How to use the gstools.tools.special.tplstable_cor function in gstools
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GeoStat-Framework / GSTools / gstools / covmodel / tpl_models.py View on Github 
.. math::
\rho(r) =
2H \cdot
\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+2H}\left[\frac{r}{\ell_{\mathrm{up}}}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+2H}\left[\frac{r}{\ell_{\mathrm{low}}}\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, 1)
return (
self.len_up ** (2 * self.hurst)
* tplstable_cor(r, self.len_up, self.hurst, 1)
- self.len_low ** (2 * self.hurst)
* tplstable_cor(r, self.len_low, self.hurst, 1)
) / (
self.len_up ** (2 * self.hurst) - self.len_low ** (2 * self.hurst)
)\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)
)The general case:
.. math::
\rho(r) =
H \cdot
\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+H}
\left[\left(\frac{r}{\ell_{\mathrm{up}}}\right)^{2}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+H}
\left[\left(\frac{r}{\ell_{\mathrm{low}}}\right)^{2}\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, 2)
return (
self.len_up ** (2 * self.hurst)
* tplstable_cor(r, self.len_up, self.hurst, 2)
- self.len_low ** (2 * self.hurst)
* tplstable_cor(r, self.len_low, self.hurst, 2)
) / (
self.len_up ** (2 * self.hurst) - self.len_low ** (2 * self.hurst)
)\right]
The general case:
.. math::
\rho(r) =
2H \cdot
\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+2H}\left[\frac{r}{\ell_{\mathrm{up}}}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+2H}\left[\frac{r}{\ell_{\mathrm{low}}}\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, 1)
return (
self.len_up ** (2 * self.hurst)
* tplstable_cor(r, self.len_up, self.hurst, 1)
- self.len_low ** (2 * self.hurst)
* tplstable_cor(r, self.len_low, self.hurst, 1)
) / (
self.len_up ** (2 * self.hurst) - self.len_low ** (2 * self.hurst)
)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)
)\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+H}
\left[\left(\frac{r}{\ell_{\mathrm{up}}}\right)^{2}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+H}
\left[\left(\frac{r}{\ell_{\mathrm{low}}}\right)^{2}\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, 2)
return (
self.len_up ** (2 * self.hurst)
* tplstable_cor(r, self.len_up, self.hurst, 2)
- self.len_low ** (2 * self.hurst)
* tplstable_cor(r, self.len_low, self.hurst, 2)
) / (
self.len_up ** (2 * self.hurst) - self.len_low ** (2 * self.hurst)
)\rho(r) =
2H \cdot
\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+2H}\left[\frac{r}{\ell_{\mathrm{up}}}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+2H}\left[\frac{r}{\ell_{\mathrm{low}}}\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, 1)
return (
self.len_up ** (2 * self.hurst)
* tplstable_cor(r, self.len_up, self.hurst, 1)
- self.len_low ** (2 * self.hurst)
* tplstable_cor(r, self.len_low, self.hurst, 1)
) / (
self.len_up ** (2 * self.hurst) - self.len_low ** (2 * self.hurst)
)\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)
)\rho(r) =
H \cdot
\frac{\ell_{\mathrm{up}}^{2H} \cdot
E_{1+H}
\left[\left(\frac{r}{\ell_{\mathrm{up}}}\right)^{2}\right]
- \ell_{\mathrm{low}}^{2H} \cdot
E_{1+H}
\left[\left(\frac{r}{\ell_{\mathrm{low}}}\right)^{2}\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, 2)
return (
self.len_up ** (2 * self.hurst)
* tplstable_cor(r, self.len_up, self.hurst, 2)
- self.len_low ** (2 * self.hurst)
* tplstable_cor(r, self.len_low, self.hurst, 2)
) / (
self.len_up ** (2 * self.hurst) - self.len_low ** (2 * self.hurst)
)
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