SpaceFillingC2

class SpaceFillingC2(*args)

Space filling C2 (centered L2-discrepancy) computation.

Notes

Compute the centered L2 discrepancy:

\begin{multline*}
C^2(X_{d}^N) = \left(\frac{13}{12}\right)^{d} - \frac{2}{N} \sum_{i=1}^{N} \prod_{k=1}^{d} \left( 1 + \frac{1}{2} |x_k^{(i)} - 0.5| - \frac{1}{2} |x_k^{(i)} - 0.5|^2 \right)\\
         + \frac{1}{N^2} \sum_{i,j=1}^{N} \prod_{k=1}^{d} \left( 1 + \frac{1}{2} |x_k^{(i)} - 0.5| + \frac{1}{2} |x_k^{(j)} - 0.5| - \frac{1}{2} |x_k^{(i)} - x_k^{(j)}| \right)
\end{multline*}

Methods

evaluate(sample) Compute the C2 criterion for a specific design.
getClassName() Accessor to the object’s name.
getId() Accessor to the object’s id.
getName() Accessor to the object’s name.
getShadowedId() Accessor to the object’s shadowed id.
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
isMinimizationProblem() Minimization flag accessor.
perturbLHS(oldDesign, oldCriterion, row1, …) Elementary perturbation.
setName(name) Accessor to the object’s name.
setShadowedId(id) Accessor to the object’s shadowed id.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)
evaluate(sample)

Compute the C2 criterion for a specific design.

Parameters:

design : Sample or 2d array like

The design

Returns:

crit : float

The C2 criterion

Examples

>>> import openturns as ot
>>> # Build an LHS using openturns class
>>> lhs = ot.LHSExperiment(ot.Uniform(), 100)
>>> design = lhs.generate()
>>> # Compute the C2 criterion
>>> crit = ot.SpaceFillingC2().evaluate(design)
getClassName()

Accessor to the object’s name.

Returns:

class_name : str

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns:

visible : bool

Visibility flag.

hasName()

Test if the object is named.

Returns:

hasName : bool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:

hasVisibleName : bool

True if the name is not empty and not the default one.

isMinimizationProblem()

Minimization flag accessor.

Returns:

isMinimization : bool

Whether the problem is a minimization.

perturbLHS(oldDesign, oldCriterion, row1, row2, column)

Elementary perturbation.

Parameters:

design : Sample

The design to perturb (in-place)

oldCriterion : float

The previous value of the criterion

row1 : int

First row index

row2 : int

Second row index

Returns:

criterion : float

The value of the criterion

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

id : int

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.