def prepare_next_tree(self):
"""Prepare conditional U matrix for next tree."""
for edge in self.edges:
copula_theta = edge.theta
if self.level == 1:
left_u = self.u_matrix[:, edge.L]
right_u = self.u_matrix[:, edge.R]
else:
left_parent, right_parent = edge.parents
left_u, right_u = Edge.get_conditional_uni(
left_parent, right_parent)
# compute conditional cdfs C(i|j) = dC(i,j)/duj and dC(i,j)/du
left_u = [x for x in left_u if x is not None]
right_u = [x for x in right_u if x is not None]
X_left_right = np.array([[x, y] for x, y in zip(left_u, right_u)])
X_right_left = np.array([[x, y] for x, y in zip(right_u, left_u)])
copula = Bivariate(edge.name)
copula.fit(X_left_right)
left_given_right = copula.partial_derivative(
X_left_right, copula_theta)
right_given_left = copula.partial_derivative(
X_right_left, copula_theta)
# correction of 0 or 1
left_given_right[left_given_right == 0] = EPSILON
right_given_left[right_given_left == 0] = EPSILON
left_given_right[left_given_right == 1] = 1 - EPSILON
right_given_left[right_given_left == 1] = 1 - EPSILON
edge.U = np.array([left_given_right, right_given_left])
def test_fit(self):
"""fit checks that the given values are independent."""
# Setup
instance = Bivariate(CopulaTypes.INDEPENDENCE)
data = np.array([[1, 2], [4, 3]])
# Run
instance.fit(data)
# Check
instance.tau is None
instance.theta is None
def test_partial_derivative_scalar(self, derivative_mock):
"""partial_derivative_scalar calls partial_derivative with its arguments in an array."""
# Setup
instance = Bivariate(copula_type=CopulaTypes.CLAYTON)
instance.fit(self.X)
# Run
result = instance.partial_derivative_scalar(0.5, 0.1)
# Check
assert result == derivative_mock.return_value
expected_args = ((np.array([[0.5, 0.1]]), 0), {})
assert len(expected_args) == len(derivative_mock.call_args)
assert (derivative_mock.call_args[0][0] == expected_args[0][0]).all()
def test_to_dict(self):
"""To_dict returns the defining parameters of a copula in a dict."""
# Setup
instance = Bivariate('frank')
instance.fit(self.X)
expected_result = {
'copula_type': 'FRANK',
"tau": 0.014492753623188406,
"theta": 0.13070829945417198
}
# Run
result = instance.to_dict()
# Check
assert result == expected_result
def test_to_dict(self):
"""To_dict returns the defining parameters of a copula in a dict."""
# Setup
instance = Bivariate(copula_type='frank')
instance.fit(self.X)
expected_result = {
'copula_type': 'FRANK',
"tau": 0.9128709291752769,
"theta": 44.2003852484162
}
# Run
result = instance.to_dict()
# Check
assert result == expected_result
def test_save(self, json_mock):
"""Save stores the internal dictionary as a json in a file."""
# Setup
instance = Bivariate('frank')
instance.fit(self.X)
expected_content = {
"copula_type": "FRANK",
"tau": 0.014492753623188406,
"theta": 0.13070829945417198
}
# Run
instance.save('test.json')
# Check
assert json_mock.called
compare_nested_dicts(json_mock.call_args[0][0], expected_content)
def test_save(self, json_mock, open_mock):
"""Save stores the internal dictionary as a json in a file."""
