Python for Scientific ComputingLecture 1: The Python Calculator

Albert DeFuscoCenter for Simulation and Modeling

September 23, 2013

Section 1

Computer Programming

a · b =

nÿ

i=1

aibi

Assembler1 g l o b a l _mult32 sum equ 163 s e c t i o n . t e x t4 _mult3 :5 push ebp

6 mov ebp , esp

7 push e s i

8 push e d i

9 sub esp , 410 mov e s i , [ ebp+12 ]11 mov edi , [ ebp+8 ]12 mov dword [ ebp≠sum ] , 013 mov ecx , 314 . f o r l o o p :15 mov eax , [ e d i ]16 imul dword [ e s i ]17 add edi , 418 add e s i , 419 add [ ebp≠sum ] , eax

20 l oop . f o r l o o p21 mov eax , [ ebp≠sum ]22 add esp , 423 pop e d i

24 pop e s i

25 pop ebp

26 r e t

C source1

1 i n t mult 3 ( i n t � dst , i n t � s r c )2 {3 i n t sum = 0 , i ;45 f o r ( i = 0 ; i < 3 ; i ++)6 sum += d s t [ i ] � s r c [ i ] ;78 r e t u r n sum ;9 }

1011 i n t main ( vo id )12 {13 i n t d [ 3 ] = { 1 , 2 , 3 } ;14 i n t s [ 3 ] = {8 , 9 , 10 } ;1516 p r i n t f ( " answer is %i\n" , mult 3 ( d , s ) ) ;17 r e t u r n 0 ;18 }

1The first compiler was written by Grace Hopper in 1952 for the A-0 language

a · b =

nÿ

i=1

aibi

Python1 import numpy2 d i s t = numpy . a r r a y ( [ 1 , 2 , 3 ] )3 s r c = numpy . a r r a y ( [ 8 , 9 , 10 ] )45 p r i n t d i s t . dot ( s r c )

Choices

Computer Time Programmer Time

History of Python

I December 1989I Implementation by Guido van Rossum as successor of ABC to

provide exception handlingI February 1991

I Python 0.9.0 had classes with inheritance, exception handling,functions, and the core datatypes

I January 1994I Version 1.0 has functional programming features

I October 2000I Python 2.0 brings garbage collectionsI Python 2.2 improves Python’s types to be purely object oriented

I December 2008I Python 3I

Reduce feature duplication by removing old ways of doing things

I Not backwards compatible with Python 2.x

What’s so great about Python?

I PortableI Your program will run if the interpreter works and the modules are

installed

What’s so great about Python?

I E�cientI Rich language features built inI Simple syntax for ease of readingI Focus shifts to “algorithm” and away from implementation

What’s so great about Python?

I FlexibleI ImperativeI Object-orientedI Functional

What’s so great about Python?

I ExtendibleI Plenty of easy-to-use modules

IIf you can imagine it, then someone has probably developed a module

for it

I Your program can adjust the way the interpreter works

Why use python for science?

I A highly programmable calculatorI Fast proto-typing new algorithms or program designI Use C or Fortran routines directlyI Many science and mathematics modules already exist

Development Environment

I Frank1. Launch Putty2. Connect to

login0a.frank.sam.pitt.edu

Read the documentation

> pydoc

> python>>> help()

Disclaimer

Python 2.7 ! = 3.0

http://wiki.python.org/moin/Python2orPython3

Python syntax

I Extremely simplified syntaxI Nearly devoid of special charactersI Intended to be nearly English

I Dynamic typesI It is the responsibility of the programmerI Still “strongly typed”

Python objects

I All data in Python is represented by objectsI Objects have

I an identityI a typeI a valueI a name (“variable”)2

I Variables are names assigned to objects

2http://python.net/~goodger/projects/pycon/2007/idiomatic/handout.html#other-languages-have-variables

Section 2

Hands-on Python

Numerical objects

I IntegersI a = 1

I FloatsI a = 1.0

I Complex numbersI a = 1.5 + 0.5jI a. real and a.imag return each component

I Type castsI myFloat = float(myInteger)I myInt = int(myFloat)

I OperatorsI Addition +I Subtraction ≠I Multiplication �I Exponentiation ��I Division /I Modulus %

Mathematical functions

I many functions exist with the math module

1 import math23 h e l p ( math )45 p r i n t math . cos ( 0 )6 p r i n t math . p i

