"""
FAST sensitivity indices
========================
"""

# %%
# This example will demonstrate how to quantify the correlation between the input
# variables and the output variable of a model using the FAST method,
# based upon the Fourier decomposition of the model response,
# which is a relevant alternative to the classical
# simulation approach for computing Sobol sensitivity indices.
#
# The FAST indices, like the Sobol indices, allow one to
# evaluate the importance of a single variable or a specific set of variables.
#
# In theory, FAST indices range is :math:`\left[0; 1\right]` ; the closer to 1 the
# index is, the greater the model response sensitivity to the variable is.
#
# The FAST method compute the first and total order indices.
# The first order indices evaluate the importance of one variable at a time
# (:math:`d` indices, with :math:`d` the input dimension of the model).
#
# The :math:`d` total indices give the relative importance of every variables except
# the variable :math:`X_i`, for every variable.

# %%
from openturns.usecases import ishigami_function
import openturns as ot
import openturns.viewer as otv

# %%
# We load the :ref:`Ishigami model <use-case-ishigami>` from the usecases module :
im = ishigami_function.IshigamiModel()

# %%
# The `IshigamiModel` data class contains the input independent joint distribution :
distribution = im.distribution

# %%
# and the Ishigami function :
model = im.model


# %%
size = 400
sensitivityAnalysis = ot.FAST(model, distribution, size)
# Compute the first order indices (first and total order indices are
# computed together)
firstOrderIndices = sensitivityAnalysis.getFirstOrderIndices()
# Retrieve total order indices
totalOrderIndices = sensitivityAnalysis.getTotalOrderIndices()

# %%
# Print indices
print("First order FAST indices:", firstOrderIndices)
print("Total order FAST indices:", totalOrderIndices)

# %%
graph = ot.SobolIndicesAlgorithm.DrawImportanceFactors(
    firstOrderIndices, distribution.getDescription(), "FAST first order indices"
)
view = otv.View(graph)

# %%
graph = ot.SobolIndicesAlgorithm.DrawImportanceFactors(
    totalOrderIndices, distribution.getDescription(), "FAST total order indices"
)
view = otv.View(graph)

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