Scientific Programming in Python

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Scientific Programming in Python

Eric Christiansen

UCSD

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What is Python?

Python in a very high level (scripting) language which has gained widespread popularity in recent years.

It is:

cross platform object oriented open source

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What is Python?

It is:

cross platform

object oriented open source

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What is Python?

It is:

cross platform object oriented

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What is Python?

It is:

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...

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Why should I care?

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Why should I care?

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Python’s Scientific Libraries

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

Suppose you want:

standard science and engineering functions or plotting (MATLAB)

SciPy, Matplotlib

a computer algebra system (Mathematica)

SAGE

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

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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Python’s Scientific Libraries

Suppose you want:

SciPy, Matplotlib

SAGE

data processing

Biopython

PyML, mlpy, SHOGUN

neural nets

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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

Advantages of MATLAB: already widely used

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Python vs MATLAB

designed specifically for scientific computing

easy to find documentation

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Python vs MATLAB

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Python vs MATLAB

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Python vs MATLAB

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Python vs MATLAB

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Python vs MATLAB

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

appears to approximately superset MATLAB’s functionality modern language with support for object orientation

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Python vs MATLAB

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Python Intro - 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 g

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Python Intro - Vectors and Matrices

Many of these functions come from SciPy. from s c i p y import ∗ Vectors: N = 5 # a s c a l a r v = [ 1 , 2 , 3 ] # a l i s t v = a r r a y ( [ 1 , 2 , 3 ] ) # a column v e c t o r v = a r r a y ( [ [ 1 ] , [ 2 ] , [ 3 ] ] ) # a column v e c t o r v = a r r a y ( [ [ 1 , 2 , 3 ] ] ) # a column v e c t o r v = t r a n s p o s e ( v ) # t r a n s p o s e a v e c t o r # ( row t o column # o r column t o row ) v = a r a n g e ( −4 ,4) # a v e c t o r i n # a s p e c i f i e d r a n g e : v = p i ∗ a r a n g e ( −4 ,4)/4 v = a r a n g e ( − 4 , 4 , . 5 ) # a r a n g e ( s t a r t , s t o p , s t e p ) v = [ ] # empty l i s t

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Python Intro

Matrices: m = z e r o s ( [ 2 , 3 ] ) # a m a t r i x o f z e r o s v = o n e s ( [ 1 , 3 ] ) # a m a t r i x o f o n e s v = r a n d ( 3 , 1 ) # r a n d m a t r i x ( s e e a l s o r a n d n ) m = e y e ( 3 ) # i d e n t i t y m a t r i x ( 3 x3 )

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Python Intro - Vectors and Matrices

v = a r r a y ( [ 5 , 6 , 7 ] ) # a c c e s s a v e c t o r e l e m e n t v [ 2 ] # v e c t o r ( i n d e x ) − a r r a y s a r e # z e r o −i n d e x e d l e n ( v ) # number o f e l e m e n t s i n # a v e c t o r m = a r r a y ( [ [ 1 , 2 , 3 ] , \ [ 4 , 5 , 6 ] ] ) # a 2 x3 m a t r i x m[ 1 , 2 ] == m [ 1 ] [ 2 ] # a c c e s s a m a t r i x e l e m e n t # m a t r i x [ row , column ]

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blah

m [ 1 , : ] # a c c e s s a m a t r i x row # ( bottom row ) m [ : , 0 ] # a c c e s s a m a t r i x column # ( l e f t column ) m. r e s h a p e ( [ 4 , 1 ] ) # t u r n m a t r i x i n t o a column # v e c t o r ( c o n c a t e n a t e r o w s ) m. s h a p e # s i z e o f a m a t r i x [ rows , c o l s ] m. s h a p e [ 0 ] # number o f r o w s m. s h a p e [ 1 ] # number o f c o l u m n s z e r o s (m. s h a p e ) # c r e a t e a new m a t r i x w i t h # s i z e o f m m = a r r a y ( [ [ ’ h e l l o ’ , sum ] , \ [ 1 , 2 ] ] ) # p u t w h a t e v e r you want # i n t o an a r r a y

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Python Intro - Vectors and Matrices

