def psi(self, s):
assert not np.isnan(self.params), "Copula must have parameters to calculate psi"
s = np.asarray(s)
if self.params <= -36:
return -log1pexp(-s - self.params) / self.params
elif self.params < 0:
return -np.log1p(np.exp(-s) * np.expm1(-self.params)) / self.params
elif self.params == 0:
return np.exp(-s)
else:
const = log1mexp(self.params)
m = np.less(s, const, where=~np.isnan(s))
s[m] = np.nan
s[~m] = -log1mexp(s[~m] - log1mexp(self.params)) / self.params
return s.item(0) if s.size == 1 else s
def pdf(self, u: Array, log=False):
assert not np.isnan(self.params), "Copula must have parameters to calculate parameters"
n, d = u.shape
theta = self.params
ok = valid_rows_in_u(u)
res = np.repeat(np.nan, n)
u_ = u[ok]
u_sum = u_.sum(1)
lp = log1mexp(theta)
lpu = log1mexp(theta * u_)
lu = lpu.sum(1)
li_arg = np.exp(lp + (lpu - lp).sum(1))
li = poly_log(li_arg, 1 - d, log=True)
res[ok] = (d - 1) * np.log(theta) + li - theta * u_sum - lu
return res if log else np.exp(res)
def random(self, n: int, seed: int = None):
u = random_uniform(n, self.dim, seed)
if abs(self.params) < 1e-7:
return u
if self.dim == 2:
v = u[:, 1]
a = -abs(self.params)
v = -1 / a * np.log1p(-v * np.expm1(-a) / (np.exp(-a * u[:, 0]) * (v - 1) - v))
u[:, 1] = 1 - v if self.params > 0 else v
return u
# alpha too large
if log1mexp(self.params) == 0:
return np.ones((n, self.dim))
fr = random_log_series_ln1p(-self.params, n)[:, None]
return self.psi(-np.log(u) / fr)