up the data for the problem.

The following code creates the constraints for the problem.

Here are the complete programs for the CP-SAT solution.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

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Python Operators

Precedence and associativity of operators in python.

• Python Arithmetic Operators
• Difference between / vs. // operator in Python
• Python - Star or Asterisk operator ( * )
• What does the Double Star operator mean in Python?
• Division Operators in Python
• Modulo operator (%) in Python
• Python Logical Operators
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• Difference between 'and' and '&' in Python
• not Operator in Python | Boolean Logic

Ternary Operator in Python

• Python Bitwise Operators

Python Assignment Operators

Assignment operators in python.

• Walrus Operator in Python 3.8
• Increment += and Decrement -= Assignment Operators in Python
• Merging and Updating Dictionary Operators in Python 3.9
• New '=' Operator in Python3.8 f-string

Python Relational Operators

• Comparison Operators in Python
• Python NOT EQUAL operator
• Difference between == and is operator in Python
• Chaining comparison operators in Python
• Python Membership and Identity Operators
• Difference between != and is not operator in Python

In Python programming, Operators in general are used to perform operations on values and variables. These are standard symbols used for logical and arithmetic operations. In this article, we will look into different types of Python operators. 

• OPERATORS: These are the special symbols. Eg- + , * , /, etc.
• OPERAND: It is the value on which the operator is applied.

Types of Operators in Python

• Arithmetic Operators
• Comparison Operators
• Logical Operators
• Bitwise Operators
• Assignment Operators
• Identity Operators and Membership Operators

Arithmetic Operators in Python

Python Arithmetic operators are used to perform basic mathematical operations like addition, subtraction, multiplication , and division .

In Python 3.x the result of division is a floating-point while in Python 2.x division of 2 integers was an integer. To obtain an integer result in Python 3.x floored (// integer) is used.

Example of Arithmetic Operators in Python

Division operators.

In Python programming language Division Operators allow you to divide two numbers and return a quotient, i.e., the first number or number at the left is divided by the second number or number at the right and returns the quotient. 

There are two types of division operators: 

Float division

• Floor division

The quotient returned by this operator is always a float number, no matter if two numbers are integers. For example:

Example: The code performs division operations and prints the results. It demonstrates that both integer and floating-point divisions return accurate results. For example, ’10/2′ results in ‘5.0’ , and ‘-10/2’ results in ‘-5.0’ .

Integer division( Floor division)

The quotient returned by this operator is dependent on the argument being passed. If any of the numbers is float, it returns output in float. It is also known as Floor division because, if any number is negative, then the output will be floored. For example:

Example: The code demonstrates integer (floor) division operations using the // in Python operators . It provides results as follows: ’10//3′ equals ‘3’ , ‘-5//2’ equals ‘-3’ , ‘ 5.0//2′ equals ‘2.0’ , and ‘-5.0//2’ equals ‘-3.0’ . Integer division returns the largest integer less than or equal to the division result.

Precedence of Arithmetic Operators in Python

The precedence of Arithmetic Operators in Python is as follows:

• P – Parentheses
• E – Exponentiation
• M – Multiplication (Multiplication and division have the same precedence)
• D – Division
• A – Addition (Addition and subtraction have the same precedence)
• S – Subtraction

The modulus of Python operators helps us extract the last digit/s of a number. For example:

• x % 10 -> yields the last digit
• x % 100 -> yield last two digits

Arithmetic Operators With Addition, Subtraction, Multiplication, Modulo and Power

Here is an example showing how different Arithmetic Operators in Python work:

Example: The code performs basic arithmetic operations with the values of ‘a’ and ‘b’ . It adds (‘+’) , subtracts (‘-‘) , multiplies (‘*’) , computes the remainder (‘%’) , and raises a to the power of ‘b (**)’ . The results of these operations are printed.

Note: Refer to Differences between / and // for some interesting facts about these two Python operators.

Comparison of Python Operators

In Python Comparison of Relational operators compares the values. It either returns True or False according to the condition.

= is an assignment operator and == comparison operator.

Precedence of Comparison Operators in Python

In Python, the comparison operators have lower precedence than the arithmetic operators. All the operators within comparison operators have the same precedence order.

Example of Comparison Operators in Python

Let’s see an example of Comparison Operators in Python.

Example: The code compares the values of ‘a’ and ‘b’ using various comparison Python operators and prints the results. It checks if ‘a’ is greater than, less than, equal to, not equal to, greater than, or equal to, and less than or equal to ‘b’ .

