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GNU GENERAL PUBLIC LICENSE
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How to Apply These Terms to Your New Programs
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the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<https://www.gnu.org/licenses/why-not-lgpl.html>.

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README.md Normal file
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# packsim

3
build.sh Normal file
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cd src
python3 setup.py build_ext --inplace --quiet
mv *.so ../

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check_width_exists.py Normal file
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from pathlib import Path
import sys, numpy as np
def main():
n = int(sys.argv[1])
all_widths = set(np.round(np.arange(3, 10.05, 0.05), 2))
for file in Path(f"simulations/Radial[T]T - N{n}R4.0").iterdir():
i = file.name.index("x")
all_widths.remove(float(file.name[i-4:i]))
remain_widths = sorted(list(all_widths))[::-1]
print(remain_widths)
print([int(round((10-w)/.05)) for w in remain_widths])
if __name__ == "__main__":
main()

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packsim.py Normal file
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#!/usr/bin/env python3
from __future__ import annotations
import argparse, json
from simulation import Diagram, Flow, Search, Shrink
def get_diagram(sim, t):
if t == "flow":
diagram = Diagram(sim, np.array([["voronoi", "energy"]]))
elif t == "stats":
diagram = Diagram(sim, np.array([
["voronoi", "eigs", "site_edge_count"],
["site_isos", "site_energies", "edge_lengths"]
]), cumulative=False)
elif t == "eigs":
diagram = Diagram(sim, np.array([["voronoi", "eigs"]]))
elif t == "shrink":
diagram = Diagram(sim, np.array([["voronoi", "avg_radius", "isoparam_avg"]]), cumulative=False)
return diagram
def main():
# Loading configuration and settings.
parser = argparse.ArgumentParser("Processes packing simulations.")
parser.add_argument('sim_conf', metavar='path/to/config',
help="configuration file for a simulation")
parser.add_argument('-q', '--quiet', dest='quiet', action='store_true', default=False,
help="suppress all normal output")
parser.add_argument('-l', '--log', dest='log_steps', action='store_true', default=50,
help="number of iterations before logging")
parser.add_argument('-i', '--input', dest='input_file')
parser.add_argument('-o', '--output', dest='output_file')
args = parser.parse_args()
if args.input_file is None:
config_sim(args)
else:
loaded_sim(args)
def config_sim(args):
with open(args.sim_conf) as f:
params = json.load(f)
calc_params, sim_params = params["calc"], params["sim"]
n, w, h, r, energy = calc_params["n_objects"], calc_params["width"], calc_params["height"], \
calc_params["natural_radius"], calc_params["energy"]
mode, thres, step = sim_params["mode"], sim_params["threshold"], sim_params["step_size"]
# Running simulation
if mode == "flow":
sim = Flow(n, w, h, r, energy, thres, step)
elif mode == "search":
sim = Search(n, w, h, r, energy, thres, step, sim_params["manifold_step"],
sim_params["count"])
elif mode == "shrink":
sim = Shrink(n, w, h, r, energy, thres, step, sim_params["delta_width"],
sim_params["stop_width"])
sim.initialize()
sim.run(not args.quiet, args.log_steps)
def loaded_sim(args):
pass
if __name__ == '__main__':
try:
main()
except KeyboardInterrupt:
print("Program terminated by user.")

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requirements.txt Normal file
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cycler==0.10.0
Cython==0.29.24
kiwisolver==1.3.1
matplotlib==3.4.3
numpy==1.21.2
Pillow==8.3.1
pyparsing==2.4.7
python-dateutil==2.8.2
scipy==1.7.1
six==1.16.0

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shrink_energy_comparison.py Normal file
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#!/usr/bin/env python3
from __future__ import annotations
from typing import List
from simulation import Diagram, Simulation
import argparse, numpy as np
import matplotlib.pyplot as plt
from pathlib import Path
def get_torus_config_energies(n: int, widths: np.ndarray, h: float, r: float,
energy: str) -> Tuple[np.ndarray, np.ndarray]:
torus_min_energies, torus_max_energies = np.empty(widths.shape), np.empty(widths.shape)
for i, w in enumerate(widths):
sim = Simulation(n, w, h, r, energy)
for c in range(1,n): # Ignore 0, tends to error.
sim.add_frame(torus=(1,c))
sim.add_frame(torus=(c,1))
hashes = int(21*i/len(widths))
print(f'Generating at width {w:.02f}... ' + \
f'|{"#"*hashes}{" "*(20-hashes)}| {i+1}/{len(widths)}, {2*c}/{2*(n-1)}' + \
f' completed.', flush=True, end='\r')
torus_min_energies[i] = min([frame.energy for frame in sim.frames])
torus_max_energies[i] = max([frame.energy for frame in sim.frames])
print(flush=True)
return torus_min_energies, torus_max_energies
# def equal_shape_eigs(n, widths, h, r):
# n,w,h,r = 57, 10, 10, 4 # Domain settings
# thres, step_size = 10e-5, 5e-2 # Simulation settings
# log_steps = 50
# energy = "radial-t"
# sims = [None]*n*2
# energies = {}
# for x in range(1,n):
# sim = TravelEQ(n, w, h, r, energy, thres, step_size, log_steps)
# sim2 = TravelEQ(n, w, h, r, energy, thres, step_size, log_steps)
# #frame = FindEQ(n, w, h, r, "radial-t", POOL, thres, step_size, log_steps)
# for j in range(141):
# sim.w = 10-j*.05
# sim2.w = 10-j*.05
# sim.add_frame(None, (1,x), 0)
# sim2.add_frame(None, (x, 1), 0)
# #sim.initialize(torus=(1,x))
# energies[(1,x)] = sim[0].energy
# energies[(x,1)] = sim2[0].energy
# sims[x] = list([y.energy for y in sim.frames])
# sims[x+n] = list([y.energy for y in sim2.frames])
# #k1 = np.concatenate(sim.frames[0].process(sim.frames[0].grad, sim.frames[0].get_ranges()))
# #print(np.linalg.norm(k1))
# # hess = sim.frames[0].hessian(10e-5)
# # eigs = np.sort(np.linalg.eig(hess)[0])
# # sim.frames[0].stats["eigs"] = eigs
# # diagram = Diagram(sim, np.array([["voronoi", "eigs"]]))
# #diagram = Diagram(sim, np.array([["voronoi"]]))
# #diagram.render_static(0, filename=f'EqualShape/EqualShapeN{n}/{str((1, x))}')
# print(min(energies, key=energies.get))
# return sims
def main():
# Loading arguments.
parser = argparse.ArgumentParser("Compiles the equilibriums for each width into a diagram.")
parser.add_argument('sims_path', metavar='path/to/folder',
help="folder that contains simulation files.")
parser.add_argument('-q', '--quiet', dest='quiet', action='store_true', default=False,
help="suppress all normal output")
parser.add_argument('-o', '--output', dest='output_file')
args = parser.parse_args()
sims = []
files = list(Path(args.sims_path).iterdir())
for i, file in enumerate(files):
sims.append(Simulation.load(file))
hashes = int(21*i/len(files))
print(f'Loading simulations... |{"#"*hashes}{" "*(20-hashes)}|' + \
f' {i+1}/{len(files)} simulations loaded.', flush=True, end='\r')
print(flush=True)
sims.sort(key=lambda x: x.w)
widths = np.asarray([sim.w for sim in sims])
min_frames = [min(sim.frames, key=lambda x: x.energy) for sim in sims]
max_frames = [max(sim.frames, key=lambda x: x.energy) for sim in sims]
min_energies = np.asarray([frame.energy for frame in min_frames])
max_energies = np.asarray([frame.energy for frame in max_frames])
torus_min_energies, torus_max_energies = get_torus_config_energies(
sims[0].n, widths, sims[0].h, sims[0].r, sims[0].energy
)
min_markers = [np.var(frame.stats["site_areas"]) <= 1e-8 for frame in min_frames]
max_markers = [np.var(frame.stats["site_areas"]) <= 1e-8 for frame in max_frames]
# Torus minimum energies used as reference.
fig, ax = plt.subplots(figsize=(16, 8))
#ax.plot(widths, nums)
# for i, equal_sim in enumerate(equal_sims):
# if i in [0, n]:
# continue
# ax.plot(widths,
# np.asarray(equal_sims[i]) - reference,
# color="orange", alpha=0.5, linewidth=0.5, zorder=3
# )
ax.plot(widths, torus_min_energies - torus_min_energies, color='C1')
ax.plot(widths, min_energies - torus_min_energies, color='C0')
ax.plot(widths, max_energies - torus_min_energies, color='C0', linestyle='dotted')
#ax.plot(widths, torus_max_energies - torus_min_energies, color='C1', linestyle='dotted')
for i, marker in enumerate(min_markers):
if marker:
ax.scatter(widths[i], min_energies[i]-torus_min_energies[i],
marker='H', color="orange", s=20, zorder=4)
else:
ax.scatter(widths[i], min_energies[i]-torus_min_energies[i],
marker='d', color="blue", s=20, zorder=4)
for i, marker in enumerate(max_markers):
if marker:
ax.scatter(widths[i], max_energies[i]-torus_min_energies[i],
marker='H', edgecolors="orange", s=20, facecolors='none', zorder=4)
else:
ax.scatter(widths[i], max_energies[i]-torus_min_energies[i],
marker='d', edgecolors="blue", s=20, facecolors='none', zorder=4)
ax.invert_xaxis()
ax.title.set_text('Reduced Energy vs. Width')
ax.set_xlabel("Width")
ax.set_ylabel("Reduced Energy")
ax.grid(zorder=0)
#ax.set_xticks([round(w,2) for w in widths[::-2]])
#ax.set_yticks(np.arange(-920, 1120, 40))
#ax.set_xticklabels(ax.get_xticks(), rotation = 90)
plt.tight_layout()
fig.savefig(f"figures/WidthsEnergyComparison - N{sims[0].n}.png")
if __name__ == "__main__":
try:
main()
except KeyboardInterrupt:
print("Program terminated by user.")

