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)

Initialize self. See help(type(self)) for accurate signature.

evaluate(sample)

Compute the C2 criterion for a specific design.

Parameters
designSample or 2d array like

The design

Returns
critfloat

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_namestr

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

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

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

isMinimizationProblem()

Minimization flag accessor.

Returns
isMinimizationbool

Whether the problem is a minimization.

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

Elementary perturbation.

Parameters
designSample

The design to perturb (in-place)

oldCriterionfloat

The previous value of the criterion

row1int

First row index

row2int

Second row index

Returns
criterionfloat

The value of the criterion

setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.