Lotka-Volterra Predator-Prey Model in Three Part Harmony

#!/usr/bin/env python

import os

def system( u, v, w, uinit, vinit, winit, time ):
ut = list(); ut.append( uinit )
vt = list(); vt.append( vinit )
wt = list(); wt.append( winit )
for i in range( time ):
ut.append( u.update( ut[-1], vt[-1], wt[-1] ) )
vt.append( v.update( vt[-1], ut[-1], wt[-1] ) )
wt.append( w.update( wt[-1], ut[-1], vt[-1] ) )
return ( ut, vt, wt )

class Component:
def __init__( self, a, b, g, h ):
self.alpha = a
self.beta = b
self.gamma = g
self.step = h
def update( self, x, y, z ):
self.body = self.alpha*x + self.beta*x*y + self.gamma*x*z
return x + self.step*self.body

step = 0.08
u = Component( -1.0, 0.025, 0.035, step )
v = Component( 1.5, -0.45, -0.024, step )
w = Component( 1.45, -0.75, 0.026, step )
( ut, vt, wt ) = system( u, v, w, 5.0, 50.0, 20.0, 4000 )

ubuff = open( "ut.txt", "w" )
vbuff = open( "vt.txt", "w" )
wbuff = open( "wt.txt", "w" )

for i in range( len( ut ) ):
ubuff.write( str( ut[i] ) )
ubuff.write('\n')
vbuff.write( str( vt[i] ) )
vbuff.write('\n')
wbuff.write( str( wt[i] ) )
wbuff.write('\n')

ubuff.close(); vbuff.close(); wbuff.close()

foo = list()
foo.append('#!/usr/bin/env octave\n')
foo.append('\n')
foo.append('load ut.txt ; load vt.txt ; load wt.txt ;\n')
foo.append('t = 0:4000 ; plot( t, ut, t, vt, t, wt ) ;\n')
foo.append('print -djpeg foo.jpeg;\n')

f = open( "foo.o", "w" )
f.writelines( foo )
f.close()

os.system( 'octave -qf foo.o' )
os.system( 'evince foo.jpeg &' )

os.system( 'rm ut.txt' )
os.system( 'rm vt.txt' )
os.system( 'rm wt.txt' )
os.system( 'rm foo.o' )

Variance

Different programs implement variance in different ways. This can lead to confusing results when you move from one set of functions to another.

scipy.stats.cov() normalizes by (N-1), by default, bias=False. By setting bias=True, you will normalize by N.

However, scipy.var() normalizes by N.

In Octave, var( x, 0 ) biases by N-1, and var( x, 1 ) biases by N.

Matlab and R, I think, do things slightly differently.

GNU Octave

GNU Octave Manual, version 3, is found here.