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fixed docstring and added more explanation

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Eric Kalosa-Kenyon 2020-01-08 16:09:59 -08:00
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commit c58104c943
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17
doc/source/tuto_creating_new_kernels.rst
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@ -173,16 +173,23 @@ is set to each ``param``. ::
This function is required for GPLVM, BGPLVM, sparse models and uncertain inputs.
Computes the derivative of the likelihood with respect to the inputs
``X`` (a :math:`n \times q` np.array). The result is returned by the
function which is a :math:`n \times q` np.array. ::
``X`` (a :math:`n \times q` np.array), that is, it calculates the quantity:
.. math::
\frac{\partial L}{\partial K} \frac{\partial K}{\partial X}
The partial derivative matrix is, in this case, comes out as an :math:`n \times q` np.array.
Were the number of parameters to be larger than 1 or the number of dimensions likewise any larger
than 1, the calculated partial derivitive would be a 3- or 4-tensor. ::
def gradients_X(self,dL_dK,X,X2):
"""derivative of the covariance matrix with respect to X."""
"""derivative of the likelihood matrix with respect to X, calculated using dK_dX"""
if X2 is None: X2 = X
dist2 = np.square((X-X2.T)/self.lengthscale)
dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1)
return np.sum(dL_dK*dX,1)[:,None]
dK_dX = -self.variance*self.power * (X-X2.T)/self.lengthscale**2 * (1 + dist2/2./self.lengthscale)**(-self.power-1)
return np.sum(dL_dK*dK_dX,1)[:,None]
:py:func:`~GPy.kern.src.kern.Kern.gradients_X_diag` ``(self,dL_dKdiag,X)``
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~