Logicals

I Boolean typeI a = (3 > 4)

I ComparisonsI ==I !=,<>I >I <I <=I >=

Strings

I a = ’single quoted’

I a = "double quoted"

I Triple quotes preserve whitespace and newlines

1 a = """ t r i p l e2 quoted3 s t r i n g """

I “\” is the escape character

String operations

I TypecastingI doubleA = float(a)I intA = int(a)

I Comparisons return a BooleanI A == B

I concatenated = a + b

Formatted stringsI width placeholders

\%s string\%d integer\%f float with 6 decimals\%E scientific notation

\%\% the % sign

I modifiersI integers after % adjust with width to printI decimal points are specified after the width as “.x”I use a hyphen after % to left justifyI printing long strings or large numbers will skew columns

1 from math import pi , e23 p r i n t "pi is %d and e is %d" % ( pi , e )4 p r i n t "pi is %6.4f and e is %6.4f" % ( pi , e )5 p r i n t "pi is %f and e is %f" % ( pi , e )6 p r i n t "pi is %10.8 e and e is %10.8 e" % ( pi , e )7 p r i n t "pi is %15.8 e and e is %15.8 e" % ( pi , e )

Writing a script file

I save the file to hello.py

1 #/ u s r / b i n / env python23 #This i s my comment about the f o l l o w i n g s c r i p t4 p r i n t ’Hello , world !’

I run the file

> module load python/epd-7.2> python hello.pyHello, world!

Structured blocks

1 i f ( a>b ) :2 p r i n t ’a is bigger ’3 e l i f ( b>a ) :4 p r i n t ’big is bigger ’5 e l s e :6 p r i n t ’a must equal b’

I Why is it indented?

Structured blocks

1 i f ( a>b ) :2 p r i n t ’a is bigger ’3 e l i f ( b>a ) :4 p r i n t ’big is bigger ’5 e l s e :6 p r i n t ’a must equal b’

I Why is it indented?

Logical operations

Inot, and, or

I be careful with assignmentsI Just use if statements

Structured blocks

1 i=02 w h i l e ( i <10 ) :3 p r i n t i4 i=i+1

Structured blocks

1 f o r i i n range ( 4 ) :2 p r i n t i

Ifor is not limited to arithmetic

Simple loops

I range( start ,stop, step)I list of integers from start to stop-1 in step incrementsI End point is always omitted

1 f o r i i n range ( 4 ) :2 p r i n t i

Simple Functions

I Simplify your programI Easier debuggingI Improved elegance

1 import math2 def a r ea ( r a d i u s ) :3 r e t u r n math . p i � r a d i u s ��2

Simple Functions

I Functions must be defined before being usedI Arguments are passed by reference to the object

3

I Variables do not have values, objects doI Functions are first class citizens

12 def y ( x ) :3 x=x+14 r e t u r n x ��256 x=57 y ( x )8 p r i n t x

3http://me.veekun.com/blog/2012/05/23/python-faq-passing/

Mathematical Exercises

I Print a table of temperature conversion

C =59 (F ≠ 32)

I Compute Pi using the Wallis formula

fi = 2ŒŸ

i=1

4i2

4i2 ≠ 1

Python for Scientific ComputingLecture 2: Data Structures

Albert DeFuscoCenter for Simulation and Modeling

September 18, 2013

Download your own Python

https://www.enthought.com/products/epd/free/

Review fi

fi = 2

ŒŸ

i=1

4i

2

4i

2 ≠ 1

1 p i = 2 .

2 f o r i i n range ( 1 , n ) :

3 p i �= 4 . � i ��2 / ( 4 . � i ��2 ≠ 1 )

4 p r i n t p i

Review fi

fi = 2

ŒŸ

i=1

4i

2

4i

2 ≠ 1

1 p i = 2 .

