def cosine_kernel(x):
'''
Raised cosine basis kernel, normalized such that it integrates to 1
centered at zero. Time is rescaled so that the kernel spans from
-2 to 2
Parameters
----------
x : vector
Returns
-------
vector
$\\tfrac 1 4 + \\tfrac 1 2 cos(x)$ if $x\in[-\pi,\pi]$, otherwise 0.
'''
x = np.float64(np.abs(x))/2.0*np.pi
return np.piecewise(x,[x<=np.pi],[lambda x:(np.cos(x)+1)/4.0])
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