fips.Matern#

class fips.Matern(levels, scale, nu=1.5, *, within=None, metric='euclidean')[source]#

Bases: _Decay

A Matérn correlation, of smoothness \(\nu\).

\[C(d) = \frac{2^{1-\nu}}{\Gamma(\nu)} \, r^\nu K_\nu(r), \qquad r = \sqrt{2\nu} \, d / \ell,\]

where \(K_\nu\) is the modified Bessel function of the second kind (Rasmussen and Williams 2006, eq. 4.14). \(\nu = 1/2\) is Exponential, and \(\nu \to \infty\) is Gaussian.

Parameters:

levels (str | Sequence[str]) – The levels the distance is measured along (see Exponential).
scale (float | str | Timedelta) – The length scale \(\ell\), positive.
nu (float) – The smoothness \(\nu\), in (0, 50]: past that, use Gaussian.
within (str | Sequence[str] | None) – Correlate only labels the same on these levels (see Exponential).
metric (str) – How the distance is measured (see Exponential); "haversine" only for \(\nu \le 1/2\) (positive-definite there).

Raises:

ValueError – As Exponential, and if nu is not in (0, 50].

Examples

>>> import pandas as pd
>>> from fips import Matern
>>> coords = pd.DataFrame({"x": [0.0, 1.0]})
>>> Matern("x", 1.0, nu=0.5).correlation(coords).round(4)
array([[1.    , 0.3679],
       [0.3679, 1.    ]])

Attributes

`metric`	How the distance is measured, `"euclidean"`, `"haversine"` or `"chordal"`.
`nu`	The smoothness, 1/2 for the exponential and smoother as it grows.
`scale`	The length scale, a time for a datetime or timedelta level, else in the levels' units (km on the Earth).
`within`	The levels on which two labels must be the same to be correlated (`"time.hour"` is an attribute of a datetime level).

Methods

correlation(coords)

Return the correlation between the rows of coords, zero between groups (see CorrelationModel.correlation()).

Inherited

From CorrelationModel: levels, with_std