def cross_cov_grad_data(self, inputs_1, inputs_2):
# NOTE: This is the gradient wrt the inputs of inputs_2
# The gradient wrt the inputs of inputs_1 is -1 times this
r2 = np.abs(kernel_utils.dist2(self.ls.value, inputs_1, inputs_2))
r = np.sqrt(r2)
grad_r2 = (5.0/6.0)*np.exp(-SQRT_5*r)*(1 + SQRT_5*r)
return grad_r2[:,:,np.newaxis] * kernel_utils.grad_dist2(self.ls.value, inputs_1, inputs_2)
def cross_cov_grad_data(self, inputs_1, inputs_2):
# NOTE: This is the gradient wrt the inputs of inputs_2
# The gradient wrt the inputs of inputs_1 is -1 times this
r2 = np.abs(kernel_utils.dist2(self.ls.value, inputs_1, inputs_2))
r = np.sqrt(r2)
grad_K_r2 = np.exp(-0.5 * r2) * (-r)
grad_r2_x1 = kernel_utils.grad_dist2(self.ls.value, inputs_1, inputs_2)
grad_r2_x2 = -grad_r2_x1
return grad_K_r2[:, :, None] * grad_r2_x2
def cross_cov_grad_data(self, inputs_1, inputs_2):
# NOTE: This is the gradient wrt the inputs of inputs_2
# The gradient wrt the inputs of inputs_1 is -1 times this
# This is sloppily coded -- the gradient that comes from kernel_utils is w.r.t. inputs_1
# but a minus sign is dropped to make it w.r.t. inputs_2
# oh well...
r2 = np.abs(kernel_utils.dist2(self.ls.value, inputs_1, inputs_2))
r = np.sqrt(r2)
grad_r2 = (5.0 / 6.0) * np.exp(-SQRT_5 * r) * (1 + SQRT_5 * r)
return grad_r2[:, :, np.newaxis] * kernel_utils.grad_dist2(
self.ls.value, inputs_1, inputs_2)
def cross_cov(self, inputs_1, inputs_2):
r2 = np.abs(kernel_utils.dist2(self.ls.value, inputs_1, inputs_2))
cov = np.exp(-0.5 * r2)
return cov
def cross_cov(self, inputs_1, inputs_2):
r2 = np.abs(kernel_utils.dist2(self.ls.value, inputs_1, inputs_2))
r = np.sqrt(r2)
cov = (1.0 + SQRT_5 * r + (5.0 / 3.0) * r2) * np.exp(-SQRT_5 * r)
return cov
def cross_cov(self, inputs_1, inputs_2):
r2 = np.abs(kernel_utils.dist2(self.ls.value, inputs_1, inputs_2))
r = np.sqrt(r2)
cov = (1.0 + SQRT_5*r + (5.0/3.0)*r2) * np.exp(-SQRT_5*r)
return cov