Generate a random (noisy) draw from a Gaussian Process with a RBF kernel.

def gen_gausprocess_se(ntrain, ntest, noise=1., lenscale=1., scale=1.,
                       xmin=-10, xmax=10):
    """
    Generate a random (noisy) draw from a Gaussian Process with a RBF kernel.
    """

    # Xtrain = np.linspace(xmin, xmax, ntrain)[:, np.newaxis]
    Xtrain = np.random.rand(ntrain)[:, np.newaxis] * (xmin - xmax) - xmin
    Xtest = np.linspace(xmin, xmax, ntest)[:, np.newaxis]
    Xcat = np.vstack((Xtrain, Xtest))

    K = scale * np.exp(-cdist(Xcat, Xcat, metric='sqeuclidean') /
                       (2 * lenscale**2))
    U, S, V = np.linalg.svd(K)
    L = U.dot(np.diag(np.sqrt(S))).dot(V)
    f = np.random.randn(ntrain + ntest).dot(L)

    ytrain = f[0:ntrain] + np.random.randn(ntrain) * noise
    ftest = f[ntrain:]

    return Xtrain, ytrain, Xtest, ftest