Tile Coding Software

tiles.py

# tiles.py -- Tile Coding Software
# Copyright (C) <2018>  <Germano Gabbianelli>
#
# Based on Tiles3 by Richard S. Sutton:
#  http://incompleteideas.net/tiles/tiles3.html
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

import numpy as np

def tiles(a, n=None, d=None):
    a = np.expand_dims(np.atleast_2d(a), 1)
    k = a.shape[2] # number of dimensions

    if n is None:
        n = 4
        while n < 4 * k:
            n <<= 1 # same as * 2
    else:
        # n should be >= 4 * k
        n = int(n)

    if d is None:
        d = np.arange(1, k * 2, 2) # first k odd numbers
    else:
        d = np.asanyarray(d)

    a = np.floor(a * n)
    d = np.arange(n).reshape(-1, 1) * d
    return np.floor((a + d) / n)


def indices(a, min=0, max=1):
    a = np.atleast_3d(a)
    n = a.shape[1]
    k = a.shape[2]

    min = np.broadcast_to(min, k)
    max = np.broadcast_to(max, k)
    min, max = tiles([min, max], n)
    n_tiles = max - min + 1

    assert np.all(n_tiles == n_tiles[0])
    n_tiles = n_tiles[0]
    order = n_tiles.copy()
    order[1:] = order[:-1] # shift all elements 1 to the right
    order[0] = 1

    a = ((a - min) * np.cumprod(order)).sum(-1)

    idx = np.full(n, n_tiles.prod())
    idx[0] = 0
    idx = np.cumsum(idx)
    return a + idx