2 f o r i i n range ( 1 , n ) :

3 p i �= 4 . � i ��2 / ( 4 . � i ��2 ≠ 1 )

4 p r i n t p i

Containers

I tuples, lists and stringsI Elements are accessed with container[ ]

IIndexed starting at 0

I Arguments for len(container)

I Each type has special features

Tuples

ITuple = (1,3 ., ’red’)

I Contain references to other objectsI The structure cannot be changedI A convenient way to pass multiple objects

I Packing and un-packing

Lists

IList = [’red’,’green’,’blue’]

I ResizableI List-of-Lists is a multi-dimensional listI Lists are not arraysI

range() is a list

Dictionaries

I Key - value pairsProtons = {’Oxygen’: 8, ’Hydrogen’: 1}

Protons[’Carbon’] = 6

I Any type can be a key or valueI Look-up tablesI Sorting and searching operations

Indexing Lists and tuples

I Slicing just like Fortran 90L[ start : stop: stride ]

start Æ i < stop; i+ = stride

I Negative indices start at the end of the listI -1 is the last element

Other operations

I Search for value with in

I Concatenate with + or *

I Count number of occurrences

Loops

I Iterate over any sequenceI string, list, keys in dictionary, lines in file

1 vowe l s = ’aeiouy ’2 f o r i i n ’orbital ’ :

3 i f i i n vowe l s :

4 p r i n t ( i )

Loops

I Keep a counter

1 s h e l l s = ( ’s’ , ’p’ , ’d’ , ’f’ )

2 f o r i ndex , t h i s S h e l l i n enumerate ( s h e l l s ) :

3 p r i n t i ndex , t h i s S h e l l

Loops

I List comprehension

1 even = [ i f o r i i n range ( 100 ) i f i%2 == 0 ]

2

3 l i s t X = [≠1 , 0 , 1 ]

4 l i s t Y = [ 2 , 4 ]

5 myTuple = [ ( x , y ) f o r x i n l i s t X f o r y i n l i s t Y ]

Mutability of objects

I Immutable objects get created and destroyed upon assignment andcollection

I StringsI Numbers (no ++ operator)I Tuples

I Mutable objects create references to contained objects uponassignment

I ListsI Dictionaries

Hands-on: Mutability

Tuples or Lists?

I List: homogeneous dataI Elements can be added or deletedI Elements can be in any orderI Mutable

I Tuples: heterogeneous data (structs)I Constant sizeI Order mattersI Immutable

Container examples

I ListI ParticlesI Lines in an input file

I TupleI Position data

I DictionaryI Associated listsI Look-up tablesI HistogramsI NetworksI Graphs

Functions

I Doc stringsI Default valuesI Optional argumentsI Returns

Functions

1 def d i v i d e ( x , y ) :

2 """ D i v i d e t a k e s two i n t e g e r s as i n p u t

3 r e t u r n s a tupe o f q u o t i e n t and rema inde r """

4 r e t u r n x/y , x%y

Mathematical Exercises

I Write a function to di�erentiate another function

f

Õ(x) ¥ f (x + h) ≠ f (x ≠ h)

2h

If (x) and h are arguments

I make h = 0.01 the default valueI Practice with the following functions

If (x) = x

2 at x = 1I

f (x) = cos(x) at x = 2fiI

f (x) = e

≠2x

2 at x = 0

Mathematical Exercises

I Write a function to di�erentiate another function

f

Õ(x) ¥ f (x + h) ≠ f (x ≠ h)

2h

If (x) and h are arguments

I make h = 0.01 the default valueI Practice with the following functions

If (x) = x

2 at x = 1I

f (x) = cos(x) at x = 2fiI

f (x) = e

≠2x

2 at x = 0

recursions

n! =nŸ

k=1k

1 def f a c t o r i a l ( n ) :

2 i f ( n==0 ) :

3 r e t u r n 1

4 r e t u r n n� f a c t o r i a l ( n≠1 )

Python for Scientific ComputingLecture 3: Object-oriented Programming

Albert DeFuscoCenter for Simulation and Modeling

September 20, 2013

Modules

I Import math.py such that math becomes the object nameimport math

print math.pi

print math.sin(math.pi)

I AlternativesI from math import sin

I import math as maths

I AvoidI from math import �

If you can imagine it, someone probably has a module that can do it.

http://docs.python.org/2/py-modindex.html

http://wiki.python.org/moin/UsefulModules

Modules

I Any python script can be importedI The contents are run when importedI Use __main__ to just import definitionsI Name space defaults to the script’s file name

Functions and variablesI Functions can be documented easily

1 def p i ( i ) :

2 """ Compute the i t h term o f the W a l l i s f o rmu la """

3 r e t u r n 4 . � i ��2 / ( 4 . � i ��2 ≠ 1 )

4

5 h e l p ( p i )

I Multiple returns are tuples1 def myFunction ( x , y ) :

