scientific programming in python

Why Python? Introduction to Python Further Info

Scientific Programming in Python

Eric Christiansen

UCSD CSE

September 16, 2008

This work is licensed under the Creative Commons Attribution 3.0 License.

Based on a MATLAB tutorial by Tim Marks

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What is Python?

Python in a very high level (scripting) language which has gainedwidespread popularity in recent years.It is:

cross platform

object oriented

open source

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What is Python?

cross platform

object oriented

open source

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What is Python?

cross platform

object oriented

open source

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What is Python?

cross platform

object oriented

open source

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Why should I care?

You may need to use a computer to

run simulations

crunch data

display data...

Python’s 3rd-party libraries can help you with these tasks.

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Why should I care?

run simulations

crunch data

display data...

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Why should I care?

run simulations

crunch data

display data...

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Python’s Scientific Libraries

Python is enhanced by a large set of scientific libraries that arebeing actively developed.

standard science and engineering functions or plotting (MATLAB)

SciPy, Matplotlib

a computer algebra system (Mathematica)

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SciPy, Matplotlib

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SciPy, Matplotlib

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data processing

Modular toolkit for Data Processing (MDP)

bioinformatics functions

Biopython

machine learning functions

PyML, mlpy, SHOGUN

neural nets

Fast Artificial Neural Network (FANN) Library

artificial intelligence or robotics routines

Python Robotics (Pyro)

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data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Is it hard to learn?

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Is it hard to learn?

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Python vs MATLAB

Advantages of MATLAB:

already widely used

designed specifically for scientific computing

easy to find documentation

good IDE with debugging and profiling support “out of the box”

Advantages of Python:

open source means no limits on use

appears to approximately superset MATLAB’s functionality

modern language with support for object orientation

support for calling functions in other languages

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used

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Basics

To get information on an object from the interpreter

h e l p <o b j e c t >

Commenting:

Inline comments are preceded with #

Block comments are surrounded with ”””

Code blocks are denoted with indentation:

i f x == 2 :p r i n t x

Python is dynamically typed:

a = ” h e l l o ” # a i s a s t r i n ga = 4 # a i s now an i n t e g e r

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VectorsMany of these functions come from SciPy.

from s c i p y import ∗

Vectors:

N = 5 # a s c a l a rv = [ 1 , 2 , 3 ] # a l i s tv = a r r a y ( [ 1 , 2 , 3 ] ) # a column v e c t o rv = a r r a y ( [ [ 1 ] , [ 2 ] , [ 3 ] ] )# a column v e c t o rv = a r r a y ( [ [ 1 , 2 , 3 ] ] ) # a column v e c t o rv = t r a n s p o s e ( v ) # t r an s p o s e a v e c t o r

# ( row to column# or column to row )

v = a ran ge (−4 ,4) # a ve c t o r i n# a s p e c i f i e d range :

v = p i ∗ ar an ge (−4 ,4)/4v = a ran ge (−4 ,4 , .5) # arange ( s t a r t , stop , s t e p )v = [ ] # empty l i s t

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Matrices

v = a r r a y ( [ 5 , 6 , 7 ] ) # acc e s s a v e c t o r e l ementv [ 2 ] # ve c t o r ( i nd ex ) − a r r a y s a r e

# zero−i ndexedl e n ( v ) # number o f e l ement s i n a v e c t o r

m = a r r a y ( [ [ 1 , 2 , 3 ] , \[ 4 , 5 , 6 ] ] ) # a 2x3 mat r i x

m[ 1 , 2 ] == m[ 1 ] [ 2 ] # acc e s s a mat r i x e l ement# mat r i x [ row , column ]

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Syntax and Special Functions

Matrices:

m = z e r o s ( [ 2 , 3 ] ) # a mat r i x o f z e r o sv = ones ( [ 1 , 3 ] ) # a mat r i x o f onesv = rand ( 3 , 1 ) # rand mat r i x ( s e e a l s o randn )m = eye ( 3 ) # i d e n t i t y mat r i x (3 x3 )

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Syntax and Special Functions (cont)

m[ 1 , : ] # acc e s s a mat r i x row ( second row )m[ : , 0 ] # acc e s s a mat r i x column ( l e f t column )m[ 1 : , 1 : ] # lowe r r i g h t submat r i xm. r e s h a p e ( [ 4 , 1 ] ) # turn mat r i x i n t o a column

# ve c t o r ( conca t ena t e rows )m. shape # s i z e o f a mat r i x [ rows , c o l s ]m. shape [ 0 ] # number o f rowsm. shape [ 1 ] # number o f columnsz e r o s (m. shape ) # c r e a t e a new mat r i x w i th

# s i z e o f m

m = a r r a y ( [ [ ’ h e l l o ’ , sum ] ,\[ 1 , 2 ] ] ) # put whatever you want

# i n t o an a r r a ym[ 0 , 1 ] (m[ 1 ] ) # c a l l sum on bottom row o f m

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Syntax and Special Functions (cont)

Arithmetic operations performed on arrays are done “element byelement”.