Arithmetic operations performed on arrays are done “element by element”. a = a r r a y ( [ 1 , 2 , 3 , 4 ] ) # v e c t o r 2 ∗ a # s c a l a r m u l t i p l i c a t i o n a / 4 # s c a l a r d i v i s i o n b = a r r a y ( [ 5 , 6 , 7 , 8 ] ) # v e c t o r a + b # p o i n t w i s e v e c t o r a d d i t i o n a − b # p o i n t w i s e v e c t o r s u b t r a c t i o n a ∗∗ 2 # p o i n t i s e v e c t o r s q u a r i n g a ∗ b # p o i n t w i s e v e c t o r m u l t i p l y a / b # p o i n t w i s e v e c t o r d i v i d e l o g ( a ) # p o i n t w i s e l o g a r i t h m a r o u n d ( a r r a y ( [ [ . 6 ] , \ [ . 5 ] ] ) ) # p o i n t w i s e r o u n d i n g # ( . 5 r o u n d s t o 0 )

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Vector Operations

a = a r r a y ( [ 1 , 4 , 6 , 3 ] ) # v e c t o r sum ( a ) # sum o f v e c t o r e l e m e n t s mean ( a ) # mean o f v e c t o r e l e m e n t s v a r ( a ) # v a r i a n c e s t d ( a ) # s t a n d a r d d e v i a t i o n max ( a ) # maximum a = a r r a y ( [ [ 1 , 2 , 3 ] , \ [ 4 , 5 , 6 ] ] ) # m a t r i x

mean ( a , 0 ) # mean o f e a c h column

amax ( a , 1 ) # max o f e a c h row

amax ( a ) # t o o b t a i n max o f m a t r i x # n o t e we u s e 2

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Matrix Operations

d o t ( 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 1 x3 t i m e s column # v e c t o r 3 x1 r e s u l t s i n a # s i n g l e number , a l s o known # a s d o t / i n n e r p r o d u c t d o t ( a r r a y ( [ [ 1 ] , [ 2 ] , [ 3 ] ] ) , \ a r r a y ( [ [ 4 , 5 , 6 ] ] ) ) # column v e c t o r 3 x1 t i m e s row # v e c t o r 1 x3 r e s u l t s i n 3 x3 # m a t r i x , a l s o known # a s o u t e r p r o d u c t a = r a n d ( 3 , 2 ) # 3 x2 m a t r i x b = r a n d ( 2 , 4 ) # 2 x4 m a t r i x d o t ( a , b ) # 3 x4 m a t r i x

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Saving Your Work

import c P i c k l e a s p i c k l e # t h i s module l e t s you # s a v e 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 e p i c k l e . dump ( o b j , f ) # dump o b j e c t t o a r c h i v e f . c l o s e ( ) # c l o s e a r c h i v e f i l e d e l o b j # c l e a r o b j e c t # f r o m memory f = open ( ’ s a v e f i l e ’ , ’ r ’ ) # open a r c h i v e f i l e o b j = p i c k l e . l o a d ( f ) # r e a d o b j e c t # f r o m a r c h i v e f . 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 if they are greater than 0, and equal to 0 if they less than or equal to 0.

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 s f o r i i n r a n g e ( l e n ( v ) ) :

i f v ( i ) > 0 : u ( i ) = v ( i )

Using list comprehension:

v = [ 3 , 5 , − 2 , 5 , − 1 , 0 ]

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Importing Functions

Save the following code to “mylib.py”:

d e f myfunc ( a , b ) : r e t u r n a+b ∗∗2

Import and use myfunc. Note, we might need to configure PYTHONPATH.

from m y l i b import myfunc myfunc ( 1 , 2 )

myfunc ( b =2 , a =1) # same a s a b o v e

Python also supports class creation:

c l a s s M y C l a s s :

d e f 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 = M y C l a s s ( )

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Plotting

The library matplotlib / pylab is your friend:

from p y l a b import ∗ x s = a r a n g e ( − 2 , 2 , . 0 1 ) p l o t ( x s , s i n ( x s ) ) 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 c a n d i s p l a y t h e i m a g e ima = a r r a y ( im ) # t y p e c a s t i n g t o a r r a y # e x t r a c t s p i x e l v a l u e s i m r = Image . f r o m s t r i n g ( ’RGB ’ , \ ( ima . s h a p e [ 1 ] , ima . s h a p e [ 0 ] ) , \ ima . t o s t r i n g ( ) ) # c o n v e r t a r r a y i n t o i m a g e img = ima . mean ( 2 ) # a v e r a g e c o l o r i n t e n s i t i e s

# f o r e a c h p i x e l imshow ( img )

autumn ( ) # s e t d e f a u l t c o l o r m a p t o autumn show ( )

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How do I start?

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 be found at http://www.awaretek.com/tutorials.html

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How do I start?

Many guides and tutorials are available online: Dive Into Python

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How do I start?

Many guides and tutorials are available online: Dive Into Python

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