##### https://github.com/GPflow/GPflow
Tip revision: 2a30405
reference.py
``````import numpy as np

def ref_rbf_kernel(X, lengthscale, signal_var):
N, _ = X.shape
kernel = np.zeros((N, N))
for row_index in range(N):
for column_index in range(N):
vecA = X[row_index, :]
vecB = X[column_index, :]
delta = vecA - vecB
distance_squared = np.dot(delta.T, delta)
kernel[row_index, column_index] = \
signal_var * np.exp(-0.5 * distance_squared / lengthscale ** 2)
return kernel

def ref_arccosine_kernel(X, order, weightVariances, biasVariance, signal_var):
num_points = X.shape[0]
kernel = np.empty((num_points, num_points))
for row in range(num_points):
for col in range(num_points):
x = X[row]
y = X[col]

numerator = (weightVariances * x).dot(y) + biasVariance

x_denominator = np.sqrt((weightVariances * x).dot(x) +
biasVariance)
y_denominator = np.sqrt((weightVariances * y).dot(y) +
biasVariance)
denominator = x_denominator * y_denominator

theta = np.arccos(np.clip(numerator / denominator, -1., 1.))
if order == 0:
J = np.pi - theta
elif order == 1:
J = np.sin(theta) + (np.pi - theta) * np.cos(theta)
elif order == 2:
J = 3. * np.sin(theta) * np.cos(theta)
J += (np.pi - theta) * (1. + 2. * np.cos(theta)**2)

kernel[row, col] = signal_var * (1. / np.pi) * J * \
x_denominator ** order * \
y_denominator ** order
return kernel

def ref_periodic_kernel(X, lengthscale, signal_var, period):
# Based on the GPy implementation of standard_period kernel
base = np.pi * (X[:, None, :] - X[None, :, :]) / period
exp_dist = np.exp(-0.5 *
np.sum(np.square(np.sin(base) / lengthscale), axis=-1))
return signal_var * exp_dist
``````