circulargaussian2d

probnum.problems.zoo.quad.circulargaussian2d(m=None, v=None)[source]

The two-dimensional circular Gaussian integrated wrt the Lebesgue measure. [1]

The integrand is

\[f(x) = (2\pi v)^{-\frac{1}{2}} r^2 e^{-\frac{(r - m)^2}{2 v}}\]

on the domain \(\Omega=[-3, 3]^2\). Above, \(v\) is the v parameter, \(m\) is the m parameter and \(r = \|x\|\) is the norm of the input vector \(x\).

Parameters:
  • m (float | Real | floating | None) – The non-negative mean of the circular Gaussian in units of radius. Defaults to 0.0.

  • v (float | Real | floating | None) – The positive variance of the circular Gaussian. Defaults to 1.0.

Returns:

The quadrature problem.

Return type:

quad_problem

References