Download Basics of Python - AG Tremblay

Python - Tutorial
Python is a very simple language, and has a very straightforward syntax. It has efficient high-level
data structures and a simple but effective approach to object-oriented programming. The Python
interpreter and the extensive standard library are freely available. This tutorial introduces many
of Python’s most noteworthy features, and will give you a good idea of the language’s flavor and
style.
How to Start Python
Invoking the Interpreter
The Python interpreter is usually installed as /usr/local/bin/python. The path /usr/local/bin is
put in the Unix shell’s search. This makes it possible to start python by typing the command
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python
Invocation of a Script
The most common use case is, of course, a simple invocation of a script:
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p y t h o n m y s c r i p t . py
When a script file is used, it is sometimes useful to be able to run the script and enter interactive
mode afterwards. This can be done by passing −i before the script:
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p y t h o n − i m y s c r i p t . py
Hello, World!
The simplest directive in Python is the print directive - it simply prints out a line.
To print a string, just write:
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p r i n t ’ H e l l o , World ! ’
Comments in Python start with the hash character # and extend to the end of the physical line.
A comment may appear at the start of a line or following whitespace or code, but not within a
string literal.
Indentation
Python uses indentation for blocks, instead of curly braces. Both tabs and spaces are supported,
but the standard indentation requires standard Python code to use four spaces. For example:
x = 1
i f x == 1 :
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# indented four spaces
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print ’x i s 1. ’
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Variables and Types
Python is completely object oriented, and not "statically typed". You do not need to declare
variables before using them, or declare their type. Every variable in Python is an object.
This tutorial will go over a few basic types of variables.
Number
Python supports two types of numbers - integers and floating point numbers.
To define an integer, use the following syntax:
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myint = 7
To define a floating point number, you may use one of the following notations:
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myfloat = 7.0
myfloat = f l o a t (7)
Strings
Strings are defined either with a single quote or a double quotes.
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mystring = ’ h e l l o ’
mystring = " h e l l o "
The difference between the two is that using double quotes makes it easy to include apostrophes
(whereas these would terminate the string if using single quotes)
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m y s t r i n g = "Don ’ t w o r r y a b o u t a p o s t r o p h e s "
Simple operators can be executed on numbers and strings:
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one = 1
two = 2
t h r e e = one + two
hello = " hello "
world = " world "
h e l l o w o r l d = h e l l o + " " + world
Assignments can be done on more than one variable "simultaneously" on the same line like this
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a, b = 3, 4
Mixing operators between numbers and strings is not supported:
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# T h i s w i l l n o t work !
p r i n t one + two + h e l l o
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Lists
Lists are very similar to arrays. They can contain any type of variable, and they can contain as
many variables as you wish. Here is an example of how to build a list.
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mylist = []
m y l i s t . append ( 1 )
m y l i s t . append ( 2 )
m y l i s t . append ( 3 )
print ( mylist [ 0 ] ) # prints
print ( mylist [ 1 ] ) # prints
print ( mylist [ 2 ] ) # prints
mylist2 = range (1 ,20 ,2) #
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range ( s t a r t i n g p o i n t , endpoint , s t e p s i z e )
Accessing an index which does not exist generates an exception (an error).
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mylist = [1 ,2 ,3]
print ( mylist [10])
To find out the length of a list, just use
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len ( mylist )
Basic Operators
This section explains how to use basic operators in Python.
Arithmetic Operators
Just as any other programming languages, the addition, subtraction, multiplication, and division
operators can be used with numbers.
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number = 1 + 2 ∗ 3 / 4 . 0
Try to predict what the answer will be. Does python follow order of operations?
Another operator available is the modulo % operator, which returns the integer remainder of the
division.
dividend % divisor = remainder
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r e m a i n d e r = 11 % 3
Using two multiplication symbols makes a power relationship.