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from __future__ import annotations
from typing import Tuple, List
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator, FormatStrFormatter
import os, math, random, time, pickle, scipy, numpy as np
from packsim import VoronoiContainer, AreaEnergy, RadialALEnergy, RadialTEnergy
from timeit import default_timer as timer
INT = np.int64
FLOAT = np.float64
SYMM = np.array([[1,0], [1,1], [0,1], [-1,1], [-1,0], [-1,-1], [0,-1], [1,-1]])
def gen_filepath(sim: Simulation, ext: str, parent_dir='figures') -> str:
"""
Generates a filename based on the simulation.
:param sim: [Simulation] simulation to generate file for.
:param ext: [str] file extension.
:return: [str] string for filename.
"""
energy = {AreaEnergy: "Area", RadialALEnergy: "Radial[AL]",
RadialTEnergy: "Radial[T]"}[sim.energy]
mode = {Flow: "F", Search: "T", Shrink: "S"}[type(sim)]
base_filename = f'{energy}{mode} - N{sim[0].n}R{sim[0].r} - {round(sim[0].w, 2):.2f}x{sim[0].h}'
base_path = f'{parent_dir}/{base_filename}'
i = 1
if ext == "":
path = base_path
while os.path.isdir(path):
path = base_path + f'({i})'
i += 1
else:
path = base_path + "." + ext
while os.path.isfile(path):
path = base_path + f'({i}).{ext}'
i += 1
return path
class Diagram():
"""
Class for generating diagrams.
:param sim: [Simulation] Simulation class containing dynamics.
:param diagrams: [np.ndarray] selects which diagrams to show.
"""
__slots__ = ['sim', 'diagrams', 'cumulative']
def __init__(self, sim: Simulation, diagrams: np.ndarray, cumulative: bool = True):
self.sim = sim
self.diagrams = np.atleast_2d(diagrams)
self.cumulative = cumulative
def generate_frame(self, frame: int):
"""
Generates one frame for the plot.
:param frame: [int] frame index to draw.
:param scale: [float] how much of the domain to draw.
:param area: [bool] set to false to not label areas.
:param only: [bool] set to True to only render diagram.
"""
shape = self.diagrams.shape
fig, axes = plt.subplots(*shape, figsize=(shape[1]*8, shape[0]*8))
if self.diagrams.shape == (1,1):
getattr(self, str(self.diagrams[0][0]) + '_plot')(frame, axes)
else:
axes = np.atleast_2d(axes)
it = np.nditer(self.diagrams, flags=["multi_index"])
for diagram in it:
if diagram == "":
continue
getattr(self, str(diagram) + '_plot')(frame, axes[it.multi_index])
plt.tight_layout()
def voronoi_plot(self, i: int, ax):
n,w,h = self.sim[i].n, self.sim[i].w, self.sim[i].h
scale = 1.5
area = n <= 60
scipy.spatial.voronoi_plot_2d(self.sim[i].vor_data, ax, show_vertices=False,
point_size = 7-n/100)
ax.plot([-w, 2*w], [0, 0], 'r')
ax.plot([-w, 2*w], [h, h], 'r')
ax.plot([0,0], [-h, 2*h], 'r')
ax.plot([w, w], [-h, 2*h], 'r')
ax.axis('equal')
ax.set_xlim([(1-scale)*w/2, (1+scale)*w/2])
ax.set_ylim([(1-scale)*h/2, (1+scale)*h/2])
ax.title.set_text("Voronoi Visualization")
props = dict(boxstyle='round', facecolor='wheat', alpha=0.8)
# if area:
# global SYMM
# for site_index in range(n):
# for s in np.concatenate(([[0,0]], SYMM)):
# txt = ax.text(*(site.vec + s*self.sim[i].dim),
# str(round(site.cache("area"), 3)))
# txt.set_clip_on(True)
ax.text(0.05, 0.95, f'Energy: {self.sim[i].energy}', transform=ax.transAxes, fontsize=14,
verticalalignment='top', bbox=props)
def energy_plot(self, i: int, ax):
ax.set_xlim([0, len(self.sim)])
try:
ax.plot([0, len(self.sim)], [self.sim[i].minimum, self.sim[i].minimum], 'red')
except AttributeError:
pass
energies = [self.sim[j].energy for j in range(i+1)]
ax.plot(list(range(i+1)), energies)
ax.title.set_text('Energy vs. Time')
max_value = round(self.sim[0].energy)
min_value = round(self.sim[-1].energy)
diff = max_value-min_value
ax.set_yticks(np.arange(int(min_value-diff/5), int(max_value+diff/5), diff/25))
ax.set_xlabel("Iterations")
ax.set_ylabel("Energy")
ax.grid()
def site_areas_plot(self, i: int, ax):
regular_area = self.sim[i].w*self.sim[i].h/self.sim[i].n
y, x = self.sim.generate_bar_info("site_areas", i, self.cumulative,
avg=True, reg=regular_area)
ax.bar(x, y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Site Areas')
ax.set_xlabel("Area")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.ticklabel_format(useOffset=False)
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
# for xtick, color in zip(ax.get_xticklabels(), areas_bar[2]):
# if color != 'C0':
# xtick.set_color(color)
def site_edge_count_plot(self, i: int, ax):
y, x = self.sim.generate_bar_info("site_edge_count", i, self.cumulative,
bounds=(1, 11), avg=True)
ax.bar(x, y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Edges per Site')
ax.set_xlabel("Number of Edges")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.set_xticklabels([int(z) for z in x])
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
def site_isos_plot(self, i: int, ax):
regular_area = self.sim[i].w*self.sim[i].h/self.sim[i].n
regular_edge = math.sqrt(2*regular_area/(3*math.sqrt(3)))
regular_isoparam = 4*math.pi*regular_area/(6*regular_edge)**2
y, x = self.sim.generate_bar_info("site_isos", i, self.cumulative, bounds=(0,1),
avg=True, reg=regular_isoparam)
ax.bar(x, y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Isoparametric Values')
ax.set_xlabel("Isoparametric Value")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.ticklabel_format(useOffset=False)
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
# for xtick, color in zip(ax.get_xticklabels(), isoparam_bar[2]):
# if color != 'C0':
# xtick.set_color(color)
def site_energies_plot(self, i: int, ax):
y, x = self.sim.generate_bar_info("site_energies", i, self.cumulative, avg=True)
ax.bar(x, y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Site Energies')
ax.set_xlabel("Energy")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.ticklabel_format(useOffset=False)
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
def avg_radius_plot(self, i: int, ax):
y, x = self.sim.generate_bar_info("avg_radius", i, self.cumulative, avg=True)
ax.bar(x, y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Site Average Radii')
ax.set_xlabel("Average Radius")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.ticklabel_format(useOffset=False)
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
def isoparam_avg_plot(self, i: int, ax):
y, x = self.sim.generate_bar_info("isoparam_avg", i, self.cumulative, avg=True)
ax.bar(x,y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Site Isoperimetric Averages')
ax.set_xlabel("Isoperimetric Average")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.ticklabel_format(useOffset=False)
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
def edge_lengths_plot(self, i: int, ax):
regular_area = self.sim[i].w*self.sim[i].h/self.sim[i].n
regular_edge = math.sqrt(2*regular_area/(3*math.sqrt(3)))
y, x = self.sim.generate_bar_info("edge_lengths", i, self.cumulative,
30, avg=True, reg=regular_edge)
ax.bar(x, y, width=0.8*(x[1]-x[0]))
ax.title.set_text('Edge Lengths')
ax.set_xlabel("Length")
ax.set_ylabel("Average Occurances")
ax.set_xticks(x)
ax.set_xticklabels(ax.get_xticks(), rotation = 90)
ax.xaxis.set_major_formatter(FormatStrFormatter('%.3f'))
#ax.ticklabel_format(useOffset=False)
ax.yaxis.set_major_locator(MaxNLocator(integer=True))
# for xtick, color in zip(ax.get_xticklabels(), lengths_bar[2]):
# if color != 'C0':
# xtick.set_color(color)
def eigs_plot(self, i: int, ax):
eigs = self.sim[i].stats["eigs"]
ax.plot(list(range(len(eigs))), eigs, marker='o', linestyle='dashed', color='C0')
ax.plot([0,len(eigs)], [0, 0], color="red")
ax.title.set_text('Hessian Eigenvalues')
ax.set_xlabel("")
ax.set_ylabel("Value")
def render_static(self, i: int, j: int = None, filename = None):
"""
Renders single frames.
:param filename: [str] name of file.
:param i: [int] index of frame to start rendering.
:param j: [j] index of frame to stop rendering.
:param only: [bool] set to True to only render diagram.
"""
if j is None:
j = len(self.sim)-1
length = j+1-i
if length == 1:
if filename is None:
path = gen_filepath(self.sim, "png")
else:
path = f'figures/{filename}.png'
self.generate_frame(i)
plt.savefig(path)
plt.close()
print(f'Wrote to \"{path}\"')
else:
if filename is None:
path = gen_filepath(self.sim, "")
else:
path = f'figures/{filename}'
os.mkdir(path)
for frame in range(i, j+1):
self.generate_frame(frame)
if frame % 20 == 0:
print(f'Rendered frame {frame}/{length} : {100*frame/length:.2f}%')
plt.savefig(f'{path}/img{frame:03}.png')
plt.close()
print(f'Wrote to folder \"{path}\"')
def render_video(self, time = 30, fps = None, filename = None):
"""
Renders plot(s) into image.
:param scale: [float] how much of the domain to draw.
:param area: [bool] set to false to not label area.
:param filename: [str] name for static image.
:param fps: [float] fps for image.
:param only: [bool] set to True to only render diagram.
"""
if fps is None:
if type(self.sim) == Flow:
fps = min(len(self.sim)/time, 30)
else:
fps = 5
step = len(self.sim)/(fps*time) if fps == 30 else 1
# Iterate through desired frames.
try:
os.mkdir("figures/temp")
except FileExistsError:
pass
print("Generating frames...")
frames = min(len(self.sim), int(fps * time))
for j in range(frames):
self.generate_frame(int(j*step))
if j % 20 == 0:
print(f'Rendered frame {j}/{frames} : {100*j/frames:.2f}%')
plt.savefig(f'figures/temp/img{j:03}.png')
plt.close()
if filename is None:
path = gen_filepath(self.sim, "mp4")
else:
path = f'figures/{filename}.mp4'
# Convert to gif.
print("Assembling MP4...")
os.system(f'ffmpeg -hide_banner -loglevel error -r {fps} -i figures/temp/img%03d.png' + \
f' -c:v libx264 -crf 18 -preset slow -pix_fmt yuv420p -vf' + \
f' "scale=trunc(iw/2)*2:trunc(ih/2)*2" -f mp4 "{path}"')
# Remove files.
for j in range(frames):
os.remove(f'figures/temp/img{j:03}.png')
os.rmdir("figures/temp")
print(f'Wrote to \"{path}\".')
class Simulation:
"""
Class for running simulations.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param energy: energy to use to calculate. Can
pass in class directly or use string.
"""
__slots__ = ['n', 'w', 'h', 'r', 'energy', 'frames']
def __init__(self, n: int, w: float, h: float, r: float, energy: str):
self.n, self.w, self.h, self.r = int(n), w, h, r
self.frames = []
if self.n < 2:
raise ValueError("Number of objects should be larger than 2!")
if self.w <= 0:
raise ValueError("Width needs to be nonzero and positive!")
if self.h <= 0:
raise ValueError("Height needs to be nonzero and positive!")
if isinstance(energy, str):
try:
self.energy = {"area": AreaEnergy, "radial-al": RadialALEnergy,
"radial-t" : RadialTEnergy}[energy.lower()]
except KeyError:
raise ValueError("Invalid Energy!")
