A Fast (and Furious) Introduction to Python¶

Luis Martí, IC/UFF¶

http://lmarti.com; lmarti@ic.uff.br

Advanced Evolutionary Computation: Theory and Practice

This notebook is based on Rick Muller's [A Crash Course in Python for Scientists

](http://nbviewer.ipython.org/gist/rpmuller/5920182)

The notebook is better viewed rendered as slides. You can convert it to slides and view them by:

• using nbconvert with a command like:

  $ ipython nbconvert --to slides --post serve <this-notebook-name.ipynb>
  

• installing Reveal.js - Jupyter/IPython Slideshow Extension
• using the online IPython notebook slide viewer (some slides of the notebook might not be properly rendered).

This and other related IPython notebooks can be found at the course github repository:

• https://github.com/lmarti/evolutionary-computation-course

A fair question: Why Python?¶

• Multi-platform language.

• object-oriented,

• imperative and

• functional programming or

• procedural styles.

• dynamic type system

• automatic memory management

• large and comprehensive standard library.

Python works out of the box¶

Many of the things I used to use a calculator for, I now use Python for:

(If you're typing this into an IPython notebook, or otherwise using notebook file, you hit shift-Enter to evaluate a cell.)

There are some gotchas compared to using a normal calculator.¶

Python integer division, like C or Fortran integer division, truncates the remainder and returns an integer. At least it does in version 2. In version 3, Python returns a floating point number. You can get a sneak preview of this feature in Python 2 by importing the module from the future features:

from __future__ import division

Alternatively, you can convert one of the integers to a floating point number, in which case the division function returns another floating point number.

The import statement¶

In the last few lines, we have sped by a lot of things that we should stop for a moment and explore a little more fully. We've seen, however briefly, two different data types: integers, also known as whole numbers to the non-programming world, and floating point numbers, also known (incorrectly) as decimal numbers to the rest of the world.

We've also seen the first instance of an import statement. Python has a huge number of libraries included with the distribution. To keep things simple, most of these variables and functions are not accessible from a normal Python interactive session. Instead, you have to import the name. For example, there is a math module containing many useful functions. To access, say, the square root function, you can either first

from math import sqrt

and then

or you can simply import the math library itself

You can define variables using the equals (=) sign:

If you try to access a variable that you haven't yet defined, you get an error:

and you need to define it:

You can name a variable almost anything you want. It needs to start with an alphabetical character or "_", can contain alphanumeric charcters plus underscores ("_"). Certain words, however, are reserved for the language:

and, as, assert, break, class, continue, def, del, elif, else, except, 
exec, finally, for, from, global, if, import, in, is, lambda, not, or,
pass, print, raise, return, try, while, with, yield

Trying to define a variable using one of these will result in a syntax error:

The Python Tutorial has more on using Python as an interactive shell. The IPython tutorial makes a nice complement to this, since IPython has a much more sophisticated iteractive shell.

Strings¶

Strings are lists of printable characters, and can be defined using either single quotes

or double quotes

But not both at the same time, unless you want one of the symbols to be part of the string.

Just like the other two data objects we're familiar with (ints and floats), you can assign a string to a variable

The print function is often used for printing character strings:

But it can also print data types other than strings:

In the above snipped, the number 600 (stored in the variable "area") is converted into a string before being printed out.

You can use the + operator to concatenate strings together:

Don't forget the space between the strings, if you want one there.

You can use + to concatenate multiple strings in a single statement:

If you have a lot of words to concatenate together, there are other, more efficient ways to do this. But this is fine for linking a few strings together.

Lists¶

Very often in a programming language, one wants to keep a group of similar items together. Python does this using a data type called lists.

You can access members of the list using the index of that item:

Python lists, like C, but unlike Fortran, use 0 as the index of the first element of a list. Thus, in this example, the 0 element is "Sunday", 1 is "Monday", and so on. If you need to access the nth element from the end of the list, you can use a negative index. For example, the -1 element of a list is the last element:

You can add additional items to the list using the .append() command:

The range() command is a convenient way to make sequential lists of numbers:

Note that range(n) starts at 0 and gives the sequential list of integers less than n. If you want to start at a different number, use range(start,stop).

The lists created above with range have a step of 1 between elements. You can also give a fixed step size via a third command:

You can find out how long a list is using the len() command:

Lists do not have to hold the same data type. For example,¶

However, it's good (but not essential) to use lists for similar objects that are somehow logically connected. If you want to group different data types together into a composite data object, it's best to use tuples, which we will learn about below.

