def localPointsBeforeTreshold(N):
def hypoTreshold(a0, a1, b0, b1):
def value(a, b):
return -np.sin(a) * np.sin(b) / (np.cos(a) * np.cos(b) - 1)
return value(a0, b0), value(a0, b1), value(a1, b0), value(a1, b1)
for i in range(N):
if i % 100 == 0:
print(f'{i+1}/{N}')
a0 = np.random.rand() * np.pi
a1 = np.random.rand() * np.pi
b0 = np.random.rand() * np.pi
b1 = np.random.rand() * np.pi
P = T.find_P(np.pi / 2, a0, a1, b0, b1)
if T.TLM(P):
# treshold = tresholdTheta(a0,a1,b0,b1, 1e-5)
tresholds = hypoTreshold(a0, a1, b0, b1)
n = 100
# Theta = np.linspace(0, treshold,n)
Theta = np.linspace(0, np.pi / 2, n)
for theta in Theta:
for tresh in tresholds:
if np.abs(theta - tresh) < 0.03:
print("facet")
P = T.find_P(theta, a0, a1, b0, b1)
nl = T.is_nonlocalPoint(P)
print(nl)
print("next")
def hypothesis2(N):
tlm0flag0 = 0
tlm0flag1 = 0
tlm1flag0 = 0
tlm1flag1 = 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.pi / 2
P = T.find_P(theta, a0, a1, b0, b1)
tlm = T.TLM(P)
# print("TLM", tlm)
flag = optimalTheta(a0, a1, b0, b1)
# print(tlm, flag, "tutaj")
if tlm:
if flag:
tlm1flag1 += 1
else:
tlm1flag0 += 1
else:
if flag:
tlm0flag1 += 1
else:
tlm0flag0 += 1
print(tlm1flag1, tlm1flag0, tlm0flag1, tlm0flag0)
def check(theta, a0, a1, b0, b1):
P = T.find_P(theta, a0, a1, b0, b1)
Qs = St.satoshiTestComment(P)
tlm = T.TLM(T.find_P(np.pi / 2, a0, a1, b0, b1))
wholeSp, thetaNew = St.SPlusCondition(P)
Qw = newTest(theta, a0, a1, b0, b1)
# flag = optimalTheta(a0,a1,b0,b1)
Qn = T.is_exposed(theta, a0, a1, b0, b1, 0.0001)
print(theta, a0, a1, b0, b1)
print(Qs, Qw, Qn, "extremal")
print(tlm, wholeSp)
def newTest(theta, a0, a1, b0, b1):
Pmax = T.find_P(np.pi / 2, a0, a1, b0, b1)
tlm = T.TLM(Pmax)
if tlm:
P = T.find_P(theta, a0, a1, b0, b1)
wholeSp, thetaNew = St.SPlusCondition(P)
if np.abs(thetaNew - theta) > acc:
print("something is wrong with theta")
if wholeSp:
return 1
return 0
def notUniquePointsInvestigating(N):
for i in range(N):
P = np.round(T.notUniquePoints(), 6)
correct, realisation, wholeSp = T.twoQubitRepresentationSpecial(P)
if correct:
print(P, "point")
theta, a0, a1, b0, b1 = realisation
# print(correct, theta, a0/np.pi, a1/np.pi, b0/np.pi, b1/np.pi, wholeSp, np.sin(theta)**2, "tu")
# print(P[0]/np.cos(theta), P[1]/np.cos(theta), P[2]/np.cos(theta), P[3]/np.cos(theta), "cosinusy prawdziwe")
print(St.STLM(P, theta), "stlm")
Ptlm = T.find_P(np.pi / 2, a0, a1, b0, b1)
print(T.find_P(theta, a0, a1, b0, b1), "Punkt zwrotny")
print(T.is_nonlocalPoint(P), "is nonlocal?")
