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*}

Attributes:
thisown

The membership flag

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.

thisown

The membership flag