How can I plot implicit functions in python?

Question

I have a two-variables function as

Z = m_1 m_2 / pow(m_1 + m_2, 2)

I want to plot the curves with constant values for Z in the m_1 - m_2 plane (contours). For example, Z=0.10, 0.15, 0.20, 0.25. What is the easiest way to do this job in python via matplotlib? Following is what I've tried but it doesn't quite what I want. I expect different results. I need to make sure if this is correct.

def etta(m_1, m_2):
    return m_1*m_2 / pow(m_1 + m_2, 2)

m_1 = linspace(4, 14, 100)
m_2 = linspace(4, 14, 100)

X,Y = meshgrid(m_1, m_2)

Z = etta(X, Y).T

print(sqrt(2))

fig, ax = plt.subplots()
cnt = contour(Z, cmap=cm.RdBu)

plt.show()

This seems like a pretty standard contour problem (isn't it?). Do you have any code that we could take a look at to see what isn't working? — mgilson
– mgilson, Commented Nov 22, 2013 at 20:54
Your code produces what I would have expected. You can also visualize it with `imshow(Z, origin='lower') to compare. What did you expect it to look like? — askewchan
– askewchan, Commented Nov 22, 2013 at 21:25

askewchan · Accepted Answer · 2013-11-22 21:34:37Z

2

Perhaps this is what you want:

V = [0.10, 0.15, 0.20, 0.25]
cnt = plt.contour(X, Y, Z, V, cmap=cm.RdBu)

Which will draw lines at values given by V. The problem though, is that the values you gave mostly don't show up in the domain given by X and Y. You can see this by looking at the full function with imshow:

plt.imshow(Z, extent=(X.min(), X.max(), Y.min(), Y.max()), origin='lower', cmap=cm.RdBu)

imshow

contour

Increase the values in V to see more lines:

V = np.linspace(.1, .3, 25)
plt.contour(X,Y,Z,V, cmap=cm.RdBu)

enter image description here

edited Nov 22, 2013 at 21:34

answered Nov 22, 2013 at 21:28

askewchan

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