# Setup
instance = Bivariate(copula_type='frank')
instance.fit(self.X)
expected_content = {
"copula_type": "FRANK",
"tau": 0.9128709291752769,
"theta": 44.2003852484162
}
# Run
instance.save('test.json')
# Check
assert open_mock.called_once_with('test.json', 'w')
assert json_mock.called
compare_nested_dicts(json_mock.call_args[0][0], expected_content)
class TestFrank(TestCase):
def setUp(self):
self.X = np.array([
[2641.16233666, 180.2425623],
[921.14476418, 192.35609972],
[-651.32239137, 150.24830291],
[1223.63536668, 156.62123653],
[3233.37342355, 173.80311908],
[1373.22400821, 191.0922843],
[1959.28188858, 163.22252158],
[1076.99295365, 190.73280428],
[2029.25100261, 158.52982435],
[1835.52188141, 163.0101334],
[1170.03850556, 205.24904026],
[739.42628394, 175.42916046],
[1866.65810627, 208.31821984],
[3703.49786503, 178.98351969],
[1719.45232017, 160.50981075],
[258.90206528, 163.19294974],
[219.42363944, 173.30395132],
[609.90212377, 215.18996298],
[1618.44207239, 164.71141696],
[2323.2775272, 178.84973821],
[3251.78732274, 182.99902513],
[1430.63989981, 217.5796917],
[-180.57028875, 201.56983421],
[-592.84497457, 174.92272693]
])
self.copula = Bivariate(CopulaTypes.FRANK)
def test_fit(self):
"""On fit, theta and tau attributes are set."""
# Setup
expected_theta = 0.1307082
expected_tau = 0.01449275
# Run
self.copula.fit(self.X)
actual_theta = self.copula.theta
actual_tau = self.copula.tau
# Check
self.assertAlmostEqual(actual_theta, expected_theta, places=3)
self.assertAlmostEqual(actual_tau, expected_tau)
def test_probability_density(self):
"""Probability_density returns the probability density for the given values."""
# Setup
self.copula.fit(self.X)
expected_result = 0.999672586804842
# Run
result = self.copula.probability_density(np.array([[0.1, 0.5]]))
# Check
assert np.isclose(result, expected_result).all()
assert isinstance(result, np.ndarray)
def test_cumulative_distribution(self):
"""Cumulative_density returns the probability distribution value for a point."""
# Setup
self.copula.fit(self.X)
expected_result = 0.05147003
# Run
result = self.copula.cumulative_distribution(np.array([[0.1, 0.5]]))
# Check
assert np.isclose(result, expected_result).all()
assert isinstance(result, np.ndarray)
def test_sample(self):
"""After being fit, copula can produce samples."""
# Setup
self.copula.fit(self.X)
# Run
result = self.copula.sample(10)
# Check
assert isinstance(result, np.ndarray)
assert result.shape == (10, 2)
class TestFrank(TestCase):
def setUp(self):
self.X = np.array([[2641.16233666, 180.2425623],
[921.14476418, 192.35609972],
[-651.32239137, 150.24830291],
[1223.63536668, 156.62123653],
[3233.37342355, 173.80311908],
[1373.22400821, 191.0922843],
[1959.28188858, 163.22252158],
[1076.99295365, 190.73280428],
[2029.25100261, 158.52982435],
[1835.52188141, 163.0101334],
[1170.03850556, 205.24904026],
[739.42628394, 175.42916046],
[1866.65810627, 208.31821984],
[3703.49786503, 178.98351969],
[1719.45232017, 160.50981075],
[258.90206528, 163.19294974],
[219.42363944, 173.30395132],
[609.90212377, 215.18996298],
[1618.44207239, 164.71141696],
[2323.2775272, 178.84973821],
[3251.78732274, 182.99902513],
[1430.63989981, 217.5796917],
[-180.57028875, 201.56983421],
[-592.84497457, 174.92272693]])
self.copula = Bivariate(CopulaTypes.FRANK)
def test_fit(self):
"""On fit, theta and tau attributes are set."""
# Setup
expected_theta = 0.1307082
expected_tau = 0.01449275
# Run
self.copula.fit(self.X)
actual_theta = self.copula.theta
actual_tau = self.copula.tau
# Check
self.assertAlmostEqual(actual_theta, expected_theta, places=3)
self.assertAlmostEqual(actual_tau, expected_tau)
def test_probability_density(self):
"""Probability_density returns the probability density for the given values."""