Iteration, Indentation, and Blocks¶

One of the most useful things you can do with lists is to iterate through them, i.e. to go through each element one at a time. To do this in Python, we use the for statement:

This code snippet goes through each element of the list called days_of_the_week and assigns it to the variable day. It then executes everything in the indented block (in this case only one line of code, the print statement) using those variable assignments. When the program has gone through every element of the list, it exists the block.

(Almost) every programming language defines blocks of code in some way. In Fortran, one uses END statements (ENDDO, ENDIF, etc.) to define code blocks. In C, C++, and Perl, one uses curly braces {} to define these blocks.

Python uses a colon (":"), followed by indentation level to define code blocks. Everything at a higher level of indentation is taken to be in the same block. In the above example the block was only a single line, but we could have had longer blocks as well:

The range() command is particularly useful with the for statement to execute loops of a specified length:

Slicing¶

Lists and strings have something in common that you might not suspect: they can both be treated as sequences. You already know that you can iterate through the elements of a list. You can also iterate through the letters in a string:

This is only occasionally useful. Slightly more useful is the slicing operation, which you can also use on any sequence. We already know that we can use indexing to get the first element of a list:

If we want the list containing the first two elements of a list, we can do this via

or simply

If we want the last items of the list, we can do this with negative slicing:

which is somewhat logically consistent with negative indices accessing the last elements of the list.

You can do:

Since strings are sequences, you can also do this to them:

If we really want to get fancy, we can pass a third element into the slice, which specifies a step length (just like a third argument to the range() function specifies the step):

Note that in this example I was even able to omit the second argument, so that the slice started at 2, went to the end of the list, and took every second element, to generate the list of even numbers less that 40.

Booleans and Truth Testing¶

We have now learned a few data types. We have integers and floating point numbers, strings, and lists to contain them. We have also learned about lists, a container that can hold any data type. We have learned to print things out, and to iterate over items in lists. We will now learn about boolean variables that can be either True or False.

We invariably need some concept of conditions in programming to control branching behavior, to allow a program to react differently to different situations. If it's Monday, I'll go to work, but if it's Sunday, I'll sleep in. To do this in Python, we use a combination of boolean variables, which evaluate to either True or False, and if statements, that control branching based on boolean values.

For example:

(Quick quiz: why did the snippet print "Go to work" here? What is the variable "day" set to?)

Let's take the snippet apart to see what happened. First, note the statement

If we evaluate it by itself, as we just did, we see that it returns a boolean value, False. The "==" operator performs equality testing. If the two items are equal, it returns True, otherwise it returns False. In this case, it is comparing two variables, the string "Sunday", and whatever is stored in the variable "day", which, in this case, is the other string "Saturday". Since the two strings are not equal to each other, the truth test has the false value.

The if statement that contains the truth test is followed by a code block (a colon followed by an indented block of code). If the boolean is true, it executes the code in that block. Since it is false in the above example, we don't see that code executed.

The first block of code is followed by an else statement, which is executed if nothing else in the above if statement is true. Since the value was false, this code is executed, which is why we see "Go to work".

You can compare any data types in Python:

We see a few other boolean operators here, all of which which should be self-explanatory. Less than, equality, non-equality, and so on.

Particularly interesting is the 1 == 1.0 test, which is true, since even though the two objects are different data types (integer and floating point number), they have the same value. There is another boolean operator is, that tests whether two objects are the same object:

We can do boolean tests on lists as well:

Finally, note that you can also string multiple comparisons together, which can result in very intuitive tests:

If statements can have elif parts ("else if"), in addition to if/else parts. For example:¶

Of course we can combine if statements with for loops, to make a snippet that is almost interesting:

This is something of an advanced topic, but ordinary data types have boolean values associated with them, and, indeed, in early versions of Python there was not a separate boolean object. Essentially, anything that was a 0 value (the integer or floating point 0, an empty string "", or an empty list []) was False, and everything else was true. You can see the boolean value of any data object using the bool() function.

Code Example: The Fibonacci Sequence¶

The Fibonacci sequence is a sequence in math that starts with 0 and 1, and then each successive entry is the sum of the previous two. Thus, the sequence goes 0,1,1,2,3,5,8,13,21,34,55,89,...

A very common exercise in programming books is to compute the Fibonacci sequence up to some number n. First I'll show the code, then I'll discuss what it is doing.

Let's go through this line by line. First, we define the variable n, and set it to the integer 20. n is the length of the sequence we're going to form, and should probably have a better variable name. We then create a variable called sequence, and initialize it to the list with the integers 0 and 1 in it, the first two elements of the Fibonacci sequence. We have to create these elements "by hand", since the iterative part of the sequence requires two previous elements.

