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==========================================
 Practical Scientific Computing in Python
==========================================

Prerequisites and audience
==========================

This is a workshop targetted at the level of a upper graduate student in
engineering or an upper undergraduate in applied mathematics or physics.  A
working knowledge of basic programming is assumed, as well as familiarity with
calculus, basic linear algebra, FFTs, and other similar topics.

The course will stay reasonably basic in the python techniques used, but the
core language itself will not be taught.  Students are expected to at the very
least work thoroughly through the official Python tutorial, as well as read
Perry Greenfield's data analysis tutorial.


Proposed agenda
===============

Day 1
-----

830-845 Introduction
Set up computers, introduce instructors, hand out course materials

845-930 Python for scientific computing
A high-level overview of the topic of Python in a scientific context.

930-1030  Workflow.

Editor: (X)Emacs, Vi(m), SPE.

ipython.  Saving and reloading files.

Getting help:
  - pydoc (-g)

  - The standard docs (bookmark them)

  - ipython ?/??, help(), the tab key.

  - The open source process: mailing lists, wikis.  Python
  cookbook. Participate!


Basic setup:
  - ipython
  - matplotlib (latex, etc).
  - Modules: import/reload, PYTHONPATH.

1030:1100 -- Break


* Define a simple function: Wallis' product for pi.  Illustrates arbitrary
size integers.

* Qsort: lists, recursion.

* Define a trapezoid rule integrator: function objects, arrays.

--- Lunch

* Univariate polynomials, root finding: poly1d objects, convolutions,
plotting. 

* Data fitting/smoothing: least squares, cubic splines, polynomial fitting.

* Numerical integration and root finding: Find t such that

 \int_0^t{ f(s) ds} = u

for a known, monotonically increasing f(s) and a fixed u.

* Prime numbers: the Sieve of Erathostenes.  Illustrates lists and sets.

* Word frequencies: use of dictionaries and text processing.


Day 2
-----

* FFTs: 2-d image denoising via FFT.

* Visual (VPython): Show some examples, explain.  Target shooting exercise.

* Eigenfaces problem, part 1.

* Eigenfaces problem, part 2.

* Speed: weave.blitz, weave.inline.


Day 3
-----

* Interactive work with IPython

Efficient use of IPython to speed up development and everyday scientific
work. Profiling, debugging and embedding of IPython into third-party codes.

* Modules, Packages, $PYTHONPATH.

* Unit testing.

* Object Oriented Programming.

* Advanced Matplotlib.

* 3d visualization.

We'll cover the use of MayaVi, which encapsulates much of the complexity of
VTK. Some examples of low-level VTK use will be shown.

  - imv.surf example, interact with it, modify and save to disk.  Wireframe
  and contour, change colormaps.

* Code wrapping - f2py, pyrex, swig, boost.

weave.inline
weave.blitz

f2py simple wrapping example, then they have to repeat the process for a
pre-written .f file given to them but unwrapped.  Then, they must write a
small .py script which actually calls the fortran .so.

* Package distribution: distutils.

* PIL.

Unused examples and exercises
-----------------------------

* Bessel functions: special functions library, array manipulations to check
recursion relation.

* Montecarlo integration to compute pi.

* One-dimensional FFT - Bode plot.

* Spectral interpolation.

* Steinman interpolation.

* More weave.inline examples.