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()

Answer 1

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