We then have a for loop over the list of integers from 2 (the next element of the list) to n (the length of the sequence). After the colon, we see a hash tag "#", and then a comment that if we had set n to some number less than 2 we would have a problem. Comments in Python start with #, and are good ways to make notes to yourself or to a user of your code explaining why you did what you did. Better than the comment here would be to test to make sure the value of n is valid, and to complain if it isn't; we'll try this later.

In the body of the loop, we append to the list an integer equal to the sum of the two previous elements of the list.

After exiting the loop (ending the indentation) we then print out the whole list. That's it!

Functions¶

We might want to use the Fibonacci snippet with different sequence lengths. We could cut an paste the code into another cell, changing the value of n, but it's easier and more useful to make a function out of the code. We do this with the def statement in Python:

We can now call fibonacci() for different sequence_lengths:

We've introduced a several new features here. First, note that the function itself is defined as a code block (a colon followed by an indented block). This is the standard way that Python delimits things. Next, note that the first line of the function is a single string. This is called a docstring, and is a special kind of comment that is often available to people using the function through the python command line:

If you define a docstring for all of your functions, it makes it easier for other people to use them, since they can get help on the arguments and return values of the function.

Next, note that rather than putting a comment in about what input values lead to errors, we have some testing of these values, followed by a warning if the value is invalid, and some conditional code to handle special cases.

Recursion and Factorials¶

Functions can also call themselves, something that is often called recursion. We're going to experiment with recursion by computing the factorial function. The factorial is defined for a positive integer n as

First, note that we don't need to write a function at all, since this is a function built into the standard math library. Let's use the help function to find out about it:

This is clearly what we want.

However, if we did want to write a function ourselves, we could do recursively by noting that

The program then looks something like:

Recursion can be very elegant, and can lead to very simple programs.

Two More Data Structures: Tuples and Dictionaries¶

Before we end the Python overview, I wanted to touch on two more data structures that are very useful (and thus very common) in Python programs.

A tuple is a sequence object like a list or a string. It's constructed by grouping a sequence of objects together with commas, either without brackets, or with parentheses:

Tuples are like lists, in that you can access the elements using indices:

However, tuples are immutable, you can't append to them or change the elements of them:

Tuples are useful anytime you want to group different pieces of data together in an object, but don't want to create a full-fledged class (see below) for them. For example, let's say you want the Cartesian coordinates of some objects in your program. Tuples are a good way to do this:

Again, it's not a necessary distinction, but one way to distinguish tuples and lists is that tuples are a collection of different things, here a name, and x and y coordinates, whereas a list is a collection of similar things, like if we wanted a list of those coordinates:

Tuples can be used when functions return more than one value. Say we wanted to compute the smallest x- and y-coordinates of the above list of objects. We could write:

Here we did two things with tuples you haven't seen before. First, we unpacked an object into a set of named variables using tuple assignment:

>>> name,x,y = obj

We also returned multiple values (minx,miny), which were then assigned to two other variables (x,y), again by tuple assignment. This makes what would have been complicated code in C++ rather simple.

Tuple assignment is also a convenient way to swap variables:

Dictionaries¶

Dictionaries are an object called "mappings" or "associative arrays" in other languages. Whereas a list associates an integer index with a set of objects:

The index in a dictionary is called the key, and the corresponding dictionary entry is the value. A dictionary can use (almost) anything as the key. Whereas lists are formed with square brackets [], dictionaries use curly brackets {}:

There's also a convenient way to create dictionaries without having to quote the keys.

The len() function works on both tuples and dictionaries:

"Advanced" Python Topics¶

The map() function¶

There are two significant changes over what we did earlier. First, I'm passing the comma character ',' into the split function, so that it breaks to a new word every time it sees a comma. Next, to simplify things a big, I'm using the map() command to repeatedly apply a single function (float()) to a list, and to return the output as a list.

Optional arguments¶

You will recall that the numpy.linspace function can take either two arguments (for the starting and ending points):

or it can take three arguments, for the starting point, the ending point, and the number of points:

You can also pass in keywords to exclude the endpoint:

Right now, we only know how to specify functions that have a fixed number of arguments. We'll learn how to do the more general cases here.

If we're defining a simple version of linspace, we would start with:

We can add an optional argument by specifying a default value in the argument list:

This gives exactly the same result if we don't specify anything:

But also let's us override the default value with a third argument:

We can add arbitrary keyword arguments to the function definition by putting a keyword argument **kwargs handle in:

What the keyword argument construction does is to take any additional keyword arguments (i.e. arguments specified by name, like "endpoint=False"), and stick them into a dictionary called "kwargs" (you can call it anything you like, but it has to be preceded by two stars). You can then grab items out of the dictionary using the get command, which also lets you specify a default value. I realize it takes a little getting used to, but it is a common construction in Python code, and you should be able to recognize it.

