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 gained
widespread popularity in recent years.
It is:

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What is Python?

It is:
cross platform

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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?

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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?

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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Python’s Scientiﬁc Libraries

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

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standard science and engineering functions or plotting (MATLAB)
SciPy, Matplotlib

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standard science and engineering functions or plotting (MATLAB)
SciPy, Matplotlib
a computer algebra system (Mathematica)
SAGE

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data processing
Modular toolkit for Data Processing (MDP)

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data processing
bioinformatics functions
Biopython

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data processing
Biopython
machine learning functions
PyML, mlpy, SHOGUN

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data processing
Biopython
PyML, mlpy, SHOGUN
neural nets
Fast Artiﬁcial Neural Network (FANN) Library

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data processing
Biopython
PyML, mlpy, SHOGUN
neural nets
Fast Artiﬁcial Neural Network (FANN) Library
artiﬁcial intelligence or robotics routines
Python Robotics (Pyro)

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Is it hard to learn?

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Python vs MATLAB

Advantages of MATLAB:

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Python vs MATLAB

already widely used

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Python vs MATLAB

already widely used
designed speciﬁcally for scientiﬁc computing

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Python vs MATLAB

already widely used
easy to ﬁnd documentation

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Python vs MATLAB

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

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Python vs MATLAB

already widely used
Advantages of Python:

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Python vs MATLAB

already widely used
open source means no limits on use

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Python vs MATLAB

already widely used
appears to approximately superset MATLAB’s functionality

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Python vs MATLAB

already widely used
modern language with support for object orientation

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Python vs MATLAB

already widely used
modern language with support for object orientation
support for calling functions in other languages

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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 :
print x
Python is dynamically typed:
a = ”hello” # a is a string
a = 4 # a i s now an i n t e g e r

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Vectors
Many of these functions come from SciPy.
from s c i p y import ∗
Vectors:
N = 5 # a scalar
v = [1 ,2 ,3] # a list
v = array ([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 = array ([[1 ,2 ,3]]) # a column v e c t o r
v = transpose (v) # transpose a vector
# ( row t o column
# o r column t o row )
v = a r a n g e ( −4 ,4) # a vector in
# a s p e c i f i e d range :
v = p i ∗ a r a n g e ( −4 ,4)/4
v = arange ( −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 = array ([5 ,6 ,7]) # access a vector element
v [2] # vector ( index ) − arrays are
# z e r o −i n d e x e d
len (v) # number o f e l e m e n t s i n a v e c t o r
m = array ([[1 ,2 ,3] ,
[4 ,5 ,6]]) # a 2 x3 m a t r i x
m[ 1 , 2 ] == m [ 1 ] [ 2 ] # access a matrix element
# m a t r i x [ row , column ]

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Syntax and Special Functions

Matrices:
m = zeros ([2 ,3]) # a matrix of zeros
v = ones ( [ 1 , 3 ] ) # a matrix of ones
v = rand (3 ,1) # rand matrix ( see a l s o randn )
m = eye (3) # i d e n t i t y m a t r i x ( 3 x3 )

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Syntax and Special Functions (cont)

m[ 1 , : ] # a c c e s s a m a t r i x row ( s e c o n d row )
m[ : , 0 ] # a c c e s s a m a t r i x column ( l e f t column )
m[ 1 : , 1 : ] # lower r i g h t submatrix
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 rows )
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 rows
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 of 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
m[ 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 by
element”.
a = array ([1 ,2 ,3 ,4]) # vector
2 ∗ a # scalar multiplication
a / 4 # scalar division
b = array ([5 ,6 ,7 ,8]) # vector
a + b # pointwise vector addition
a − b # pointwise vector subtraction
a ∗∗ 2 # pointise vector squaring
a ∗ b # pointwise vector multiply
a / b # pointwise vector divide
log (a) # pointwise logarithm
around ( a r r a y ( [ [ . 6 ] ,
[.5]])) # pointwise rounding
# ( . 5 rounds to 0)

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Vector Operations

a = array ([1 ,4 ,6 ,3]) # vector
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
var (a) # variance
std (a) # standard deviation
max ( a ) # maximum

a = array ([[1 ,2 ,3] ,
[4 ,5 ,6]]) # matrix
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
# 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 ] ) ) ,
array ([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
# as dot / i n n e r product
dot ( 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
# as outer product
a = rand (3 ,2) # 3 x2 m a t r i x
b = rand (2 ,4) # 2 x4 m a t r i x
dot ( 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 . close () # close archive f i l e

del obj # clear object
# from memory

f = open ( ’ s a v e f i l e ’ , ’ r ’ ) # open archive f i l e
obj = p i c k l e . load ( f ) # read object
# from archive
f . close () # close archive 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] ∗ len (v) # u is a l l zeros
for i in range ( len ( 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 ) :
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 bo v e
Python also supports class creation:
c l a s s MyClass :
def init ( self ):
print ” hello ! ”
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 = arange ( −2 ,2 ,.01)
p l o t ( xs , 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 can d i s p l a y t h e image
ima = a r r a y ( im ) # t y p e c a s t i n g to a r r a y
# extracts pixel values
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 image
img = mean ( ima , 2 ) # average color i n t e n s i t i e s
# f o r each 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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More Help?

Many guides and tutorials are available online:

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More Help?

Dive Into Python
python introduction for programmers

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More Help?

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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Questions?

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