Py tut-handout

Introduction Python Tutorial Numerics & Plotting Standard library
An introduction to the Python programming
language
Prabhu Ramachandran
Department of Aerospace Engineering
IIT Bombay
16, July 2007
Prabhu Ramachandran Introduction to Python
Outline
1 Introduction
Introduction to Python
2 Python Tutorial
Preliminaries
Data types
Control ﬂow, functions
Modules, exceptions, classes
Miscellaneous
3 Numerics & Plotting
NumPy Arrays
Plotting: Matplotlib
SciPy
4 Standard library
Quick Tour

Introduction
Creator and BDFL: Guido van Rossum
BDFL == Benevolent Dictator For Life
Conceived in December 1989
The name “Python”: Monty Python’s Flying Circus
Current stable version of Python is 2.5.x
PSF license (like BSD: no strings attached)
Highly cross platform
Runs on the Nokia series 60!
Resources
Available as part of any sane GNU/Linux distribution
Web: http://www.python.org
Documentation: http://www.python.org/doc
Free Tutorials:
Ofﬁcial Python tutorial:
http://docs.python.org/tut/tut.html
Byte of Python: http://www.byteofpython.info/
Dive into Python: http://diveintopython.org/

Why Python?
High level, interpreted, modular, OO
Easy to learn
Easy to read code
Much faster development cycle
Powerful interactive interpreter
Rapid application development
Powerful standard library
Interfaces well to C++, C and FORTRAN libraries
In short: there is little you can’t do with it
A quote
I came across Python and its Numerical extension in
1998 . . . I quickly fell in love with Python programming
which is a remarkable statement to make about a
programming language. If I had not seen others with the
same view, I might have seriously doubted my sanity.
– Travis Oliphant (creator of NumPy)

Why not ***lab?
Open Source, Free
Portable
Python is a real programming language: large and small
programs
Can do much more than just array and math
Wrap large C++ codes
Build large code bases via SCons
Interactive data analysis/plotting
Parallel application
Job scheduling on a custom cluster
Miscellaneous scripts
Why not Python?
Can be slow for high-performance applications
This can be fairly easily overcome by using C/C++/FORTRAN
extensions

Use cases
NASA: Python Streamlines Space Shuttle Mission Design
AstraZeneca Uses Python for Collaborative Drug Discovery
ForecastWatch.com Uses Python To Help Meteorologists
Industrial Light & Magic Runs on Python
Zope: Commercial grade CMS
RedHat: install scripts, sys-admin tools
Numerous success stories:
http://www.pythonology.com/success
Before we begin
This is only an introduction
Python is a full-ﬂedged programming language
Please read the tutorial
It is very well written and can be read in one afternoon

Preliminaries Data types Control flow, functions Modules, exceptions, classes Miscellaneous
Preliminaries: The Interpreter
Python is interpreted
Interpreted vs. Compiled
Interpreted languages allow for rapid testing/prototyping
Dynamically typed
Full introspection of code at runtime
Did I say dynamic?
Does not force OO or a particular programming paradigm
down your throat!
Preliminaries . . .
Will follow the Official Python tutorial
No lexical blocking
Indentation specifies scope
Leads to easier to read code!

Using the interpreter
Starting up: python or ipython
Quitting: Control-D or Control-Z (on Win32)
Can use it like a calculator
Can execute one-liners via the -c option: python -c
"print ’hello world’"
Other options via python -h
IPython
Recommended interpreter, IPython:
http://ipython.scipy.org
Better than the default Python shell
Supports tab completion by default
Easier object introspection
Shell access!
Command system to allow extending its own behavior
Supports history (across sessions) and logging
Can be embedded in your own Python code
Support for macros
A ﬂexible framework for your own custom interpreter
Other miscellaneous conveniences
We’ll get back to this later

Basic IPython features
Startup: ipython [options] files
ipython [-wthread|-gthread|-qthread]:
Threading modes to support wxPython, pyGTK and Qt
ipython -pylab: Support for matplotlib
TAB completion:
Type object_name.<TAB> to see list of options
Also completes on ﬁle and directory names
object? shows docstring/help for any Python object
object?? presents more docs (and source if possible)
Debugging with %pdb magic: pops up pdb on errors
Access history (saved over earlier sessions also)
Use <UpArrow>: move up history
Use <Ctrl-r> string: search history backwards
Use Esc >: get back to end of history
%run [options] file[.py] lets you run Python code
Basic concepts
Dynamically typed
Assignments need not specify a type
a = 1
a = 1.1
a = " foo "
a = SomeClass ( )
Comments:
a = 1 # In−l i n e comments
# Comment in a l i n e to i t s e l f .
a = "# This i s not a comment ! "

Basic concepts
No lexical scoping
Scope determined by indentation
for i in range ( 1 0 ) :
print " inside loop : " ,
# Do something in the loop .
print i , i ∗ i
print " loop i s done ! " # This i s outside the loop !
Assignment to an object is by reference
Essentially, names are bound to objects
Basic types
Basic objects: numbers (ﬂoat, int, long, complex), strings,
tuples, lists, dictionaries, functions, classes, types etc.
Types are of two kinds: mutable and immutable
Immutable types: numbers, strings, None and tuples
Immutables cannot be changed “in-place”
Mutable types: lists, dictionaries, instances, etc.
Mutable objects can be “changed”

