LehreWiki

Python Quick Start

Why Python?

Starting the IPython shell as a Notebook

# On the ZMAW system you have to select the newest version with notebooks available
module load python/2.7-ve3

# Start the notebook server in the background
ipython notebook &

# The notebook server provides some information about where to find the dashboard

[NotebookApp] Serving notebooks from /home/zmaw/u242023/sync/python/notebooks
[NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888/

The dashboard is the central place to collect your scripts (notebooks). Different ports (here :8888) are used if there are additional notebook servers running on the same machine.

You should use firefox to interact with the notebook server. Make sure the Java script is enable when you want to use other browsers.

Starting the IPython shell

module load python/2.7-ve2

ipython --pylab

loads matplotlib module and enables interactive plotting

module load is a ZMAW specific environment setting! Version 2.7-ve2 is needed for the notebook version (see below).

Quit with CTRL-D

Getting help 

help()
help modules

list available modules

Features of IPython:

Are you a Matlab user?

The exercise is to plot a sine wave:

Matlab/Octave: 

>> x=linspace(0,2*pi,100)
>> y=sin(x)
>> plot(x,y)

Python 

In [1]: x=linspace(0,2*pi,100)
In [2]: y=sin(x)
In [3]: plot(x,y)

So, it works pretty much the same way!

Of course there are some differences but many similarities.

Unix basics

The ampersand & at the end of a line starts a process in the background. You can get the process in the foreground by typing fg. You can stop a process in the foreground by pressing Control-C.

Within the IPython shell you can use the exclamation mark ! to spawn unix commands. E.g. 

# List directory content
!ls

# Make new directory
!mkdir new_name

# Change to directory
!cd new_name

# Change to an upper level
!cd ..

# Move or rename file or directory
!mv filename_old filename_new

Python modules

There a several modules which are already included in the standard Python distribution:

Other modules for scientific computing have to be installed separately, e.g. Numpy, Scipy, Pylab, IPython.

Some distributions including precompiled modules are available, e.g.

It is important to know where to find the functions that you need. We will go through some useful examples.

Numpy

Numpy is the core library for multidimensional array objects (ndarray) and linear algebra. Most other scientific modules use the numpy array object. Numpy arrays and standard Python sequences have important differences:

The User's guide PDF provides a good introduction.

Scipy

The Scipy module is built on Numpy and offers a collection of mathematical algorithms such as

Furthermore it includes very handy routines for data input and output of binary and ASCII-tables, Matlab and Netcdf data files

Pylab

Pylab (aka Matplotlib) uses Numpy and Scipy and offers high-level functions that are similar in the name and syntax to those offered by Matlab. Matplotlib is the name of the core library and pylab provides the Matlab similarity. Pylab produces figures of great quality suitable for publications.

Making plots is easy. Start reading the User's guide. For a specific problem look at the Gallery for a similar plot you would like to have and learn from the source code.

IPython

IPython is an environment for interactive and exploratory computing. Useful features are TAB-completion, magic commands, e.g. %run, %whos, input cache and many more convenient functions that are not available in the standard Python shell.

Importing the scientific environment

The statement 

from pylab import *

imports the most important functions/objects for numerical computation and plotting. When using the interactive IPyhon shell this import is already done with 

ipython --pylab

For more complex applications it is useful but not necessary to follow the conventions that the community has adopted: 

   1 import numpy as np
   2 import scipy as sp
   3 import matplotlib as mpl
   4 import matplotlib.pyplot as plt

Arrays

Numpy provides a multidimensional array data type. An array can hold arbitrary Python objects but usually they are used for N-dimensional numeric data types.

Array creation

Arrays can also be created from special functions, e.g. random

Array indexing

Example and exercise

Write two programs, a test and a plotting program. The test program shall create a simulated dataset and the plotting routine shall read and display the data on the screen.

We start with a simple linear relation of two variables x and y. The measurement y shall be influenced by noise with a Gaussian distribution.

Generate test data

We first would like to generate x including 11 numbers in the intervall [-5,5] 

x=linspace(-5,5,11)

The variable y depends on x and includes the random noise 

y=x+randn(x.size)

We write both variables in a file 

save('data.txt',(x,y))

Now we combine this in a script. First we open an editor (xemacs, nedit, geany, vi or whatever you like) from the Unix shell 

nedit generate_test_data.py &

Create a new file, copy and paste the sourcode, and save (Ctrl-S). 

   1 from pylab import *
   2 
   3 x=linspace(-5,5,11)
   4 y=x+randn(x.size)
   5 savetxt('data.txt',(x,y))
   6 print('Finished!')

Now you can run the script from IPython 

In [7]: run generate_test_data.py
Finished!

Have a look at the variables (objects): 

In [3]: whos
Variable   Type       Data/Info
-------------------------------
x          ndarray    11: 11 elems, type `float64`, 88 bytes
y          ndarray    11: 11 elems, type `float64`, 88 bytes

In [5]: x
Out[5]: array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.,  5.])

In [6]: y
Out[6]: 
array([-5.0387728 , -4.28591892, -3.30766546, -1.65761351, -0.19178245,
       -1.52643416,  0.52628016,  0.74130426,  2.99303495,  4.91713939,
        5.13835735])

Plot test data

The following code can be used as a template 

   1 from pylab import *
   2 
   3 x,y=loadtxt('data.txt')
   4 
   5 figure() # Opens a new window for plotting
   6 plot(x,y,'ko') # Plots the data
   7 show() # Displays the result on the screen
   8 savefig('plot.pdf') # Saves the plot on disc

Exercise

Hints:

Pure Python essentials

Python basic data types

Loop

   1 for i in range(3):
   2     print i

Symbolic math

Use isympy or import sympy to obtain a computer algebra system 

isympy 
IPython console for SymPy 0.7.1 (Python 2.7.0-64-bit) (ground types: python)

These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z, t = symbols('x y z t')
>>> k, m, n = symbols('k m n', integer=True)
>>> f, g, h = symbols('f g h', cls=Function)

Documentation can be found at http://www.sympy.org

Derivatives 

In [1]: f=sin(x)

In [2]: diff(f,x)
Out[2]: cos(x)

Series expansion 

In [3]: f.series()
Out[3]: 
     3     5          
    x     x           
x - ── + ─── + O(x**6)
    6    120

Simplification 

In [4]: g=sin(x)**2+cos(x)**2

In [5]: simplify(g)
Out[5]: 1

Integration 

In [7]: F=sin(x)
In [8]: f=diff(F,x)
In [9]: f.integrate()
Out[9]: sin(x)

Calculus 

In [12]: Rational(1,3)+Rational(1,4)
Out[12]: 7/12

Documentation and tutorials

LehreWiki: PythonQuickstart (last edited 2015-04-07 20:28:27 by anonymous)