else:
if energy not in [AreaEnergy, RadialALEnergy, RadialTEnergy]:
raise ValueError("Invalid Energy!")
self.energy = energy
def __getitem__(self, key: int) -> VoronoiContainer:
return self.frames[key]
def __len__(self):
return len(self.frames)
def initialize(self, points = None, torus = None, jitter = 0):
"""
Initializes the simulation
:param points: Can be multiple types. Takes list-like data types.
:param torus: Used or generating torus points. L value.
:param jitter: [int] Add random*jitter movement to initial data.
"""
self.add_frame(points, torus, jitter)
def add_frame(self, points = None, torus = None, jitter = 0.0):
"""
Adds a new frame to this simulation.
:param points: Can be multiple types. Takes list-like data types.
:param torus: Used or generating torus points. L value.
:param jitter: [int] Add random*jitter movement to initial data.
"""
dim = np.array([self.w, self.h])
if not (points is None):
points = np.asarray(points)
if points.shape[1] != 2:
raise ValueError("Improper shape, points are 2 dimensional.")
elif not torus is None:
points = Simulation.torus_sites(self.n, self.w, self.h, torus)
else:
points = dim * np.random.random_sample((self.n, 2))
points += (jitter*np.random.random_sample((self.n, 2)).astype(FLOAT)) % dim
self.frames.append(self.energy(self.n, self.w, self.h, self.r, points))
def generate_bar_info(self, stat: str, i: int, cumulative: bool, bins: int = 10,
bounds: Tuple[float] = None, avg: bool = False, reg = None) -> Tuple:
"""
Gets the bar info for matplotlib from the ith to jth frame.
:param stat: [str] name of statistic to obtain.
:param i: [int] frame to obtain
:param cumulative: [bool] Will obtain all stats up to the ith frame if True.
:param bins: [int] number of bins for the bar graph.
:param bound: [Tuple[float]] lower and upper bounds for the bins. If not set,
automatically take the min and max value.
:param avg: [bool] Averages the counts over the number of frames if True.
:param mark: If not None, set a specific marker.
:return: [Tuple] returns a tuple of labels, values, and colors.
"""
if cumulative:
values = np.concatenate([f.stats[stat] for f in self.frames[:(i+1)]])
else:
values = self.frames[i].stats[stat]
bins = 9
if np.var(values) <= 1e-8:
hist = np.zeros((bins,))
val = np.average(values)
hist[(bins+1) // 2 - 1] = len(values)
bin_list = np.linspace(0, val, bins//2+1, endpoint=True)
bin_list = np.concatenate((bin_list, (bin_list+val)[1:]))
return hist, bin_list[not (bins%2):]
hist, bin_edges = np.histogram(values, bins=bins, range=bounds)
bin_list = [(bin_edges[i] + bin_edges[i+1])/2 for i in range(len(bin_edges)-1)]
if avg and cumulative:
return hist / (i+1), bin_list
return hist, bin_list
# colors = ["C0"]*bins
# if reg >= lb and reg <= ub:
# colors[int((reg-lb)*bins/diff)] = "C3"
# return (labels, count, colors)
def get_distinct(self) -> Simulation:
distinct_eigs = []
new_frames = []
for frame in self.frames:
new_eigs = frame.stats["eigs"]
is_in = False
for eigs in distinct_eigs:
if np.allclose(new_eigs, eigs, atol=1e-4):
is_in = True
if not is_in:
distinct_eigs.append(new_eigs)
new_frames.append(frame)
continue
new_sim = self.__class__(self.n, self.w, self.h, self.r, self.energy)
new_sim.frames = new_frames
return new_sim
def save(self, filename: str = None):
"""
Saves the points at every point into a file.
:filename: [str] name of the file
"""
if filename is None:
path = gen_filepath(self, "sim", "simulations")
else:
path = f'simulations/{filename}.sim'
# Convert sites to NumPy array.
arr = np.zeros((len(self.frames), self.n, 2))
arr = np.stack([frame.site_arr for frame in self.frames])
#stats = [frame.stats for frame in self.frames]
all_info = []
for frame in self.frames:
frame_info = dict()
frame_info["arr"] = frame.site_arr
frame_info["energy"] = {AreaEnergy: "Area", RadialALEnergy: "Radial[AL]",
RadialTEnergy: "Radial[T]"}[sim.energy]
frame_info["params"] = (frame.n, frame.w, frame.h, frame.r)
all_info.append(frame_info)
with open(path, 'wb') as output:
pickle.dump((all_info, self.__class__), output, pickle.HIGHEST_PROTOCOL)
print("Wrote to " + path)
@staticmethod
def load(filename: str) -> Simulation:
"""
Loads the points at every point into a file.
:param filename: [str] name of the file
"""
frames = []
with open(filename, 'rb') as data:
all_info, sim_class = pickle.load(data)
sim = sim_class(*all_info[0]["params"], all_info[0]["energy"], 0, 0, 0, 0)
for frame_info in all_info:
frames.append(frame_info["energy"](*frame_info["params"], frame_info["arr"]))
frames[-1].stats = frame_info["stats"]
sim.frames = frames
return sim
@staticmethod
def torus_sites(n: int, w: float, h: float, L: Tuple[int]):
"""
Returns the points when you wrap a line
around a torus, like in the periodic domain.
:param n: [int] amount of points.
:param w: [float] width of the domain.
:param h: [float] height of the domain.
:param L: [Tuple[int]] L = (u,v)
"""
dim = np.array([[w, h]])
L = np.array(L)
return (np.array([1,1])/2 + np.concatenate([(i*dim*L/n) for i in range(n)])) % dim
class Flow(Simulation):
"""
Class for finding an equilibrium from initial points.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param energy: [str] energy to use to calculate.
:param thres: [float] threshold for close enough to equilibrium.
:param step_size: [float] size to step by for iteration.
"""
__slots__ = ['thres', 'step_size']
def __init__(self, n: int, w: float, h: float, r: float, energy: str, thres: float,
step_size: float):
super().__init__(n, w, h, r, energy)
self.thres, self.step_size = thres, step_size
def run(self, log, log_steps):
"""
Runs the simulation.
:param log: [bool] will log if True.
"""
if log:
print(f'Find - N = {self.n}, R = {self.r}, {self.w} X {self.h}', flush=True)
i, grad_mag = 0, float('inf')
## Replace with adaptive step size eventually!!!!!!
trial = 2
while grad_mag > self.thres: # Get to threshold.
# Iterate and generate next frame using Euler method.
start = timer()
new_sites, DE = self.frames[i].iterate(self.step_size)
orig_step = self.energy(self.n, self.w, self.h, self.r, new_sites)
grad_mag = np.linalg.norm(DE)
end = timer()
if orig_step.energy < self.frames[i].energy: # If energy decreases.
if trial < 20: # Try increasing step size for 10 times.
factor = 1 + .1**trial
test_step = self.energy(self.n, self.w, self.h, self.r,
self.frames[i].add_sites(self.step_size*factor*DE))
# If increased step has less energy than original step.
if test_step.energy < orig_step.energy:
self.step_size *= factor
trial = max(2, trial-1)
grad_mag = np.linalg.norm(DE)
new_step = test_step
else: # Otherwise, increases trials, and use original.
trial += 1
new_step = orig_step
else:
new_step = orig_step
else: # Step size too large, decrease and reset trial counter.
self.step_size /= (1 + .1**(trial-1))
trial = 1
new_sites, DE = self.frames[i].iterate(self.step_size)
new_step = self.energy(self.n, self.w, self.h, self.r, new_sites)
self.frames.append(new_step)
self.step_size = max(10e-4, self.step_size)
i += 1
if(log and i % log_steps == 0):
print(f'Iteration: {i:05} | Energy: {self.frames[i].energy: .5f}' + \
f' | Gradient: {grad_mag:.8f} | Step: {self.step_size: .5f} | ' + \
f'Time: {end-start: .3f}', flush=True)
class Search(Simulation):
"""
Class for traversing to other equilibriums from an equilbrium.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param energy: [str] energy to use to calculate.
:param thres: [float] threshold for when to stop.
:param kernel_step: [float] size to step when jumping off kernel.
:param iter_step: [float] size to step by for iteration.
:param iter: [int] number of iterations
"""
__slots__ = ['thres', 'iter_step', 'kernel_step', 'iter']
def __init__(self, n: int, w: float, h: float, r: float, energy: str, thres,
iter_step: float, kernel_step: float, iter: int):
super().__init__(n, w, h, r, energy)
self.thres, self.iter = thres, iter
self.kernel_step, self.iter_step = kernel_step, iter_step
def run(self, log, log_steps):
"""
Runs the simulation.
:param log: [bool] will log if True.
"""
if log:
print(f'Travel - N = {self.n}, R = {self.r}, {self.w} X {self.h}', flush=True)
dim = np.array([self.w, self.h])
fixed = random.randint(0, self.n-1)
center = dim / 2
new_sites = self.frames[0].site_arr
# Move fixed point to center.
for i in range(self.iter):
# Get to equilibrium.
sim = Flow(self.n, self.w, self.h, self.r, self.energy, self.thres,
self.iter_step)
sim.initialize(new_sites)
sim.run(log, log_steps)
self.frames[i] = sim[-1] # Replace frame with equilibrium frame.
if log:
print(f'Equilibrium: {i:04}\n')
# Calculate kernel, and travel in some direction.
hess = self.frames[i].hessian(10e-5)
ns = scipy.linalg.null_space(hess, 10e-4).T
#self.frames[i].get_statistics()
eigs = np.sort(np.linalg.eig(hess)[0])
self.frames[i].stats["eigs"] = eigs
zero_eigs = np.count_nonzero(np.isclose(eigs, np.zeros((len(eigs),)), atol=1e-4))
if zero_eigs != 2:
print("WARNING, 0 EIGS NOT 2", zero_eigs)
if i == self.iter-1:
break
if len(ns) <= 2:
new_sites = dim * np.random.random_sample((self.n, 2))
else:
vec = ns[random.randint(0, len(ns)-1)] # Choose random vector
new_sites = self.frames[i].add_sites(self.kernel_step*vec.reshape((self.n, 2)))
new_sites += (center - new_sites[fixed]) % dim # Offset
self.frames.append(None)
class Shrink(Simulation):
"""
Class for traversing to other equilibriums from an equilbrium.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param energy: [str] energy to use to calculate.
:param thres: [float] threshold for when to stop.
:param w_change: [float] percent to change w each iteration.
:param stop_w: [int] percentage at which to stop iterating.
:param step_size: [float] size to step by for iteration.
"""
__slots__ = ['thres', 'w_change', 'stop_w', 'step_size']
def __init__(self, n: int, w: float, h: float, r: float, energy: str, thres: float,
step_size: float, w_change: float, stop_w: float):
super().__init__(n, w, h, r, energy)
self.thres, self.step_size = thres, step_size
self.w_change, self.stop_w = w*w_change, w*stop_w
def run(self, log, log_steps):
"""
Runs the simulation.
:param log: [bool] will log if True.
"""
if log:
print(f'Shrink - N = {self.n}, R = {self.r}, {self.w} X {self.h}', flush=True)
while self.w >= self.stop_w:
# Get to equilibrium.
sim = Flow(self.n, self.w, self.h, self.r, self.energy, self.thres,
self.step_size)
sim.initialize(self.frames[-1].site_arr)
sim.run(log, log_steps)
self.frames.append(sim[-1]) # Replace frame with equilibrium frame.
self.frames[-1].get_statistics()
if log:
print(f'Width: {self.w:.4f}\n')
self.w -= self.w_change
del self.frames[0]
TravelEQ = Search

