def generalDoubleTiltedRegion(D):
A = np.linspace(0, 2, D)
Phi = np.linspace(0, np.pi / 2, D)
Plane = np.zeros((D, D))
for i, phi in enumerate(Phi):
print(f'{i+1}/{D}')
for j, a in enumerate(A):
B = GDT.functional(a, phi)
accuracy = 0.001
P, Qn = T.Best_point(B, accuracy)
Qs = St.satoshiTest(P)
if Qn:
if Qs:
Plane[i][j] = 1
else:
Plane[i][j] = 2
else:
if Qs:
Plane[i][j] = 3
else:
Plane[i][j] = 0
plt.imshow(Plane.T, extent=[0, np.pi / 2, 2, 0])
plt.colorbar()
plt.show()
def compareSatoshiAndNumeric(N):
bothEx = 0
bothNoEx = 0
SatEx = 0
NumEx = 0
for i in range(N):
if i % 100 == 0:
print(f'{i+1}/{N}')
theta = np.random.rand() * np.pi / 4
a0 = np.random.rand() * 2 * np.pi
a1 = np.random.rand() * 2 * np.pi
b0 = np.random.rand() * 2 * np.pi
b1 = np.random.rand() * 2 * np.pi
P = T.find_P(theta, a0, a1, b0, b1)
isExtremal = St.satoshiTest(P)
accuracy = 0.001
isExtremal2 = T.is_exposed(theta, a0, a1, b0, b1, accuracy, limit=1)
if isExtremal:
if isExtremal2:
bothEx += 1
else:
SatEx += 1
else:
if isExtremal2:
NumEx += 1
else:
bothNoEx += 1
print(bothNoEx, bothEx, SatEx, NumEx)
def optimalTheta(a0, a1, b0, b1):
n = 100
Theta = np.linspace(0, np.pi / 2, n)
flag = 0
for theta in Theta:
P = T.find_P(theta, a0, a1, b0, b1)
Q = St.satoshiTest(P)
print(theta, Q)
def research(theta, a0, a1, b0, b1):
def maximum(S):
m = 0
for x in range(2):
for y in range(2):
if S[x][y] > m:
m = S[x][y]
return m
def getThetaFromSinSquared(s):
return np.arccos(np.sqrt(1 - s))
P = T.find_P(theta, a0, a1, b0, b1)
S_p, S_m = St.SPlusTemp(P)
print(S_p)
print(S_m)
flag = False
for x in range(2):
for y in range(2):
thetaNew = getThetaFromSinSquared(S_p[x][y])
Pnew = T.find_P(thetaNew, a0, a1, b0, b1)
stlm = St.STLM(Pnew, thetaNew)
print(stlm, "STLM")
Qs = St.satoshiTest(Pnew)
print(Qs, thetaNew)
if Qs:
flag = True
for x in range(2):
for y in range(2):
thetaNew = getThetaFromSinSquared(S_m[x][y])
Pnew = T.find_P(thetaNew, a0, a1, b0, b1)
stlm = St.STLM(Pnew, thetaNew)
print(stlm, "STLM")
Qs = St.satoshiTest(Pnew)
print(Qs, thetaNew)
if Qs:
flag = True
print("i co?", flag)
def pointsWithTwoSolutions(N):
for i in range(N):
if i % 100 == 0:
print(f'{i+1}/{N}')
a = np.random.rand() * 0.25 - 0.125
b = np.random.rand() * 2 - 1
c = np.random.rand() * 2 - 1
# a = 1/4
# b = 1/8
c = 1 / np.sqrt(2)
P = [a, a, b, b, c, c, c, -c]
isExtremal = St.satoshiTest(P)
print(isExtremal)
def plotExposed(D):
acc = 1e-4
x0 = 0
x_end = np.pi / 2
y0 = 0
y_end = 1
Y = np.linspace(y0, y_end, D)
X = np.linspace(x0, x_end, D)
Map = np.zeros((D, D))
for y, CosA in enumerate(Y):
for x, theta in enumerate(X):
a0 = 0
b0 = 0
a1 = np.arccos(CosA)
b1 = -np.arccos(CosA) + 2 * np.pi
