UNIVERSITY OF CAPE TOWN

UCT Physics PHY321F - Computational Physics

Useful Python code fragments

Importing

from math import *

Frequently, the array and other facilities provided by the Numeric extension are useful

from Numeric import *

includes the normal math functions as well.

Animation of the results can also be useful; the visual extensions can be used for this.

from visual import *

also imports Numeric.

Finally, visual can also be used for plotting graphs.

from visual.graph import *

imports visual, etc. as well.

Writing to a file

outfile=open("myfile","w") # open file in write mode ... print >> outfile, x, y, x # print to outfile x,y and z ... outfile.close() # close the file

Plotting a graph

from visual.graph import * # Fft on Windows ? ... points is an array of Python tuples of x,y values ... data=array([(x1,y1),(x2,y2), ... ]) myplot=gcurve( pos=data, color=color.blue ) # colour is optional ...

It may be simpler to plot the curve point by point in some loop:

from visual.graph import * # Fft on Windows ? myplot=gcurve( color=color.blue ) # colour is optional ... for .... ... calculate x and y myplot.plot( pos=(x,y) )

Power spectrum via FFT

from FFT import * # Fft on Windows ? ... data is Numeric array ... transform=fft(data) # transform is complex powerspectrum=abs(transform*conjugate(transform))/len(data)**2

It may be useful to `window' the data (see Numerical Recipes):

from FFT import fft # from Fft on Windows ? from MLab import hanning ... data is Numeric array ... transform=fft(data*hanning(len(data))) # transform is complex powerspectrum=abs(transform*conjugate(transform))/len(data)**2

Note that if the time step is dt and the total time slice of the data is T=N dt, the step size in angular frequency is d omega = 2pi/T and the range of frequencies in the transform is from -(N/2)domega .. (N/2)domega.