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s q u a r e d = 7 ∗∗ 2
cubed = 2 ∗∗ 3
Using Operators with Strings
Python supports concatenating strings using the addition operator:
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h e l l o w o r l d = " h e l l o " + " " + " world "
Python also supports multiplying strings to form a string with a repeating sequence:
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l o t s o f h e l l o s = " h e l l o " ∗ 10
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Using Operators with Lists
Lists can be joined with the addition operators:
even_numbers = [ 2 , 4 , 6 , 8 ]
odd_numbers = [ 1 , 3 , 5 , 7 ]
3 a l l _ n u m b e r s = odd_numbers + even_numbers
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Just as in strings, Python supports forming new lists with a repeating sequence using the
multiplication operator:
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print [1 ,2 ,3] ∗ 3
String Formatting
Python uses C-style string formatting to create new, formatted strings. The % operator is used
to format a set of variables enclosed in a ’tuple’ (a fixed size list), together with a format string,
which contains normal text together with ’argument specifiers’, special symbols like %s (strings)
and %d (integers).
Let’s say you have a variable called name with your user name in it, and you would then like to
print out a greeting to that user.
# T h i s p r i n t s o u t " H e l l o , John ! "
name = " John "
3 p r i n t " H e l l o , %s ! " % name
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To use two or more argument specifiers, use a tuple (parentheses):
# T h i s p r i n t s o u t " John i s 23 y e a r s o l d . "
name = " John "
3 age = 23
4 p r i n t "%s i s %d y e a r s o l d . " % ( name , age )
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Any object which is not a string can be formatted using the %s operator as well. For example:
# This p r i n t s out : A l i s t : [ 1 , 2 , 3 ]
mylist = [1 ,2 ,3]
3 p r i n t "A l i s t : %s " % m y l i s t
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Here are some basic argument specifiers you should know:
• %s - String (or any object with a string representation, like numbers)
• %d - Integers
• %f - Floating point numbers
• %.<number of digits>f - Floating point numbers with a fixed amount of digits to the right
of the dot.
• %x/%X - Integers in hex representation (lowercase/uppercase)
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Conditions
Python uses boolean variables to evaluate conditions. The boolean values True and False are
returned when an expression is compared or evaluated. For example:
x = 2
2 p r i n t x == 2 # p r i n t s o u t True
3 p r i n t x == 3 # p r i n t s o u t F a l s e
4 p r i n t x < 3 # p r i n t s o u t True
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Notice that variable assignment is done using a single equals operator =, whereas comparison
between two variables is done using the double equals operator ==. The "not equals" operator
is marked as !=.
Boolean Operators
The and and or boolean operators allow building complex boolean expressions, for example:
name = " John "
2 age = 23
3 i f name == " John " and age == 2 3 :
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p r i n t " Your name i s John , and you a r e a l s o 23 y e a r s o l d . "
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i f name == " John " or name == " R i c k " :
p r i n t " Your name i s e i t h e r John o r R i c k . "
The in Operator
The in operator could be used to check if a specified object exists within an iterable object
container, such as a list:
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i f name i n [ " John " , " R i c k " ] :
p r i n t " Your name i s e i t h e r John o r R i c k . "
Here is an example for using Python’s statement if using code blocks:
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i f <s t a t e m e n t i s t r u e >:
<do s o m e t h i n g >
....
....
e l i f <a n o t h e r s t a t e m e n t i s t r u e >: # e l s e i f
<do s o m e t h i n g e l s e >
....
....
else :
<do a n o t h e r t h i n g >
....
....
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For example:
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x = 2
i f x == 2 :
p r i n t " x e q u a l s two ! "
else :
p r i n t " x d o e s n o t e q u a l t o two . "
A statement is evaluated as true if one of the following is correct:
1. The True boolean variable is given, or calculated using an expression, such as an arithmetic
comparison.
2. An object which is not considered "empty" is passed.
Here are some examples for objects which are considered as empty:
1. An empty string: ""
2. An empty list: []
3. The number zero: 0
4. The false boolean variable: False
The is Operator
Unlike the double equals operator ==, the is operator does not match the values of the variables,
but the instances themselves. For example:
x = [1 ,2 ,3]
2 y = [1 ,2 ,3]
3 p r i n t x == y # P r i n t s o u t True
4 p r i n t x i s y # P r i n t s out F a l s e
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The not Operator
Using not before a boolean expression inverts it:
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p r i n t not F a l s e # P r i n t s o u t True
p r i n t ( not F a l s e ) == ( F a l s e ) # P r i n t s o u t F a l s e
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Loops
There are two types of loops in Python, for and while.
