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.

getName()

Accessor to the object's name.

hasName()

Test if the object is named.

isMinimizationProblem()

Minimization flag accessor.

perturbLHS(oldDesign, oldCriterion, row1, ...)

Elementary perturbation.

setName(name)

Accessor to the object's name.
__init__(*args)
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__).

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

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.

Examples using the class

Kriging: configure the optimization solver

Kriging: configure the optimization solver

Various design of experiments

Various design of experiments

Optimize an LHS design of experiments

Optimize an LHS design of experiments