from __future__ import absolute_import, division, print_function
__doc__ = """
.. autofunction:: generate_list1_gallery
"""
__copyright__ = "Copyright (C) 2017 - 2018 Xiaoyu Wei"
__license__ = """
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
import numpy as np
# {{{ TreeBox class
class TreeBox:
"""
A minimalistic tree class.
Courtesy of: Andreas Klockner
"""
def __init__(self, center, radius, child_nlevels):
self.center = center
self.radius = radius
self.children = []
if child_nlevels:
child_radius = radius // 2
assert child_radius
dimensions = len(center)
for i in range(2 ** dimensions):
child_center = center.copy()
for idim in range(dimensions):
# 1 if that dimension bit is set, 0 if not
dim_indicator = int(bool(i & 1 << idim))
child_center[idim] += (2 * dim_indicator - 1) * child_radius
self.children.append(
TreeBox(child_center, child_radius, child_nlevels - 1)
)
def draw(self):
lx, ly = self.center - self.radius * 0.95
hx, hy = self.center + self.radius * 0.95
import matplotlib.pyplot as plt
plt.plot([lx, lx, hx, hx, lx], [ly, hy, hy, ly, ly])
# }}} End TreeBox class
def build_tree(dimensions):
"""
Courtesy of: Andreas Klockner
"""
# four levels deep
# -> centers on a 2**4 x 2**4 grid
nlevels = 4
root_radius = 2 ** (nlevels - 1)
root = TreeBox(
center=np.array(dimensions * [root_radius], np.int),
radius=root_radius,
child_nlevels=nlevels - 1,
)
return root
def generate_boxes_on_level(box, ilevel):
"""
Courtesy of: Andreas Klockner
"""
if ilevel:
for child in box.children:
for result in generate_boxes_on_level(child, ilevel - 1):
yield result
else:
yield box
def generate_boxes(box):
"""
Courtesy of: Andreas Klockner
"""
yield box
for child in box.children:
for result in generate_boxes(child):
yield result
def linf_dist(box1, box2):
"""
Courtesy of: Andreas Klockner
"""
return np.max(np.abs(box1.center - box2.center) - (box1.radius + box2.radius))
def generate_interactions(dimensions):
"""
Courtesy of: Andreas Klockner
"""
root = build_tree(dimensions)
root_radius = root.radius
min_cutoff = root_radius >> 2
max_cutoff = 2 * root_radius - min_cutoff
target_boxes = [
box
for box in generate_boxes_on_level(root, 2)
if np.min(box.center) > min_cutoff and np.max(box.center) < max_cutoff
]
near_neighbor_interactions = [
(tbox, sbox)
for tbox in target_boxes
for sbox in generate_boxes(root)
if linf_dist(tbox, sbox) == 0
]
if 0:
import matplotlib.pyplot as plt
for tbox, sbox in near_neighbor_interactions:
plt.figure()
plt.gca().set_aspect("equal")
tbox.draw()
sbox.draw()
return near_neighbor_interactions
def postprocess_interactions(near_neighbor_interactions):
unique_interaction_vectors = set()
for (tbox, sbox) in near_neighbor_interactions:
unique_interaction_vectors.add(tuple(tbox.center - sbox.center))
# Add interactions within the same box
tb0, wb0 = near_neighbor_interactions[0]
unique_interaction_vectors.add(tuple(tb0.center - tb0.center))
list1_interactions = sorted(list(unique_interaction_vectors))
return list1_interactions
[docs]def generate_list1_gallery(dim):
"""Generate a *list1* that servers as the gallery for all possible *list1*
interactions with given dimension and order.
"""
# contains each sourcebox.center-to-targetbox.center vector
# source box is 4x4 to make all involved lengths to be integers
vec_list = postprocess_interactions(generate_interactions(dim))
distinct_numbers = set()
for vec in vec_list:
for cvc in vec:
distinct_numbers.add(cvc)
# contains a lookup table for case indices
base = len(range(min(distinct_numbers), max(distinct_numbers) + 1))
case_indices = -np.ones(base ** dim, dtype=int)
shift = -min(distinct_numbers)
def case_encode(case_vec):
table_id = 0
for cvc in case_vec:
table_id = table_id * base + (cvc + shift)
return int(table_id)
case_id = 0
for vec in vec_list:
case_indices[case_encode(vec)] = case_id
case_id += 1
assert len(vec_list) == case_id
return (vec_list, case_encode, case_indices)
# vim: ft=pyopencl:fdm=marker