wavy.GPfcts
===========

.. py:module:: wavy.GPfcts


Functions
---------

.. autoapisummary::

   wavy.GPfcts.kernel
   wavy.GPfcts.posterior_predictive_nigp
   wavy.GPfcts.nll_fn_nigp


Module Contents
---------------

.. py:function:: kernel(X1, X2, l=1.0, sigma_f=1.0)

   Isotropic squared exponential kernel. Computes
   a covariance matrix from points in X1 and X2.
   Args:
       X1: Array of m points (m x d).
       X2: Array of n points (n x d).
   Returns:
       Covariance matrix (m x n).


.. py:function:: posterior_predictive_nigp(X_s, X_train, Y_train, l=None, sigma_f=None, sigma_y=None, sigma_x=None, Grad_fmean=None)

   Computes statistics of the GP posterior predictive distribution
   from m training data X_train and Y_train and n new inputs X_s.
   Args:
       X_s: New input locations (n x d)
       X_train: Training locations (m x d)
       Y_train: Training targets (m x 1)
       l: length scale parameter
       sigma_f: signal variance parameter
       sigma_y: noise paramter on y
       sigma_x: noise parameter on x
   Returns:
       Posterior mean vector (n x d) and covariance matrix (n x n)


.. py:function:: nll_fn_nigp(X_train, Y_train, Grad_fmean, naive=False)

   Returns a function that computes the negative log marginal
   likelihood for training data X_train and Y_train and given
   noise level.
   Args:
       X_train: training locations (m x d).
       Y_train: training targets (m x 1).
       noise: known noise level of Y_train.
       naive: if True use a naive implementation of Eq. (7), if
              False use a numerically more stable implementation.
   Returns:
       Minimization objective.