# Setup
self.copula.fit(self.X)
expected_result = 0.999672586804842
# Run
result = self.copula.probability_density(np.array([[0.1, 0.5]]))
# Check
assert np.isclose(result, expected_result).all()
assert isinstance(result, np.ndarray)
def test_cumulative_distribution(self):
"""Cumulative_density returns the probability distribution value for a point."""
# Setup
self.copula.fit(self.X)
expected_result = 0.05147003
# Run
result = self.copula.cumulative_distribution(np.array([[0.1, 0.5]]))
# Check
assert np.isclose(result, expected_result).all()
assert isinstance(result, np.ndarray)
@patch('copulas.bivariate.base.np.random.uniform')
def test_sample(self, uniform_mock):
"""Sample use the inverse-transform method to generate new samples."""
# Setup
instance = Bivariate(CopulaTypes.FRANK)
instance.tau = 0.5
instance.theta = instance.compute_theta()
uniform_mock.return_value = np.array([0.1, 0.2, 0.4, 0.6, 0.8])
expected_result = np.array([[6.080069565509917e-06, 0.1],
[6.080069565509917e-06, 0.2],
[6.080069565509917e-06, 0.4],
[6.080069565509917e-06, 0.6],
[4.500185268624483e-06, 0.8]])
expected_uniform_call_args_list = [((0, 1, 5), {}), ((0, 1, 5), {})]
# Run
result = instance.sample(5)
# Check
assert isinstance(result, np.ndarray)
assert result.shape == (5, 2)
compare_nested_iterables(result, expected_result)
assert uniform_mock.call_args_list == expected_uniform_call_args_list
def test_cdf_zero_if_single_arg_is_zero(self):
"""Test of the analytical properties of copulas on a range of values of theta."""
# Setup
instance = Bivariate(CopulaTypes.FRANK)
tau_values = np.linspace(-1.0, 1.0, 20)[1:-1]
# Run/Check
for tau in tau_values:
instance.tau = tau
instance.theta = instance.compute_theta()
copula_zero_if_arg_zero(instance)
def test_cdf_value_if_all_other_arg_are_one(self):
"""Test of the analytical properties of copulas on a range of values of theta."""
# Setup
instance = Bivariate(CopulaTypes.FRANK)
tau_values = np.linspace(-1.0, 1.0, 20)[1:-1]
# Run/Check
for tau in tau_values:
instance.tau = tau
instance.theta = instance.compute_theta()
copula_single_arg_not_one(instance, tolerance=1E-03)
def test_sample_random_state(self):
"""If random_state is set, the samples are the same."""
# Setup
instance = Bivariate(CopulaTypes.FRANK, random_seed=0)
instance.tau = 0.5
instance.theta = instance.compute_theta()
expected_result = np.array([[3.66330927e-06, 5.48813504e-01],
[6.08006957e-06, 7.15189366e-01],
[5.27582646e-06, 6.02763376e-01],
[5.58315848e-06, 5.44883183e-01],
[6.08006957e-06, 4.23654799e-01]])
# Run
result = instance.sample(5)
# Check
compare_nested_iterables(result, expected_result)
class TestClayton(TestCase):
def setUp(self):
self.copula = Bivariate(CopulaTypes.CLAYTON)
self.X = np.array([[2641.16233666, 180.2425623],
[921.14476418, 192.35609972],
[-651.32239137, 150.24830291],
[1223.63536668, 156.62123653],
[3233.37342355, 173.80311908],
[1373.22400821, 191.0922843],
[1959.28188858, 163.22252158],
[1076.99295365, 190.73280428],
[2029.25100261, 158.52982435],
[1835.52188141, 163.0101334],
[1170.03850556, 205.24904026],
[739.42628394, 175.42916046],
[1866.65810627, 208.31821984],
[3703.49786503, 178.98351969],
[1719.45232017, 160.50981075],
[258.90206528, 163.19294974],
[219.42363944, 173.30395132],
[609.90212377, 215.18996298],
[1618.44207239, 164.71141696],
[2323.2775272, 178.84973821],
[3251.78732274, 182.99902513],
[1430.63989981, 217.5796917],
[-180.57028875, 201.56983421],
[-592.84497457, 174.92272693]])
def test_fit(self):
"""On fit, theta and tau attributes are set."""
