Hints to Exercises: Python
Problem Set 1

Computational Physics with Numerical Recipes
James P. Sethna
Physics 480/680, Spring 2008
http://www.physics.cornell.edu/~sethna/teaching/ComputationalPhysics/

1.1 Preliminaries

I recommend using the ipython shell, the scientific library scipy, and the 
plotting package pylab.

These are all installed on the computers in Rockefeller B3 and B6.
Or, you can set them up on your own machine. On PC's, Enthought bundles
all of these nicely (http://code.enthought.com/enthon/);
otherwise you can download and install from www.python.org/, 
ipython.scipy.org/, www.scipy.org, and sourceforge.net/projects/matplotlib
(matplotlib includes pylab). Many details can be found on Chris Myers' 
installation page 
	http://pages.physics.cornell.edu/~myers/teaching/
		ComputationalMethods/python/WorldPy.html
and many useful links are at the bottom of his course Web page
	http://pages.physics.cornell.edu/~myers/teaching/ComputationalMethods/

You can see if these packages are working:
	> ipython -pylab
	In [1]: import scipy
	In [2]: import pylab
Or, even better, write a file (say Preliminaries.py) with your commands, and 
use %run
	> ipython -pylab
	In [1]: run Preliminaries
	...
If you start ipython in a different directory than your files are in (for 
example, if you run Windows and launch it from the desktop icon), you'll
want to cd to the relevant directory or folder, e.g.:
	In [1]: cd C:\\Documents\ and\ Settings\\sethna\\Desktop

(a) You'll want to use scipy.arange or scipy.linspace to generate x,
and scipy.exp and scipy.sin to generate y. You should not need to use
loops: exp and sin work as array operations on vectors too. In using
pylab.plot, you will need the option "g" for a green
line, and linewidth=3. Remember to use pylab.show() to see the plot.
pylab.ylim will be useful too: try help(pylab.plot), help(pylab.ylim), etc.
Save the plot using the button on the pylab window.

(b) Reading in a file of numbers can be done using scipy.fromfile, but
you need to reshape them. NoisyYofT has 1025 pairs of points:
	numbers = scipy.fromfile("NoisyYOfT.dat", dtype=float, sep=" ")
	numbers = numbers.reshape(1025,2)
	t = numbers[:,0]
	y = numbers[:,1]
Use help(pylab.plot) to figure out how to plot black points.


1.2 Condition Number

To type in a scipy array, you need to explicitly convert it from a list, e.g.
	b = scipy.array([0.217, 0.254])
You'll want to import scipy.linalg as well as scipy.
The functions scipy.dot, scipy.linalg.svd, and scipy.linalg.solve will
be useful. (Use help(scipy.linalg.svd), etc.)

1.3 Sherman Morrison formula

In addition, scipy.linalg.inv, scipy.transpose, and scipy.outer might be
useful.

1.4 Timing Sine.

You'll want to import the package "time", and set up your x-array using
scipy.linspace before timing with time.clock().