I need to draw a graph in python using this function: b²x²+a²z²+2dxz²+d²z²-a²b²=0 where b, a and d will be different each time. The problem here for me is that I cannot separate X and Z. I've tried something like that.
import numpy as np
import matplotlib.pyplot as plt
z = -np.linspace(9,15,100)
x = np.linspace(-26,26,1000)
x,z = np.meshgrid(x,z)
a = 4
b = 2
d = 1
Z = a**2*z**2+2*d*z**2-a**2*b**2
X = b**2*x**2
plt.contour(x,z,(X+Z),[0])
plt.xlim([-1.5,1.5])
plt.ylim([-11.5,-8.5])
I don't know if matplotlib can create an implicit plot; a quick search of their documentation didn't turn up anything. But it appears you can use Sympy for that. From this SO question:
from sympy import var, Plot
var('x y')
Plot(x*y**3 - y*x**3)
Working code here:
from functools import partial
import numpy
import scipy.optimize
import matplotlib.pyplot as pp
a = 4
b = 3
d = 0.6
def z(x, y):
return b**2*x**2+a**2*y**2+2*d*x*y**2+d**2*y**2-a**2*b**2
x_window = 0, 5
y_window = 0, 5
xs = []
ys = []
for x in numpy.linspace(*x_window, num=200):
try:
# A more efficient technique would use the last-found-y-value as a
# starting point
y = scipy.optimize.brentq(partial(z, x), *y_window)
except ValueError:
# Should we not be able to find a solution in this window.
pass
else:
xs.append(x)
ys.append(y)
pp.plot(xs, ys)
pp.xlim(*x_window)
pp.ylim(*y_window)
pp.show()
np.all(X+Z > 0), so there is nothing.