def pair_eval(self, X, Y):
"""Evaluate k(x1, y1), k(x2, y2), ..."""
sigma2s = self.sigma2s
Xs = old_div(X, np.sqrt(sigma2s))
Ys = old_div(Y, np.sqrt(sigma2s))
k = KGauss(1.0)
return k.pair_eval(Xs, Ys)
def eval(self, X, Y):
"""
Equivalent to dividing each dimension with the corresponding width (not
width^2) and using the standard Gaussian kernel.
"""
sigma2s = self.sigma2s
Xs = old_div(X, np.sqrt(sigma2s))
Ys = old_div(Y, np.sqrt(sigma2s))
k = KGauss(1.0)
return k.eval(Xs, Ys)
def pair_gradXY_sum(self, X, Y):
"""
Compute \sum_{i=1}^d \frac{\partial^2 k(X, Y)}{\partial x_i \partial y_i}
evaluated at each x_i in X, and y_i in Y.
X: n x d numpy array.
Y: n x d numpy array.
Return a one-dimensional length-n numpy array of the derivatives.
"""
d = X.shape[1]
sigma2 = self.sigma2
D2 = np.sum((X - Y)**2, 1)
Kvec = np.exp(old_div(-D2, (2.0 * self.sigma2)))
G = Kvec / sigma2 * (d - old_div(D2, sigma2))
return G
def gradXY_sum(self, X, Y):
r"""
Compute \sum_{i=1}^d \frac{\partial^2 k(X, Y)}{\partial x_i \partial y_i}
evaluated at each x_i in X, and y_i in Y.
X: nx x d numpy array.
Y: ny x d numpy array.
Return a nx x ny numpy array of the derivatives.
"""
(n1, d1) = X.shape
(n2, d2) = Y.shape
assert d1==d2, 'Dimensions of the two inputs must be the same'
d = d1
sigma2 = self.sigma2
D2 = np.sum(X**2, 1)[:, np.newaxis] - 2*np.dot(X, Y.T) + np.sum(Y**2, 1)
K = np.exp(old_div(-D2,(2.0*sigma2)))
G = K/sigma2*(d - old_div(D2,sigma2))
return G
def pair_eval(self, X, Y):
"""
Evaluate k(x1, y1), k(x2, y2), ...
Parameters
----------
X, Y : n x d numpy array
Return
-------
a numpy array with length n
"""
(n1, d1) = X.shape
(n2, d2) = Y.shape
assert n1 == n2, 'Two inputs must have the same number of instances'
assert d1 == d2, 'Two inputs must have the same dimension'
D2 = np.sum((X - Y)**2, 1)
Kvec = np.exp(old_div(-D2, (2.0 * self.sigma2)))
return Kvec
def eval(self, X, Y):
"""
Evaluate the Gaussian kernel on the two 2d numpy arrays.
Parameters
----------
X : n1 x d numpy array
Y : n2 x d numpy array
Return
------
K : a n1 x n2 Gram matrix.
"""
#(n1, d1) = X.shape
#(n2, d2) = Y.shape
#assert d1==d2, 'Dimensions of the two inputs must be the same'
sumx2 = np.reshape(np.sum(X**2, 1), (-1, 1))
sumy2 = np.reshape(np.sum(Y**2, 1), (1, -1))
D2 = sumx2 - 2 * np.dot(X, Y.T) + sumy2
K = np.exp(old_div(-D2, (2.0 * self.sigma2)))
return K