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Small tweaks to Matern Covariance Documentation #7859

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Jul 22, 2025
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Small tweaks to Matern Covariance Documentation #7859

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matern doc
elc45 Jul 20, 2025
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elc45 Jul 21, 2025
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32 changes: 30 additions & 2 deletions pymc/gp/cov.py
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Original file line number Diff line number Diff line change
Expand Up @@ -617,13 +617,27 @@ def full_from_distance(self, dist: TensorLike, squared: bool = False) -> TensorV

class Matern52(Stationary):
r"""
The Matern kernel with nu = 5/2.
The Matérn kernel with :math:`\nu = \frac{5}{2}`.

.. math::

k(x, x') = \left(1 + \frac{\sqrt{5(x - x')^2}}{\ell} +
\frac{5(x-x')^2}{3\ell^2}\right)
\mathrm{exp}\left[ - \frac{\sqrt{5(x - x')^2}}{\ell} \right]

Read more `here <https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function>`_.

Parameters
----------
input_dim : int
The number of input dimensions
ls : scalar or array, optional
Lengthscale parameter :math:`\ell`; if `input_dim` > 1, a list or array of scalars.
If `input_dim` == 1, a scalar.
ls_inv : scalar or array, optional
Inverse lengthscale :math:`1 / \ell`. One of `ls` or `ls_inv` must be provided.
active_dims : list of int, optional
The dimension(s) the covariance function operates on.
"""

def full_from_distance(self, dist: TensorLike, squared: bool = False) -> TensorVariable:
Expand Down Expand Up @@ -657,12 +671,26 @@ def power_spectral_density(self, omega: TensorLike) -> TensorVariable:

class Matern32(Stationary):
r"""
The Matern kernel with nu = 3/2.
The Matérn kernel with :math:`\nu = \frac{3}{2}`.

.. math::

k(x, x') = \left(1 + \frac{\sqrt{3(x - x')^2}}{\ell}\right)
\mathrm{exp}\left[ - \frac{\sqrt{3(x - x')^2}}{\ell} \right]

Read more `here <https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function>`_.

Parameters
----------
input_dim : int
The number of input dimensions
ls : scalar or array, optional
Lengthscale parameter :math:`\ell`; if `input_dim` > 1, a list or array of scalars.
If `input_dim` == 1, a scalar.
ls_inv : scalar or array, optional
Inverse lengthscale :math:`1 / \ell`. One of `ls` or `ls_inv` must be provided.
active_dims : list of int, optional
The dimension(s) the covariance function operates on.
"""

def full_from_distance(self, dist: TensorLike, squared: bool = False) -> TensorVariable:
Expand Down