What is an object?
A loose and informal but handy description
An object is a particular instance of a general class of things
Real world example
Consider the class of cars made by Honda
A Honda Accord on the road, is a particular instance of the
general class of cars
It is an object in the general sense of the term
Objects in a programming language
The object in the computer follows a similar idea
An object has attributes (or state) and behavior
Object contains or manages data (attributes) and has
methods (behavior)
Together this lets one create representation of “real” things on
the computer
Programmers then create objects and manipulate them
through their methods to get things done
In Python everything is essentially an object – you don’t have
to worry about it

Numbers
>>> a = 1 # I n t .
>>> l = 1000000L # Long
>>> e = 1.01325e5 # f l o a t
>>> f = 3.14159 # f l o a t
>>> c = 1+1 j # Complex !
>>> print f ∗c / a
(3.14159+3.14159 j )
>>> print c . real , c . imag
1.0 1.0
>>> abs ( c )
1.4142135623730951
Boolean
>>> t = True
>>> f = not t
False
>>> f or t
True
>>> f and t
False

Strings
s = ’ t h i s i s a s t r i n g ’
s = ’ This one has " quotes " inside ! ’
s = "The reverse with ’ single−quotes ’ inside ! "
l = "A long s t r i n g spanning several l i n e s
one more l i n e
yet another "
t = " " "A t r i p l e quoted s t r i n g
does not need to be escaped at the end and
" can have nested quotes " and whatnot . " " "
Strings
>>> word = " hello "
>>> 2∗word + " world " # Arithmetic on s t r i n g s
h e l l o h e l l o world
>>> print word [ 0 ] + word [ 2 ] + word[ −1]
hlo
>>> # Strings are " immutable "
. . . word [ 0 ] = ’H ’
Traceback ( most recent c a l l l a s t ) :
F i l e "<stdin >" , l i n e 1 , in ?
TypeError : object doesnt support item assignment
>>> len ( word ) # The length of the s t r i n g
5
>>> s = u ’ Unicode s t r i n g s ! ’ # unicode s t r i n g
>>> # Raw s t r i n g s ( note the leading ’ r ’ )
. . . raw_s = r ’A LaTeX s t r i n g $ alpha nu$ ’

More on strings
>>> a = ’ hello world ’
>>> a . s t a r t s w i t h ( ’ h e l l ’ )
True
>>> a . endswith ( ’ ld ’ )
True
>>> a . upper ( )
’HELLO WORLD’
>>> a . upper ( ) . lower ( )
’ hello world ’
>>> a . s p l i t ( )
[ ’ hello ’ , ’ world ’ ]
>>> ’ ’ . j o i n ( [ ’a ’ , ’b ’ , ’ c ’ ] )
’ abc ’
>>> x , y = 1 , 1.234
>>> ’ x i s %s , y i s %s ’%(x , y )
’ x i s 1 , y i s 1.234 ’
>>> # could also do : ’ x i s %d , y i s %f ’%(x , y )
See http://docs.python.org/lib/typesseq-strings.html
Lists
Lists are mutable
Items are indexed at 0
Last element is -1
Length: len(list)

List: examples
>>> a = [ ’spam ’ , ’ eggs ’ , 100 , 1234]
>>> a [ 0 ]
’spam ’
>>> a [ 3 ]
1234
>>> a[ −2]
100
>>> a[1: −1]
[ ’ eggs ’ , 100]
>>> a [ : 2 ] + [ ’ bacon ’ , 2∗2]
[ ’spam ’ , ’ eggs ’ , ’ bacon ’ , 4]
>>> 2∗a [ : 3 ] + [ ’Boe ! ’ ]
[ ’spam ’ , ’ eggs ’ , 100 , ’spam ’ , ’ eggs ’ , 100 , ’Boe ! ’ ]
Lists are mutable
>>> a = [ ’spam ’ , ’ eggs ’ , 100 , 1234]
>>> a [ 2 ] = a [ 2 ] + 23
>>> a
[ ’spam ’ , ’ eggs ’ , 123 , 1234]
>>> a = [ ’spam ’ , ’ eggs ’ , 100 , 1234]
>>> a [ 0 : 2 ] = [1 , 12] # Replace some items
>>> a
[1 , 12 , 123 , 1234]
>>> a [ 0 : 2 ] = [ ] # Remove some items
>>> a
[123 , 1234]

List methods
>>> a = [ ’spam ’ , ’ eggs ’ , 100 , 1234]
>>> len ( a )
4
>>> a . reverse ( )
>>> a
[1234 , 100 , ’ eggs ’ , ’spam ’ ]
>>> a . append ( [ ’ x ’ , 1 ] ) # L i s t s can contain l i s t s .
>>> a
[1234 , 100 , ’ eggs ’ , ’spam ’ , [ ’ x ’ , 1 ] ]
>>> a . extend ( [ 1 , 2 ] ) # Extend the l i s t .
>>> a
[1234 , 100 , ’ eggs ’ , ’spam ’ , [ ’ x ’ , 1] , 1 , 2]
Tuples
>>> t = (0 , 1 , 2)
>>> print t [ 0 ] , t [ 1 ] , t [ 2 ] , t [ −1] , t [ −2] , t [ −3]
0 1 2 2 1 0
>>> # Tuples are immutable !
. . . t [ 0 ] = 1
TypeError : object doesn ’ t support item assignment

