import tensorflow as tf

import numpy as np

from scipy.spatial.distance import pdist, cdist, squareform

def rbf(X, X2=None, lengthscale=1.0, variance=1.0):

lengthscale = tf.convert_to_tensor(lengthscale, tf.float64)

variance = tf.convert_to_tensor(variance, tf.float64)

X = tf.convert_to_tensor(X)

X = X / lengthscale

Xs = tf.reduce_sum(tf.square(X), 1)

if X2 is None:

X2 = X

X2s = Xs

else:

X2 = tf.convert_to_tensor(X2)

X2 = X2 / lengthscale

X2s = tf.reduce_sum(tf.square(X2), 1)

square = tf.reshape(Xs, [-1, 1]) + tf.reshape(X2s, [1, -1]) - \

2 * tf.matmul(X, X2, transpose_b=True)

output = variance * tf.exp(-square / 2)

return output

def RationalQuadratic(X, X2=None, lengthScale=0.5, alpha=0.1, variance=1.0):

lengthScale = tf.convert_to_tensor(lengthScale, tf.float64)

alpha = tf.convert_to_tensor(alpha, tf.float64)

X = tf.convert_to_tensor(X)

X = X / alpha

X = X / lengthScale

Xs = tf.reduce_sum(tf.square(X), 1)

if X2 is None:

X2 = X

X2s = Xs

else:

X2 = tf.convert_to_tensor(X2)

X2 = X2 / alpha

X2 = X2 / lengthScale

X2s = tf.reduce_sum(tf.square(X2), 1)

square = tf.reshape(Xs, [-1, 1]) + tf.reshape(X2s, [1, -1]) - 2 *\

tf.matmul(X, X2, transpose_b=True)

output = 1 + (square / 2)

K = variance * tf.pow(output, - alpha)

return K

def ExpSineSquared(X, Xs=None, lengthScale=0.5, period=8.0, sigma=1.0):

if Xs is None:

X = X.eval(session=tf.Session())

dists = squareform(pdist(X, metric='euclidean'))

arg = np.pi * dists / period

sin_arg = np.sin(arg)

K = np.exp(- 2 * (sin_arg / lengthScale) ** 2)

else:

X = X.eval(session=tf.Session())

Xs = Xs.eval(session=tf.Session())

dists = cdist(X, Xs, metric='euclidean')

K = np.exp(- 2 * (np.sin(np.pi / period * dists) / lengthScale) ** 2)

K = sigma * K

return tf.convert_to_tensor(K, tf.float64)