GPy Kernel Cheatsheet:: All the kernels in GPy (example realizations, covariance matrix, kernel equation)

gpy_kernel_cheatsheet.py

%pylab inline
import numpy as np
import pylab as plt
import GPy
import re

def get_equation(kern):
    match = re.search(r'(math::)(\r\n|\r|\n)*(?P<equation>.*)(\r\n|\r|\n)*', kern.__doc__)
    return '' if match is None else match.group('equation').strip()

for kernel_name in dir(GPy.kern):
    Kernel = getattr(GPy.kern, kernel_name)
    
    if Kernel.__class__ == GPy.kern.Exponential.__class__ == GPy.kern._src.kernel_slice_operations.KernCallsViaSlicerMeta:        
        # Try plotting sample paths here
        try:
            k = Kernel(input_dim=1)
            
            X = np.linspace(0.,1.,500) # define X to be 500 points evenly spaced over [0,1]
            X = X[:,None] # reshape X to make it n*p --- we try to use 'design matrices' in GPy 

            mu = np.zeros((500))# vector of the means --- we could use a mean function here, but here it is just zero.
            C = k.K(X,X) # compute the covariance matrix associated with inputs X

            # Generate 20 separate samples paths from a Gaussian with mean mu and covariance C
            Z = np.random.multivariate_normal(mu,C,20)

                        
            kernel_equation = get_equation(k)
            #print kernel_equation
            from IPython.display import Math, display
            display(Math(kernel_equation))
            
            fig = plt.figure()     # open a new plotting window
            plt.subplot(121)
            for i in range(3):
                plt.plot(X[:],Z[i,:])

            plt.title('{} samples'.format(kernel_name))
            
            plt.subplot(122)
            plt.imshow(C, interpolation='nearest')
            plt.title('{} covariance'.format(kernel_name))
        except:
            continue