Revision

**138cd0ccaea183c3b4c17c6bbeafbdf148521170**authored by James Hensman on**08 June 2017, 09:58:17 UTC**, committed by James Hensman on**08 June 2017, 09:58:17 UTC****1 parent**0b3ce9b

reference.py

```
import numpy as np
def referenceRbfKernel( X, lengthScale, signalVariance ):
(nDataPoints, inputDimensions ) = X.shape
kernel = np.zeros( (nDataPoints, nDataPoints ) )
for row_index in range( nDataPoints ):
for column_index in range( nDataPoints ):
vecA = X[row_index,:]
vecB = X[column_index,:]
delta = vecA - vecB
distanceSquared = np.dot( delta.T, delta )
kernel[row_index, column_index ] = signalVariance * np.exp( -0.5*distanceSquared / lengthScale** 2)
return kernel
def referenceArcCosineKernel( X, order, weightVariances, biasVariance, signalVariance ):
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) + (np.pi - theta) * (1. + 2. * np.cos(theta) ** 2)
kernel[row, col] = signalVariance * (1. / np.pi) * J * \
x_denominator ** order * \
y_denominator ** order
return kernel
def referencePeriodicKernel( X, lengthScale, signalVariance, 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 signalVariance * exp_dist
```

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