Plotting ODEs, Isoclines using Python

Question

I am looking for a Python package that will allow me to plot something similar to the Java applet seen below:

http://math.mit.edu/mathlets/mathlets/isoclines/

Does anyone know any ODE plotting packages for this? I can code something from scratch using Numpy, Matplotlib, but I wanted to ask around first.

Thanks,

Will matplotlib's quiver do something like this? matplotlib.sourceforge.net/api/… and matplotlib.sourceforge.net/examples/pylab_examples/… — Thomas K
– Thomas K, Commented Jun 16, 2011 at 11:55
yes quiver apparently can help here, i saw some examples for it too. — BBSysDyn
– BBSysDyn, Commented Jun 16, 2011 at 12:35

BBSysDyn · Accepted Answer · 2011-06-16 13:09:26Z

3

I wrote something like this, it seems to work for y'=y^2-x

from pylab import *
xmax = 4.0
xmin = -xmax
D = 20
ymax = 4.0
ymin = -ymax
x = linspace(xmin, xmax, D)
y = linspace(ymin, ymax, D)
X, Y = meshgrid(x, y)
deg = arctan(Y**2 - X)
QP = quiver(X,Y,cos(deg),sin(deg))
show()

enter image description here

answered Jun 16, 2011 at 13:09

BBSysDyn

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Comments

DSM · Accepted Answer · 2011-06-16 12:14:07Z

1

Sage will do this:

x,y = var("x y")
eq = y^3-3*y-x
p = implicit_plot(eq==0,(x,-4,4),(y,-4,4))
p += plot_slope_field(eq, (x,-4,4),(y,-4,4), headlength=1e-8)
p.show(aspect_ratio=1)

although it's simply wrapping matplotlib functionality for the graphics. (To be perfectly honest, the matplotlib wrapping isn't as good as it could be yet, which often causes me headaches.)

example

answered Jun 16, 2011 at 12:14

DSM

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4 Comments

BBSysDyn Over a year ago

i looked at sage, the source code is huge, does it support python out of the box? is the code above python code?

DSM Over a year ago

Yeah, it's pretty big: it's a collection of math tools and libraries wrapped in Python. But if everything you're doing is numerical, and you don't need symbolics, then it's probably easiest just to use matplotlib directly (as, after all, that's what Sage is doing behind the scenes.)

Thomas K Over a year ago

You can use sage on the web, without installing it, if you prefer: sagenb.org

BBSysDyn Over a year ago

thx for the info, but I got into this so I would have local code instead of "mathlets" that are applets.

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