def correlation(self, r):
r"""Truncated-Power-Law with Stable modes - correlation function.
If ``len_low=0`` we have a simple representation:
.. math::
\rho(r) =
\frac{2H}{\alpha} \cdot
E_{1+\frac{2H}{\alpha}}
\left[
\left(\frac{r}{\ell}\right)^{\alpha}
\right]
The general case:
.. math::
\rho(r) =
\frac{2H}{\alpha} \cdot
\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+\frac{2H}{\alpha}}
\left[\left(\frac{r}{\ell_{\mathrm{up}}}\right)^{\alpha}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+\frac{2H}{\alpha}}
\left[\left(\frac{r}{\ell_{\mathrm{low}}}\right)^{\alpha}\right]}
{\ell_{\mathrm{up}}^{2H}-\ell_{\mathrm{low}}^{2H}}
"""
# if lower limit is 0 we use the simplified version (faster)
if np.isclose(self.len_low, 0.0):
return tplstable_cor(r, self.len_scale, self.hurst, self.alpha)
return (self.len_up**(2 * self.hurst) *
tplstable_cor(r, self.len_up, self.hurst, self.alpha) -
self.len_low**(2 * self.hurst) *
tplstable_cor(r, self.len_low, self.hurst, self.alpha)) / (
self.len_up**(2 * self.hurst) -
self.len_low**(2 * self.hurst))
def correlation(self, r):
"""TPL with Stable modes - correlation function."""
# if lower limit is 0 we use the simplified version (faster)
if np.isclose(self.len_low_rescaled, 0.0):
return tplstable_cor(r, self.len_rescaled, self.hurst, self.alpha)
return (self.len_up_rescaled**(2 * self.hurst) * tplstable_cor(
r, self.len_up_rescaled, self.hurst, self.alpha) -
self.len_low_rescaled**(2 * self.hurst) *
tplstable_cor(r, self.len_low_rescaled, self.hurst, self.alpha)
) / (self.len_up_rescaled**(2 * self.hurst) -
self.len_low_rescaled**(2 * self.hurst))
def cor(self, h):
"""TPL with Stable modes - normalized correlation function."""
return tplstable_cor(h, 1.0, self.hurst, self.alpha)
def cor(self, h):
"""TPL with Exponential modes - normalized correlation function."""
return tplstable_cor(h, 1.0, self.hurst, 1)
def cor(self, h):
"""TPL with Gaussian modes - normalized correlation function."""
return tplstable_cor(h, 1.0, self.hurst, 2)