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

.. currentmodule:: lsqfitgp

.. _kernels:

Predefined kernels
==================

This is a list of all the specific kernels implemented in `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
`CrossKernel` (or their specific superclass), while there are no positional
arguments when instantiating the kernel and the call signature of instances is
always `x`, `y`.

Example: the kernel `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.

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
`Constant`.

.. warning::

   You may encounter problems with second derivatives for `CausalExpQuad`,
   `FracBrownian`, `NNKernel`, and with first derivatives too for `Wendland`
   (but only in more than one dimension). :class:`Color` stops working for
   :math:`n > 20`.

Index
-----

Isotropic kernels
^^^^^^^^^^^^^^^^^
  * :class:`Bessel`
  * :class:`Cauchy`
  * :class:`CausalExpQuad`
  * :class:`Constant`
  * :class:`ExpQuad`
  * :class:`GammaExp`
  * :class:`Log`
  * :class:`Matern`
  * :class:`Maternp`
  * :class:`Wendland`
  * :class:`White`

Stationary kernels
^^^^^^^^^^^^^^^^^^
  * :class:`AR`
  * :class:`Celerite`
  * :class:`Circular`
  * :class:`Color`
  * :class:`Cos`
  * :class:`Expon`
  * :class:`Harmonic`
  * :class:`HoleEffect`
  * :class:`MA`
  * :class:`Periodic`
  * :class:`Pink`
  * :class:`Sinc`
  * :class:`StationaryFracBrownian`
  * :class:`Zeta`

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

Documentation
-------------
.. autoclass:: AR(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/AR.png
.. image:: kernelsref/AR-samples.png
.. autoclass:: BART(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/BART.png
.. image:: kernelsref/BART-samples.png
.. autoclass:: BagOfWords(**kw)
    :members:
    :class-doc-from: class
.. autoclass:: Bessel(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Bessel.png
.. image:: kernelsref/Bessel-samples.png
.. autoclass:: BrownianBridge(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/BrownianBridge.png
.. image:: kernelsref/BrownianBridge-samples.png
.. autoclass:: Categorical(**kw)
    :members:
    :class-doc-from: class
.. autoclass:: Cauchy(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Cauchy.png
.. image:: kernelsref/Cauchy-samples.png
.. autoclass:: CausalExpQuad(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/CausalExpQuad.png
.. image:: kernelsref/CausalExpQuad-samples.png
.. autoclass:: Celerite(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Celerite.png
.. image:: kernelsref/Celerite-samples.png
.. autoclass:: Circular(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Circular.png
.. image:: kernelsref/Circular-samples.png
.. autoclass:: Color(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Color.png
.. image:: kernelsref/Color-samples.png
.. autoclass:: Constant(**kw)
    :members:
    :class-doc-from: class
.. autoclass:: Cos(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Cos.png
.. image:: kernelsref/Cos-samples.png
.. autoclass:: Decaying(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Decaying.png
.. image:: kernelsref/Decaying-samples.png
.. autoclass:: ExpQuad(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/ExpQuad.png
.. image:: kernelsref/ExpQuad-samples.png
.. autoclass:: Expon(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Expon.png
.. image:: kernelsref/Expon-samples.png
.. autoclass:: FracBrownian(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/FracBrownian.png
.. image:: kernelsref/FracBrownian-samples.png
.. autoclass:: GammaExp(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/GammaExp.png
.. image:: kernelsref/GammaExp-samples.png
.. autoclass:: Gibbs(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Gibbs.png
.. image:: kernelsref/Gibbs-samples.png
.. autoclass:: Harmonic(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Harmonic.png
.. image:: kernelsref/Harmonic-samples.png
.. autoclass:: HoleEffect(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/HoleEffect.png
.. image:: kernelsref/HoleEffect-samples.png
.. autoclass:: Linear(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Linear.png
.. image:: kernelsref/Linear-samples.png
.. autoclass:: Log(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Log.png
.. image:: kernelsref/Log-samples.png
.. autoclass:: MA(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/MA.png
.. image:: kernelsref/MA-samples.png
.. autoclass:: Matern(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Matern.png
.. image:: kernelsref/Matern-samples.png
.. autoclass:: Maternp(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Maternp.png
.. image:: kernelsref/Maternp-samples.png
.. autoclass:: NNKernel(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/NNKernel.png
.. image:: kernelsref/NNKernel-samples.png
.. autoclass:: OrnsteinUhlenbeck(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/OrnsteinUhlenbeck.png
.. image:: kernelsref/OrnsteinUhlenbeck-samples.png
.. autoclass:: Periodic(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Periodic.png
.. image:: kernelsref/Periodic-samples.png
.. autoclass:: Pink(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Pink.png
.. image:: kernelsref/Pink-samples.png
.. autoclass:: Rescaling(**kw)
    :members:
    :class-doc-from: class
.. autoclass:: Sinc(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Sinc.png
.. image:: kernelsref/Sinc-samples.png
.. autoclass:: StationaryFracBrownian(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/StationaryFracBrownian.png
.. image:: kernelsref/StationaryFracBrownian-samples.png
.. autoclass:: Taylor(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Taylor.png
.. image:: kernelsref/Taylor-samples.png
.. autoclass:: Wendland(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Wendland.png
.. image:: kernelsref/Wendland-samples.png
.. autoclass:: White(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/White.png
.. image:: kernelsref/White-samples.png
.. autoclass:: Wiener(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Wiener.png
.. image:: kernelsref/Wiener-samples.png
.. autoclass:: WienerIntegral(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/WienerIntegral.png
.. image:: kernelsref/WienerIntegral-samples.png
.. autoclass:: Zeta(**kw)
    :members:
    :class-doc-from: class
.. image:: kernelsref/Zeta.png
.. image:: kernelsref/Zeta-samples.png