def _force_psd(self):
"""
Forces covariance matrix to be positive semi-definite. This is useful when user is overwriting covariance
parameters
"""
cov = near_psd(self.sigma)
self._rhos = cov[tri_indices(self.dim, 1, 'lower')]
def fit_cor(copula: Copula, data: np.ndarray, typ: str) -> np.ndarray:
"""
Constructs parameter matrix from matrix of Kendall's Taus or Spearman's Rho
Parameters
----------
copula: AbstractCopula
Copula instance
data: ndarray
Data to fit copula with
typ: {'irho', 'itau'}
The type of rank correlation measure to use. 'itau' uses Kendall's tau while 'irho' uses Spearman's rho
Returns
-------
ndarray
Parameter matrix is copula is elliptical. Otherwise, a vector
"""
indices = tri_indices(copula.dim, 1, 'lower')
if typ == 'itau':
tau = kendall_tau(data)[indices]
theta = copula.itau(tau)
elif typ == 'irho':
rho = spearman_rho(data)[indices]
theta = copula.irho(rho)
else:
raise ValueError("Correlation Inversion must be either 'itau' or 'irho'")
if is_elliptical(copula):
theta = near_psd(create_cov_matrix(theta))[indices]
return theta
def _force_psd(self):
"""
Forces covariance matrix to be positive semi-definite. This is useful when user is overwriting covariance
parameters
"""
cov = near_psd(self.sigma)
self._rhos = cov[tri_indices(self.dim, 1, 'lower')]
def fit_cor(copula, data: np.ndarray, typ: str) -> np.ndarray:
"""
Constructs parameter matrix from matrix of Kendall's Taus or Spearman's Rho
Parameters
----------
copula: BaseCopula
Copula instance
data: ndarray
Data to fit copula with
typ: {'irho', 'itau'}
The type of rank correlation measure to use. 'itau' uses Kendall's tau while 'irho' uses Spearman's rho
Returns
-------
ndarray
Parameter matrix is copula is elliptical. Otherwise, a vector
"""
indices = tri_indices(copula.dim, 1, 'lower')
if typ == 'itau':
tau = kendall_tau(data)[indices]
theta = copula.itau(tau)
elif typ == 'irho':
rho = spearman_rho(data)[indices]
theta = copula.irho(rho)
else:
raise ValueError(
"Correlation Inversion must be either 'itau' or 'irho'")
if is_elliptical(copula):
theta = near_psd(create_cov_matrix(theta))[indices]
return theta
def __setitem__(self, index: Union[int, Tuple[Union[slice, int],
Union[slice, int]], slice],
value: Union[float, Collection[float], np.ndarray]):
d = self.dim
if np.isscalar(value):
if value < -1 or value > 1:
raise ValueError("correlation value must be between -1 and 1")
else:
value = np.asarray(value)
if not np.all((value >= -1 - EPS) & (value <= 1 + EPS)):
raise ValueError("correlation value must be between -1 and 1")
if isinstance(index, slice):
value = near_psd(value)
if value.shape != (d, d):
raise ValueError(
f"The value being set should be a matrix of dimension ({d}, {d})"
)
self._rhos = value[tri_indices(d, 1, 'lower')]
return
if isinstance(index, int):
self._rhos[index] = value
else:
index = tuple(index)
if len(index) != 2:
raise IndexError('index can only be 1 or 2-dimensional')
x, y = index
# having 2 slices for indices is equivalent to self[:]
if isinstance(x, slice) and isinstance(y, slice):
self[:] = value
return
elif isinstance(x, slice) or isinstance(y, slice):
value = np.repeat(
value, d) if np.isscalar(value) else np.asarray(value)
if len(value) != d:
raise ValueError(
f"value must be a scalar or be a vector with length {d}"
)
# one of the item is
for i, v in enumerate(value):
idx = (i, y) if isinstance(x, slice) else (x, i)
if idx[0] == idx[1]: # skip diagonals
continue
idx = _get_rho_index(d, idx)
self._rhos[idx] = v
else:
# both are integers
idx = _get_rho_index(d, index)
self._rhos[idx] = float(value)
self._force_psd()
def _get_rho_index(dim: int, index: Tuple[int, int]) -> int:
x, y = index
if x < 0 or y < 0:
raise IndexError('Only positive indices are supported')
elif x >= dim or y >= dim:
raise IndexError('Index cannot be greater than dimension of copula')
elif x == y:
raise IndexError('Cannot set values along the diagonal')
for j, v in enumerate(zip(*tri_indices(dim, 1, 'upper' if x < y else 'lower'))):
if (x, y) == v:
return j
raise IndexError(f"Unable to find index {(x, y)}")
def __setitem__(self, i, value):
d = self.dim
if isinstance(i, slice):
value = near_psd(value)
if value.shape != (d, d):
return IndexError(f"The value being set should be a matrix of dimension ({d}, {d})")
self._rhos = value[tri_indices(d, 1, 'lower')]
return
if isinstance(i, int):
self._rhos[i] = value
else:
i = _get_rho_index(d, i)
self._rhos[i] = value
self._force_psd()
def __setitem__(self, i, value):
d = self.dim
if isinstance(i, slice):
value = near_psd(value)
if value.shape != (d, d):
return IndexError(f"The value being set should be a matrix of dimension ({d}, {d})")
self._rhos = value[tri_indices(d, 1, 'lower')]
return
assert -1.0 <= value <= 1.0, "correlation value must be between -1 and 1"
if isinstance(i, int):
self._rhos[i] = value
else:
i = _get_rho_index(d, i)
self._rhos[i] = value
self._force_psd()
def initial_params(self) -> np.ndarray:
if self.x0 is not None:
return self.x0
if is_elliptical(self.copula):
corr = pearson_rho(self.data)
rhos = corr[tri_indices(self.copula.dim, 1, 'lower')]
if hasattr(self.copula, '_df'):
# T-distribution
return np.array([4.669,
*rhos]) # set df as Feigenbaum's constant
else:
# Gaussian
return rhos
try:
start = CorrInversionEstimator(self.copula, self.data,
self.verbose).fit('itau')
ll = self.copula.log_lik(self.data)
if np.isfinite(ll):
return start
else:
if self.copula.name.lower(
) == 'clayton' and self.copula.dim == 2:
