I'm trying to find how many local minimas the function have in the defined region but I don't quite understand how you can tell which one is a local minima from a 2D plot. From videos I have seen, it's fairly trivial to see them in 3D but how do you determine them in a 2D plot with a defined region? Would appreciate any insight into this since im quite confused.
I have the isocontour plotted of the function $ \phi(x) := |F(x)|$
$F_1(x,y)=x^2+2y^2+sin(2x)=0$ using python.
def F1(x, y):
return x**2 + 2 * y**2 + np.sin(2 * x)
x = np.linspace(-2, 2, 50)
y = np.linspace(-2, 2, 50)
X, Y = np.meshgrid(x, y)
magnitude_F1 = np.sqrt(F1(X, Y)**2)
fig, ax = plt.subplots()
CS = ax.contour(X, Y, magnitude_F1, np.array([1,5,10,50,100]))
ax.clabel(CS, inline=True, fontsize=10)