The for Loop
for loops iterate over a given sequence. Here is an example:
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primes = [2 , 3 , 5 , 7]
for prime in primes :
print prime
for loops can iterate over a sequence of numbers using the "range" and "xrange" functions. The
difference between range and xrange is that the range function returns a new list with numbers
of that specified range, whereas xrange returns an iterator, which is more efficient. Note that
the xrange function is zero based.
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# P r i n t s o u t t h e numbers 0 , 1 , 2 , 3 , 4
for x in xrange ( 5 ) : # or range (5)
print x
# P r i n t s out 3 ,4 ,5
fo r x in xrange (3 , 6 ) : # or range (3 , 6)
print x
# P r i n t s out 3 ,5 ,7
f o r x in xrange (3 , 8 , 2 ) : # or range (3 , 8 , 2)
print x
while Loops
while loops repeat as long as a certain boolean condition is met. For example:
# P r i n t s out 0 ,1 ,2 ,3 ,4
count = 0
3 while count < 5:
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print count
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c o u n t += 1 # T h i s i s t h e same a s c o u n t = c o u n t + 1
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break and continue Statements
break is used to exit a for loop or a while loop, whereas continue is used to skip the current
block, and return to the for or while statement. A few examples:
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# P r i n t s out 0 ,1 ,2 ,3 ,4
count = 0
w h i l e True :
print count
c o u n t += 1
i f c o u n t >= 5 :
break
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# P r i n t s o u t o n l y odd numbers − 1 , 3 , 5 , 7 , 9
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for x in xrange (10):
# Check i f x i s e v e n
i f x % 2 == 0 :
continue
print x
Functions
What are Functions?
Functions are a convenient way to divide your code into useful blocks, allowing us to order our
code, make it more readable, reuse it and save some time. Also functions are a key way to define
interfaces so programmers can share their code.
How do you Write Functions in Python?
Functions in python are defined using the block keyword def, followed with the function’s name
as the block’s name. For example:
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def m y _ f u n c t i o n ( ) :
p r i n t " H e l l o From My F u n c t i o n ! "
Functions may also receive arguments (variables passed from the caller to the function). For
example:
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def m y _ f u n c t i o n _ w i t h _ a r g s ( username ) :
p r i n t " H e l l o , %s , From My F u n c t i o n ! " % ( username )
Functions may return a value to the caller, using the keyword return. For example:
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def sum_two_numbers ( a , b ) :
return a + b
How do you Call Functions in Python?
Simply write the function’s name followed by (), placing any required arguments within the
brackets. For example, lets call the functions written above (in the previous example):
# print a simple greeting
my_function ( )
3 #p r i n t s − " H e l l o , John Doe , From My F u n c t i o n ! "
4 m y _ f u n c t i o n _ w i t h _ a r g s ( " John Doe " )
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# a f t e r t h i s l i n e x w i l l hold the value 3!
x = sum_two_numbers ( 1 , 2 )
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Modules and Packages
Modules in Python are itself Python files, which implement a set of functions. Modules are
imported from other modules using the import command.
numpy Module
numpy is the fundamental package for scientific computing with Python. It contains among other
things:
• a powerful N-dimensional array object
• sophisticated (broadcasting) functions
• tools for integrating C/C++ and Fortran code
• useful linear algebra, Fourier transform, and random number capabilities
The main functionalities are summarized in the following example:
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import numpy
a = numpy . a r r a y ( [ [ 2 , 3 , 4 , 1 ] , [ 2 , 5 , 7 , 8 ] ] ) # a r r a y c r e a t i o n
p r i n t ( " T h i s i s a %d d i m e n s i o n a l m a t r i x " % ( a . ndim ) +
" with a shape of " , a . shape )
b1 = numpy . a r a n g e ( 0 , 2 4 . 1 , 0 . 1 )
b2 = numpy . l i n s p a c e ( 0 , 2 4 , 2 4 1 )
c = numpy . z e r o s ( ( 2 , 4 ) ) # c r e a t e s a r r a y f u l l o f z e r o s
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#
c
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f
f
B a s i c o p e r a t i o s w i t h numpy a r r a y s
+= 1 . 5
= a ∗ c # element wise product
= numpy . d o t ( a . T , c ) # d o t p r o d u c t
= numpy . sum ( a , a x i s =1) # sum o v e r s e c o n d d i m e n s i o n
= numpy . s i n ( f ) # s i n u s f u n c t i o n w o r k s a l s o w i t h cos , exp , t a n . . .