Dictionaries
Associative arrays/mappings
Indexed by “keys” (keys must be immutable)
dict[key] = value
keys() returns all keys of the dict
values() returns the values of the dict
has_key(key) returns if key is in the dict
Dictionaries: example
>>> t e l = { ’ jack ’ : 4098, ’ sape ’ : 4139}
>>> t e l [ ’ guido ’ ] = 4127
>>> t e l
{ ’ sape ’ : 4139, ’ guido ’ : 4127, ’ jack ’ : 4098}
>>> t e l [ ’ jack ’ ]
4098
>>> del t e l [ ’ sape ’ ]
>>> t e l [ ’ i r v ’ ] = 4127
>>> t e l
{ ’ guido ’ : 4127, ’ i r v ’ : 4127, ’ jack ’ : 4098}
>>> t e l . keys ( )
[ ’ guido ’ , ’ i r v ’ , ’ jack ’ ]
>>> t e l . has_key ( ’ guido ’ )
True

Control ﬂow
Control ﬂow is primarily achieved using the following:
if/elif/else
for
while
break, continue, else may be used to further control
pass can be used when syntactically necessary but nothing
needs to be done
If example
x = i n t ( raw_input ( " Please enter an integer : " ) )
# raw_input asks the user f o r input .
# i n t ( ) typecasts the r e s u l t i n g s t r i n g i n t o an i n t .
i f x < 0:
x = 0
print ’ Negative changed to zero ’
e l i f x == 0:
print ’ Zero ’
e l i f x == 1:
print ’ Single ’
else :
print ’ More ’

If example
>>> a = [ ’ cat ’ , ’ window ’ , ’ defenestrate ’ ]
>>> i f ’ cat ’ in a :
. . . print "meaw"
. . .
meaw
>>> pets = { ’ cat ’ : 1 , ’ dog ’ :2 , ’ croc ’ : 10}
>>> i f ’ croc ’ in pets :
. . . print pets [ ’ croc ’ ]
. . .
10
for example
>>> a = [ ’ cat ’ , ’ window ’ , ’ defenestrate ’ ]
>>> for x in a :
. . . print x , len ( x )
. . .
cat 3
window 6
defenestrate 12
>>> knights = { ’ gallahad ’ : ’ the pure ’ ,
. . . ’ robin ’ : ’ the brave ’ }
>>> for k , v in knights . i t e r i t e m s ( ) :
. . . print k , v
. . .
gallahad the pure
robin the brave

for and range example
>>> for i in range ( 5 ) :
. . . print i , i ∗ i
. . .
0 0
1 1
2 4
3 9
4 16
>>> a = [ ’a ’ , ’b ’ , ’ c ’ ]
>>> for i , x in enumerate ( a ) :
. . . print i , x
. . .
0 ’a ’
1 ’b ’
2 ’ c ’
while example
>>> # Fibonacci series :
. . . # the sum of two elements defines the next
. . . a , b = 0 , 1
>>> while b < 10:
. . . print b
. . . a , b = b , a+b
. . .
1
1
2
3
5
8

Functions
Support default and keyword arguments
Scope of variables in the function is local
Mutable items are passed by reference
First line after definition may be a documentation string
(recommended!)
Function definition and execution defines a name bound to the
function
You can assign a variable to a function!
Functions: examples
>>> def f i b ( n ) : # write Fibonacci series up to n
. . . " " " P r i n t a Fibonacci series up to n . " " "
. . . a , b = 0 , 1
. . . while b < n :
. . . print b ,
. . . a , b = b , a+b
. . .
>>> # Now c a l l the function we j u s t defined :
. . . f i b (2000)
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597
>>> f = f i b # Assign a variable to a function
>>> f (10)
1 1 2 3 5 8

Functions: default arguments
def ask_ok ( prompt , r e t r i e s =4 , complaint= ’Yes or no ! ’ ) :
while True :
ok = raw_input ( prompt )
i f ok in ( ’ y ’ , ’ ye ’ , ’ yes ’ ) :
return True
i f ok in ( ’n ’ , ’ no ’ , ’ nop ’ , ’ nope ’ ) :
return False
r e t r i e s = r e t r i e s − 1
i f r e t r i e s < 0:
raise IOError , ’ bad user ’
print complaint
Functions: keyword arguments
def parrot ( voltage , state= ’a s t i f f ’ ,
action= ’voom ’ , type= ’ Norwegian Blue ’ ) :
print "−− This parrot wouldn ’ t " , action ,
print " i f you put " , voltage , " Volts through i t . "
print "−− Lovely plumage , the " , type
print "−− I t ’ s " , state , " ! "
parrot (1000)
parrot ( action = ’VOOOOOM’ , voltage = 1000000)
parrot ( ’a thousand ’ , state = ’ pushing up the daisies ’ )
parrot ( ’a m i l l i o n ’ , ’ bereft of l i f e ’ , ’ jump ’ )

Modules
Define variables, functions and classes in a file with a .py
extension
This file becomes a module!
Modules are searched in the following:
Current directory
Standard: /usr/lib/python2.3/site-packages/ etc.
Directories specified in PYTHONPATH
sys.path: current path settings (from the sys module)
The import keyword “loads” a module
One can also use:
from module import name1, name2, name2
where name1 etc. are names in the module, “module”
from module import * — imports everything from
module, use only in interactive mode
Modules: example
# −−− foo . py −−−
some_var = 1
def f i b ( n ) : # write Fibonacci series up to n
" " " P r i n t a Fibonacci series up to n . " " "
a , b = 0 , 1
while b < n :
print b ,
a , b = b , a+b
# EOF
>>> import foo
>>> foo . f i b (10)
1 1 2 3 5 8
>>> foo . some_var
1

