"""
Evaluate the mean of a random vector by simulations
===================================================
"""
# %%
# Abstract
# --------
# We introduce the :class:`ExpectationSimulationAlgorithm` class which implements an incremental Monte Carlo sampling algorithm to estimate the mean of a random vector.
import openturns as ot
import openturns.viewer as otv
from matplotlib import pylab as plt

# %%
# We shall use this algorithm for the :ref:`Ishigami function <use-case-ishigami>` that we load from the `usecases` module :
#
from openturns.usecases import ishigami_function

im = ishigami_function.IshigamiModel()


# %%
# The Ishigami `model` and the distribution of the input variables are stored in
# the `im` object :
model = im.model
distribution = im.distributionX

# %%
# We create a random vector that follows the distribution of the input variables.
inputVector = ot.RandomVector(distribution)

# %%
# The output vector is a :class:`~openturns.CompositeRandomVector`.
outputVector = ot.CompositeRandomVector(model, inputVector)

# %%
# The mean of the output vector is
print("Mean of the output random vector : %.5f" % im.expectation)


# %%
# We define the algorithm simply by calling it with the output vector :
algo = ot.ExpectationSimulationAlgorithm(outputVector)

# %%
# We can also set the algorithm parameters :
algo.setMaximumOuterSampling(80000)
algo.setBlockSize(1)
algo.setCoefficientOfVariationCriterionType("NONE")


# %%
# We are then ready to launch the algorithm and store the result.
algo.run()
result = algo.getResult()


# %%
# As usual for Monte Carlo estimation we can draw the convergence history.
graphConvergence = algo.drawExpectationConvergence()
view = otv.View(graphConvergence)


# %%
# The result obtained with the previous algorithm is an instance of the
# :class:~openturns.ExpectationSimulationResult` class.

# %%
# The expected value of the mean is given by the `getExpectationEstimate` method :
expectation = result.getExpectationEstimate()
print("Estimated mean of the output random vector : %.5f" % expectation[0])

# %%
# The variance and standard deviation of the estimated mean are respectively given by `getVarianceEstimate` and `getStandardDeviation`:
expectationVariance = result.getVarianceEstimate()
print(
    "Variance of the estimated mean of the output random vector : %.5f"
    % expectationVariance[0]
)
standardDeviation = result.getStandardDeviation()
print("Standard deviation : %.5f" % standardDeviation[0])

# %%
# This variance and this standard deviation must not to be confused with the variance and the standard deviation of the Ishigami model!
print("Ishigami variance : %.5f" % im.variance)
print("Ishigami standard deviation : %.5f" % im.variance ** (1 / 2))


# %%
# The asymptotic confidence distribution of the output random vector mean estimate is
expectationDistribution = result.getExpectationDistribution()
print(expectationDistribution)

# %%
# Let us draw it:
graphExpectationDistribution = expectationDistribution.drawPDF()
graphExpectationDistribution.setTitle(
    "Normal asymptotic distribution of the mean estimate"
)
view = otv.View(graphExpectationDistribution)

# %%
# Display all figures
plt.show()
