#! /usr/bin/env python

import openturns as ot
from openturns.testing import assert_almost_equal
from openturns.usecases import ishigami_function
from math import pi


ot.TESTPREAMBLE()
ot.PlatformInfo.SetNumericalPrecision(5)

"""
Test the import of the IshigamiModel data class.
"""
im = ishigami_function.IshigamiModel()
a = 7.0
b = 0.1

# parameters
assert_almost_equal(im.dim, 3, 1e-12)
assert_almost_equal(im.a, a, 1e-12)
assert_almost_equal(im.b, b, 1e-12)

# marginals means
assert_almost_equal(im.X1.getMean()[0], 0.0, 1e-12)
assert_almost_equal(im.X2.getMean()[0], 0.0, 1e-12)
assert_almost_equal(im.X3.getMean()[0], 0.0, 1e-12)

# special value
X = ot.Point([pi / 2, pi / 2, 1.0])
assert_almost_equal(im.model(X), [1.0 + a + b], 1e-12)

# First moments
expectation = a / 2.0
assert_almost_equal(im.expectation, expectation, 1e-12)

variance = 1.0 / 2 + a**2 / 8.0 + b * pi**4 / 5.0 + b**2 * pi**8 / 18.0
assert_almost_equal(im.variance, variance, 1e-12)


# Sobol indices
S1 = (1.0 / 2.0 + b * pi**4 / 5.0 + b**2 * pi**8 / 50.0) / variance
assert_almost_equal(im.S1, S1, 1e-12)

S2 = (a**2 / 8.0) / variance
assert_almost_equal(im.S2, S2, 1e-12)

assert_almost_equal(im.S3, 0.0, 1e-12)
assert_almost_equal(im.S12, 0.0, 1e-12)

S13 = b**2 * pi**8 / 2.0 * (1.0 / 9.0 - 1.0 / 25.0) / variance
assert_almost_equal(im.S13, S13, 1e-12)

S23 = 0.0
assert_almost_equal(im.S23, 0.0, 1e-12)

S123 = 0.0
assert_almost_equal(im.S123, 0.0, 1e-12)

ST1 = S1 + S13
assert_almost_equal(im.ST1, ST1, 1e-12)

ST2 = S2
assert_almost_equal(im.ST2, ST2, 1e-12)

ST3 = S13
assert_almost_equal(im.ST3, ST3, 1e-12)