Namespaces
A mapping from names to objects
Modules introduce a namespace
So do classes
The running script’s namespace is __main__
A modules namespace is identiﬁed by its name
The standard functions (like len) are in the __builtin__
namespace
Namespaces help organize different names and their bindings
to different objects
Exceptions
Python’s way of notifying you of errors
Several standard exceptions: SyntaxError, IOError etc.
Users can also raise errors
Users can create their own exceptions
Exceptions can be “caught” via try/except blocks

Exception: examples
>>> 10 ∗ ( 1 / 0 )
ZeroDivisionError : integer d i v i s i o n or modulo by zero
>>> 4 + spam∗3
NameError : name ’spam ’ is not defined
>>> ’2 ’ + 2
TypeError : cannot concatenate ’ s t r ’ and ’ i n t ’ objects
Exception: examples
>>> while True :
. . . try :
. . . x = i n t ( raw_input ( " Enter a number : " ) )
. . . break
. . . except ValueError :
. . . print " I n v a l i d number , t r y again . . . "
. . .
>>> # To raise exceptions
. . . raise ValueError , " your error message"
ValueError : your error message

Classes: the big picture
Lets you create new data types
Class is a template for an object belonging to that class
Note: in Python a class is also an object
Instantiating a class creates an instance (an object)
An instance encapsulates the state (data) and behavior
(methods)
Allows you to deﬁne an inheritance hierarchy
“A Honda car is a car.”
“A car is an automobile.”
“A Python is a reptile.”
Programmers need to think OO
Classes: what’s the big deal?
Lets you create objects that mimic a real problem being
simulated
Makes problem solving more natural and elegant
Easier to create code
Allows for code-reuse
Polymorphism

Class deﬁnition and instantiation
Class deﬁnitions when executed create class objects
Instantiating the class object creates an instance of the class
class Foo ( object ) :
pass
# class object created .
# Create an instance of Foo .
f = Foo ( )
# Can assign an a t t r i b u t e to the instance
f . a = 100
print f . a
100
Classes . . .
All attributes are accessed via the object.attribute
syntax
Both class and instance attributes are supported
Methods represent the behavior of an object: crudely think of
them as functions “belonging” to the object
All methods in Python are “virtual”
Inheritance through subclassing
Multiple inheritance is supported
No special public and private attributes: only good
conventions
object.public(): public
object._private() & object.__priv(): non-public

Classes: examples
class MyClass ( object ) :
" " " Example class ( t h i s i s the class docstring ) . " " "
i = 12345 # A class a t t r i b u t e
def f ( s e l f ) :
" " " This i s the method docstring " " "
return ’ hello world ’
>>> a = MyClass ( ) # creates an instance
>>> a . f ( )
’ hello world ’
>>> # a . f ( ) i s equivalent to MyClass . f ( a )
. . . # This also explains why f has a ’ s e l f ’ argument .
. . . MyClass . f ( a )
’ hello world ’
Classes (continued)
self is conventionally the first argument for a method
In previous example, a.f is a method object
When a.f is called, it is passed the instance a as the first
argument
If a method called __init__ exists, it is called when the
object is created
If a method called __del__ exists, it is called before the
object is garbage collected
Instance attributes are set by simply “setting” them in self
Other special methods (by convention) like __add__ let you
define numeric types:
http://docs.python.org/ref/specialnames.html
http://docs.python.org/ref/numeric-types.html

Classes: examples
class Bag( MyClass ) : # Shows how to derive classes
def __init__ ( s e l f ) : # called on object creation .
s e l f . data = [ ] # an instance a t t r i b u t e
def add ( self , x ) :
s e l f . data . append ( x )
def addtwice ( self , x ) :
s e l f . add ( x )
s e l f . add ( x )
>>> a = Bag ( )
>>> a . f ( ) # I n h e ri t e d method
’ hello world ’
>>> a . add ( 1 ) ; a . addtwice (2)
>>> a . data
[1 , 2 , 2]
Derived classes
Call the parent’s __init__ if needed
If you don’t need a new constructor, no need to deﬁne it in
subclass
Can also use the super built-in function
class AnotherBag (Bag ) :
def __init__ ( s e l f ) :
# Must c a l l parent ’ s __init__ e x p l i c i t l y
Bag . __init__ ( s e l f )
# A l t e r n a t i v e l y use t h i s :
super ( AnotherBag , s e l f ) . __init__ ( )
# Now setup any more data .
s e l f . more_data = [ ]

Classes: polymorphism
class Drawable ( object ) :
def draw ( s e l f ) :
# Just a s p e c i f i c a t i o n .
pass
class Square ( Drawable ) :
# draw a square .
class Circle ( Drawable ) :
# draw a c i r c l e .
class A r t i s t ( Drawable ) :
for obj in s e l f . drawables :
obj . draw ( )
Stand-alone scripts
Consider a ﬁle f.py:
# ! / usr / bin / env python
" " " Module l e v e l documentation . " " "
# F i r s t l i n e t e l l s the s h e l l that i t should use Python
# to i n t e r p r e t the code in the f i l e .
def f ( ) :
print " f "
# Check i f we are running standalone or as module .
# When imported , __name__ w i l l not be ’ __main__ ’
i f __name__ == ’ __main__ ’ :
# This i s not executed when f . py i s imported .
f ( )

