import numpy as np
from mushroom_rl.utils.features import uniform_grid
[docs]class GaussianRBF:
r"""
Class implementing Gaussian radial basis functions. The value of the feature is computed using the formula:
.. math::
\sum \dfrac{(X_i - \mu_i)^2}{\sigma_i}
where X is the input, \mu is the mean vector and \sigma is the scale parameter vector.
"""
[docs] def __init__(self, mean, scale, dimensions=None):
"""
Constructor.
Args:
mean (np.ndarray): the mean vector of the feature;
scale (np.ndarray): the scale vector of the feature;
dimensions (list, None): list of the dimensions of the input to be considered by the feature. The number of
dimensions must match the dimensionality of ``mean`` and ``scale``.
"""
self._mean = mean
self._scale = scale
self._dim = dimensions
[docs] def __call__(self, x):
if self._dim is not None:
x = x[self._dim]
return np.exp(-np.sum((x - self._mean)**2 / self._scale))
def __str__(self):
name = 'GaussianRBF ' + str(self._mean) + ' ' + str(self._scale)
if self._dim is not None:
name += ' ' + str(self._dim)
return name
[docs] @staticmethod
def generate(n_centers, low, high, dimensions=None, eta=0.25):
r"""
Factory method to build uniformly spaced gaussian radial basis functions with `eta` overlap.
Args:
n_centers (list): list of the number of radial basis functions to be used for each dimension.
low (np.ndarray): lowest value for each dimension;
high (np.ndarray): highest value for each dimension;
dimensions (list, None): list of the dimensions of the input to be considered by the feature. The number of
dimensions must match the number of elements in ``n_centers`` and ``low``;
eta (float, 0.25): percentage of overlap between the features.
Returns:
The list of the generated radial basis functions.
"""
n_features = len(low)
assert len(n_centers) == n_features
assert len(low) == len(high)
assert dimensions is None or n_features == len(dimensions)
grid, w = uniform_grid(n_centers, low, high, eta)
b = 2*(w/3)**2
basis = list()
for i in range(len(grid)):
v = grid[i, :]
bf = GaussianRBF(v, b, dimensions)
basis.append(bf)
return basis