Revision: 4038
http://matplotlib.svn.sourceforge.net/matplotlib/?rev=4038&view=rev
Author: jdh2358
Date: 2007-10-28 08:00:36 -0700 (Sun, 28 Oct 2007)
Log Message:
-----------
added lotka example
Modified Paths:
--------------
trunk/py4science/examples/qsort.py
Added Paths:
-----------
trunk/py4science/examples/lotka_volterra.py
trunk/py4science/examples/skel/lotka_volterra_skel.py
Added: trunk/py4science/examples/lotka_volterra.py
===================================================================
--- trunk/py4science/examples/lotka_volterra.py (rev 0)
+++ trunk/py4science/examples/lotka_volterra.py 2007-10-28 15:00:36 UTC (rev
4038)
@@ -0,0 +1,78 @@
+import numpy as n
+import pylab as p
+import scipy.integrate as integrate
+
+def dr(r, f):
+ return alpha*r - beta*r*f
+
+def df(r, f):
+ return gamma*r*f - delta*f
+
+def derivs(state, t):
+ """
+ Map the state variable [rabbits, foxes] to the derivitives
+ [deltar, deltaf] at time t
+ """
+ #print t, state
+ r, f = state # rabbits and foxes
+ deltar = dr(r, f) # change in rabbits
+ deltaf = df(r, f) # change in foxes
+ return deltar, deltaf
+
+alpha, delta = 1, .25
+beta, gamma = .2, .05
+
+# the initial population of rabbits and foxes
+r0 = 20
+f0 = 10
+
+t = n.arange(0.0, 100, 0.1)
+
+y0 = [r0, f0] # the initial [rabbits, foxes] state vector
+y = integrate.odeint(derivs, y0, t)
+r = y[:,0] # extract the rabbits vector
+f = y[:,1] # extract the foxes vector
+
+p.figure()
+p.plot(t, r, label='rabbits')
+p.plot(t, f, label='foxes')
+p.xlabel('time (years)')
+p.ylabel('population')
+p.title('population trajectories')
+p.grid()
+p.legend()
+p.savefig('lotka_volterra.png', dpi=150)
+p.savefig('lotka_volterra.eps')
+
+
+p.figure()
+p.plot(r, f)
+p.xlabel('rabbits')
+p.ylabel('foxes')
+p.title('phase plane')
+
+
+# make a direction field plot with quiver
+rmax = 1.1 * r.max()
+fmax = 1.1 * f.max()
+R, F = n.meshgrid(n.arange(-1, rmax), n.arange(-1, fmax))
+dR = dr(R, F)
+dF = df(R, F)
+p.quiver(R, F, dR, dF)
+
+
+R, F = n.meshgrid(n.arange(-1, rmax, .1), n.arange(-1, fmax, .1))
+dR = dr(R, F)
+dF = df(R, F)
+
+p.contour(R, F, dR, levels=[0], linewidths=3, colors='black')
+p.contour(R, F, dF, levels=[0], linewidths=3, colors='black')
+p.ylabel('foxes')
+p.title('trajectory, direction field and null clines')
+
+p.savefig('lotka_volterra_pplane.png', dpi=150)
+p.savefig('lotka_volterra_pplane.eps')
+
+
+p.show()
+
Modified: trunk/py4science/examples/qsort.py
===================================================================
--- trunk/py4science/examples/qsort.py 2007-10-27 12:36:39 UTC (rev 4037)
+++ trunk/py4science/examples/qsort.py 2007-10-28 15:00:36 UTC (rev 4038)
@@ -33,5 +33,7 @@
rseq = range(10)
random.shuffle(rseq)
sseq = qsort(rseq)
+ print tseq
+ print sseq
self.assertEqual(tseq,sseq)
main()
Added: trunk/py4science/examples/skel/lotka_volterra_skel.py
===================================================================
--- trunk/py4science/examples/skel/lotka_volterra_skel.py
(rev 0)
+++ trunk/py4science/examples/skel/lotka_volterra_skel.py 2007-10-28
15:00:36 UTC (rev 4038)
@@ -0,0 +1,56 @@
+import numpy as n
+import pylab as p
+import scipy.integrate as integrate
+
+def dr(r, f):
+ 'return delta r'
+ XXX
+
+def df(r, f):
+ 'return delta f'
+ XXX
+def derivs(state, t):
+ """
+ Map the state variable [rabbits, foxes] to the derivitives
+ [deltar, deltaf] at time t
+ """
+ XXX
+
+alpha, delta = 1, .25
+beta, gamma = .2, .05
+
+# the initial population of rabbits and foxes
+r0 = 20
+f0 = 10
+
+t = XXX # pick a time vector (think about the time scales!)
+y0 = [r0, f0] # the initial [rabbits, foxes] state vector
+y = XXX # integrate derives over t starting at y0
+r = XXX # extract the rabbits vector
+f = XXX # extract the foxes vector
+
+
+# FIGURE 1: rabbits vs time and foxes vs time on the same plot with
+# legend and xlabel, ylabel and title
+
+# FIGURE 2: the phase plane
+
+# plot r vs f and label the x and y axes
+XXX
+
+# FIGURE 2 continued....
+
+# use meshgrid to make a grid over R and F
+# with a coarse 1 year sampling. evaluate dR and dF over the 2 s
+# grids and make a quiver plot. See pylab.quiver and matplotlib
+# examples/quiver_demo.py
+XXX
+
+# FIGURE 2 continued... use contour to compute the null clines over
+# dR (the rabbits null cline) and dF (the foxes null cline). You will
+# need to do a finer meshgrid for accurate null clins and pass
+# levels=[0] to contour
+XXX
+
+p.show()
+
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