More IPython features
Input and output caching:
In: a list of all entered input
Out: a dict of all output
_, __, __ are the last three results as is _N
%hist [-n] macro shows previous history, -n suppresses
line number information
Log the session using %logstart, %logon and %logoff
%run [options] file[.py] – running Python code
%run -d [-b<N>]: debug script with pdb N is the line
number to break at (defaults to 1)
%run -t: time the script
%run -p: Profile the script
%prun runs a statement/expression under the profiler
%macro [options] macro_name n1-n2 n3-n4 n6
save specified lines to a macro with name macro_name
More IPython features . . .
%edit [options] [args]: edit lines of code or file
specified in editor (configure editor via $EDITOR)
%cd changes directory, see also
%pushd, %popd, %dhist
Shell access
!command runs a shell command and returns its output
files = %sx ls or files = !ls sets files to all
result of the ls command
%sx is quiet
!ls $files passes the files variable to the shell
command
%alias alias_name cmd creates an alias for a system
command
%colors lets you change the color scheme to
NoColor, Linux, LightBG

More IPython features . . .
Use ; at the end of a statement to suppress printing output
%who, %whos: print information on variables
%save [options] filename n1-n2 n3-n4: save
lines to a file
%time statement: Time execution of a Python statement
or expression
%timeit [-n<N> -r<R> [-t|-c]] statement: time
execution using Python’s timeit module
Can define and use profiles to setup IPython differently:
math, scipy, numeric, pysh etc.
%magic: Show help on all magics
File handling
>>> # Reading f i l e s :
. . . f = open ( ’ / path / to / file_name ’ )
>>> data = f . read ( ) # Read e n t i r e f i l e .
>>> l i n e = f . readline ( ) # Read one l i n e .
>>> # Read e n t i r e f i l e appending each l i n e i n t o a l i s t
. . . l i n e s = f . readlines ( )
>>> f . close ( ) # close the f i l e .
>>> # Writing f i l e s :
. . . f = open ( ’ / path / to / file_name ’ , ’w ’ )
>>> f . write ( ’ hello world n ’ )
tell(): returns int of current position
seek(pos): moves current position to specified byte
Call close() when done using a file

Math
math module provides basic math routines for floats
cmath module provides math routies for complex numbers
random: provides pseudo-random number generators for
various distributions
These are always available and part of the standard library
More serious math is provided by the NumPy/SciPy modules
– these are not standard and need to be installed separately
Timing and profiling
Timing code: use the time module
Read up on time.time() and time.clock()
timeit: is a better way of doing timing
IPython has handy time and timeit macros (type
timeit? for help)
IPython lets you debug and profile code via the run macro
(type run? on the prompt to learn more)

Odds and ends
dir([object]) function: attributes of given object
type(object): returns type information
str(), repr(): convert object to string representation
isinstance, issubclass
assert statements let you do debugging assertions in code
csv module: reading and writing CSV files
pickle: lets you save and load Python objects (serialization)
os.path: common path manipulations
Check out the Python Library reference:
http://docs.python.org/lib/lib.html
NumPy Arrays Plotting: Matplotlib SciPy
The numpy module
Manipulating large Python lists for scientific computing is slow
Most complex computations can be reduced to a few standard
operations
The numpy module provides:
An efficient and powerful array type for various common data
types
Abstracts out the most commonly used standard operations on
arrays
Numeric was the first, then came numarray. numpy is the
latest and is the future
This course uses numpy and only covers the absolute basics

Basic concepts
numpy arrays are of a ﬁxed size (arr.size) and have the
same type (arr.dtype)
numpy arrays may have arbitrary dimensionality
The shape of an array is the extent (length) of the array along
each dimension
The rank(arr) of an array is the “dimensionality” of the
array
The arr.itemsize is the number of bytes (8-bits) used for
each element of the array
Note: The shape and rank may change as long as the
size of the array is ﬁxed
Note: len(arr) != arr.size in general
Note: By default array operations are performed elementwise
Indices start from 0
Examples of numpy
# Simple array math example
>>> from numpy import ∗
>>> a = array ( [ 1 , 2 , 3 , 4 ] )
>>> b = array ( [ 2 , 3 , 4 , 5 ] )
>>> a + b # Element wise addition !
array ( [ 3 , 5 , 7 , 9 ] )
>>> print pi , e # Pi and e are defined .
3.14159265359 2.71828182846
# Create array from 0 to 10
>>> x = arange (0.0 , 10.0 , 0.05)
>>> x ∗= 2∗ pi /10 # m u l t i p l y array by scalar value
array ( [ 0 . , 0 . 0 3 1 4 , . . . , 6 . 2 5 2 ] )
# apply functions to array .
>>> y = sin ( x )

More examples of numpy
# Size , shape , rank , type etc .
>>> x = array ( [ 1 . , 2 , 3 , 4 ] )
>>> size ( x )
4
>>> x . dtype # or x . dtype . char
’d ’
>>> x . shape
(4 ,)
>>> print rank ( x ) , x . itemsize
1 8
>>> x . t o l i s t ( )
[ 1. 0 , 2.0 , 3.0 , 4.0]
# Array indexing
>>> x [ 0 ] = 10
>>> print x [ 0 ] , x[ −1]
10.0 4.0
Multi-dimensional arrays
>>> a = array ( [ [ 0 , 1 , 2 , 3] ,
. . . [10 ,11 ,12 ,13]])
>>> a . shape # ( rows , columns )
(2 , 4)
# Accessing and s e t t i n g values
>>> a [1 , 3 ]
13
>>> a [1 , 3 ] = −1
>>> a [ 1 ] # The second row
array ([10 ,11 ,12 , −1])
# Flatten / ravel arrays to 1D arrays
>>> a . f l a t # or ravel ( a )
array ([0 ,1 ,2 ,3 ,10 ,11 ,12 , −1])
# Note : f l a t references o r i g i n a l memory

