How define a boundary in matplotlib python?

Question

I want to plot the following field equations:

dx/dt = x*(4*y+3*x-3)
dy/dt = y*(4*y+3*x-4)

but I do not know how can I restrict the boundary to a triangle: x>=0, y>=0, x<=1-y:

# stream plot with matplotlib
import numpy as np
import matplotlib.pyplot as plt
def velocity_i(x,y):
    vx = x*(3*x+4*y-3)
    vy = y*(3*x+4*y-4)
    return vx, vy
n=100
x = np.linspace(0, 1, n)
y = np.linspace(0, 1, n)
X, Y = np.meshgrid(x, y)
Ux, Uy = velocity_i(X, Y)
vels = (Ux**2+Uy**2)**0.5
plt.figure(figsize=(5,4))
stream = plt.streamplot(X, Y,
              Ux,Uy,
              arrowsize=1,
              arrowstyle='->',
              color= vels,
              density=1,
              linewidth=1,
                       )
plt.xlabel(r"$\Omega_{\rm m}$",fontsize='14')
plt.ylabel(r"$\Omega_{\rm r}$",fontsize='14')
plt.colorbar(stream.lines)

plt.xlim((-.05,1.05))
plt.ylim((-.05,1.05))
plt.show()

@MadPhysicist: I have reminded the OP couple of times as he seemed a new user. But he asked me a new question on 3d which is a completely different task. So I quit asking :) — Sheldore
– Sheldore, Commented Jan 2, 2019 at 13:34

Sheldore · Accepted Answer · 2018-12-31 16:00:20Z

4

This is quite straightforwardly achievable using NumPy masking and np.where function. I am only showing the relevant two lines of code (highlighted by a comment) needed to get the job done.

Explanation: X<=1-Y checks your required boundary condition and then at all those indices where this condition holds True, it assigns the actual computed value of Ux (or Uy) and at indices where the condition is False, it assigns 0. Here X<=1-Y acts as kind of a conditional mask.

Ux, Uy = velocity_i(X, Y)
Ux = np.where(X<=1-Y, Ux, 0) # <--- Boundary condition for Ux
Uy = np.where(X<=1-Y, Uy, 0) # <--- Boundary condition for Uy
vels = (Ux**2+Uy**2)**0.5

edited Dec 31, 2018 at 16:00

answered Dec 31, 2018 at 15:55

Sheldore

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5 Comments

user9812604 Over a year ago

Then, how can we plot 3d: dx/dt = x*(4*y+3*x+2*z-3) , dy/dt = y*(4*y+3*x+2*z-4) , dz/dt = z*(4*y+3*x+2*z-2) , for between x,y,z>=0 and x+y+z=1 ?

Sheldore Over a year ago

That's a new problem. You wanted to get the plot similar to what you posted in the question. I helped you with that. Post a new question for a 3d. Show in your new question, what is the expected 3d output. On Stack overflow you ask one question at a time. Plotting 3d would require some thoughts and efforts. People will help you if you first show them your attempt. No one will write a code from scratch for you.

user9812604 Over a year ago

Plz see stackoverflow.com/questions/53995222/…

Mad Physicist Over a year ago

Would it be useful to select X and Y before you compute Ux and Uy to begin with?

Sheldore Over a year ago

@MadPhysicist: I tried that using Ux, Uy = velocity_i(X[X<=1-Y], Y[X<=1-Y]) but then X and Y are meshgrid and so for me the straightforward solution was to simply assign 0 values later. Choosing X, Y = np.meshgrid(x[x<1-y], y[x<1-y]) would be wrong

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