Logical Operators in Python

Python Logical operators perform Logical AND , Logical OR , and Logical NOT operations. It is used to combine conditional statements.

Precedence of Logical Operators in Python

The precedence of Logical Operators in Python is as follows:

• Logical not
• logical and

Example of Logical Operators in Python

The following code shows how to implement Logical Operators in Python:

Example: The code performs logical operations with Boolean values. It checks if both ‘a’ and ‘b’ are true ( ‘and’ ), if at least one of them is true ( ‘or’ ), and negates the value of ‘a’ using ‘not’ . The results are printed accordingly.

Bitwise Operators in Python

Python Bitwise operators act on bits and perform bit-by-bit operations. These are used to operate on binary numbers.

Precedence of Bitwise Operators in Python

The precedence of Bitwise Operators in Python is as follows:

• Bitwise NOT
• Bitwise Shift
• Bitwise AND
• Bitwise XOR

Here is an example showing how Bitwise Operators in Python work:

Example: The code demonstrates various bitwise operations with the values of ‘a’ and ‘b’ . It performs bitwise AND (&) , OR (|) , NOT (~) , XOR (^) , right shift (>>) , and left shift (<<) operations and prints the results. These operations manipulate the binary representations of the numbers.

Python Assignment operators are used to assign values to the variables.

Let’s see an example of Assignment Operators in Python.

Example: The code starts with ‘a’ and ‘b’ both having the value 10. It then performs a series of operations: addition, subtraction, multiplication, and a left shift operation on ‘b’ . The results of each operation are printed, showing the impact of these operations on the value of ‘b’ .

Identity Operators in Python

In Python, is and is not are the identity operators both are used to check if two values are located on the same part of the memory. Two variables that are equal do not imply that they are identical. 

Example Identity Operators in Python

Let’s see an example of Identity Operators in Python.

Example: The code uses identity operators to compare variables in Python. It checks if ‘a’ is not the same object as ‘b’ (which is true because they have different values) and if ‘a’ is the same object as ‘c’ (which is true because ‘c’ was assigned the value of ‘a’ ).

Membership Operators in Python

In Python, in and not in are the membership operators that are used to test whether a value or variable is in a sequence.

Examples of Membership Operators in Python

The following code shows how to implement Membership Operators in Python:

Example: The code checks for the presence of values ‘x’ and ‘y’ in the list. It prints whether or not each value is present in the list. ‘x’ is not in the list, and ‘y’ is present, as indicated by the printed messages. The code uses the ‘in’ and ‘not in’ Python operators to perform these checks.

in Python, Ternary operators also known as conditional expressions are operators that evaluate something based on a condition being true or false. It was added to Python in version 2.5. 

It simply allows testing a condition in a single line replacing the multiline if-else making the code compact.

Syntax :   [on_true] if [expression] else [on_false] 

Examples of Ternary Operator in Python

The code assigns values to variables ‘a’ and ‘b’ (10 and 20, respectively). It then uses a conditional assignment to determine the smaller of the two values and assigns it to the variable ‘min’ . Finally, it prints the value of ‘min’ , which is 10 in this case.

In Python, Operator precedence and associativity determine the priorities of the operator.

Operator Precedence in Python

This is used in an expression with more than one operator with different precedence to determine which operation to perform first.

Let’s see an example of how Operator Precedence in Python works:

Example: The code first calculates and prints the value of the expression 10 + 20 * 30 , which is 610. Then, it checks a condition based on the values of the ‘name’ and ‘age’ variables. Since the name is “ Alex” and the condition is satisfied using the or operator, it prints “Hello! Welcome.”

Operator Associativity in Python

If an expression contains two or more operators with the same precedence then Operator Associativity is used to determine. It can either be Left to Right or from Right to Left.

The following code shows how Operator Associativity in Python works:

Example: The code showcases various mathematical operations. It calculates and prints the results of division and multiplication, addition and subtraction, subtraction within parentheses, and exponentiation. The code illustrates different mathematical calculations and their outcomes.

To try your knowledge of Python Operators, you can take out the quiz on Operators in Python . 

Python Operator Exercise Questions

Below are two Exercise Questions on Python Operators. We have covered arithmetic operators and comparison operators in these exercise questions. For more exercises on Python Operators visit the page mentioned below.

Q1. Code to implement basic arithmetic operations on integers

Q2. Code to implement Comparison operations on integers

Explore more Exercises: Practice Exercise on Operators in Python

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