Slicing arrays
>>> a = array ( [ [ 1 , 2 , 3 ] , [4 ,5 ,6] , [ 7 , 8 , 9 ] ] )
>>> a [ 0 , 1 : 3 ]
array ( [ 2 , 3 ] )
>>> a [ 1 : , 1 : ]
array ( [ [ 5 , 6] ,
[8 , 9 ] ] )
>>> a [ : , 2 ]
array ( [ 3 , 6 , 9 ] )
# S t r i d i n g . . .
>>> a [ 0 : : 2 , 0 : : 2 ]
array ( [ [ 1 , 3] ,
[7 , 9 ] ] )
# A l l these s l i c e s are references to the same memory !
Array creation functions
array(object, dtype=None,
copy=1,order=None, subok=0,ndmin=0)
arange(start, stop=None, step=1,
dtype=None)
linspace(start, stop, num=50,
endpoint=True, retstep=False)
ones(shape, dtype=None, order=’C’)
zeros((d1,...,dn),dtype=float,order=’C’)
identity(n)
empty((d1,...,dn),dtype=float,order=’C’)
ones_like(x), zeros_like(x), empty_like(x)

Array math
Basic elementwise math (given two arrays a, b):
a + b → add(a, b)
a - b, → subtract(a, b)
a * b, → multiply(a, b)
a / b, → divide(a, b)
a % b, → remainder(a, b)
a ** b, → power(a, b)
Inplace operators: a += b, or add(a, b, a) etc.
Logical operations: equal (==), not_equal (!=),
less (<), greater (>) etc.
Trig and other functions: sin(x), arcsin(x),
sinh(x), exp(x), sqrt(x) etc.
sum(x, axis=0), product(x, axis=0): sum and
product of array elements
dot(a, b)
Advanced
Only scratched the surface of numpy
Ufunc methods: reduce, accumulate, outer,
reduceat
Typecasting
More functions: take, choose, where, compress,
concatenate
Array broadcasting and None

About matplotlib
Easy to use, scriptable, “Matlab-like” 2D plotting
Publication quality ﬁgures and interactive capabilities
Plots, histograms, power spectra, bar charts, errorcharts,
scatterplots, etc.
Also does polar plots, maps, contours
Support for simple TEX markup
Multiple output backends (images, EPS, SVG, wx, Agg, Tk,
GTK)
Cross-platform: Linux, Win32, Mac OS X
Good idea to use via IPython: ipython -pylab
From scripts use: import pylab
More information
More information here: http://matplotlib.sf.net
http://matplotlib.sf.net/tutorial.html
http://matplotlib.sf.net/screenshots.html

Basic plotting with matplotlib
>>> x = arange (0 , 2∗pi , 0.05)
>>> p l o t ( x , sin ( x ) ) # Same as p l o t ( x , sin ( x ) , ’b− ’)
>>> p l o t ( x , sin ( x ) , ’ ro ’ )
>>> axis ([0 ,2∗ pi , −1 ,1])
>>> xlabel ( r ’$ chi$ ’ , color= ’g ’ )
>>> ylabel ( r ’ sin ( $ chi$ ) ’ , color= ’ r ’ )
>>> t i t l e ( ’A simple f i g u r e ’ , fo nts iz e =20)
>>> savefig ( ’ / tmp / t e s t . eps ’ )
# M ul ti pl e plots in one f i g u r e
>>> t = arange (0.0 , 5.2 , 0.2)
# red dashes , blue squares and green t r i a n g l e s
>>> p l o t ( t , t , ’ r−−’ , t , t ∗∗2 , ’ bs ’ , t , t ∗∗3 , ’g^ ’ )
Basic plotting . . .
# Set properties of objects :
>>> p l o t ( x , sin ( x ) , l i n e w i d t h =2.0 , color= ’ r ’ )
>>> l , = p l o t ( x , sin ( x ) )
>>> setp ( l , l i n e w i d t h =2.0 , color= ’ r ’ )
>>> l . set_linewidth ( 2 . 0 ) ; l . set_color ( ’ r ’ )
>>> draw ( ) # Redraws current f i g u r e .
>>> setp ( l ) # Prints available properties
>>> close ( ) # Closes the f i g u r e .
# M ul ti pl e figure s :
>>> f i g u r e ( 1 ) ; p l o t ( x , sin ( x ) )
>>> f i g u r e ( 2 ) ; p l o t ( x , tanh ( x ) )
>>> f i g u r e ( 1 ) ; t i t l e ( ’ Easy as 1 ,2 ,3 ’ )

Basic plotting . . .
>>> f i g u r e (1)
>>> subplot (211) # Same as subplot (2 , 1 , 1)
>>> p l o t ( x , cos (5∗x )∗ exp(−x ) )
>>> subplot (2 , 1 , 2)
>>> p l o t ( x , cos (5∗x ) , ’ r−−’ , label = ’ cosine ’ )
>>> p l o t ( x , sin (5∗x ) , ’g−−’ , label = ’ sine ’ )
>>> legend ( ) # Or legend ( [ ’ cosine ’ , ’ sine ’ ] )
>>> t e x t (1 ,0 , ’ (1 ,0) ’ )
>>> axes = gca ( ) # Current axis
>>> f i g = gcf ( ) # Current f i g u r e
X-Y plot
Example code
t1 = arange (0.0 , 5.0 , 0.1)
t2 = arange (0.0 , 5.0 , 0.02)
t3 = arange (0.0 , 2.0 , 0.01)
subplot (211)
p l o t ( t1 , cos(2∗ pi∗t1 )∗exp(−t1 ) , ’ bo ’ ,
t2 , cos(2∗ pi∗t2 )∗exp(−t2 ) , ’ k ’ )
grid ( True )
t i t l e ( ’A t a l e of 2 subplots ’ )
ylabel ( ’Damped ’ )
subplot (212)
p l o t ( t3 , cos(2∗ pi∗t3 ) , ’ r−−’ )
grid ( True )
xlabel ( ’ time ( s ) ’ )
ylabel ( ’Undamped ’ )

