Deterministic design of experiments

In this example we present the available deterministic design of experiments.

Four types of deterministic design of experiments are available:

• Axial

• Factorial

• Composite

• Box

Each type of deterministic design is discretized differently according to a number of levels.

Functionally speaking, a design is a Sample that lies within the unit cube and can be scaled and moved to cover the desired box.

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)

We will use the following function to plot bi-dimensional samples.

def drawBidimensionalSample(sample, title):
    n = sample.getSize()
    graph = ot.Graph("%s, size=%d" % (title, n), "X1", "X2", True, '')
    cloud = ot.Cloud(sample)
    graph.add(cloud)
    return graph

Axial design

levels = [1.0, 1.5, 3.0]
experiment = ot.Axial(2, levels)
sample = experiment.generate()
graph = drawBidimensionalSample(sample, "Axial")
view = viewer.View(graph)

Scale and to get desired location.

sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Axial")
view = viewer.View(graph)

Factorial design

experiment = ot.Factorial(2, levels)
sample = experiment.generate()
sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Factorial")
view = viewer.View(graph)

Composite design

experiment = ot.Composite(2, levels)
sample = experiment.generate()
sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Composite")
view = viewer.View(graph)

Grid design

levels = [3, 4]
experiment = ot.Box(levels)
sample = experiment.generate()
sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Box")
view = viewer.View(graph)
plt.show()