Python modules

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

http://docs.python.org/modindex.html

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

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

http://www.pythonxy.com/ Python(x,y) is a scientific python distribution with many modules included
http://www.enthought.com/products/epd.php

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

Numpy, Scipy, Pylab and IPython

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:

Numpy arrays have a fixed size at creation, unlike Python lists
Numpy arrays facilitate mathematical operations on large numbers of data efficiently

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

Clustering algorithms
Fast Fourier Transform routines
Integration and ordinary differential equation solvers
Interpolation and smoothing splines
Linear algebra
Maximum entropy methods
N-dimensional image processing and signal processing
Optimization and root-finding routines
Statistical distributions and functions

Furthermore it includes very handy routines for data input and output.

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

empty((d1,d2),dtype) returns uninitialized array of shape d1,d2.
zeros((d1,d2),dtype) returns array of shape d1,d2 filled with zeros
ones((d1,d2),dtype) returns array of shape d1,d2 filled with ones
array(object,dtype) returns an array from an object, e.g. a list
dtype fundamental C data type e.g. uint8, int16, int64, float32, float64

Array indexing

A[y,x] returns (y,x) element of the array
A[:,x] returns all elements of the y-dimension at x
A[y1:y2,x]
A[:,:] returns a copy of two dimensional array A
A[:,:,0] returns the first sub-image of a 3-dimensional array

Links and References

http://heim.ifi.uio.no/~hpl/scripting/all-nosplit/index.html
http://www.springer.com/math/cse/book/978-3-540-73915-9 Python Scripting for Computational Science