Errorbar
Example code
t = arange (0.1 , 4 , 0.1)
s = exp(−t )
e = 0.1∗abs ( randn ( len ( s ) ) )
f = 0.1∗abs ( randn ( len ( s ) ) )
g = 2∗e
h = 2∗f
errorbar ( t , s , [ e , g ] , f , fmt= ’o ’ )
xlabel ( ’ Distance (m) ’ )
ylabel ( ’ Height (m) ’ )
t i t l e ( ’Mean and standard error ’
’ as a function of distance ’ )
Semi-log and log-log plots
Example code
dt = 0.01
t = arange ( dt , 20.0 , dt )
subplot (311)
semilogy ( t , exp(−t / 5 . 0 ) )
ylabel ( ’ semilogy ’ )
grid ( True )
subplot (312)
semilogx ( t , sin (2∗ pi∗t ) )
ylabel ( ’ semilogx ’ )
grid ( True )
# minor grid on too
gca ( ) . xaxis . grid ( True , which= ’ minor ’ )
subplot (313)
loglog ( t , 20∗exp(−t / 1 0 . 0 ) , basex=4)
grid ( True )
ylabel ( ’ loglog base 4 on x ’ )

Histogram
Example code
mu, sigma = 100 , 15
x = mu + sigma∗randn (10000)
# the histogram of the data
n , bins , patches = h i s t ( x , 100 , normed=1)
# add a ’ best f i t ’ l i n e
y = normpdf ( bins , mu, sigma )
l = p l o t ( bins , y , ’ r−−’ , l i n e w i d t h =2)
xlim (40 , 160)
xlabel ( ’ Smarts ’ )
ylabel ( ’P ’ )
t i t l e ( r ’$ rm{ IQ : } / mu=100 ,/ sigma=15$ ’ )
Bar charts
Example code
N = 5
menMeans = (20 , 35 , 30 , 35 , 27)
menStd = ( 2 , 3 , 4 , 1 , 2)
# the x locations f o r the groups
ind = arange (N)
# the width of the bars
width = 0.35
p1 = bar ( ind , menMeans, width ,
color= ’ r ’ , yerr=menStd )
womenMeans = (25 , 32 , 34 , 20 , 25)
womenStd = ( 3 , 5 , 2 , 3 , 3)
p2 = bar ( ind+width , womenMeans, width ,
color= ’ y ’ , yerr=womenStd)
ylabel ( ’ Scores ’ )
t i t l e ( ’ Scores by group and gender ’ )
x t i c k s ( ind+width ,
( ’G1 ’ , ’G2 ’ , ’G3 ’ , ’G4 ’ , ’G5 ’ ) )
xlim(−width , len ( ind ) )
y t i c k s ( arange (0 ,41 ,10))
legend ( ( p1 [ 0 ] , p2 [ 0 ] ) ,
( ’Men ’ , ’Women ’ ) , shadow=True )

Pie charts
Example code
# make a square f i g u r e and axes
f i g u r e (1 , f i g s i z e =(8 ,8))
ax = axes ( [ 0 . 1 , 0.1 , 0.8 , 0 . 8 ] )
labels = ’ Frogs ’ , ’Hogs ’ , ’Dogs ’ , ’ Logs ’
fracs = [15 ,30 ,45 , 10]
explode =(0 , 0.05 , 0 , 0)
pie ( fracs , explode=explode , labels=labels ,
autopct= ’ %1.1 f%%’ , shadow=True )
t i t l e ( ’ Raining Hogs and Dogs ’ ,
bbox={ ’ facecolor ’ : ’ 0.8 ’ , ’ pad ’ : 5 } )
Scatter plots
Example code
N = 30
x = 0.9∗rand (N)
y = 0.9∗rand (N)
# 0 to 10 point radiuses
area = pi ∗(10 ∗ rand (N))∗∗2
volume = 400 + rand (N)∗450
scat ter ( x , y , s=area , marker= ’o ’ , c=volume ,
alpha =0.75)
xlabel ( r ’$ Delta_i$ ’ , size= ’ x−large ’ )
ylabel ( r ’$ Delta_ { i +1}$ ’ , size= ’ x−large ’ )
t i t l e ( r ’ Volume and percent change ’ )
grid ( True )
colorbar ( )
savefig ( ’ scatt er ’ )