a = a r r a y ( [ 1 , 2 , 3 , 4 ] ) # ve c t o r2 ∗ a # s c a l a r m u l t i p l i c a t i o na / 4 # s c a l a r d i v i s i o nb = a r r a y ( [ 5 , 6 , 7 , 8 ] ) # ve c t o ra + b # po i n tw i s e v e c t o r a d d i t i o na − b # po i n tw i s e v e c t o r s u b t r a c t i o na ∗∗ 2 # p o i n t i s e v e c t o r s qu a r i n ga ∗ b # po i n tw i s e v e c t o r mu l t i p l ya / b # po i n tw i s e v e c t o r d i v i d el o g ( a ) # po i n tw i s e l o g a r i t hmaround ( a r r a y ( [ [ . 6 ] , \

[ . 5 ] ] ) ) # po i n tw i s e round ing# ( . 5 rounds to 0)

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Vector Operations

a = a r r a y ( [ 1 , 4 , 6 , 3 ] ) # ve c t o rsum ( a ) # sum of v e c t o r e l ement smean ( a ) # mean o f v e c t o r e l ement sv a r ( a ) # va r i a n c es t d ( a ) # standa rd d e v i a t i o nmax ( a ) # maximum

a = a r r a y ( [ [ 1 , 2 , 3 ] , \[ 4 , 5 , 6 ] ] ) # mat r i x

mean ( a , 0 ) # mean o f each columnamax ( a , 1 ) # max o f each rowamax ( a ) # to ob t a i n max o f mat r i x

# note we use 2# d i f f e r e n t max f u n c t i o n s

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Matrix Operations

dot ( t r a n s p o s e ( a r r a y ( [ 1 , 2 , 3 ] ) ) , \a r r a y ( [ 4 , 5 , 6 ] ) ) # row v e c t o r 1x3 t imes column

# ve c t o r 3x1 r e s u l t s i n a# s i n g l e number , a l s o known# as dot / i n n e r p roduc t

dot ( a r r a y ( [ [ 1 ] , [ 2 ] , [ 3 ] ] ) , \a r r a y ( [ [ 4 , 5 , 6 ] ] ) ) # column v e c t o r 3x1 t imes row

# ve c t o r 1x3 r e s u l t s i n 3x3# matr ix , a l s o known# as ou t e r p roduc t

a = rand ( 3 , 2 ) # 3x2 mat r i xb = rand ( 2 , 4 ) # 2x4 mat r i xdot ( a , b ) # 3x4 mat r i x

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Saving Your Work

import c P i c k l e as p i c k l e # t h i s module l e t s you# save and r e l o a d o b j e c t s

f = open ( ’ s a v e f i l e ’ , ’w ’ ) # open a r c h i v e f i l ep i c k l e . dump( obj , f ) # dump ob j e c t to a r c h i v ef . c l o s e ( ) # c l o s e a r c h i v e f i l e

del o b j # c l e a r o b j e c t# from memory

f = open ( ’ s a v e f i l e ’ , ’ r ’ ) # open a r c h i v e f i l eo b j = p i c k l e . l o a d ( f ) # read ob j e c t

# from a r c h i v ef . c l o s e ( ) # c l o s e a r c h i v e f i l e

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Relations and Control

Example: given a list v, create a new list u with values equal to v ifthey are greater than 0, and equal to 0 if they less than or equal to0.Using a for loop:

v = [3 ,5 ,−2 ,5 ,−1 ,0]u = [ 0 ] ∗ l e n ( v ) # u i s a l l z e r o sf o r i i n ra ng e ( l e n ( v ) ) :

i f v [ i ] > 0 :u [ i ] = v [ i ]

Using list comprehension:

v = [3 ,5 ,−2 ,5 ,−1 ,0]u = [ max ( e , 0 ) f o r e i n v ]

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Importing Functions

Save the following code to “mylib.py”:

def myfunc ( a , b ) :return a+b∗∗2

Import and use myfunc. Note, we might need to configurePYTHONPATH.

from m y l i b import myfuncmyfunc ( 1 , 2 )myfunc ( b=2,a=1) # same as above

Python also supports class creation:

c l a s s MyClass :def i n i t ( s e l f ) :

p r i n t ” h e l l o ! ”m y c l a s s = MyClass ( )

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Plotting

The library matplotlib / pylab is your friend:

from p y l a b import ∗xs = ar ang e (−2 ,2 , .01)p l o t ( xs , s i n ( xs ) )show ( )

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Imaging

We use the Python Imaging Library as well as matplotlib / pylab.

from p y l a b import ∗import Image

im = Image . open ( ’ my image . j p g ’ )im . show ( ) # we can d i s p l a y the imageima = a r r a y ( im ) # ty p e c a s t i n g to a r r a y

# e x t r a c t s p i x e l v a l u e simr = Image . f r o m s t r i n g ( ’RGB ’ ,\

( ima . shape [ 1 ] , ima . shape [ 0 ] ) , \ima . t o s t r i n g ( ) ) # conve r t a r r a y i n t o image

img = mean ( ima , 2 ) # ave rage c o l o r i n t e n s i t i e s# f o r each p i x e l

imshow ( img )autumn ( ) # se t d e f a u l t co lormap to autumnshow ( )

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More Help?

Many guides and tutorials are available online:

Dive Into Python

python introduction for programmers

A list of tutorials for Python and some of its many libraries can befound at http://www.awaretek.com/tutorials.html

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More Help?

Many guides and tutorials are available online:Dive Into Python

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More Help?

Many guides and tutorials are available online:Dive Into Python

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Questions?

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scientific programming in python

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