Fix RBF kernel length scale calculation

This commit fixes the implementation of the RBF kernel function to correctly match the standard mathematical definition. Previously, the length scale parameter ls was used without squaring, resulting in a kernel formula of exp(- (1/(2*ls)) * ||x1 - x2||^2 ). The corrected implementation now uses ls**2 in the denominator, so the kernel is computed as exp(- (1/(2*ls**2)) * ||x1 - x2||^2 ), which is consistent with the conventional RBF kernel definition.

Author: whiteode

chapter_gaussian-processes/gp-priors.md

@@ -117,7 +117,7 @@ We illustrate this process in the figure below.
 ```{.python .input}
 def rbfkernel(x1, x2, ls=4.):  #@save
     dist = distance_matrix(np.expand_dims(x1, 1), np.expand_dims(x2, 1))
-    return np.exp(-(1. / ls / 2) * (dist ** 2))
+    return np.exp(-(1. / ls**2 / 2) * (dist ** 2))
 
 x_points = np.linspace(0, 5, 50)
 meanvec = np.zeros(len(x_points))