"""
Create mixed deterministic and probabilistic designs of experiments
===================================================================
"""

# %%
#
# In this example we build a mixed deterministic and probabilistic design of
# experiments in which levels are defined from the probabilistic distribution
# of the input random vector. More precisely, we show how to create an `Axial`
# design of experiments whose points are updated so that they match the mean
# and variance of the distribution.
#
# The example here is an axial design of experiments where levels are
# proportional to the standard deviation of each component of the random input
# vector, and centered on the mean vector of the random input vector.

# %%
import openturns as ot
import math as m
import openturns.viewer as otv

# %%
# Define the underlying random vector.
dim = 2
R = ot.CorrelationMatrix(dim)
distribution = ot.Normal([2.0, 3.0], [0.5, 2.0], R)
rv = ot.RandomVector(distribution)

# %%
# Define the structure of the design of experiments.
levels = [1.0, 2.0, 3.0]
experiment = ot.Axial(dim, levels)
sample = experiment.generate()

# %%
# Scale the design proportionnally to the standard deviation of each component.

# %%
covariance = rv.getCovariance()
scaling = [m.sqrt(covariance[i, i]) for i in range(dim)]
print("scaling=", scaling)
sample *= scaling

# %%
# Center the design around the mean point of the distribution.

# %%
center = rv.getMean()
print("center=", center)
sample += center

# %%
# Draw the design as well as the distribution iso-values.

# %%
graph = distribution.drawPDF()
doe = ot.Cloud(sample)
doe.setColor("red")
doe.setLegend("design")
graph.add(doe)
view = otv.View(graph)

# %%
# Display all figures
otv.View.ShowAll()