# The support of bivariate claytonCopula with negative parameter is not
# the full unit square; the further from 0, the more restricted.
while start < 0:
start += .2
self.copula.params = start
if np.isfinite(self.copula.log_lik(self.data)):
break
if not np.isnan(ll) and np.isinf(ll):
# for perfectly correlated data
return start
return self.copula.params
except NotImplementedError:
return self.copula.params
def _get_rho_index(d: int, i: Tuple[int, int]) -> int:
i = tuple(i)
if not isinstance(i, tuple):
raise IndexError("only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean "
"arrays are valid indices")
if len(i) != 2:
raise IndexError('only 2-dimensional indices supported')
x, y = i
if x < 0 or y < 0:
raise IndexError('Only positive indices are supported')
elif x >= d or y >= d:
raise IndexError('Index cannot be greater than dimension of copula')
elif x == y:
raise IndexError('Cannot set values along the diagonal')
for j, v in enumerate(zip(*tri_indices(d, 1, 'upper' if x < y else 'lower'))):
if i == v:
return j
raise IndexError(f"Unable to find index {i}")
def initial_params(copula: Copula, data: np.ndarray, x0: np.ndarray):
# ensure that initial is defined. If it is defined, checks that all x0 values are finite
# neither infinite nor nan
if x0 is not None and \
((np.isscalar(x0) and not np.isfinite(x0)) or (not np.isscalar(x0) and all(np.isfinite(x0)))):
return x0
if is_elliptical(copula):
corr = pearson_rho(data)
rhos = corr[tri_indices(copula.dim, 1, 'lower')]
if copula.name.lower() == 'student':
# T-distribution
return np.array([4.669, *rhos]) # set df as Feigenbaum's constant
else:
# Gaussian
return rhos
try:
start = estimate_corr_inverse_params(copula, data, 'itau')
ll = copula.log_lik(data)
if np.isfinite(ll):
return start
else:
if copula.name.lower() == 'clayton' and copula.dim == 2:
# The support of bivariate claytonCopula with negative parameter is not
# the full unit square; the further from 0, the more restricted.
while start < 0:
start += .2
copula.params = start
if np.isfinite(copula.log_lik(data)):
break
if not np.isnan(ll) and np.isinf(ll):
# for perfectly correlated data
return start
return copula.params
except NotImplementedError:
return copula.params
def _get_rho_index(d: int, i: Tuple[int, int]) -> int:
i = tuple(i)
if not isinstance(i, tuple):
raise IndexError("only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean "
"arrays are valid indices")
if len(i) != 2:
raise IndexError('only 2-dimensional indices supported')
x, y = i
if x < 0 or y < 0:
raise IndexError('Only positive indices are supported')
elif x >= d or y >= d:
raise IndexError('Index cannot be greater than dimension of copula')
elif x == y:
raise IndexError('Cannot set values along the diagonal')
for j, v in enumerate(zip(*tri_indices(d, 1, 'upper' if x < y else 'lower'))):
if i == v:
return j
raise IndexError(f"Unable to find index {i}")
def initial_params(self):
if self._x0 is not None:
return self._x0
if is_elliptical(self.copula):
corr = pearson_rho(self.data)
rhos = corr[tri_indices(self.copula.dim, 1, 'lower')]
if hasattr(self.copula, '_df'):
# T-distribution
return np.array([4.669, *rhos]) # set df as Feigenbaum's constant
else:
# Gaussian
return rhos
try:
start = (CorrInversionEstimator(self.copula, self.data, False, self._verbose).fit('itau'))
ll = self.copula.log_lik(self.data)
if np.isfinite(ll):
return start
else:
if self.copula.name.lower() == 'clayton' and self.copula.dim == 2:
# The support of bivariate claytonCopula with negative parameter is not
# the full unit square; the further from 0, the more restricted.
while start < 0:
start += .2
self.copula.params = start
if np.isfinite(self.copula.log_lik(self.data)):
break
if not np.isnan(ll) and np.isinf(ll):
# for perfectly correlated data
return start
return self.copula.params
except NotImplementedError:
return self.copula.params