I want to calculate and plot a gradient of any scalar function of two variables. If you really want a concrete example, lets say f=x^2+y^2 where x goes from -10 to 10 and same for y. How do I calculate and plot grad(f)? The solution should be vector and I should see vector lines. I am new to python so please use simple words.
EDIT:
@Andras Deak: thank you for your post, i tried what you suggested and instead of your test function (fun=3*x^2-5*y^2) I used function that i defined as V(x,y); this is how the code looks like but it reports an error
import numpy as np
import math
import sympy
import matplotlib.pyplot as plt
def V(x,y):
t=[]
for k in range (1,3):
for l in range (1,3):
t.append(0.000001*np.sin(2*math.pi*k*0.5)/((4*(math.pi)**2)* (k**2+l**2)))
term = t* np.sin(2 * math.pi * k * x/0.004) * np.cos(2 * math.pi * l * y/0.004)
return term
return term.sum()
x,y=sympy.symbols('x y')
fun=V(x,y)
gradfun=[sympy.diff(fun,var) for var in (x,y)]
numgradfun=sympy.lambdify([x,y],gradfun)
X,Y=np.meshgrid(np.arange(-10,11),np.arange(-10,11))
graddat=numgradfun(X,Y)
plt.figure()
plt.quiver(X,Y,graddat[0],graddat[1])
plt.show()
AttributeError: 'Mul' object has no attribute 'sin'
And lets say I remove sin, I get another error:
TypeError: can't multiply sequence by non-int of type 'Mul'
I read tutorial for sympy and it says "The real power of a symbolic computation system such as SymPy is the ability to do all sorts of computations symbolically". I get this, I just dont get why I cannot multiply x and y symbols with float numbers.
What is the way around this? :( Help please!
UPDATE
@Andras Deak: I wanted to make things shorter so I removed many constants from the original formulas for V(x,y) and Cn*Dm. As you pointed out, that caused the sin function to always return 0 (i just noticed). Apologies for that. I will update the post later today when i read your comment in details. Big thanks!
UPDATE 2 I changed coefficients in my expression for voltage and this is the result:
It looks good except that the arrows point in the opposite direction (they are supposed to go out of the reddish dot and into the blue one). Do you know how I could change that? And if possible, could you please tell me the way to increase the size of the arrows? I tried what was suggested in another topic (Computing and drawing vector fields):
skip = (slice(None, None, 3), slice(None, None, 3))
This plots only every third arrow and matplotlib does the autoscale but it doesnt work for me (nothing happens when i add this, for any number that i enter) You were already of huge help , i cannot thank you enough!