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Merge 65707a6 into 3117c23
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@ahaselsteiner
ahaselsteiner committed Jul 27, 2020
2 parents 3117c23 + 65707a6 commit 9018caa
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156 changes: 77 additions & 79 deletions tests/test_distributions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -16,29 +16,27 @@ class MultivariateDistributionTest(unittest.TestCase):
Create an example MultivariateDistribution (Vanem2012 model).
"""

# Define dependency tuple.
dep1 = (None, 0, None)
dep2 = (0, None, 0)

# Define parameters.
# Create a MultivariateDistribution, the joint distribution for Hs-Tz
# presented in Vanem et al. (2012).
# Start with a Weibull distribution for wave height, Hs.
shape = ConstantParam(1.471)
loc = ConstantParam(0.8888)
scale = ConstantParam(2.776)
par1 = (shape, loc, scale)
par0 = (shape, loc, scale)
dist0 = WeibullDistribution(*par0)

shape = FunctionParam('exp3', 0.0400, 0.1748, -0.2243)
loc = None
scale = FunctionParam('power3', 0.1, 1.489, 0.1901)
par2 = (shape, loc, scale)
# Conditional lognormal distribution for period, Tz.
mu = FunctionParam('power3', 0.1, 1.489, 0.1901)
sigma = FunctionParam('exp3', 0.0400, 0.1748, -0.2243)
dist1 = LognormalDistribution(mu=mu, sigma=sigma)

del shape, loc, scale
distributions = [dist0, dist1]

# Create distributions.
dist1 = WeibullDistribution(*par1)
dist2 = LognormalDistribution(*par2)
dep0 = (None, None, None)
dep1 = (0, None, 0)
dependencies = [dep0, dep1]

distributions = [dist1, dist2]
dependencies = [dep1, dep2]
mul_var_dist = MultivariateDistribution(distributions, dependencies)


def test_add_distribution_err_msg(self):
Expand All @@ -47,8 +45,10 @@ def test_add_distribution_err_msg(self):
dependency.
"""

dep0 = (None, 0, None)
dependencies = [dep0, self.dep1]
with self.assertRaises(ValueError):
MultivariateDistribution(self.distributions, self.dependencies)
MultivariateDistribution(self.distributions, dependencies)


def test_add_distribution_iter(self):
Expand All @@ -70,8 +70,8 @@ def test_add_distribution_length(self):
are of unequal length.
"""

dep3 = (0, None, None)
dependencies = [self.dep1, self.dep2, dep3]
dep2 = (0, None, None)
dependencies = [self.dep0, self.dep1, dep2]
with self.assertRaises(ValueError):
MultivariateDistribution(self.distributions, dependencies)

Expand All @@ -81,8 +81,8 @@ def test_add_distribution_dependencies_length(self):
has not length 3.
"""

dep1 = (None, None)
dependencies = [dep1, self.dep2]
dep0 = (None, None)
dependencies = [dep0, self.dep1]
with self.assertRaises(ValueError):
MultivariateDistribution(self.distributions, dependencies)

Expand All @@ -91,8 +91,8 @@ def test_add_distribution_dependencies_value(self):
Tests if an exception is raised when dependencies has an invalid value.
"""

dep1 = (-3, None, None)
dependencies = [dep1, self.dep2]
dep0 = (-3, None, None)
dependencies = [dep0, self.dep1]
with self.assertRaises(ValueError):
MultivariateDistribution(self.distributions, dependencies)

Expand All @@ -111,33 +111,8 @@ def test_multivariate_draw_sample(self):
"""
Tests the draw_sample() function of MulvariateDistribution.
"""

# Create a MultivariateDistribution, the joint distribution for Hs-Tz
# presented in Vanem et al. (2012).
# Start with a Weibull distribution for wave height, Hs.
shape = ConstantParam(1.471)
loc = ConstantParam(0.8888)
scale = ConstantParam(2.776)
par0 = (shape, loc, scale)
dist0 = WeibullDistribution(*par0)