There's an analogous *args that dumps any additional arguments into a list called "args". Think about the range function: it can take one (the endpoint), two (starting and ending points), or three (starting, ending, and step) arguments. How would we define this?

List Comprehensions and Generators¶

List comprehensions are a streamlined way to make lists. They look something like a list definition, with some logic thrown in. For example:

You can also put some boolean testing into the construct:

Here i%2 is the remainder when i is divided by 2, so that i%2==1 is true if the number is odd. Even though this is a relative new addition to the language, it is now fairly common since it's so convenient.

iterators are a way of making virtual sequence objects.¶

Consider if we had the nested loop structure:

for i in range(1000000):
    for j in range(1000000):

Inside the main loop, we make a list of 1,000,000 integers, just to loop over them one at a time. We don't need any of the additional things that a lists gives us, like slicing or random access, we just need to go through the numbers one at a time. And we're making 1,000,000 of them.

iterators are a way around this.¶

For example, the range function is the iterator version of range. This simply makes a counter that is looped through in sequence, so that the analogous loop structure would look like:

for i in range(1000000):
    for j in range(1000000):

Even though we've only added two characters, we've dramatically sped up the code, because we're not making 1,000,000 big lists.

We can define our own iterators using the yield statement:

We can always turn an iterator into a list using the list command:

There's a special syntax called a generator expression that looks a lot like a list comprehension:

Factory Functions¶

A factory function is a function that returns a function. They have the fancy name lexical closure, which makes you sound really intelligent in front of your CS friends. But, despite the arcane names, factory functions can play a very practical role.

Suppose you want the Gaussian function centered at 0.5, with height 99 and width 1.0. You could write a general function.

But what if you need a function with only one argument, like f(x) rather than f(x,y,z,...)? You can do this with Factory Functions:

Everything in Python is an object, including functions. This means that functions can be returned by other functions. (They can also be passed into other functions, which is also useful, but a topic for another discussion.) In the gauss_maker example, the g function that is output "remembers" the A, a, x0 values it was constructed with, since they're all stored in the local memory space (this is what the lexical closure really refers to) of that function.

Factories are one of the more important of the Software Design Patterns, which are a set of guidelines to follow to make high-quality, portable, readable, stable software. It's beyond the scope of the current work to go more into either factories or design patterns, but I thought I would mention them for people interested in software design.

Functional programming¶

Functional programming is a very broad subject. The idea is to have a series of functions, each of which generates a new data structure from an input, without changing the input structure at all. By not modifying the input structure (something that is called not having side effects), many guarantees can be made about how independent the processes are, which can help parallelization and guarantees of program accuracy. There is a Python Functional Programming HOWTO in the standard docs that goes into more details on functional programming. I just wanted to touch on a few of the most important ideas here.

There is an operator module that has function versions of most of the Python operators. For example:

These are useful building blocks for functional programming.¶

The lambda operator allows us to build anonymous functions, which are simply functions that aren't defined by a normal def statement with a name. For example, a function that doubles the input is:

We could also write this as:

And assign it to a function separately:

lambda is particularly convenient (as we'll see below) in passing simple functions as arguments to other functions.

map is a way to repeatedly apply a function to a list:

reduce is a way to repeatedly apply a function to the first two items of the list. There already is a sum function in Python that is a reduction:

Object Oriented Programming¶

We've seen a lot of examples of objects in Python. We create a string object with quote marks:

and we have a bunch of methods we can use on the object:

Object oriented programming simply gives you the tools to define objects and methods for yourself. It's useful anytime you want to keep some data (like the characters in the string) tightly coupled to the functions that act on the data (length, split, startswith, etc.).

As an example, we're going to bundle the functions we did to make the 1d harmonic oscillator eigenfunctions with arbitrary potentials, so we can pass in a function defining that potential, some additional specifications, and get out something that can plot the orbitals, as well as do other things with them, if desired.

The __init__() function specifies what operations go on when the object is created. The self argument is the object itself, and we don't pass it in. The only required argument is the function that defines the QM potential. We can also specify additional arguments that define the numerical grid that we're going to use for the calculation.

For example, to do an infinite square well potential, we have a function that is 0 everywhere. We don't have to specify the barriers, since we'll only define the potential in the well, which means that it can't be defined anywhere else.

We can similarly redefine the Harmonic Oscillator potential.