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import array, scipy.spatial, numpy as np
from cython.parallel import parallel, prange
cimport numpy as np
from cpython cimport array
from libc.stdlib cimport malloc, realloc, calloc, free
from libc.math cimport isnan, NAN, pi as PI, M_PI_2 as PI_2, \
sqrt, log, sin, cos, tan, acos, fabs
from packsim cimport INT_T, FLOAT_T, Init, IArray, FArray, BitSet, Vector2D, Matrix2x2, \
VectorSelfOps, VectorCopyOps, MatrixSelfOps, MatrixCopyOps, \
SiteCacheMap, EdgeCacheMap, VoronoiInfo, Site, HalfEdge
#### Constants ####
INT = np.int64
FLOAT = np.float64
cdef FLOAT_T TAU = 2*PI
# In most cases, the amount of edges relevant to a gradient will
# not exceed this number. However, we assign a growth rate of 8 edges,
# when dynamically allocating.
cdef INT_T EDGE_ARR_SIZE = 32
cdef Init init
init.IArray, init.FArray, init.BitSet, init.Vector2D, init.Matrix2x2 = \
init_iarray, init_farray, init_bitset, init_vector2d, init_matrix2x2
cdef VectorSelfOps VSO
cdef VectorCopyOps VCO
cdef MatrixSelfOps MSO
cdef MatrixCopyOps MCO
VSO.neg, VSO.vadd, VSO.vsub, VSO.vmul, VSO.vdiv, VSO.sadd, VSO.ssub, VSO.smul, VSO.sdiv = \
v_neg_s, v_vadd_s, v_vsub_s, v_vmul_s, v_vdiv_s, v_sadd_s, v_ssub_s, v_smul_s, v_sdiv_s
VSO.matmul = v_matmul_s
VCO.neg, VCO.vadd, VCO.vsub, VCO.vmul, VCO.vdiv, VCO.sadd, VCO.ssub, VCO.smul, VCO.sdiv = \
v_neg_c, v_vadd_c, v_vsub_c, v_vmul_c, v_vdiv_c, v_sadd_c, v_ssub_c, v_smul_c, v_sdiv_c
VCO.matmul = v_matmul_c
MSO.neg, MSO.madd, MSO.msub, MSO.mmul, MSO.mdiv, MSO.sadd, MSO.ssub, MSO.smul, MSO.sdiv = \
m_neg_s, m_madd_s, m_msub_s, m_mmul_s, m_mdiv_s, m_sadd_s, m_ssub_s, m_smul_s, m_sdiv_s
MSO.matmul = m_matmul_s
MCO.neg, MCO.madd, MCO.msub, MCO.mmul, MCO.mdiv, MCO.sadd, MCO.ssub, MCO.smul, MCO.sdiv = \
m_neg_c, m_madd_c, m_msub_c, m_mmul_c, m_mdiv_c, m_sadd_c, m_ssub_c, m_smul_c, m_sdiv_c
MCO.matmul = m_matmul_c
cdef Vector2D NAN_VECTOR = init.Vector2D(NAN, NAN)
cdef Matrix2x2 NAN_MATRIX = init.Matrix2x2(NAN, NAN, NAN, NAN)
cdef FLOAT_T[18] SYMM = [0,0, 1,0, 1,1, 0,1, -1,1, -1,0, -1,-1, 0,-1, 1,-1]
cdef Matrix2x2 R = init.Matrix2x2(0, -1, 1, 0)
"""
If bound checking is desired, uncomment out ..._valid_indices functions.
"""
#### IArray Methods ####
cdef inline IArray init_iarray(INT_T* arr, (INT_T, INT_T) shape) nogil:
cdef IArray iarray
iarray.arr, iarray.shape = arr, shape
iarray.get = iarray_get
iarray.set = iarray_set
return iarray
cdef inline bint iarray_valid_indices(IArray* self, (INT_T, INT_T) index) nogil:
if index[0] > self.shape[0] or index[1] > self.shape[1]:
with gil:
raise IndexError(f"Index out of range for IArray with shape {self.shape}")
cdef inline INT_T iarray_get(IArray* self, (INT_T, INT_T) index) nogil:
#iarray_valid_indices(&self, index)
return self.arr[index[0]*self.shape[1] + index[1]]
cdef inline void iarray_set(IArray* self, (INT_T, INT_T) index, INT_T val) nogil:
#iarray_valid_indices(&self, index)
self.arr[index[0]*self.shape[1] + index[1]] = val
#### FArray Methods ####
cdef inline FArray init_farray(FLOAT_T* arr, (INT_T, INT_T) shape) nogil:
cdef FArray farray
farray.arr, farray.shape = arr, shape
farray.get = farray_get
farray.set = farray_set
return farray
cdef inline bint farray_valid_indices(FArray* self, (INT_T, INT_T) index) nogil:
if index[0] > self.shape[0] or index[1] > self.shape[1]:
with gil:
raise IndexError(f"Index out of range for FArray with shape {self.shape}")
cdef inline FLOAT_T farray_get(FArray* self, (INT_T, INT_T) index) nogil:
#iarray_valid_indices(&self, index)
return self.arr[index[0]*self.shape[1] + index[1]]
cdef inline void farray_set(FArray* self, (INT_T, INT_T) index, FLOAT_T val) nogil:
#iarray_valid_indices(&self, index)
self.arr[index[0]*self.shape[1] + index[1]] = val
#### IList Methods ####
# cdef inline IList init_ilist() nogil:
# cdef IList ilist
# ilist.size = EDGE_ARR_SIZE
# ilist.length = 0
# ilist.data = <INT_T*> malloc(self.size * sizeof(INT_T))
# ilist.append, ilist.free = ilist_append, ilist_free
# return ilist
# cdef inline void ilist_append(IList* self, INT_T) nogil:
# if self.size == self.length:
# ilist.data = <INT_T*> realloc((self.size+8) * sizeof(INT_T))
# self.size += 8
# self.data[self.length] == INT_T
# self.length += 1
# cdef inline void ilist_free(IList* self) nogil:
# free(self.data)
#### BitSet Methods ####
cdef inline BitSet init_bitset(INT_T elements) nogil:
cdef BitSet bitset
bitset.bits = <INT_T*> calloc(((elements/sizeof(INT_T))+1), sizeof(INT_T))
bitset.add, bitset.free = bitset_add, bitset_free
return bitset
cdef inline bint bitset_add(BitSet* self, INT_T val) nogil:
cdef INT_T index, rel_index, old
index = val/sizeof(INT_T)
old = self.bits[index]
rel_index = val - index*sizeof(INT_T)
self.bits[index] = (1 << rel_index) | old # New value.
return old == self.bits[index] # Means 1 was already there.
cdef inline void bitset_free(BitSet* self) nogil:
free(self.bits)
#### Vector2D Methods ####
"""
Prefix 'v' stands for vector, element by element operation.
Prefix 's' stands for scalar, broadcasted operation.
Suffix 'w' stands for write, overwriting current value.
Suffix 'n' stands for new, copying to a new location.
While it's possible to chain 'new' operations, when possible,
avoid this, so fewer objects are needed.
"""
cdef inline Vector2D init_vector2d(FLOAT_T x, FLOAT_T y) nogil:
cdef Vector2D vec
vec.x, vec.y = x, y
vec.self, vec.copy = VSO, VCO
vec.equals, vec.rot, vec.dot, vec.mag = v_equals, rot, dot, mag
return vec
cdef inline bint v_equals(Vector2D* self, Vector2D w) nogil:
return ((self.x == w.x) and (self.y == w.y))
cdef inline Vector2D* v_neg_s(Vector2D* self) nogil:
self.x = -self.x
self.y = -self.y
return self
cdef inline Vector2D* v_vadd_s(Vector2D* self, Vector2D w) nogil:
self.x += w.x
self.y += w.y
return self
cdef inline Vector2D* v_vsub_s(Vector2D* self, Vector2D w) nogil:
self.x -= w.x
self.y -= w.y
return self
cdef inline Vector2D* v_vmul_s(Vector2D* self, Vector2D w) nogil:
self.x *= w.x
self.y *= w.y
return self
cdef inline Vector2D* v_vdiv_s(Vector2D* self, Vector2D w) nogil:
self.x /= w.x
self.y /= w.y
return self
cdef inline Vector2D* v_sadd_s(Vector2D* self, FLOAT_T s) nogil:
self.x += s
self.y += s
return self
cdef inline Vector2D* v_ssub_s(Vector2D* self, FLOAT_T s) nogil:
self.x -= s
self.y -= s
return self
cdef inline Vector2D* v_smul_s(Vector2D* self, FLOAT_T s) nogil:
self.x *= s
self.y *= s
return self
cdef inline Vector2D* v_sdiv_s(Vector2D* self, FLOAT_T s) nogil:
self.x /= s
self.y /= s
return self
cdef inline Vector2D* v_matmul_s(Vector2D* self, Matrix2x2 m) nogil:
self.x, self.y = self.x*m.a + self.y*m.c, self.x*m.b + self.y*m.d
return self
cdef inline Vector2D v_neg_c(Vector2D* self) nogil:
return init.Vector2D(-self.x, -self.y)
cdef inline Vector2D v_vadd_c(Vector2D* self, Vector2D w) nogil:
return init.Vector2D(self.x + w.x, self.y + w.y)
cdef inline Vector2D v_vsub_c(Vector2D* self, Vector2D w) nogil:
return init.Vector2D(self.x - w.x, self.y - w.y)
cdef inline Vector2D v_vmul_c(Vector2D* self, Vector2D w) nogil:
return init.Vector2D(self.x * w.x, self.y * w.y)
cdef inline Vector2D v_vdiv_c(Vector2D* self, Vector2D w) nogil:
return init.Vector2D(self.x / w.x, self.y / w.y)
cdef inline Vector2D v_sadd_c(Vector2D* self, FLOAT_T s) nogil:
return init.Vector2D(self.x + s, self.y + s)
cdef inline Vector2D v_ssub_c(Vector2D* self, FLOAT_T s) nogil:
return init.Vector2D(self.x + s, self.y + s)
cdef inline Vector2D v_smul_c(Vector2D* self, FLOAT_T s) nogil:
return init.Vector2D(self.x * s, self.y * s)
cdef inline Vector2D v_sdiv_c(Vector2D* self, FLOAT_T s) nogil:
return init.Vector2D(self.x / s, self.y / s)
cdef inline Vector2D v_matmul_c(Vector2D* self, Matrix2x2 m) nogil:
return init.Vector2D(
self.x*m.a + self.y*m.c, self.x*m.b + self.y*m.d
)
cdef inline Vector2D rot(Vector2D* self) nogil:
return init.Vector2D(-self.y, self.x)
cdef inline FLOAT_T dot(Vector2D* self, Vector2D w) nogil:
return self.x*w.x + self.y*w.y
cdef inline FLOAT_T mag(Vector2D* self) nogil:
return <FLOAT_T>sqrt(<double>(self.x*self.x + self.y*self.y))
#### Matrix2x2 Methods ####
cdef inline Matrix2x2 init_matrix2x2(FLOAT_T a, FLOAT_T b, FLOAT_T c, FLOAT_T d) nogil:
cdef Matrix2x2 matrix
matrix.a, matrix.b, matrix.c, matrix.d = a, b, c, d
matrix.self, matrix.copy = MSO, MCO
matrix.equals, matrix.vecmul = m_equals, m_vecmul
return matrix
cdef inline bint m_equals(Matrix2x2* self, Matrix2x2 m) nogil:
return (
(self.a == m.a) and (self.b == m.b) and (self.c == m.c) and (self.d == m.d)
)
cdef inline Vector2D m_vecmul(Matrix2x2* self, Vector2D v) nogil:
return init.Vector2D(
self.a*v.x + self.b*v.y, self.c*v.x + self.d*v.y
)
cdef inline Matrix2x2* m_neg_s(Matrix2x2* self) nogil:
self.a, self.b, self.c, self.d = -self.a, -self.b, -self.c, -self.d
return self
cdef inline Matrix2x2* m_madd_s(Matrix2x2* self, Matrix2x2 m) nogil:
self.a += m.a
self.b += m.b
self.c += m.c
self.d += m.d
return self
cdef inline Matrix2x2* m_msub_s(Matrix2x2* self, Matrix2x2 m) nogil:
self.a -= m.a
self.b -= m.b
self.c -= m.c
self.d -= m.d
return self
cdef inline Matrix2x2* m_mmul_s(Matrix2x2* self, Matrix2x2 m) nogil:
self.a *= m.a
self.b *= m.b
self.c *= m.c
self.d *= m.d
return self
cdef inline Matrix2x2* m_mdiv_s(Matrix2x2* self, Matrix2x2 m) nogil:
self.a /= m.a
self.b /= m.b
self.c /= m.c
self.d /= m.d
return self
cdef inline Matrix2x2* m_sadd_s(Matrix2x2* self, FLOAT_T s) nogil:
self.a += s
self.b += s
self.c += s
self.d += s
return self
cdef inline Matrix2x2* m_ssub_s(Matrix2x2* self, FLOAT_T s) nogil:
self.a -= s
self.b -= s
self.c -= s
self.d -= s
return self
cdef inline Matrix2x2* m_smul_s(Matrix2x2* self, FLOAT_T s) nogil:
self.a *= s
self.b *= s
self.c *= s
self.d *= s
return self
cdef inline Matrix2x2* m_sdiv_s(Matrix2x2* self, FLOAT_T s) nogil:
self.a /= s
self.b /= s
self.c /= s
self.d /= s
return self
cdef inline Matrix2x2* m_matmul_s(Matrix2x2* self, Matrix2x2 m) nogil:
self.a, self.b, self.c, self.d = \
self.a*m.a + self.b*m.c, self.a*m.b + self.b*m.d, \
self.c*m.a + self.d*m.c, self.c*m.b + self.d*m.d
return self
cdef inline Matrix2x2 m_neg_c(Matrix2x2* self) nogil:
return init.Matrix2x2(-self.a, -self.b, -self.c, -self.d)
cdef inline Matrix2x2 m_madd_c(Matrix2x2* self, Matrix2x2 m) nogil:
return init.Matrix2x2(self.a+m.a, self.b+m.b, self.c+m.c, self.d+m.d)
cdef inline Matrix2x2 m_msub_c(Matrix2x2* self, Matrix2x2 m) nogil:
return init.Matrix2x2(self.a-m.a, self.b-m.b, self.c-m.c, self.d-m.d)
cdef inline Matrix2x2 m_mmul_c(Matrix2x2* self, Matrix2x2 m) nogil:
return init.Matrix2x2(self.a*m.a, self.b*m.b, self.c*m.c, self.d*m.d)
cdef inline Matrix2x2 m_mdiv_c(Matrix2x2* self, Matrix2x2 m) nogil:
return init.Matrix2x2(self.a/m.a, self.b/m.b, self.c/m.c, self.d/m.d)
cdef inline Matrix2x2 m_sadd_c(Matrix2x2* self, FLOAT_T s) nogil:
return init.Matrix2x2(self.a+s, self.b+s, self.c+s, self.d+s)
cdef inline Matrix2x2 m_ssub_c(Matrix2x2* self, FLOAT_T s) nogil:
return init.Matrix2x2(self.a-s, self.b-s, self.c-s, self.d-s)
cdef inline Matrix2x2 m_smul_c(Matrix2x2* self, FLOAT_T s) nogil:
return init.Matrix2x2(self.a*s, self.b*s, self.c*s, self.d*s)
cdef inline Matrix2x2 m_sdiv_c(Matrix2x2* self, FLOAT_T s) nogil:
return init.Matrix2x2(self.a/s, self.b/s, self.c/s, self.d/s)
cdef inline Matrix2x2 m_matmul_c(Matrix2x2* self, Matrix2x2 m) nogil:
return init.Matrix2x2(
self.a*m.a + self.b*m.c, self.a*m.b + self.b*m.d,
self.c*m.a + self.d*m.c, self.c*m.b + self.d*m.d
)