# Conditonal lognormal distribution for period, Tz.
dist1_shape = FunctionParam('exp3', 0.0400, 0.1748, -0.2243)
dist1_loc = None
dist1_scale = FunctionParam('power3', 0.1, 1.489, 0.1901)
par1 = (dist1_shape, dist1_loc, dist1_scale)
dist1 = LognormalDistribution(*par1)

distributions = [dist0, dist1]

dep0 = (None, None, None)
dep1 = (0, None, 0)
dependencies = [dep0, dep1]

mul_var_dist = MultivariateDistribution(distributions, dependencies)

n=10000
sample = mul_var_dist.draw_sample(n)
sample = self.mul_var_dist.draw_sample(n)
self.assertEqual(n, sample[0].size)
self.assertEqual(n, sample[1].size)

Expand All @@ -152,47 +127,70 @@ def test_multivariate_draw_sample(self):
fit = Fit(sample, [dist_description_0, dist_description_1])
fitted_dist0 = fit.mul_var_dist.distributions[0]
fitted_dist1 = fit.mul_var_dist.distributions[1]
self.assertAlmostEqual(fitted_dist0.shape(0), shape(0), delta=0.1)
self.assertAlmostEqual(fitted_dist0.loc(0), loc(0), delta=0.1)
self.assertAlmostEqual(fitted_dist0.scale(0), scale(0), delta=0.1)
self.assertAlmostEqual(fitted_dist0.shape(0), self.shape(0), delta=0.1)
self.assertAlmostEqual(fitted_dist0.loc(0), self.loc(0), delta=0.1)
self.assertAlmostEqual(fitted_dist0.scale(0), self.scale(0), delta=0.1)
self.assertAlmostEqual(fitted_dist1.shape.a, 0.04, delta=0.1)
self.assertAlmostEqual(fitted_dist1.shape.b, 0.1748, delta=0.1)
self.assertAlmostEqual(fitted_dist1.shape.c, -0.2243, delta=0.15)
self.assertAlmostEqual(fitted_dist1.scale(1), dist1_scale(1), delta=0.1)
self.assertAlmostEqual(fitted_dist1.scale(2), dist1_scale(2), delta=0.1)

def test_multivariate_cdf(self):
"""
Tests the cdf() function of MulvariateDistribution.
"""
p = self.mul_var_dist.cdf([2, 2], lower_integration_limit=[0, 0])
self.assertAlmostEqual(p, 0, delta=0.01)

p = self.mul_var_dist.cdf([[2, 20], [2, 16]], lower_integration_limit=[0, 0])
np.testing.assert_allclose(p, [0, 1], atol=0.01)

# Create a bivariate normal distribution, where we know that at the
# peak, the CDF must evaluate to 0.25.
dist = NormalDistribution(shape=None, loc=ConstantParam(1), scale=ConstantParam(1))
dep = (None, None, None)
bivariate_dist = MultivariateDistribution([dist, dist], [dep, dep])

p = bivariate_dist.cdf([1, 1])
self.assertAlmostEqual(p, 0.25, delta=0.001)

def test_multivariate_pdf(self):
"""
Tests the pdf() function of MulvariateDistribution.
"""
# Let's compare the density values with density values presented in
# Haselsteiner et al. (2017), Fig. 5, DOI: 10.1016/j.coastaleng.2017.03.002
f = self.mul_var_dist.pdf([10, 13])
self.assertAlmostEqual(f, 0.000044, delta=0.00002)

f = self.mul_var_dist.pdf([[8, 10, 12], [12.5, 13, 13.4]])
np.testing.assert_allclose(f, [0.000044, 0.000044, 0.000044], atol=0.00002)

