sombrero2d

probnum.problems.zoo.quad.sombrero2d(w=None)

The two-dimensional sombrero function integrated wrt the Lebesgue measure. [1]

The integrand is

\[f(x) = \frac{\operatorname{sin}(\pi r w)}{\pi r w}\]

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

Parameters:

w (float | Real | floating | None) – The positive frequency parameter. Defaults to 1.0.

Returns:

The quadrature problem.

Return type:

quad_problem

References

[1]

Emukit docs on sombrero2d .