def brute_force_t1():
print "Now attempting to find \mathbb{G}_{T=1} by brute-force simulation..."
num = 25
(impossible,suboptimal,optimal) = ([],[],[])
(basis0,basis1,basis2) = (np.array([0,1,1]), np.array([1,0,1]), np.array([1,1,0]))
(c0,c1,c2) = np.meshgrid(np.linspace(0,1,num), np.linspace(0,1,num), np.linspace(0,1,num))
(c0,c1,c2) = (c0.ravel(),c1.ravel(),c2.ravel())
print "We must iterate through " + str(len(c0)) + " simulated points ... "
# The case of i=0 is when all the components are zero.
for i in range(1,len(c0)):
if i % 100000 == 0:
print "Now on point " + str(i)
p = c0[i]*basis0 + c1[i]*basis1 + c2[i]*basis2
w = np.array([c0[i], c1[i], c2[i]])
w = w / np.sum(w)
six_points = par.get_six_points(p, w, False)
result = position_t0(six_points)
if result == "Impossible":
impossible.append(p)
elif result == "Suboptimal":
suboptimal.append(p)
else:
optimal.append(p)
print "Number of impossible, suboptimal, and optimal points: {0}, {1}, {2}.".format(
len(impossible),len(suboptimal),len(optimal))
# Next step is to plot. There are several ways we can do this.
plt3d = plt.figure().gca(projection='3d')
x_coordinates = [point[0] for point in impossible]
y_coordinates = [point[1] for point in impossible]
z_coordinates = [point[2] for point in impossible]
plt3d.plot_surface(x_coordinates, y_coordinates, z_coordinates)
plt.xlabel('X axis')
plt.ylabel('Y axis')
plt.show()
np.array([0,2,2]),np.array([2,0,2]),np.array([2,2,0]),
np.array([1.5,1.5,1./3]),np.array([1./3,1.5,1.5]),np.array([1.5,1./3,1.5])]
(basis0,basis1,basis2) = (np.array([0,2,2]), np.array([2,0,2]), np.array([2,2,0]))
rationals = par.generate_rationals(30, 1)
print "There are a total of " + str(len(rationals)) + " possible values for a single basis... "
points_tested = 0
for first in range(0, len(rationals)):
for second in range(first, len(rationals)):
for third in range(second, len(rationals)):
(c0,c1,c2) = (rationals[first],rationals[second],rationals[third])
p = c0*basis0 + c1*basis1 + c2*basis2
if np.sum(p) < 2:
continue
w = np.array([c0, c1, c2])
w = w / np.sum(w)
six_points = par.get_six_points(p, w, False)
points_tested += 1
if points_tested % 250000 == 0:
print "Points tested: {}.".format(points_tested)
done = False
for s in six_points:
if par.position_t1(s) == "Impossible":
done = True
break
if not done:
for s in six_points:
if par.position_t1(s) == "Optimal":
symmetrical_points = replicate(p)
for pt in symmetrical_points:
optimal.append(pt)
done = True