def test_latex_representation(self):
"""
Tests if the latex representation is correct.
"""
dep1 = (None, None, None)
dep2 = (0, None, 0)
dependencies = [dep1, dep2]
m = MultivariateDistribution(self.distributions, dependencies)
m = self.mul_var_dist
computed_latex = m.latex_repr(['Hs', 'Tp'])
correct_latex = \
['\\text{ joint PDF: }',
'f(h_{s},t_{p})=f_{H_{s}}(h_{s})f_{T_{p}|H_{s}}(t_{p}|h_{s})',
'',
'1\\text{. variable, }H_{s}: ',
'f_{H_{s}}(h_{s})=\\dfrac{\\beta_{h_{s}}}{\\alpha_{h_{s}}}'
'\\left(\\dfrac{h_{s}-\\gamma_{h_{s}}}{\\alpha_{h_{s}}}'
'\\right)^{\\beta_{h_{s}}-1}\\exp\\left[-\\left(\\dfrac{h_{s}-'
'\\gamma_{h_{s}}}{\\alpha_{h_{s}}}\\right)^{\\beta_{h_{s}}}\\right]',
'\\quad\\text{ with }\\alpha_{h_{s}}=2.776,',
'\\quad\\qquad\\;\\; \\beta_{h_{s}}=1.471,',
'\\quad\\qquad\\;\\; \\gamma_{h_{s}}=0.8888.',
'',
'2\\text{. variable, }T_{p}: ',
'f_{T_{p}|H_{s}}(t_{p}|h_{s})=\\dfrac{1}{t_{p}\\tilde{\\sigma}_'
'{t_{p}}\\sqrt{2\\pi}}\\exp\\left[-\\dfrac{(\\ln t_{p}-\\tilde{'
'\\mu}_{t_{p}})^2}{2\\tilde{\\sigma}_{t_{p}}^2}\\right]',
'\\quad\\text{ with }\\exp{\\tilde{\\mu}}_{t_{p}}='
'0.1+1.489h_{s}^{0.1901},',
'\\quad\\qquad\\;\\; \\tilde{\\sigma}_{t_{p}}='
'0.04+0.1748e^{-0.2243h_{s}}.']
assert(computed_latex, correct_latex)
['\\text{ joint PDF: }',
'f(h_{s},t_{p})=f_{H_{s}}(h_{s})f_{T_{p}|H_{s}}(t_{p}|h_{s})', '',
'1\\text{. variable, }H_{s}: ',
'f_{H_{s}}(h_{s})=\\dfrac{\\beta_{h_{s}}}{\\alpha_{h_{s}}}'
'\\left(\\dfrac{h_{s}-\\gamma_{h_{s}}}{\\alpha_{h_{s}}}\\right)^'
'{\\beta_{h_{s}}-1}\\exp\\left[-\\left(\\dfrac{h_{s}-'
'\\gamma_{h_{s}}}{\\alpha_{h_{s}}}\\right)^{\\beta_{h_{s}}}'
'\\right]', '\\quad\\text{ with }\\alpha_{h_{s}}=2.776,',
'\\quad\\qquad\\;\\; \\beta_{h_{s}}=1.471,',
'\\quad\\qquad\\;\\; \\gamma_{h_{s}}=0.8888.', '',
'2\\text{. variable, }T_{p}: ',
'f_{T_{p}|H_{s}}(t_{p}|h_{s})=\\dfrac{1}'
'{t_{p}\\tilde{\\sigma}_{t_{p}}\\sqrt{2\\pi}}\\exp\\left[-'
'\\dfrac{(\\ln t_{p}-\\tilde{\\mu}_{t_{p}})^2}'
'{2\\tilde{\\sigma}_{t_{p}}^2}\\right]',
'\\quad\\text{ with }\\tilde{\\mu}_{t_{p}}=0.1 + 1.489h_{s}^(0.1901),',
'\\quad\\qquad\\;\\; \\tilde{\\sigma}_{t_{p}}=0.04 + 0.1748e^{-0.2243h_{s}}.']

self.assertEqual(computed_latex, correct_latex)


class ParametricDistributionTest(unittest.TestCase):
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