Utility module

Data generation

References

• MD McKay, RJ Beckman, and WJ Conover, “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, vol. 42, no. 1, p. 55-61, 2000.

class nubo.utils.latin_hypercube.LatinHypercubeSampling(dims: int)

Bases: object

Latin hypercube sampling.

Generates a space-filling design. Two options are possible: sampling from a random or a maximin Latin hypercube. To sample \(n\) points, the random Latin hypercube divides each dimension into \(n\) equal parts and places \(n\) points such that for every dimension each equal part contains exactly one point. The maximin Latin hypercube takes a simple approach and draws a large number of random Latin hypercube samples and returns the one with the largest minimal distance between points.

Attributes:

dimsint

Number of dimensions

Methods

maximin(points[, samples])	Draw a maximin Latin hypercube sample.
random(points)	Draw a random Latin hypercube sample.

maximin(points: int, samples: int | None = 1000) → Tensor

Draw a maximin Latin hypercube sample.

Draws a large number of random Latin hypercube samples and selects the one with the largest minimal distance between points.

Parameters:

pointsint

Number of points.

samplesint

Number of random Latin hypercube samples.

Returns:

torch.Tensor

(size points x dims) Maximin Latin hypercube sample.

random(points: int) → Tensor

Draw a random Latin hypercube sample.

To sample \(n\) points, the random Latin hypercube divides each dimension into \(n\) equal parts and places \(n\) points such that for every dimension each equal part contains exactly one point.

Parameters:

pointsint

Number of points.

Returns:

torch.Tensor

(size points x dims) Random Latin hypercube sample.

nubo.utils.generate_inputs.gen_inputs(num_points: int, num_dims: int, bounds: Tensor | None = None, num_lhd: int | None = 1000) → Tensor

Generate data inputs from a maximin Latin hypercube design or from a uniform distribution for one data point.

Parameters:

num_pointsint

Number of points.

num_dimsint

Number of input dimensions.

boundstorch.Tensor, optional

(size 2 x num_dims) Bounds of input space, default is none. If none, bounds are a [0, 1]^`num_dims`.

num_lhdint, optional

Number of Latin hypercube designs to consider, default is 1000.

Returns:

torch.Tensor

(size num_points x num_dims) Input data.

Data transformations

nubo.utils.transform.standardise(y: Tensor) → Tensor

Standardise data by subtracting the mean and dividing by the standard deviation:

\[\hat{\boldsymbol y} = \frac{\boldsymbol y - \mu}{\sigma},\]

where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Parameters:

ytorch.Tensor

(size n) Data.

Returns:

torch.Tensor

(size n) Standardised data.

nubo.utils.transform.normalise(x: Tensor, bounds: Tensor) → Tensor

Normalise data to the unit cube \([0, 1]^d\).

\[\hat{\boldsymbol x} = \frac{\boldsymbol x - lb}{ub - lb},\]

where \(lb\) are the lower bounds and \(ub\) are the upper bounds.

Parameters:

xtorch.Tensor

(size n x d) Data.

boundstorch.Tensor

(size 2 x d) Bounds of input space.

Returns:

torch.Tensor

Normalised data.

nubo.utils.transform.unnormalise(x: Tensor, bounds: Tensor) → Tensor

Revere normalisation to the provided bounds.

\[\boldsymbol x = \hat{\boldsymbol x} (ub - lb) + lb,\]

where \(lb\) are the lower bounds and \(ub\) are the upper bounds.

Parameters:

xtorch.Tensor

(size n x d) Normalised data.

boundstorch.Tensor

(size 2 x d) Bounds of input space.

Returns:

torch.Tensor

Data scaled to bounds.