.. 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 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 :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::

   You may encounter problems with second derivatives for
   :class:`CausalExpQuad`, :class:`FracBrownian`, :class:`NNKernel`,
   :class:`Taylor`, and with first derivatives too for :class:`Wendland` (but
   only in more than one dimension). :class:`Color` stops working for :math:`n
   > 20`. The following kernels are not compatible with the JAX JIT:
   :class:`Bessel`, :class:`Matern`, :class:`Taylor`.

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:`Fourier`
  * :class:`Harmonic`
  * :class:`HoleEffect`
  * :class:`MA`
  * :class:`Periodic`
  * :class:`Pink`
  * :class:`Sinc`
  * :class:`StationaryFracBrownian`

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(delta, phi=None, gamma=None, maxlag=None, slnr=None, lnc=None, norm=False)
    :members:
    :class-doc-from: class
.. image:: kernelsref-AR.png
.. image:: kernelsref-AR-samples.png
.. autoclass:: BART(x, y, alpha=0.95, beta=2, maxd=2, splits=None)
    :members:
    :class-doc-from: class
.. image:: kernelsref-BART.png
.. image:: kernelsref-BART-samples.png
.. autoclass:: BagOfWords(x, y)
    :members:
    :class-doc-from: class
.. autoclass:: Bessel(r2, nu=0)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Bessel.png
.. image:: kernelsref-Bessel-samples.png
.. autoclass:: BrownianBridge(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-BrownianBridge.png
.. image:: kernelsref-BrownianBridge-samples.png
.. autoclass:: Categorical(x, y, cov=None)
    :members:
    :class-doc-from: class
.. autoclass:: Cauchy(r2, alpha=2, beta=2)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Cauchy.png
.. image:: kernelsref-Cauchy-samples.png
.. autoclass:: CausalExpQuad(r, alpha=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-CausalExpQuad.png
.. image:: kernelsref-CausalExpQuad-samples.png
.. autoclass:: Celerite(delta, gamma=1, B=0)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Celerite.png
.. image:: kernelsref-Celerite-samples.png
.. autoclass:: Circular(delta, tau=4, c=0.5)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Circular.png
.. image:: kernelsref-Circular-samples.png
.. autoclass:: Color(delta, n=2)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Color.png
.. image:: kernelsref-Color-samples.png
.. autoclass:: Constant(x, y)
    :members:
    :class-doc-from: class
.. autoclass:: Cos(delta)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Cos.png
.. image:: kernelsref-Cos-samples.png
.. autoclass:: Decaying(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Decaying.png
.. image:: kernelsref-Decaying-samples.png
.. autoclass:: ExpQuad(r2)
    :members:
    :class-doc-from: class
.. image:: kernelsref-ExpQuad.png
.. image:: kernelsref-ExpQuad-samples.png
.. autoclass:: Expon(delta)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Expon.png
.. image:: kernelsref-Expon-samples.png
.. autoclass:: Fourier(delta, n=2)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Fourier.png
.. image:: kernelsref-Fourier-samples.png
.. autoclass:: FracBrownian(x, y, H=0.5, K=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-FracBrownian.png
.. image:: kernelsref-FracBrownian-samples.png
.. autoclass:: GammaExp(r2, gamma=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-GammaExp.png
.. image:: kernelsref-GammaExp-samples.png
.. autoclass:: Gibbs(x, y, scalefun=<function <lambda> at 0x130bc8670>)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Gibbs.png
.. image:: kernelsref-Gibbs-samples.png
.. autoclass:: Harmonic(delta, Q=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Harmonic.png
.. image:: kernelsref-Harmonic-samples.png
.. autoclass:: HoleEffect(delta)
    :members:
    :class-doc-from: class
.. image:: kernelsref-HoleEffect.png
.. image:: kernelsref-HoleEffect-samples.png
.. autoclass:: Linear(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Linear.png
.. image:: kernelsref-Linear-samples.png
.. autoclass:: Log(r)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Log.png
.. image:: kernelsref-Log-samples.png
.. autoclass:: MA(delta, w=None)
    :members:
    :class-doc-from: class
.. image:: kernelsref-MA.png
.. image:: kernelsref-MA-samples.png
.. autoclass:: Matern(r2, nu=None)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Matern.png
.. image:: kernelsref-Matern-samples.png
.. autoclass:: Maternp(r2, p=None)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Maternp.png
.. image:: kernelsref-Maternp-samples.png
.. autoclass:: NNKernel(x, y, sigma0=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-NNKernel.png
.. image:: kernelsref-NNKernel-samples.png
.. autoclass:: OrnsteinUhlenbeck(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-OrnsteinUhlenbeck.png
.. image:: kernelsref-OrnsteinUhlenbeck-samples.png
.. autoclass:: Periodic(delta, outerscale=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Periodic.png
.. image:: kernelsref-Periodic-samples.png
.. autoclass:: Pink(delta, dw=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Pink.png
.. image:: kernelsref-Pink-samples.png
.. autoclass:: Rescaling(x, y, stdfun=None)
    :members:
    :class-doc-from: class
.. autoclass:: Sinc(delta)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Sinc.png
.. image:: kernelsref-Sinc-samples.png
.. autoclass:: StationaryFracBrownian(delta, H=0.5)
    :members:
    :class-doc-from: class
.. image:: kernelsref-StationaryFracBrownian.png
.. image:: kernelsref-StationaryFracBrownian-samples.png
.. autoclass:: Taylor(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Taylor.png
.. image:: kernelsref-Taylor-samples.png
.. autoclass:: Wendland(r, k=0, alpha=1)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Wendland.png
.. image:: kernelsref-Wendland-samples.png
.. autoclass:: White(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-White.png
.. image:: kernelsref-White-samples.png
.. autoclass:: Wiener(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-Wiener.png
.. image:: kernelsref-Wiener-samples.png
.. autoclass:: WienerIntegral(x, y)
    :members:
    :class-doc-from: class
.. image:: kernelsref-WienerIntegral.png
.. image:: kernelsref-WienerIntegral-samples.png