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cdef class AreaEnergy(VoronoiContainer):
"""
Class for formulas relevant to the Area energy.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param sites: [np.ndarray] collection of sites.
"""
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
np.ndarray[FLOAT_T, ndim=2] site_arr):
self.edge_cache_map = &AREA_EDGE_CACHE_MAP
self.energy = 0.0
super().__init__(n, w, h, r, site_arr)
self.minimum = (<FLOAT_T>n)*(w*h/(<FLOAT_T>n)-PI*r**2)**2
cdef void precompute(self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
cdef Site xi
cdef HalfEdge em, e, ep
cdef Vector2D vdiff
cdef FLOAT_T A = PI*self.r**2
cdef FLOAT_T energy = 0
cdef INT_T i, j
for i in prange(self.sites.shape[0], nogil=True):
xi = init.Site(i, &info)
e = xi.edge(&xi)
xi.cache.energy(&xi,
(xi.cache.area(&xi, NAN) - A)**2
)
if i < self.n:
energy += xi.cache.energy(&xi, NAN)
for j in prange(xi.edge_num(&xi)):
em, ep = e.prev(&e), e.next(&e)
vdiff = em.origin(&em)
vdiff.self.vsub(&vdiff, ep.origin(&ep))
e.cache.dVdv(&e, R.vecmul(&R, vdiff))
e.cache.H(&e, VoronoiContainer.calc_H(em, e))
e = e.next(&e)
self.energy = energy
cdef void calc_grad(self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
cdef Site xi, xf
cdef HalfEdge e, f
cdef Vector2D dedxi_p
cdef BitSet edge_set
cdef INT_T num_edges = self.edges.shape[0]
cdef FLOAT_T A = PI*self.r**2
cdef FLOAT_T [:, ::1] dedx = np.zeros((self.n, 2), dtype=FLOAT)
cdef INT_T i, j
for i in prange(self.n, nogil=True):
xi = init.Site(i, &info)
e = xi.edge(&xi)
edge_set = init.BitSet(num_edges)
for j in prange(xi.edge_num(&xi)): # Looping through site edges.
f = e
while True: # Circling this vertex.
if not edge_set.add(&edge_set, f.arr_index):
xf = f.face(&f)
dedxi_p = f.cache.dVdv(&f, NAN_VECTOR) #dVdv
dedxi_p.self.smul(&dedxi_p, xf.cache.area(&xf, NAN) - A)
dedxi_p.self.matmul(&dedxi_p, e.cache.H(&e, NAN_MATRIX))
dedx[i][0] -= dedxi_p.x
dedx[i][1] -= dedxi_p.y
f = f.twin(&f)
f = f.next(&f)
if f.arr_index == e.arr_index:
break
e = e.next(&e)
edge_set.free(&edge_set)
self.grad = dedx
cdef class RadialALEnergy(VoronoiContainer):
"""
Class for formulas relevant to the Area energy.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param sites: [np.ndarray] collection of sites.
"""
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
np.ndarray[FLOAT_T, ndim=2] site_arr):
#self.edge_cache_map = &AREA_EDGE_CACHE_MAP
self.energy = 0.0
super().__init__(n, w, h, r, site_arr)
cdef void precompute(self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
pass
cdef void calc_grad(self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
pass
cdef class RadialTEnergy(VoronoiContainer):
"""
Class for formulas relevant to the Area energy.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param sites: [np.ndarray] collection of sites.
"""
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
np.ndarray[FLOAT_T, ndim=2] site_arr):
self.edge_cache_map = &RADIALT_EDGE_CACHE_MAP
self.energy = 0.0
super().__init__(n, w, h, r, site_arr)
cdef void precompute(self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
cdef Site xi
cdef HalfEdge em, e
cdef Vector2D Rnla, i2p
# All energy has a 2pir_0 term.
cdef FLOAT_T [:] site_energy = np.full(self.sites.shape[0], TAU*self.r**2)
cdef FLOAT_T [:] avg_radii = np.zeros(self.sites.shape[0])
cdef FLOAT_T energy, r0, t, tp, B, lntan, cot, cscm, cscp, FA, int_r2d, int_rd
energy, r0 = 0, self.r
cdef INT_T i, j
for i in prange(self.sites.shape[0], nogil=True):
xi = init.Site(i, &info)
e = xi.edge(&xi)
for j in prange(xi.edge_num(&xi)):
em = e.prev(&e)
e.cache.H(&e, VoronoiContainer.calc_H(em, e))
t = Calc.phi(e)
e.cache.phi(&e, t)
Rnla = e.cache.la(&e, NAN_VECTOR)
Rnla.self.neg(&Rnla)
Rnla = Rnla.rot(&Rnla)
if Rnla.x < 0:
e.cache.B(&e, -<FLOAT_T>acos(<double>(Rnla.y/e.cache.la_mag(&e, NAN))))
else:
e.cache.B(&e, <FLOAT_T>acos(<double>(Rnla.y/e.cache.la_mag(&e, NAN))))
i2p = Calc.I2(e, r0, t)
e.cache.i2p(&e, i2p)
e = e.next(&e)
# For looping again to calculate integrals.
em = xi.edge(&xi)
for j in prange(xi.edge_num(&xi)):
e = em.next(&em)
B = em.cache.B(&em, NAN)
t, tp = em.cache.phi(&em, NAN), e.cache.phi(&e, NAN)
lntan = <FLOAT_T>(log(fabs(tan(<double>((tp+B)/2))))) - \
<FLOAT_T>(log(fabs(tan(<double>((t+B)/2)))))
cot = -1/(<FLOAT_T>(tan(<double>(tp+B)))) + \
1/(<FLOAT_T>(tan(<double>(t+B))))
cscm, cscp = 1/(<FLOAT_T>(sin(<double>(t+B)))), \
1/(<FLOAT_T>(sin(<double>(tp+B))))
em.cache.lntan(&em, lntan)
em.cache.cot(&em, cot)
em.cache.csc(&em, cscp-cscm)
em.cache.csc2(&em, cscp**2 - cscm**2)
FA = (em.cache.F(&em, NAN)/em.cache.la_mag(&em, NAN))
int_r2d, int_rd = FA**2*cot, FA*lntan
avg_radii[i] += int_rd
site_energy[i] += int_r2d - 2*r0*int_rd
em = em.next(&em)
xi.cache.avg_radius(&xi, avg_radii[i]/TAU)
xi.cache.energy(&xi, site_energy[i])
if i < self.n:
energy += site_energy[i]
self.energy = energy
cdef void calc_grad(self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
cdef Site xi
cdef HalfEdge e, fm, f
cdef Vector2D dedxi_p
cdef BitSet edge_set
cdef INT_T num_edges = self.edges.shape[0]
cdef FLOAT_T r0 = self.r
cdef FLOAT_T [:, ::1] dedx = np.zeros((self.n, 2), dtype=FLOAT)
cdef INT_T i, j
for i in prange(self.n, nogil=True):
xi = init.Site(i, &info)
e = xi.edge(&xi)
edge_set = init.BitSet(num_edges)
for j in prange(xi.edge_num(&xi)): # Looping through site edges.
f = e
while True: # Circling this vertex.
fm = f.prev(&f)
if not edge_set.add(&edge_set, f.arr_index):
dedxi_p = Calc.radialt_edge_grad(f, xi, r0)
dedx[i][0] -= dedxi_p.x
dedx[i][1] -= dedxi_p.y
if not edge_set.add(&edge_set, fm.arr_index):
dedxi_p = Calc.radialt_edge_grad(fm, xi, r0)
dedx[i][0] -= dedxi_p.x
dedx[i][1] -= dedxi_p.y
f = f.twin(&f)
f = f.next(&f)
if f.arr_index == e.arr_index:
break
e = e.next(&e)
edge_set.free(&edge_set)
self.grad = dedx
cdef class Calc:
@staticmethod
cdef inline FLOAT_T phi(HalfEdge e) nogil:
cdef Vector2D da = e.cache.da(&e, NAN_VECTOR)
cdef FLOAT_T angle = <FLOAT_T>acos(<double>(da.x/e.cache.da_mag(&e, NAN)))
return angle if da.y >= 0 else TAU - angle
@staticmethod
cdef inline Vector2D I2(HalfEdge e, FLOAT_T r0, FLOAT_T t) nogil:
cdef Vector2D Rda = e.cache.da(&e, NAN_VECTOR)
Rda = Rda.rot(&Rda)
cdef Vector2D Rcircle = init.Vector2D(
-<FLOAT_T>sin(<double>t), <FLOAT_T>cos(<double>t)
)
cdef FLOAT_T p = e.cache.F(&e, NAN) / Rcircle.dot(&Rcircle, e.cache.la(&e, NAN_VECTOR))
p = ((p - r0)**2)/(Rda.dot(&Rda, Rda))
Rda.self.smul(&Rda, p)
return Rda
@staticmethod
cdef Vector2D radialt_edge_grad(HalfEdge e, Site xi, FLOAT_T r0) nogil:
cdef Site xe
cdef HalfEdge ep
cdef Vector2D Rda, i2ps, fp, gterms, q
cdef Matrix2x2 ha, hap, hdiff
cdef FLOAT_T t1, t2, lntan, cot, csc, csc2, sinB, cosB, sinBp, cosBp, F, A, B
xe = e.face(&e)
ep = e.next(&e)
F, A, B = e.cache.F(&e, NAN), e.cache.la_mag(&e, NAN), e.cache.B(&e, NAN)
t1, t2 = e.cache.phi(&e, NAN), ep.cache.phi(&ep, NAN)
lntan, cot, csc, csc2 = e.cache.lntan(&e, NAN), e.cache.cot(&e, NAN), \
e.cache.csc(&e, NAN), e.cache.csc2(&e, NAN)
sinB, cosB = <FLOAT_T>(sin(<double>(B))), <FLOAT_T>(cos(<double>(B)))
sinBp, cosBp = <FLOAT_T>(sin(<double>(B-PI_2))), \
<FLOAT_T>(cos(<double>(B-PI_2)))
ha, hap = e.get_H(&e, xi), ep.get_H(&ep, xi)
hdiff = hap.copy.msub(&hap, ha)
# If edge is part of differentiated site.
if xe.index(&xe) == xi.index(&xi):
ha.self.msub(&ha, init.Matrix2x2(1.0, 0.0, 0.0, 1.0))
hap.self.msub(&hap, init.Matrix2x2(1.0, 0.0, 0.0, 1.0))
i2ps = ep.cache.i2p(&ep, NAN_VECTOR)
i2ps.self.matmul(&i2ps, hap)
q = e.cache.i2p(&e, NAN_VECTOR)
q.self.matmul(&q, ha)
i2ps.self.vsub(&i2ps, q)
Rda = e.cache.da(&e, NAN_VECTOR)
Rda = Rda.rot(&Rda)
fp = e.cache.la(&e, NAN_VECTOR)
fp.self.matmul(&fp, R.copy.matmul(&R, ha))
fp.self.vadd(&fp, Rda.copy.matmul(&Rda, hdiff))
fp.self.smul(&fp, (F/A**2)*cot - (r0/A)*lntan)
gterms = init.Vector2D(
cosBp*lntan + sinBp*csc,
cosB*lntan + sinB*csc
)
gterms.self.smul(&gterms, r0*F/A**2)
q = init.Vector2D(
0.5*sinBp*csc2 + cosBp*cot,
0.5*sinB*csc2 + cosB*cot
)
q.self.smul(&q, -F**2/A**3)
gterms.self.vadd(&gterms, q)
gterms = gterms.rot(&gterms)
gterms.self.matmul(&gterms, hdiff)
fp.self.vadd(&fp, gterms)
fp.self.smul(&fp, 2)
return i2ps.copy.vadd(&i2ps, fp)

