small fixes in the kernel documentation

This commit is contained in:
Nicolas 2013-01-31 17:36:01 +00:00
parent 160568c727
commit 666f334a67
4 changed files with 4 additions and 4 deletions

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@ -14,7 +14,7 @@ class Matern32(kernpart):
.. math::
k(r) = \sigma^2 (1 + \sqrt{3} r) \exp(- \sqrt{3} r) \\qquad \\qquad \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
k(r) = \sigma^2 (1 + \sqrt{3} r) \exp(- \sqrt{3} r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
:param D: the number of input dimensions
:type D: int

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@ -13,7 +13,7 @@ class Matern52(kernpart):
.. math::
k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r) \\qquad \\qquad \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
:param D: the number of input dimensions
:type D: int

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@ -13,7 +13,7 @@ class exponential(kernpart):
.. math::
k(r) = \sigma^2 \exp(- r) \\qquad \\qquad \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
k(r) = \sigma^2 \exp(- r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
:param D: the number of input dimensions
:type D: int

View file

@ -12,7 +12,7 @@ class rbf(kernpart):
.. math::
k(r) = \sigma^2 \exp(- \frac{1}{2}r^2) \\qquad \\qquad \\text{ where } r^2 = \sum_{i=1}^d \frac{ (x_i-x^\prime_i)^2}{\ell_i^2}}
k(r) = \sigma^2 \exp(- \frac{1}{2}r^2) \ \ \ \ \ \\text{ where } r^2 = \sum_{i=1}^d \frac{ (x_i-x^\prime_i)^2}{\ell_i^2}}
where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input.