Polar
Example code
f i g u r e ( f i g s i z e =(8 ,8))
ax = axes ( [ 0 . 1 , 0.1 , 0.8 , 0 . 8 ] , polar=True ,
axisbg= ’#d5de9c ’ )
r = arange (0 ,1 ,0.001)
theta = 2∗2∗pi∗r
polar ( theta , r , color= ’#ee8d18 ’ , lw =3)
# the radius of the grid labels
setp ( ax . thetagridlabels , y=1.075)
t i t l e ( r "$ theta =4 pi r " , fo nts iz e =20)
Contours
Example code
x = arange( −3.0 , 3.0 , 0.025)
y = arange( −2.0 , 2.0 , 0.025)
X, Y = meshgrid ( x , y )
Z1 = bivariate_normal (X, Y, 1.0 , 1.0 , 0.0 , 0.0)
Z2 = bivariate_normal (X, Y, 1.5 , 0.5 , 1 , 1)
# difference of Gaussians
Z = 10.0 ∗ (Z2 − Z1)
im = imshow (Z , i n t e r p o l a t i o n = ’ b i l i n e a r ’ ,
o r i g i n = ’ lower ’ ,
cmap=cm. gray , extent =(−3,3,−2,2))
leve ls = arange( −1.2 , 1.6 , 0.2)
# label every second l e v e l
clabel (CS, levels [ 1 : : 2 ] , i n l i n e =1 ,
fmt= ’ %1.1 f ’ , f o n ts iz e =14)
CS = contour (Z , levels ,
o r i g i n = ’ lower ’ ,
linewidths =2 ,
extent =(−3,3,−2,2))
# make a colorbar f o r the contour l i n e s
CB = colorbar (CS, shrink =0.8 , extend= ’ both ’ )
t i t l e ( ’ Lines with colorbar ’ )
hot ( ) ; f l a g ( )

Velocity vectors
Example code
X,Y = meshgrid ( arange (0 ,2∗ pi , . 2 ) ,
arange (0 ,2∗ pi , . 2 ) )
U = cos (X)
V = sin (Y)
Q = quiver (X [ : : 3 , : : 3 ] , Y [ : : 3 , : : 3 ] ,
U[ : : 3 , : : 3 ] , V [ : : 3 , : : 3 ] ,
color= ’ r ’ , units = ’ x ’ ,
linewidths =(2 ,) ,
edgecolors =( ’ k ’ ) ,
headaxislength=5 )
qk = quiverkey (Q, 0.5 , 0.03 , 1 , ’1 m/ s ’ ,
f o n t p r o p e r t i e s =
{ ’ weight ’ : ’ bold ’ } )
axis ([ −1 , 7 , −1, 7 ] )
t i t l e ( ’ t r i a n g u l a r head ; scale ’
’ with x view ; black edges ’ )
Maps
For details see http://matplotlib.sourceforge.net/screenshots/plotmap.py

Using SciPy
SciPy is Open Source software for mathematics, science, and
engineering
import scipy
Built on NumPy
Provides modules for statistics, optimization, integration, linear
algebra, Fourier transforms, signal and image processing,
genetic algorithms, ODE solvers, special functions, and more
Used widely by scientists world over
Details are beyond the scope of this tutorial
Quick Tour
Standard library
Very powerful
“Batteries included”
Example standard modules taken from the tutorial
Operating system interface: os
System, Command line arguments: sys
Regular expressions: re
Math: math, random
Internet access: urllib2, smtplib
Data compression: zlib, gzip, bz2, zipfile, and
tarfile
Unit testing: doctest and unittest
And a whole lot more!
Check out the Python Library reference:
http://docs.python.org/lib/lib.html

Quick Tour
Stdlib: examples
>>> import os
>>> os . system ( ’ date ’ )
F r i Jun 10 22:13:09 IST 2005
0
>>> os . getcwd ( )
’ /home/ prabhu ’
>>> os . chdir ( ’ / tmp ’ )
>>> import os
>>> d i r ( os )
<returns a l i s t of a l l module functions >
>>> help ( os )
<extensive manual page from module ’ s docstrings >
Quick Tour
Stdlib: examples
>>> import sys
>>> # P r i n t the l i s t of command l i n e args to Python
. . . print sys . argv
[ ’ ’ ]
>>> import re # Regular expressions
>>> re . f i n d a l l ( r ’ bf [ a−z ]∗ ’ ,
. . . ’ which foot or hand f e l l f a s t e s t ’ )
[ ’ foot ’ , ’ f e l l ’ , ’ f a s t e s t ’ ]
>>> re . sub ( r ’ ( b [ a−z ] + ) 1 ’ , r ’ 1 ’ ,
. . . ’ cat in the the hat ’ )
’ cat in the hat ’

Quick Tour
Stdlib: examples
>>> import math
>>> math . cos ( math . pi / 4.0)
0.70710678118654757
>>> math . log (1024 , 2)
10.0
>>> import random
>>> random . choice ( [ ’ apple ’ , ’ pear ’ , ’ banana ’ ] )
’ pear ’
Quick Tour
Stdlib: examples
>>> import u r l l i b 2
>>> f = u r l l i b 2 . urlopen ( ’ http : / /www. python . org / ’ )
>>> print f . read (100)
<!DOCTYPE html PUBLIC " −//W3C/ / DTD HTML 4.01 T r a n s i t i o n a l /
<?xml−stylesheet href=" . / css / ht2html

Quick Tour
Stdlib: examples
>>> import z l i b
>>> s = ’ witch which has which witches w r i s t watch ’
>>> len ( s )
41
>>> t = z l i b . compress ( s )
>>> len ( t )
37
>>> z l i b . decompress ( t )
’ witch which has which witches w r i s t watch ’
>>> z l i b . crc32 ( t )
−1438085031
Quick Tour
Summary
Introduced Python
Basic syntax
Basic types and data structures
Control ﬂow
Functions
Modules
Exceptions
Classes
Standard library

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