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cimport numpy as np
# Cython Types.
ctypedef np.int64_t INT_T
ctypedef np.float64_t FLOAT_T
# Stores initialization functions.
cdef struct Init:
IArray (*IArray)(INT_T*, (INT_T, INT_T)) nogil
FArray (*FArray)(FLOAT_T*, (INT_T, INT_T)) nogil
#IList (*IList)() nogil
BitSet (*BitSet)(INT_T) nogil
Vector2D (*Vector2D)(FLOAT_T, FLOAT_T) nogil
Matrix2x2 (*Matrix2x2)(FLOAT_T, FLOAT_T, FLOAT_T, FLOAT_T) nogil
SiteCacheMap (*SiteCacheMap)(INT_T, INT_T, INT_T, INT_T, INT_T) nogil
EdgeCacheMap (*EdgeCacheMap)(INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T,
INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T) nogil
VoronoiInfo (*VoronoiInfo)(INT_T [:, ::1], INT_T[:, ::1], FLOAT_T[:, ::1],
FLOAT_T[:, ::1], FLOAT_T[:, ::1], FLOAT_T[:, ::1],
EdgeCacheMap*) nogil
Site (*Site)(INT_T, VoronoiInfo*) nogil
HalfEdge (*HalfEdge)(INT_T, VoronoiInfo*) nogil
# Integer Array psuedo-class for continguous arrays.
cdef struct IArray:
INT_T* arr
(INT_T, INT_T) shape
INT_T (*get)(IArray*, (INT_T, INT_T)) nogil
void (*set)(IArray*, (INT_T, INT_T), INT_T) nogil
# Float Array psuedo-class for continguous arrays.
ctypedef struct FArray:
FLOAT_T* arr
(INT_T, INT_T) shape
FLOAT_T (*get)(FArray*, (INT_T, INT_T)) nogil
void (*set)(FArray*, (INT_T, INT_T), FLOAT_T) nogil
# Simple append-only dynamic integer array.
# ctypedef struct IList:
# INT_T* data
# INT_T size, length
# void (*append)(IList*, INT_T) nogil
# void (*free)(IList*) nogil
# Uses an array of bits to determine if value in set.
ctypedef struct BitSet:
INT_T* bits
bint (*add)(BitSet*, INT_T) nogil
void (*free)(BitSet*) nogil
# Psuedo-operator definitions.
ctypedef Vector2D* (*VectorSelfVecOp)(Vector2D*, Vector2D) nogil
ctypedef Vector2D (*VectorCopyVecOp)(Vector2D*, Vector2D) nogil
ctypedef Vector2D* (*VectorSelfSclOp)(Vector2D*, FLOAT_T) nogil
ctypedef Vector2D (*VectorCopySclOp)(Vector2D*, FLOAT_T) nogil
ctypedef Matrix2x2* (*MatrixSelfMatOp)(Matrix2x2*, Matrix2x2) nogil
ctypedef Matrix2x2 (*MatrixCopyMatOp)(Matrix2x2*, Matrix2x2) nogil
ctypedef Matrix2x2* (*MatrixSelfSclOp)(Matrix2x2*, FLOAT_T) nogil
ctypedef Matrix2x2 (*MatrixCopySclOp)(Matrix2x2*, FLOAT_T) nogil
ctypedef struct VectorSelfOps:
Vector2D* (*neg)(Vector2D*) nogil
VectorSelfVecOp vadd
VectorSelfVecOp vsub
VectorSelfVecOp vmul
VectorSelfVecOp vdiv
Vector2D* (*matmul)(Vector2D*, Matrix2x2) nogil
VectorSelfSclOp sadd
VectorSelfSclOp ssub
VectorSelfSclOp smul
VectorSelfSclOp sdiv
ctypedef struct VectorCopyOps:
Vector2D (*neg)(Vector2D*) nogil
VectorCopyVecOp vadd
VectorCopyVecOp vsub
VectorCopyVecOp vmul
VectorCopyVecOp vdiv
Vector2D (*matmul)(Vector2D*, Matrix2x2) nogil
VectorCopySclOp sadd
VectorCopySclOp ssub
VectorCopySclOp smul
VectorCopySclOp sdiv
ctypedef struct MatrixSelfOps:
Matrix2x2* (*neg)(Matrix2x2*) nogil
MatrixSelfMatOp madd
MatrixSelfMatOp msub
MatrixSelfMatOp mmul
MatrixSelfMatOp mdiv
MatrixSelfMatOp matmul
MatrixSelfSclOp sadd
MatrixSelfSclOp ssub
MatrixSelfSclOp smul
MatrixSelfSclOp sdiv
ctypedef struct MatrixCopyOps:
Matrix2x2 (*neg)(Matrix2x2*) nogil
MatrixCopyMatOp madd
MatrixCopyMatOp msub
MatrixCopyMatOp mmul
MatrixCopyMatOp mdiv
MatrixCopyMatOp matmul
MatrixCopySclOp sadd
MatrixCopySclOp ssub
MatrixCopySclOp smul
MatrixCopySclOp sdiv
# Psuedo-class for a 2-dimensional vector. No orientation.
ctypedef struct Vector2D:
FLOAT_T x, y
VectorSelfOps self
VectorCopyOps copy
bint (*equals)(Vector2D*, Vector2D) nogil
Vector2D (*rot)(Vector2D*) nogil
FLOAT_T (*dot)(Vector2D*, Vector2D) nogil
FLOAT_T (*mag)(Vector2D*) nogil
# Psuedo-class for a 2x2 matrix.
ctypedef struct Matrix2x2:
FLOAT_T a, b, c, d
MatrixSelfOps self
MatrixCopyOps copy
bint (*equals)(Matrix2x2*, Matrix2x2) nogil
Vector2D (*vecmul)(Matrix2x2*, Vector2D) nogil
# Psuedo-class that handles caching for sites.
ctypedef struct SiteCacheMap:
INT_T iarea, iperim, iisoparam, ienergy, iavg_radius
FLOAT_T (*area)(Site*, FLOAT_T) nogil
FLOAT_T (*perim)(Site*, FLOAT_T) nogil
FLOAT_T (*isoparam)(Site*, FLOAT_T) nogil
FLOAT_T (*energy)(Site*, FLOAT_T) nogil
FLOAT_T (*avg_radius)(Site*, FLOAT_T) nogil
# Psuedo-class that handles caching for edges.
ctypedef struct EdgeCacheMap:
INT_T iH, ila, ila_mag, ida, ida_mag, ixij, idVdv, iphi, iB, iF, ii2p,\
ilntan, icot, icsc, icsc2, size
Matrix2x2 (*H)(HalfEdge*, Matrix2x2) nogil
Vector2D (*la)(HalfEdge*, Vector2D) nogil
Vector2D (*da)(HalfEdge*, Vector2D) nogil
Vector2D (*xij)(HalfEdge*, Vector2D) nogil
Vector2D (*dVdv)(HalfEdge*, Vector2D) nogil
Vector2D (*i2p)(HalfEdge*, Vector2D) nogil
FLOAT_T (*la_mag)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*da_mag)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*phi)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*B)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*F)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*lntan)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*cot)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*csc)(HalfEdge*, FLOAT_T) nogil
FLOAT_T (*csc2)(HalfEdge*, FLOAT_T) nogil
# Psuedo-class to just contain all pertaining info for sites and edges.
ctypedef struct VoronoiInfo:
IArray sites, edges
FArray points, vertices, site_cache, edge_cache
EdgeCacheMap* edge_cache_map
# Psuedo-class for a Site.
ctypedef struct Site:
INT_T arr_index
VoronoiInfo* info
SiteCacheMap* cache
INT_T (*index)(Site*) nogil
Vector2D (*vec)(Site*) nogil
HalfEdge (*edge)(Site*) nogil
INT_T (*edge_num)(Site*) nogil
# Psuedo-class for an HalfEdge.
ctypedef struct HalfEdge:
INT_T orig_arr_index, arr_index
VoronoiInfo* info
EdgeCacheMap* cache
INT_T (*origin_index)(HalfEdge*) nogil
Vector2D (*origin)(HalfEdge*) nogil
Site (*face)(HalfEdge*) nogil
HalfEdge (*next)(HalfEdge*) nogil
HalfEdge (*prev)(HalfEdge*) nogil
HalfEdge (*twin)(HalfEdge*) nogil
Matrix2x2 (*get_H)(HalfEdge*, Site) nogil
cdef class VoronoiContainer:
cdef readonly INT_T n
cdef readonly FLOAT_T w, h, r, energy
cdef FLOAT_T [2] dim
cdef FLOAT_T [:, ::1] points, vertices, site_cache, edge_cache, grad
cdef INT_T [:, ::1] sites, edges
cdef EdgeCacheMap* edge_cache_map
cdef dict __dict__
cdef void calculate_voronoi(VoronoiContainer self,
np.ndarray[FLOAT_T, ndim=2] site_arr) except *
cdef void generate_dcel(VoronoiContainer self) except *
cdef void common_cache(VoronoiContainer self) except *
cdef void precompute(self) except *
cdef void calc_grad(self) except *
cdef void get_statistics(VoronoiContainer self) except *
@staticmethod
cdef inline Matrix2x2 calc_H(HalfEdge, HalfEdge) nogil
@staticmethod
cdef inline bint sign(FLOAT_T [::1], FLOAT_T [::1], FLOAT_T [::1])
cdef class AreaEnergy(VoronoiContainer):
cdef readonly FLOAT_T minimum
cdef void precompute(self) except *
cdef void calc_grad(self) except *
cdef class RadialALEnergy(VoronoiContainer):
cdef void precompute(self) except *
cdef void calc_grad(self) except *
cdef class RadialTEnergy(VoronoiContainer):
cdef void precompute(self) except *
cdef void calc_grad(self) except *
cdef class Calc:
@staticmethod
cdef inline FLOAT_T phi(HalfEdge) nogil
@staticmethod
cdef inline Vector2D I2(HalfEdge, FLOAT_T, FLOAT_T) nogil
@staticmethod
cdef Vector2D radialt_edge_grad(HalfEdge, Site, FLOAT_T) nogil

