emukit.test_functions.quadrature package

Submodules

emukit.test_functions.quadrature.baselines.univariate_approximate_ground_truth_integral(func, integral_bounds)

Estimate the 1D ground truth integral.

Parameters:

Returns:

The integral estimate (output of scipy.integrate.quad).

emukit.test_functions.quadrature.baselines.bivariate_approximate_ground_truth_integral(func, integral_bounds)

Estimate the 2D ground truth integral.

Parameters:

func – A bivariate function.
integral_bounds (List[Tuple[float, float]]) – Bounds of the integral.

Returns:

The integral estimate (output of scipy.integrate.dblquad).

emukit.test_functions.quadrature.circular_gaussian.circular_gaussian(mean=0.0, variance=1.0)

2D toy integrand that is a Gaussian on a circle.

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

where \(\sigma^2\) is the variance attribute, \(\mu\) is the mean attribute and \(r = \|x\|\) is the length of the input \(x\).

Parameters:

mean (float) – The mean of the circular Gaussian in units of radius (must be >= 0, defaults to 0).
variance (float) – The variance of the Gaussian (must be > 0, defaults to 1.).

Return type:

Returns:

The wrapped test function, and the integrals bounds (the latter defaults to [-3, 3]^2).

emukit.test_functions.quadrature.hennig1D.hennig1D()

1D toy integrand coined by Philipp Hennig.

One of the earlier mentions e.g., in this talk (external link).

\[f(x) = e^{-x^2 -\sin^2(3x)}\]

Return type:: Tuple[UserFunctionWrapper, List[Tuple[float, float]]]
Returns:: The wrapped test function, and the integrals bounds (the latter default to [-3, 3]).

emukit.test_functions.quadrature.sombrero2D.sombrero2D(freq=1.0)

2D Sombrero function.

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

where \(\omega\) is the freq parameter and \(r=\|x\|\) is the length of the input vector \(x\).

Parameters:: freq (float) – The frequency of the sombrero (must be > 0, defaults to 1).
Return type:: Tuple[UserFunctionWrapper, List[Tuple[float, float]]]
Returns:: The wrapped test function, and the integrals bounds (the latter defaults to [-3, 3]^2).