Rotate 2D Gaussian given parameters

[schniefen]

I have a Gaussian function of the form:

def f(x,y):
  a=some number
  b=...
  c=...
  return 3*np.exp(-a*(-0.5 + x)**2+b*(x-0.5)*(y-0.5)-c*(-0.5 + y)**2)

This is a Gaussian function symmetric around y=x, and I'd like to rotate it 45 degrees (counter)clockwise. Wikipedia gives an overdetermined system of equations for the variances of x and y respectively, but it looks cumbersome. Is there a simple way to do this?

Gaussian parameters