3
src/packsim.pyx Normal file
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include "core.pyx"
include "voronoi_dcel.pyx"
include "energy.pyx"

22
src/setup.py Normal file
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from setuptools import Extension, setup
from Cython.Build import cythonize
import numpy
MODULE_NAME = "packsim"
ext_modules = [
Extension(
MODULE_NAME,
[f'{MODULE_NAME}.pyx'],
extra_compile_args=['-fopenmp'],
extra_link_args=['-fopenmp']
)
]
setup(
name=MODULE_NAME,
ext_modules = cythonize(ext_modules, compiler_directives={
'language_level': 3, 'boundscheck' : False, 'wraparound': False, 'cdivision' : True
}),
include_dirs = [numpy.get_include()]
)

722
src/voronoi_dcel.pyx Normal file
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from packsim cimport SiteCacheMap, EdgeCacheMap, VoronoiInfo, Site, HalfEdge
#### Constants ####
init.SiteCacheMap, init.EdgeCacheMap, init.VoronoiInfo, init.Site, init.HalfEdge = \
init_sitecachemap, init_edgecachemap, init_voronoiinfo, init_site, init_halfedge
cdef SiteCacheMap SITE_CACHE_MAP = init.SiteCacheMap(0, 1, 2, 3, 4)
cdef EdgeCacheMap AREA_EDGE_CACHE_MAP = init.EdgeCacheMap(0, 4, 6, 8, 10, -1, 12, 13,
-1, -1, -1, -1, -1, -1, -1, 14)
cdef EdgeCacheMap RADIALT_EDGE_CACHE_MAP = init.EdgeCacheMap(0, 4, 6, 8, -1, 10, 12, 13,
14, 15, 16, 17, 18, 19, 20, 21)
#### SiteCacheMap Methods ####
cdef inline SiteCacheMap init_sitecachemap(INT_T iarea, INT_T iperim, INT_T iisoparam,
INT_T ienergy, INT_T iavg_radius) nogil:
cdef SiteCacheMap sc
sc.iarea, sc.iperim, sc.iisoparam, sc.ienergy, sc.iavg_radius = \
iarea, iperim, iisoparam, ienergy, iavg_radius
sc.area, sc.perim, sc.isoparam, sc.energy, sc.avg_radius = \
area, perim, isoparam, energy, avg_radius
return sc
cdef inline FLOAT_T area(Site* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.site_cache.get(&self.info.site_cache,
(self.arr_index, self.cache.iarea)
)
else:
self.info.site_cache.set(&self.info.site_cache,
(self.arr_index, self.cache.iarea), val)
return val
cdef inline FLOAT_T perim(Site* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.site_cache.get(&self.info.site_cache,
(self.arr_index, self.cache.iperim)
)
else:
self.info.site_cache.set(&self.info.site_cache,
(self.arr_index, self.cache.iperim), val)
return val
cdef inline FLOAT_T isoparam(Site* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.site_cache.get(&self.info.site_cache,
(self.arr_index, self.cache.iisoparam)
)
else:
self.info.site_cache.set(&self.info.site_cache,
(self.arr_index, self.cache.iisoparam), val)
return val
cdef inline FLOAT_T energy(Site* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.site_cache.get(&self.info.site_cache,
(self.arr_index, self.cache.ienergy)
)
else:
self.info.site_cache.set(&self.info.site_cache,
(self.arr_index, self.cache.ienergy), val)
return val
cdef inline FLOAT_T avg_radius(Site* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.site_cache.get(&self.info.site_cache,
(self.arr_index, self.cache.iavg_radius)
)
else:
self.info.site_cache.set(&self.info.site_cache,
(self.arr_index, self.cache.iavg_radius), val)
return val
#### EdgeCacheMap Methods ####
cdef inline EdgeCacheMap init_edgecachemap(INT_T iH, INT_T ila, INT_T ida, INT_T ixij,
INT_T idVdv, INT_T ii2p, INT_T ila_mag, INT_T ida_mag, INT_T iphi, INT_T iB,
INT_T iF, INT_T ilntan, INT_T icot, INT_T icsc, INT_T icsc2, INT_T size) nogil:
cdef EdgeCacheMap ec
ec.iH, ec.ila, ec.ida, ec.ixij, ec.idVdv, ec.ii2p, ec.ila_mag, ec.ida_mag, ec.iphi, \
ec.iB, ec.iF, ec.ilntan, ec.icot, ec.icsc, ec.icsc2 = iH, ila, ida, ixij, idVdv, ii2p, \
ila_mag, ida_mag, iphi, iB, iF, ilntan, icot, icsc, icsc2
ec.size = size
ec.H, ec.la, ec.da, ec.xij, ec.dVdv, ec.i2p, ec.la_mag, ec.da_mag, ec.phi, ec.B, ec.F, \
ec.lntan, ec.cot, ec.csc, ec.csc2 = H, la, da, xij, dVdv, i2p, la_mag, da_mag, phi, \
B, F, lntan, cot, csc, csc2
return ec
cdef inline Matrix2x2 H(HalfEdge* self, Matrix2x2 val) nogil:
if isnan(<double>val.a):
return init.Matrix2x2(
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iH)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iH+1)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iH+2)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iH+3)
),
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iH), val.a)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iH+1), val.b)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iH+2), val.c)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iH+3), val.d)
return val
cdef inline Vector2D la(HalfEdge* self, Vector2D val) nogil:
if isnan(<double>val.x):
return init.Vector2D(
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ila)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ila+1)
)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ila), val.x)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ila+1), val.y)
return val
cdef inline Vector2D da(HalfEdge* self, Vector2D val) nogil:
if isnan(<double>val.x):
return init.Vector2D(
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ida)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ida+1)
)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ida), val.x)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ida+1), val.y)
return val
cdef inline Vector2D xij(HalfEdge* self, Vector2D val) nogil:
if isnan(<double>val.x):
return init.Vector2D(
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ixij)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ixij+1)
)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ixij), val.x)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ixij+1), val.y)
return val
cdef inline Vector2D dVdv(HalfEdge* self, Vector2D val) nogil:
if isnan(<double>val.x):
return init.Vector2D(
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.idVdv)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.idVdv+1)
)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.idVdv), val.x)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.idVdv+1), val.y)
return val
cdef inline Vector2D i2p(HalfEdge* self, Vector2D val) nogil:
if isnan(<double>val.x):
return init.Vector2D(
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ii2p)
),
self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ii2p+1)
)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ii2p), val.x)
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ii2p+1), val.y)
return val
cdef inline FLOAT_T la_mag(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ila_mag)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ila_mag), val)
return val
cdef inline FLOAT_T da_mag(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ida_mag)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ida_mag), val)
return val
cdef inline FLOAT_T phi(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iphi)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iphi), val)
return val
cdef inline FLOAT_T B(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iB)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iB), val)
return val
cdef inline FLOAT_T F(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.iF)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.iF), val)
return val
cdef inline FLOAT_T lntan(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.ilntan)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.ilntan), val)
return val
cdef inline FLOAT_T cot(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.icot)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.icot), val)
return val
cdef inline FLOAT_T csc(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.icsc)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.icsc), val)
return val
cdef inline FLOAT_T csc2(HalfEdge* self, FLOAT_T val) nogil:
if isnan(<double>val):
return self.info.edge_cache.get(&self.info.edge_cache,
(self.arr_index, self.cache.icsc2)
)
else:
self.info.edge_cache.set(&self.info.edge_cache,
(self.arr_index, self.cache.icsc2), val)
return val
#### VoronoiInfo Methods ####
cdef inline VoronoiInfo init_voronoiinfo(INT_T [:, ::1] sites, INT_T [:, ::1] edges,
FLOAT_T [:, ::1] points, FLOAT_T [:, ::1] vertices,
FLOAT_T [:, ::1] site_cache, FLOAT_T [:, ::1] edge_cache,
EdgeCacheMap* edge_cache_map) nogil:
cdef VoronoiInfo info
info.sites = init_iarray(&sites[0,0], (<INT_T>sites.shape[0], <INT_T>sites.shape[1]))
info.edges = init_iarray(&edges[0,0], (<INT_T>edges.shape[0], <INT_T>edges.shape[1]))
info.points = init_farray(&points[0,0], (<INT_T>points.shape[0], <INT_T>points.shape[1]))
info.vertices = init_farray(&vertices[0,0],
(<INT_T>vertices.shape[0], <INT_T>vertices.shape[1])
)
info.site_cache = init_farray(&site_cache[0,0],
(<INT_T>site_cache.shape[0], <INT_T>site_cache.shape[1])
)
info.edge_cache = init_farray(&edge_cache[0,0],
(<INT_T>edge_cache.shape[0], <INT_T>edge_cache.shape[1])
)
info.edge_cache_map = edge_cache_map
return info
#### Site Methods ####
cdef inline Site init_site(INT_T arr_index, VoronoiInfo* info) nogil:
cdef Site site
site.arr_index, site.info, site.cache = arr_index, info, &SITE_CACHE_MAP
site.index, site.vec, site.edge, site.edge_num = index, vec, edge, edge_num
return site
cdef inline INT_T index(Site* self) nogil:
return self.info.sites.get(&self.info.sites, (self.arr_index, 0))
cdef inline Vector2D vec(Site* self) nogil:
return init.Vector2D(
self.info.points.get(&self.info.points, (self.index(self), 0)),
self.info.points.get(&self.info.points, (self.index(self), 1))
)
cdef inline HalfEdge edge(Site* self) nogil:
return init.HalfEdge(
self.info.sites.get(&self.info.sites, (self.arr_index, 1)), self.info
)
cdef inline INT_T edge_num(Site* self) nogil:
return self.info.sites.get(&self.info.sites, (self.arr_index, 2))
#### HalfEdge Methods ####
cdef inline HalfEdge init_halfedge(INT_T arr_index, VoronoiInfo* info) nogil:
cdef HalfEdge edge
edge.arr_index, edge.info, edge.cache = arr_index, info, info.edge_cache_map
edge.orig_arr_index = arr_index
edge.origin_index, edge.origin, edge.face, edge.next, edge.prev, edge.twin, edge.get_H = \
origin_index, origin, face, edge_next, prev, twin, get_H
return edge
cdef inline INT_T origin_index(HalfEdge* self) nogil:
return self.info.edges.get(&self.info.edges, (self.arr_index, 0))
cdef inline Vector2D origin(HalfEdge* self) nogil:
return init.Vector2D(
self.info.vertices.get(&self.info.vertices, (self.origin_index(self), 0)),
self.info.vertices.get(&self.info.vertices, (self.origin_index(self), 1))
)
cdef inline Site face(HalfEdge* self) nogil:
return init.Site(
self.info.edges.get(&self.info.edges, (self.arr_index, 1)), self.info
)
cdef inline HalfEdge edge_next(HalfEdge* self) nogil:
return init.HalfEdge(
self.info.edges.get(&self.info.edges, (self.arr_index, 2)), self.info
)
cdef inline HalfEdge prev(HalfEdge* self) nogil:
return init.HalfEdge(
self.info.edges.get(&self.info.edges, (self.arr_index, 3)), self.info
)
cdef inline HalfEdge twin(HalfEdge* self) nogil:
return init.HalfEdge(
