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"""
Various design of experiments
=============================
"""
# %%
#
# The goal of this example is to present several design of experiments available in the library.
# %%
# Distribution
# ------------
# %%
import openturns as ot
import openturns.viewer as otv
# %%
# Monte-Carlo sampling in 2D
# --------------------------
# %%
dim = 2
X = [ot.Uniform()] * dim
distribution = ot.JointDistribution(X)
bounds = distribution.getRange()
# %%
sampleSize = 10
sample = distribution.getSample(sampleSize)
# %%
fig = otv.PlotDesign(sample, bounds)
# %%
# We see that there a empty zones in the input space.
# %%
# Monte-Carlo sampling in 3D
# --------------------------
# %%
dim = 3
X = [ot.Uniform()] * dim
distribution = ot.JointDistribution(X)
bounds = distribution.getRange()
# %%
sampleSize = 10
sample = distribution.getSample(sampleSize)
# %%
fig = otv.PlotDesign(sample, bounds)
fig.set_size_inches(10, 10)
# %%
# Latin Hypercube Sampling
# ------------------------
# %%
distribution = ot.JointDistribution([ot.Uniform()] * 3)
samplesize = 5
experiment = ot.LHSExperiment(distribution, samplesize, False, False)
sample = experiment.generate()
# %%
# In order to see the LHS property, we need to set the bounds.
# %%
bounds = distribution.getRange()
# %%
fig = otv.PlotDesign(sample, bounds)
fig.set_size_inches(10, 10)
# %%
# We see that each column or row exactly contains one single point.
# This shows that a LHS design of experiments has good 1D projection properties, and, hence, is a good candidate for a space filling design.
# %%
# Optimized LHS
# -------------
# %%
distribution = ot.JointDistribution([ot.Uniform()] * 3)
samplesize = 10
# %%
bounds = distribution.getRange()
# %%
lhs = ot.LHSExperiment(distribution, samplesize)
lhs.setAlwaysShuffle(True) # randomized
space_filling = ot.SpaceFillingC2()
temperatureProfile = ot.GeometricProfile(10.0, 0.95, 1000)
algo = ot.SimulatedAnnealingLHS(lhs, space_filling, temperatureProfile)
# optimal design
sample = algo.generate()
# %%
fig = otv.PlotDesign(sample, bounds)
fig.set_size_inches(10, 10)
# %%
# We see that this LHS is optimized in the sense that it fills the space more evenly than a non-optimized does in general.
# %%
# Sobol' low discrepancy sequence
# -------------------------------
# %%
dim = 2
distribution = ot.JointDistribution([ot.Uniform()] * dim)
bounds = distribution.getRange()
# %%
sequence = ot.SobolSequence(dim)
# %%
samplesize = 2**5 # Sobol' sequences are in base 2
experiment = ot.LowDiscrepancyExperiment(sequence, distribution, samplesize, False)
sample = experiment.generate()
# %%
samplesize
# %%
subdivisions = [2**2, 2**1]
fig = otv.PlotDesign(sample, bounds, subdivisions)
fig.set_size_inches(6, 6)
# %%
# We have elementary intervals in 2 dimensions, each having a volume equal to 1/8.
# Since there are 32 points, the Sobol' sequence is so that each elementary interval contains exactly 32/8 = 4 points.
# Notice that each elementary interval is closed on the left (or bottom) and open on the right (or top).
# %%
# Halton low discrepancy sequence
# -------------------------------
# %%
dim = 2
distribution = ot.JointDistribution([ot.Uniform()] * dim)
bounds = distribution.getRange()
# %%
sequence = ot.HaltonSequence(dim)
# %%
# Halton sequence uses prime numbers 2 and 3 in two dimensions.
samplesize = 2**2 * 3**2
experiment = ot.LowDiscrepancyExperiment(sequence, distribution, samplesize, False)
sample = experiment.generate()
# %%
samplesize
# %%
subdivisions = [2**2, 3]
fig = otv.PlotDesign(sample, bounds, subdivisions)
fig.set_size_inches(6, 6)
# %%
# We have elementary intervals in 2 dimensions, each having a volume equal to 1/12.
# Since there are 36 points, the Halton sequence is so that each elementary interval contains exactly 36/12 = 3 points.
# Notice that each elementary interval is closed on the left (or bottom) and open on the right (or top).
# %%
# Display all figures
otv.View.ShowAll()
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