Gamma Graph

Se muestran diferentes ejemplos de los gamma vecindarios para diferentes \(n\) puntos, \(\gamma_0\), \(\gamma_1\).

import proximitygraphs as pg
import time

vcolor = '#051650'
ecolor = '#0A2472'

uniform_sphere = pg.SetPoints.uniform_sphere(n=512*24, dims = 2, seed=0)
uniform_sphere.draw(figsize=(6,6))

(<Figure size 600x600 with 1 Axes>, <Axes: >)

Single Neighborhood, 512*24=12288 points

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0, gamma1=0, block_size=512)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  10.909894943237305

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0, gamma1=0, block_size=16)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  12.347464561462402

Two Neighborhoods

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0.2, gamma1=0.2)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  19.422595500946045

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0.2, gamma1=0.2, block_size=16)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  23.289004802703857

Special cases, 100 points

uniform_sphere = pg.SetPoints.uniform_sphere(n=100, dims = 2, seed=0)
uniform_sphere.draw(figsize=(6,6))

(<Figure size 600x600 with 1 Axes>, <Axes: >)

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=1, gamma1=1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.0060346126556396484

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=-1, gamma1=-1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.04416966438293457

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=1, gamma1=-1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.028722047805786133

Examples 100 points

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0.25, gamma1=0.5)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.016045093536376953

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0.1, gamma1=0.1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.037732601165771484

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0, gamma1=0)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.013146638870239258

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0, gamma1=-0.5)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.027077674865722656

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=-0.2, gamma1=-0.2)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.02505350112915039

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=-0.25, gamma1=-0.25)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.02154374122619629

Special cases, 1000 points

uniform_sphere = pg.SetPoints.uniform_sphere(n=1000, dims = 2, seed=0)
uniform_sphere.draw(figsize=(6,6))

(<Figure size 600x600 with 1 Axes>, <Axes: >)

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=1, gamma1=1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.009044170379638672

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=1, gamma1=-1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.01305842399597168

Examples 1000 points

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0.25, gamma1=0.5)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.3076331615447998

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0.1, gamma1=0.1)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.17214369773864746

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0, gamma1=0)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  0.12284183502197266

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=0, gamma1=-0.5)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  13.261591911315918

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=-0.2, gamma1=-0.2)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  24.830246448516846

start = time.time()
H = pg.Gamma_Graph(uniform_sphere, gamma0=-0.25, gamma1=-0.25)
H.draw2(title=True, details=True, figsize=(6,6), v_size=3, e_size=1, v_color=vcolor, e_color=ecolor, fontsize=10)
end = time.time()
print("Time taken: ", end - start)

Time taken:  25.226677656173706