self.info.edges.get(&self.info.edges, (self.arr_index, 4)), self.info
)
cdef inline Matrix2x2 get_H(HalfEdge* self, Site xi) nogil:
cdef INT_T this_e = self.origin_index(self)
cdef HalfEdge s_e = xi.edge(&xi)
cdef INT_T i
for i in range(xi.edge_num(&xi)):
if s_e.origin_index(&s_e) == this_e:
return s_e.cache.H(&s_e, NAN_MATRIX)
s_e = s_e.next(&s_e)
return init.Matrix2x2(0.0, 0.0, 0.0, 0.0)
cdef class VoronoiContainer:
"""
Class for Voronoi diagrams, stored in a modified DCEL.
:param n: [int] how many sites to generate.
:param w: [float] width of the bounding domain.
:param h: [float] height of the bounding domain.
:param r: [float] radius of zero energy circle.
:param sites: np.ndarray collection of sites.
"""
def __init__(VoronoiContainer self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r, object site_arr):
self.n, self.w, self.h, self.r = n, w, h, r
self.dim = [w, h]
self.calculate_voronoi(site_arr.astype(FLOAT))
self.generate_dcel()
self.common_cache()
self.precompute()
self.calc_grad()
self.get_statistics()
# #print(np.asarray(self.site_cache[0]))
# print(np.asarray(self.edges[:6]))
# #print(np.asarray(self.edge_cache[:6]))
# print(self.gradient)
cdef void calculate_voronoi(VoronoiContainer self,
np.ndarray[FLOAT_T, ndim=2] site_arr) except *:
"""
Does all necessary computation and caching once points are set.
:param site_arr: initial points for this container.
"""
global SYMM
cdef np.ndarray[FLOAT_T, ndim=2] symm = np.asarray(SYMM).reshape(9,2)
cdef np.ndarray[FLOAT_T, ndim=1] dim = np.asarray(self.dim)
cdef np.ndarray[FLOAT_T, ndim=2] full_site_arr = np.empty((self.n*9+8, 2), dtype=FLOAT)
# Generate periodic sites and sites that bound periodic sites.
cdef INT_T i
for i in range(9):
full_site_arr[self.n*i:self.n*(i+1)] = site_arr + symm[i]*dim
if i > 0:
full_site_arr[9*self.n+i-1] = dim/2 + 2*dim*symm[i]
# Use SciPy to compute the Voronoi set.
self.scipy_vor = scipy.spatial.Voronoi(full_site_arr)
self.points = self.scipy_vor.points
self.vertices = self.scipy_vor.vertices
cdef void generate_dcel(VoronoiContainer self) except *:
cdef INT_T npoints = self.n*9+8
cdef array.array int_tmplt = array.array('q', [])
cdef np.ndarray[INT_T, ndim=1] offsets = np.zeros(self.n*9+1, dtype=INT)
cdef array.array vert_indices = array.clone(int_tmplt, 0, False)
# Flatten regions into array, so it can be used later.
cdef INT_T i
for i in range(self.n*9):
verts = self.scipy_vor.regions[self.scipy_vor.point_region[i]]
offsets[i+1] = offsets[i] + len(verts) # Build offsets.
vert_indices.extend(array.array('q', verts)) # Flatten
# Get vertices of original N sites.
cdef np.ndarray[INT_T, ndim=1] vert_indices_np = np.asarray(vert_indices)
cdef np.ndarray[INT_T, ndim=1] border_sites = np.unique(np.searchsorted(
np.asarray(offsets), # Check indices where below matches would be inserted
np.nonzero(np.isin( # Indices of other verts being in bound verts.
vert_indices_np[offsets[self.n]:], # Rest of the verts to check.
np.unique(vert_indices_np[:offsets[self.n]]) # Bound verts
))[0] + offsets[self.n],
side='right' # If on index == offset_number, should be part of the next site.
) - 1) # Subtract by one to get actual site number.
cdef INT_T border_num = len(border_sites)
# Build sites array.
# [Site Index, Edge Index/Offset, Edge Count]
self.sites = np.empty((self.n+border_num, 3), dtype=INT)
self.sites.base[:self.n, 0] = np.arange(self.n, dtype=INT)
self.sites.base[self.n:, 0] = border_sites
self.sites.base[:self.n+1, 1] = offsets[:self.n+1]
for i in range(self.n):
self.sites[i, 2] = self.sites[i+1, 1] - self.sites[i, 1]
cdef INT_T edge_count = offsets[self.n]
cdef INT_T diff
for i in range(border_num):
diff = offsets[border_sites[i]+1] - offsets[border_sites[i]]
edge_count += diff
self.sites[self.n+i, 2] = diff
if i < border_num - 1:
self.sites[self.n+i+1, 1] = self.sites[self.n+i, 1] + diff
# Build edges array
# [Origin Index, Site Index, Next Index, Prev Index, Twin Index]
self.edges = np.empty((edge_count, 5), dtype=INT)
cdef np.ndarray[INT_T, ndim=1] site_verts
cdef INT_T j, site_i, edge_i, edge_offset, vert_num, twin_index, prev_res
edge_indices = dict()
for i in range(self.n + border_num):
site_i = self.sites[i, 0]
edge_offset = self.sites[i, 1]
site_verts = vert_indices_np[offsets[site_i]:offsets[site_i+1]]
# Scipy outputs sorted vertices, but reverse if not counterclockwise.
if not VoronoiContainer.sign(self.points[site_i],
self.vertices[site_verts[0]], self.vertices[site_verts[1]]):
site_verts = np.flip(site_verts)
vert_num = offsets[site_i+1] - offsets[site_i]
for j in range(vert_num):
edge_i = edge_offset+j
self.edges[edge_i, 0] = site_verts[j]
self.edges[edge_i, 1] = i
# Add vert_num because of C modulo to get always positive.
self.edges[edge_i, 2] = (j+vert_num+1) % vert_num + edge_offset
self.edges[edge_i, 3] = (j+vert_num-1) % vert_num + edge_offset
# Get reversed tuple to theck for twin.
twin_index = edge_indices.get(
(site_verts[(j+1) % vert_num], site_verts[j]
), -1)
self.edges[edge_i, 4] = twin_index
if twin_index == -1:
edge_indices[(site_verts[j], site_verts[(j+1) % vert_num])] = \
j + edge_offset
else:
self.edges[twin_index, 4] = j + edge_offset
self.site_cache = np.empty((self.n + border_num, 5), dtype=FLOAT)
self.edge_cache = np.empty((edge_count, self.edge_cache_map.size), dtype=FLOAT)
cdef void common_cache(VoronoiContainer self) except *:
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
cdef Site xi
cdef HalfEdge em, ep
cdef Vector2D p, q, la, da, Rla
cdef FLOAT_T [:] area = np.zeros(self.sites.shape[0], dtype=FLOAT)
cdef FLOAT_T [:] perim = np.zeros(self.sites.shape[0], dtype=FLOAT)
cdef INT_T i, j
cdef FLOAT_T e_area, la_mag
for i in prange(self.sites.shape[0], nogil=True):
xi = init.Site(i, &info)
em = xi.edge(&xi)
for j in prange(xi.edge_num(&xi)):
ep = em.next(&em)
p, q = em.origin(&em), ep.origin(&ep)
la, da = q.copy.vsub(&q, p), p.copy.vsub(&p, xi.vec(&xi)) # vp - vm, vm - xi
la_mag = la.mag(&la)
e_area = la.dot(&la, da.rot(&da))
Rla = la.rot(&la)
em.cache.la(&em, la)
em.cache.la_mag(&em, la_mag)
em.cache.da(&em, da)
em.cache.da_mag(&em, da.mag(&da))
em.cache.xij(&em, Rla.copy.smul(&Rla, -e_area/la.dot(&la, la)))
if info.edge_cache_map.iF != -1:
em.cache.F(&em, e_area)
area[i] += e_area
perim[i] += la_mag
em = em.next(&em)
xi.cache.area(&xi, area[i]/2)
xi.cache.perim(&xi, perim[i])
xi.cache.isoparam(&xi, 2*PI*area[i]/(perim[i]*perim[i]))
@staticmethod
cdef inline Matrix2x2 calc_H(HalfEdge em, HalfEdge ep) nogil:
cdef Vector2D xmv, xpv, im, mp, right, Rpm, Rim, f
cdef Matrix2x2 h
cdef FLOAT_T im2, mp2
# Vectors from xi to xm and xp.
xmv, xpv = em.cache.xij(&em, NAN_VECTOR), ep.cache.xij(&ep, NAN_VECTOR)
im, mp = xmv.copy.neg(&xmv), xmv.copy.vsub(&xmv, xpv) # -xmv, xmv - xpv
im2, mp2 = -(xmv.dot(&xmv, xmv)), xmv.dot(&xmv, xmv) - xpv.dot(&xpv, xpv)
# (-xmv*xmv, xmv*xmv - xpv*xpv)
right = init.Vector2D(im2, mp2)
Rpm, Rim = R.vecmul(&R, mp.copy.neg(&mp)), im.rot(&im) # R*-mp, R*im
h = init.Matrix2x2(Rpm.x, Rim.x, Rpm.y, Rim.y) # [Rpm | Rim], h is temporary.
f = h.vecmul(&h, right) # [Rpm | Rim]*right
h = R.copy.smul(&R, mp2*(2*mp.dot(&mp, Rim))) # fp*g, g is a scalar.
# (fp*g - f*gp)/(g**2). f is a column vector, gp = 2*Rpm is a row vector.
h.self.msub(&h, init.Matrix2x2(
f.x*2*Rpm.x, f.x*2*Rpm.y, f.y*2*Rpm.x, f.y*2*Rpm.y
))
h.self.sdiv(&h, (2*mp.dot(&mp, Rim))**2)
return h
@staticmethod
cdef inline bint sign(FLOAT_T [::1] ref, FLOAT_T [::1] p, FLOAT_T [::1] q):
"""
Outputs if p2 - self is counterclockwise of p1 - self.
:param p1: [List[float]] first vector
:param p2: [List[float]] second vector
:return: [bool] returns if counterclockwise.
"""
return ((q[0] - ref[0])*-(p[1] - ref[1]) + \
(q[1] - ref[1])*(p[0] - ref[0])) >= 0
# global ROT
# cdef np.ndarray[FLOAT_T, ndim=2] rot = np.asarray(ROT).reshape(2,2)
# return (q - ref).dot(rot.dot(p - ref)) >= 0
cdef void precompute(self) except *:
pass
cdef void calc_grad(self) except *:
pass
cdef void get_statistics(self) except *:
self.stats = {}
cache = self.site_cache[:self.n, :]
self.stats["site_areas"] = np.asarray(cache[:, SITE_CACHE_MAP.iarea])
edge_count = np.empty((self.n,))
for i in range(self.n):
edge_count[i] = len(self.vor_data.regions[self.vor_data.point_region[i]])
self.stats["site_edge_count"] = edge_count
self.stats["site_isos"] = np.asarray(cache[:, SITE_CACHE_MAP.iisoparam])
self.stats["site_energies"] = np.asarray(cache[:, SITE_CACHE_MAP.ienergy])
self.stats["avg_radius"] = np.asarray(cache[:, SITE_CACHE_MAP.iavg_radius])
self.stats["isoparam_avg"] = self.stats["site_areas"] / \
(PI*self.stats["avg_radius"]**2)
edges = np.asarray(self.edges)
mask = np.nonzero(edges[:, 0] != -1)[0]
all_edges = mask[(mask % 2 == 0)]
caches = edges[all_edges, 4]
edge_cache = np.asarray(self.edge_cache)
self.stats["edge_lengths"] = edge_cache[caches, self.edge_cache_map.ila_mag]
@property
def site_arr(self):
return np.asarray(self.points[:self.n], dtype=FLOAT)
@property
def vor_data(self):
return self.scipy_vor
@property
def gradient(self):
return np.asarray(self.grad, dtype=FLOAT)
def add_sites(self, add):
return (self.site_arr + add) % np.asarray(self.dim, dtype=FLOAT)
def iterate(self, FLOAT_T step):
k1 = self.gradient
k2 = self.__class__(self.n, self.w, self.h, self.r,
self.add_sites(step*k1/2)
).gradient
k3 = self.__class__(self.n, self.w, self.h, self.r,
self.add_sites(step*(-k1+ 2*k2))
).gradient
return self.add_sites((step/6)*(k1+2*k2+k3)), k1
def hessian(self, d: float) -> np.ndarray:
"""
Obtains the approximate Hessian.
:param d: [float] small d for approximation.
:return: 2Nx2N array that represents Hessian.
"""
HE = np.zeros((2*self.n, 2*self.n))
new_sites = np.copy(self.site_arr) # Maintain one copy for speed.
for i in range(self.n):
for j in range(2):
mod = self.w if j == 0 else self.h
new_sites[i][j] = (new_sites[i][j] + d) % mod
Ep = self.__class__(self.n, self.w, self.h, self.r, new_sites)
new_sites[i][j] = (new_sites[i][j] - 2*d) % mod
Em = self.__class__(self.n, self.w, self.h, self.r, new_sites)
new_sites[i][j] = (new_sites[i][j] + d) % mod
HE[:, 2*i+j] = ((Ep.gradient - Em.gradient)/(2*d)).flatten()
# Average out discrepencies, since it should be symmetric.
for i in range(2*self.n):
for j in range(i, 2*self.n):
HE[i][j] = (HE[i][j] + HE[j][i])/2
HE[j][i] = HE[i][j]
return HE

33
test_sim.json Normal file
View File

@ -0,0 +1,33 @@
{
"calc": {
"n_objects": 10,
"width": 10.0,
"height": 10.0,
"natural_radius": 4.0,
"energy": "radial-t"
},
"sim": {
"mode": "flow",
"step_size": 0.05,
"threshold": 0.0001
}
}
/*
# ARR = np.array([
# [1, 1], [3, 1], [5, 1],
# [1, 3], [3, 3], [5, 3],
# [1, 5], [3, 5], [5, 5],
# [1, 7], [3, 7], [5, 7],
# [1, 9], [3, 9], [5, 9],
# [7, 1], [8, 1], [9, 1],
# [7, 2], [8, 2], [9, 2],
# [7, 3], [8, 3], [9, 3],
# [7, 4], [8, 4], [9, 4],
# [7, 5], [8, 5], [9, 5],
# [7, 6], [8, 6], [9, 6],
# [7, 7], [8, 7], [9, 7],
# [7, 8], [8, 8], [9, 8],
# [7, 9], [8, 9], [9, 9],
# ], dtype=float)
*/