# Setup
expected_theta = 0.0294117
expected_tau = 0.01449275
# Run
self.copula.fit(self.X)
actual_theta = self.copula.theta
actual_tau = self.copula.tau
# Check
self.assertAlmostEqual(actual_theta, expected_theta, places=3)
self.assertAlmostEqual(actual_tau, expected_tau)
def test_probability_density(self):
"""Probability_density returns the probability density for the given values."""
# Setup
self.copula.fit(self.X)
expected_result = np.array([0.98854645, 0.98607539])
# Run
result = self.copula.probability_density(
np.array([[0.1, 0.5], [0.2, 0.8]]))
# Check
assert isinstance(result, np.ndarray)
assert np.isclose(result, expected_result).all()
def test_cumulative_distribution(self):
"""Cumulative_density returns the probability distribution value for a point."""
# Setup
self.copula.fit(self.X)
expected_result = np.array([1.06658093e+06, 0.16165401])
# Run
result = self.copula.cumulative_distribution(
np.array([[1500, 180], [0.2, 0.8]]))
# Check
assert isinstance(result, np.ndarray)
assert np.isclose(result, expected_result).all()
def test_inverse_cumulative_percentile_point(self):
"""The percentile point and cumulative_distribution should be inverse one of the other."""
# Setup
self.copula.fit(self.X)
# Run
# percentile = self.copula.percent_point(0.1, 0.5)
# derivative = self.copula.partial_derivative([0.1], [0.5])
# result = self.copula.cumulative_distribution(derivative, percentile)
# Check
# assert point == result
@patch('copulas.bivariate.base.np.random.uniform')
def test_sample(self, uniform_mock):
"""Sample use the inverse-transform method to generate new samples."""
# Setup
instance = Bivariate(CopulaTypes.CLAYTON)
instance.tau = 0.5
instance.theta = instance.compute_theta()
uniform_mock.return_value = np.array([0.1, 0.2, 0.4, 0.6, 0.8])
expected_result = np.array([[0.05233100, 0.1], [0.14271095, 0.2],
[0.39959746, 0.4], [0.68567125, 0.6],
[0.89420523, 0.8]])
expected_uniform_call_args_list = [((0, 1, 5), {}), ((0, 1, 5), {})]
# Run
result = instance.sample(5)
# Check
assert isinstance(result, np.ndarray)
assert result.shape == (5, 2)
compare_nested_iterables(result, expected_result)
assert uniform_mock.call_args_list == expected_uniform_call_args_list
def test_cdf_zero_if_single_arg_is_zero(self):
"""Test of the analytical properties of copulas on a range of values of theta."""
# Setup
instance = Bivariate(CopulaTypes.CLAYTON)
tau_values = np.linspace(-1.0, 1.0, 20)[1:-1]
# Run/Check
for tau in tau_values:
instance.tau = tau
instance.theta = instance.compute_theta()
copula_zero_if_arg_zero(instance)
def test_cdf_value_if_all_other_arg_are_one(self):
"""Test of the analytical properties of copulas on a range of values of theta."""
# Setup
instance = Bivariate(CopulaTypes.CLAYTON)
tau_values = np.linspace(-1.0, 1.0, 20)[1:-1]
# Run/Check
for tau in tau_values:
instance.tau = tau
instance.theta = instance.compute_theta()
copula_single_arg_not_one(instance)
def test_sample_random_state(self):
"""If random_state is set, the samples are the same."""
# Setup
instance = Bivariate(CopulaTypes.CLAYTON, random_seed=0)
instance.tau = 0.5
instance.theta = instance.compute_theta()
expected_result = np.array([[0.68627770, 0.54881350],
[0.64059280, 0.71518937],
[0.90594782, 0.60276338],
[0.96040856, 0.54488318],
[0.40876969, 0.42365480]])
# Run
result = instance.sample(5)
# Check
compare_nested_iterables(result, expected_result)