Speeding Python: Timeit, Profiling, Cython, SWIG, and PyPy¶

The first rule of speeding up your code is not to do it at all. As Donald Knuth said:

"We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil."

The second rule of speeding up your code is to only do it if you really think you need to do it. Python has two tools to help with this process: a timing program called timeit, and a very good code profiler. We will discuss both of these tools in this section, as well as techniques to use to speed up your code once you know it's too slow.

Timeit¶

timeit helps determine which of two similar routines is faster. Recall that some time ago we wrote a factorial routine, but also pointed out that Python had its own routine built into the math module. Is there any difference in the speed of the two? timeit helps us determine this. For example, timeit tells how long each method takes:

The little % sign that we have in front of the timeit call is an example of an IPython magic function (see IPython tutorial).

In any case, the timeit function runs 3 loops, and tells us that it took on the average of 583 ns to compute 20!. In contrast:

the factorial function we wrote is about a factor of 10 slower.

Profiling¶

Profiling complements what timeit does by splitting the overall timing into the time spent in each function. It can give us a better understanding of what our program is really spending its time on.

Suppose we want to create a list of even numbers. Our first effort yields this:

Is this code fast enough? We find out by running the Python profiler on a longer run:

This looks okay, 0.05 seconds isn't a huge amount of time, but looking at the profiling shows that the append function is taking almost 20% of the time. Can we do better? Let's try a list comprehension.

By removing a small part of the code using a list comprehension, we've doubled the overall speed of the code!

Other Ways to Speed Python¶

When we compared the fact and factorial functions, above, we noted that C routines are often faster because they're more streamlined. Once we've determined that one routine is a bottleneck for the performance of a program, we can replace it with a faster version by writing it in C. This is called extending Python, and there's a good section in the standard documents. This can be a tedious process if you have many different routines to convert. Fortunately, there are several other options.

Swig (the simplified wrapper and interface generator) is a method to generate binding not only for Python but also for Matlab, Perl, Ruby, and other scripting languages. Swig can scan the header files of a C project and generate Python binding for it. Using Swig is substantially easier than writing the routines in C.

Cython is a C-extension language. You can start by compiling a Python routine into a shared object libraries that can be imported into faster versions of the routines. You can then add additional static typing and make other restrictions to further speed the code. Cython is generally easier than using Swig.

PyPy is the easiest way of obtaining fast code. PyPy compiles Python to a subset of the Python language called RPython that can be efficiently compiled and optimized. Over a wide range of tests, PyPy is roughly 6 times faster than the standard Python Distribution.

Conclusion of the Python Overview¶

There is, of course, much more to the language than I've covered here. I've tried to keep this brief enough so that you can jump in and start using Python to simplify your life and work. My own experience in learning new things is that the information doesn't "stick" unless you try and use it for something in real life.

You will no doubt need to learn more as you go. I've listed several other good references, including the Python Tutorial and Learn Python the Hard Way. Additionally, now is a good time to start familiarizing yourself with the Python Documentation, and, in particular, the Python Language Reference.

Learning Resources¶

• Official Python Documentation, including
  • Python Tutorial
  • Python Language Reference
• If you're interested in Python 3, the Official Python 3 Docs are here.
• IPython tutorial.
• Learn Python The Hard Way
• Dive Into Python, in particular if you're interested in Python 3.
• Invent With Python, probably best for kids.
• Python Functional Programming HOWTO
• The Structure and Interpretation of Computer Programs, written in Scheme, a Lisp dialect, but one of the best books on computer programming ever written.
• Generator Tricks for Systems Programmers Beazley's slides on just what generators can do for you.
• Python Module of the Week is a series going through in-depth analysis of the Python standard library in a very easy to understand way.
• 30 Python Language Features and Tricks You May Not Know About a list of Python features that you should know.

Some Python topics to look at¶

• IPython: simple shell, parallel computing.
• IPython Notebooks: simple web interface for preparing report-like documents (these slides are made with it!)
• matplotlib: a library for scientific plotting comparable to Matlab (see also bokeh).
• pandas: efficient data handling.
• scikit.learn: machine learning framework and algorithms.

Cool IPython Notebooks to look at¶

• Rob Johansson's excellent notebooks, including Scientific Computing with Python and Computational Quantum Physics with QuTiP lectures;
• XKCD style graphs in matplotlib;
• A collection of Notebooks for using IPython effectively
• A gallery of interesting IPython Notebooks
• Cross-disciplinary computational analysis IPython Notebooks From Hadoop World 2012
• Quantites Units in Python.
  • Another units module is here