P = T.find_P(theta, a0, a1, b0, b1)
P2 = symmetricPoint2(theta, CosA)
# print(np.round(P-P2,7))
# exp1 = T.is_exposed(theta, a0, a1, b0, b1, acc)
exp2 = T.is_exposed_hypo(theta, a0, a1, b0, b1)
exp3 = St.satoshiTest(P)
nonloc = T.is_nonlocalPoint(P)
print(exp2)
stlm = St.STLM(P, theta)
Ptlm = T.find_P(np.pi / 2, a0, a1, b0, b1)
tlm = T.TLM(Ptlm)
print(stlm, tlm)
Map[x][D - y - 1] = exp2
plt.imshow(Map.T, extent=[x0, x_end, y0, y_end])
plt.colorbar()
plt.xlabel("theta")
plt.ylabel("cos(a)")
plt.savefig("symmetric.png")
plt.show()
def generalWolfRegion(D):
acc = 0.001
D = 101
T = np.linspace(-1, 1, D)
R = np.linspace(0, 2, D)
Plane = np.zeros((D, D))
Plane2 = np.zeros((D, D))
for i, t in enumerate(T):
print(f'{i+1}/{D}')
for j, r in enumerate(R):
B = GW.functional(t, r)
P = GW.quantumPoint(t, r)
# print(P)
Qs = St.satoshiTest(P)
_, Qn = T.Best_point(B, acc)
Plane[i][j] = Qs
Plane2[i][j] = Qn
if Qn and (not Qs):
Qs = St.satoshiTestComment(P)
plt.imshow(Plane, extent=[0, 2 * np.pi, 4, 0])
plt.show()
plt.imshow(Plane2, extent=[0, 2 * np.pi, 4, 0])
plt.show()
def compareTests(N):
St0we0 = 0
St0we1 = 0
St1we0 = 0
St1we1 = 0
for i in range(N):
if i % 100 == 0:
print(f'{i+1}/{N}')
a0 = np.random.rand() * 2 * np.pi
a1 = np.random.rand() * 2 * np.pi
b0 = np.random.rand() * 2 * np.pi
b1 = np.random.rand() * 2 * np.pi
theta = np.random.rand() * np.pi / 2
P = T.find_P(theta, a0, a1, b0, b1)
Qs = St.satoshiTest(P)
Qw = newTest(theta, a0, a1, b0, b1)
if Qs:
if Qw:
St1we1 += 1
else:
St1we0 += 1
print(theta, a0, a1, b0, b1)
check(theta, a0, a1, b0, b1)
break
else:
if Qw:
St0we1 += 1
print(theta, a0, a1, b0, b1)
check(theta, a0, a1, b0, b1)
break
else:
St0we0 += 1
print(St1we1, St1we0, St0we1, St0we0)
def research2(theta, a0, a1, b0, b1):
def maximum(S):
m = 0
for x in range(2):
for y in range(2):
if S[x][y] > m:
m = S[x][y]
return m
def getThetaFromSinSquared(s):
return np.arccos(np.sqrt(1 - s))
def largerTheta(theta):
P = T.find_P(theta, a0, a1, b0, b1)
S_p, S_m = St.SPlusTemp(P)
# print(S_p)
# print(S_m)
thetaNew = getThetaFromSinSquared(maximum(S_p))
return thetaNew
print("Optimal theta start")
optTheta = optimalTheta(a0, a1, b0, b1)
print("Optimal theta end")
flag = False
while (theta < optTheta - acc) and (not flag):
Pnew = T.find_P(theta, a0, a1, b0, b1)
stlm = St.STLM(Pnew, theta)
Qs = St.satoshiTest(Pnew)
print(Qs, stlm, theta)
thetaNew = largerTheta(theta)
if Qs:
flag = True
if abs(thetaNew - theta) < acc:
flag = True
theta = thetaNew
print("Next")
def checkCabelloPoint():
alpha = np.random.rand() * np.pi
beta = np.random.rand() * np.pi
P = Pp.cabelloPoint(alpha, beta, 0, 0)
print(St.satoshiTest(P))