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# Printing Arrays
p r i n t " M i n i m a l / maximal v a l u e o f a : %d/%d " % ( a . min ( ) , a . max ( ) )
18 p r i n t f
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# Deep Copy
21 a_copy = a . copy ( ) # a new a r r a y o b j e c t w i t h new d a t a i s c r e a t e d
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# I n d e x i n g , S l i c i n g and I t e r a t i n g
g = numpy . a r a n g e ( 1 0 ) ∗ ∗ 3 ∗ numpy . p i
p r i n t " F i r s t e l e m e n t : %d , l a s t e l e m e n t : %d " % ( g [ 0 ] , g [ − 1 ] )
p r i n t " T h i r d e l e m e n t : %.1 f " % ( g [ 2 ] )
print " Third to f i f t h element : " , g [ 2 : 5 ]
g [ : 6 : 2 ] = −1000 # e q u i v a l e n t t o g [ 0 : 6 : 2 ] = −1000;
# from s t a r t t o p o s i t i o n 6 ,
# e x c l u s i v e , s e t e v e r y 2 nd e l e m e n t t o −1000
print "g reversed : " , g [:: −1]
Useful information for MATLAB users:
http://wiki.scipy.org/NumPy_for_Matlab_Users
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matplotlib . pyplot Module
matplotlib . pyplot is a python 2D plotting library and can be used in python scripts. matplotlib . pyplot
is a collection of command style functions that make matplotlib work like MATLAB. Each pyplot
function makes some change to a figure, e.g., create a figure, create a plotting area in a figure,
plot some lines in a plotting area, decorate the plot with labels, etc. . Here is an example which
shows some selected functionalities of matplotlib . pyplot
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import m a t p l o t l i b . p y p l o t a s p l t
x = [1 ,2 ,3 ,4]
y = [2 ,5 ,9 ,20]
p l t . p l o t ( x , y , ’ r−− ’ , l i n e w i d t h =2, l a b e l= ’ T e s t i n g ’ )
p l t . x l a b e l ( r ’ $x \ , [ \ rm{ u n i t s } ] $ ’ , f o n t s i z e =20)
p l t . y l a b e l ( r ’ $y \ , [ \ rm{a_0 } ] $ ’ , f o n t s i z e =20)
p l t . l e g e n d ( l o c= ’ l o w e r r i g h t ’ , p r o p={ ’ s i z e ’ : 2 0 } )
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# You can e i t h e r show t h e p l o t . . .
p l t . show ( )
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# . . . or save i t to a f i l e .
#f i g _ f i d = ’ t e s t . png ’
14 #p l t . s a v e f i g ( f i g _ f i d , f o r m a t =’ png ’ , d p i =100)
15 #p l t . c l o s e ( )
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Exercises
1. Write a program which determines numerically the integral of the one-dimensional sine
function
y(x) = sin (x)
in an interval of [0, π], using the summed Simpson’s rule. Hint: Simpson’s rule is defined
by
ˆ b
b−a
a+b
y (x) dx ≈
y (a) + 4y
+ y (b)
.
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a
Your task is the following: Write a function simps(x,y) computing the Simpson’s integral.
Vary systematically the number of points in the x variable and plot the integral values
against the number of grid points. Optimize the number of grid point until the error
(difference between analytical and numerical integral) is smaller than 10−7 .
2. Repeat the procedure from task 1 using the trapezoidal rule and plot the difference between
both methods on a logarithmic scale as a function of the number of grid points.
References
http://www.numpy.org/
http://matplotlib.org/index.html
http://www.learnpython.org/en/Welcome
https://docs.python.org/
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