2 r e t u r n x ��2 , y�4

3

4 a , b = myFunction ( y=2 , x=8 )

I Default and optional arguments1 def d e r i v a t i v e ( f , x , h=0 . 01 ) :

2 r e t u r n ( f ( x+h ) ≠ f ( x≠h ) ) / 2 . � h

3

4 def f ( x ) :

5 r e t u r n x ��2

6

7 d e r i v a t i v e ( f , x=0 )

Functionals and variables

I Functions are objectsI Global variables can be defined

INot always good practice

IMay reduce the usability of a module

Name Spaces and Scopes

I ModulesI

Functions

Function Scope

I Variables assigned in a function are private

1 def p i ( i ) :

2 """ Compute the i t h term o f the W a l l i s f o rmu la """

3 temp=4 . � i ��2

4 r e t u r n temp / ( temp ≠ 1 )

5

6 p r i n t p i ( 2 )

7 p r i n t temp

Function Scope

I Warning!I

Variables assigned before a function are still in scope

IIt helps to define functions first

1 myVar = 5

2 def p i ( i ) :

3 """ Compute the i t h term o f the W a l l i s f o rmu la """

4 p r i n t myVar

5 temp=4 . � i ��2

6 r e t u r n temp / ( temp ≠ 1 )

7

8 p r i n t temp

Module Scope

I Names assigned in a module are readable by functionsI Names assigned in functions do not a�ect the outer scope

Object Oriented Programming

I Focus on data, not on the procedureI Encapsulate procedures with dataI Create modular code that can be reused

Object Oriented Programming

I ClassI

The description of a type of object

I ObjectI

The realization of the description

IAn instance of a class

Object Oriented Programming

I Classes defineI

Attributes

IMethods

I Instances haveI

data stored in attributes

IMethods to operate on the data

I Objects can interact with each other by passing attributes tomethods

Our modules

/home/sam/training/python/lecture3

http://core.sam.pitt.edu/python-fall2013

Classes

1 c l a s s shape ( o b j e c t ) :

2 """ Shapes have a name and c o l o r """

3 def __init__ ( s e l f , name=’shape ’ , c o l o r=’white ’ ) :

4 s e l f . name=name

5 s e l f . c o l o r=c o l o r

6

7 c l a s s Molecu l e ( o b j e c t ) :

8 """ M o l e c u l e s have a name and c h e m i c a l f o rmu la """

9 def __init__ ( s e l f , name , fo rmu la )

10 s e l f . name = name

11 s e l f . f o rmu la = fo rmu la

Operator Overloading

Change or define the behavior of operations1 c l a s s Molecu l e ( o b j e c t ) :

2 . . .

3 def __add__( s e l f , o t h e r ) :

4 newName = s e l f . name + " + " + o t h e r . name

5 newFormula = "[" + s e l f . f o rmu la + "]" + "[" + o t h e r . f o rmu la + "]"

6 r e t u r n Molecu l e (newName , newFormula )

7

8

9 mol1=Molecu l e ( ’water ’ , ’h2o ’ )

10 mol2=Molecu l e ( ’ammonia ’ , ’nh3 ’ )

11

12 mol3 = mol1 + mol2

InheritanceI Child classes can be more specific than the parentI Subclasses can override the superclass†

1 import math

2 c l a s s shape ( o b j e c t ) :

3 def __init__ ( s e l f , name=’shape ’ , c o l o r=’white ’ ) :

4 s e l f . name=name

5 s e l f . c o l o r=c o l o r

6

7 c l a s s c i r c l e ( shape ) :

8 def __init__ ( s e l f , r a d i u s=1 . , name=’circle ’ , c o l o r=’white ’ ) :

9 super ( c i r c l e , s e l f ) . __init__ ( name , c o l o r )

10 s e l f . r a d i u s=r a d i u s

11 def a r ea ( ) :

12 r e t u r n math . p i � s e l f . r a d i u s ��2

13

14 c l a s s squa r e ( shape ) :

15 def __init__ ( s e l f , s i z e=1 . , name=’square ’ , c o l o r=’white ’ ) :

16 super ( square , s e l f ) . __init__ ( name , c o l o r )

17 s e l f . s i z e=s i z e

18 def a r ea ( ) :

19 r e t u r n s e l f . s i z e ��2

†Polymorphism in Python is achieved when classes implement the same methods, which reduces

the number of if statements