.. file generated automatically by lsqfitgp/docs/kernelsref.py

.. currentmodule:: lsqfitgp

.. _kernels:

Kernels reference
=================

This is a list of all the specific kernels implemented in :mod:`lsqfitgp`.

Kernels are reported with a simplified signature where the positional arguments
are `r` or `r2` if the kernel is isotropic, `delta` if it is stationary, or
`x`, `y` for generic kernels, and with only the keyword arguments specific to
the kernel. All kernels also understand the general keyword arguments of
:class:`Kernel` or :class:`IsotropicKernel`, while there are no positional
arguments when instantiating the kernel and the call signature of instances is
always `x`, `y`.

Example: the kernel :class:`GammaExp` is listed as ``GammaExp(r, gamma=1)``.
This means you could use it this way::

    import lsqfitgp as lgp
    import numpy as np
    kernel = lgp.GammaExp(loc=0.3, scale=2, gamma=1.4)
    x = np.random.randn(100)
    covmat = kernel(x[:, None], x[None, :])

On multidimensional input, isotropic kernels will compute the euclidean
distance. In general non-isotropic kernels will act separately on each
dimension, i.e., :math:`k(x_1,y_1,x_2,y_2) = k(x_1,y_1) k(x_2,y_2)`, apart from
kernels defined in terms of the dot product.

For all isotropic and stationary (i.e., depending only on :math:`x - y`)
kernels :math:`k(x, x) = 1`, and the typical lengthscale is approximately 1 for
default values of the keyword parameters, apart from some specific cases like
:class:`Constant`.

.. warning::

   Taking second or higher order derivatives might give problems with isotropic
   kernels with signature parameter `r`, while those with `r2` won't have any
   issue.

Index
-----

Isotropic kernels
^^^^^^^^^^^^^^^^^
  * :func:`Constant`
  * :func:`ExpQuad`
  * :func:`GammaExp`
  * :func:`Matern`
  * :func:`Matern12`
  * :func:`Matern32`
  * :func:`Matern52`
  * :func:`PPKernel`
  * :func:`RatQuad`
  * :func:`White`

Stationary kernels
^^^^^^^^^^^^^^^^^^
  * :func:`Celerite`
  * :func:`Cos`
  * :func:`Expon`
  * :func:`Fourier`
  * :func:`Harmonic`
  * :func:`Periodic`

Other kernels
^^^^^^^^^^^^^
  * :func:`BagOfWords`
  * :func:`BrownianBridge`
  * :func:`Categorical`
  * :func:`FracBrownian`
  * :func:`Gibbs`
  * :func:`Linear`
  * :func:`NNKernel`
  * :func:`OrnsteinUhlenbeck`
  * :func:`Rescaling`
  * :func:`Taylor`
  * :func:`Wiener`
  * :func:`WienerIntegral`

Documentation
-------------
.. autofunction:: BagOfWords
.. autofunction:: BrownianBridge
.. autofunction:: Categorical
.. autofunction:: Celerite
.. autofunction:: Constant
.. autofunction:: Cos
.. autofunction:: ExpQuad
.. autofunction:: Expon
.. autofunction:: Fourier
.. autofunction:: FracBrownian
.. autofunction:: GammaExp
.. autofunction:: Gibbs
.. autofunction:: Harmonic
.. autofunction:: Linear
.. autofunction:: Matern
.. autofunction:: Matern12
.. autofunction:: Matern32
.. autofunction:: Matern52
.. autofunction:: NNKernel
.. autofunction:: OrnsteinUhlenbeck
.. autofunction:: PPKernel
.. autofunction:: Periodic
.. autofunction:: RatQuad
.. autofunction:: Rescaling
.. autofunction:: Taylor
.. autofunction:: White
.. autofunction:: Wiener
.. autofunction:: WienerIntegral