fixed_rbf.py

from scipy.spatial.distance import cdist
import numpy as np
import matplotlib.pyplot as plt

# First write a covariance function. e.g. rbf
def radial_basis_kernel(x1, x2, varSigma, lengthScale):
    if x2 is None:
        d = cdist(x1, x1)
    else:
        d = cdist(x1, x2)
    s = -np.power(d, 2) / lengthScale
    
    return varSigma * np.exp(s)


# Then sample GP prior
# first, functions with one-dimensional inputs, so the infinite process indexed by reals

# choose index set for the marginal
N = 200
x = np.linspace(-6, 6, N).reshape(-1, 1)

# compute covariance matrix
sigmaSq = 2.0
scale = 1.0
K = rbf_kernel(x, None, sigmaSq, scale)

# create mean vector
mu = np.zeros(x.shape[0])#.reshape(1, 200)

# draw samples 20 from Gaussian distribution
sampleN = 20
f = np.random.multivariate_normal(mu, K, sampleN)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, f.T)
plt.show()