print(T.TLM(Ptlm), "Tlm")
print(T.is_exposed(theta, a0, a1, b0, b1, 0.001), "exposed")
def tresholdTheta(a0, a1, b0, b1, acc):
l = 0
r = np.pi / 2
P0 = T.find_P(r, a0, a1, b0, b1)
if not T.TLM(P0):
return np.pi / 2
while r - l > acc:
theta = (r + l) / 2
Q = newTest(theta, a0, a1, b0, b1)
# print(l,r,Q)
if Q:
r = theta
else:
l = theta
return (r + l) / 2
def notUniquePoint():
# P = [0.4445537842667646, 0.24544802147218514, 0.734354006208671, 0.734354006208671, 0.542908951128687, 0.542908951128687, 0.3966948365612542, 0.3966948365612542]
P5 = [0.024973, 0.058992, 0.5, 0.5, 0.07546, 0.07546, 0.092469, 0.092469]
P4 = [
0.25, 0.125, -0.262176, -0.0930301, -0.731555, -0.689269, -0.698783,
0.654382
]
P2 = [
0.5, 0.5, -np.sqrt(2 / 5), 0, -np.sqrt(5 / 2) / 2,
-np.sqrt(5 / 2) / 2 + 1 / np.sqrt(10), -np.sqrt(5 / 2) / 2,
np.sqrt(5 / 2) / 2 - 1 / np.sqrt(10)
]
P3 = [
1 / 4, 1 / 2, -np.sqrt(7 / 3) / 3, 1 / np.sqrt(21),
-37 / (12 * np.sqrt(21)), -37 / (12 * np.sqrt(21)) + 1 / 4 *
(np.sqrt(7 / 3) / 3 + 1 / np.sqrt(21)),
-np.sqrt(7 / 3) / 12 - 37 / (12 * np.sqrt(21)),
-np.sqrt(7 / 3) / 12 + 43 / (12 * np.sqrt(21))
]
b = np.random.rand()
a1 = np.random.rand()
a0 = np.random.rand()
b = 0.5
a0 = 0.25
a1 = 0.5
A0B0 = (a0 + a1 + a0 * b**2 - a1 * b**2) / (2 * b)
A0B1 = A0B0
A1B0 = A0B0 - b * (a0 - a1)
A1B1 = A0B0 - b * (a0 - a1)
P = [a0, a1, b, b, A0B0, A0B1, A1B0, A1B1]
# if A0B0 < 1:
print(P, "punkt")
correct, realisation, wholeSp = T.twoQubitRepresentation(P)
theta, a0, a1, b0, b1 = realisation
# print(correct, theta, a0/np.pi, a1/np.pi, b0/np.pi, b1/np.pi, wholeSp, np.sin(theta)**2, "tu")
# print(P[0]/np.cos(theta), P[1]/np.cos(theta), P[2]/np.cos(theta), P[3]/np.cos(theta), "cosinusy prawdziwe")
print(St.STLM(P, theta), "stlm")
Ptlm = T.find_P(np.pi / 2, a0, a1, b0, b1)
print(T.find_P(theta, a0, a1, b0, b1), "Punkt zwrotny")
print(T.TLM(Ptlm), "Tlm")
print(T.is_exposed(theta, a0, a1, b0, b1, 0.001), "exposed")
def tlmVSstlm(N):
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
P1 = T.find_P(np.pi / 2, a0, a1, b0, b1)
P2 = T.find_P(theta, a0, a1, b0, b1)
tlm = T.TLM(P1)
stlm = St.STLM(P2, theta)
wholeSp, theta = St.SPlusCondition(P2)
# print(tlm, stlm)
if stlm and (not tlm):
print(tlm, stlm)
if stlm and (not tlm) and wholeSp:
print(tlm, stlm, wholeSp)
print("aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa")
def functionalBehaviour(N):
for i in range(N):
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
F1 = []
Tet = []
MAXI = []
tlm = T.TLM(T.find_P(np.pi / 2, a0, a1, b0, b1))
print(tlm)
if tlm:
thetag = T.getThetaFromSinSquared(
T.hypoTreshold(a0, a1, b0, b1)**2)
n = 500
Theta = np.linspace(thetag, np.pi / 2, n)
for theta in Theta:
# a0 = 3/4*np.pi
# a1 = np.pi/4
# b0 = np.pi/2
# b1 = np.pi
P = T.find_P(theta, a0, a1, b0, b1)
wholeSp, thetaNew = St.SPlusCondition(P)
# if wholeSp:
# f1,m1 = T.Best_func(theta, a0, a1, b0, b1)
f2, m2 = T.Best_func_restricted(theta, a0, a1, b0, b1)
# print(m1-m2,"hmm")
# print(f1)
# print(f2)
MAXI.append(m2)
Tet.append(theta)
F1.append(f2)
# plt.plot(Tet,F1)
plt.plot(Tet, MAXI)
plt.show()
def nonnegativitySingularity(N):
for i in range(1):
a0 = 0
a1 = np.random.rand() * 2 * np.pi
b0 = 0
b1 = np.random.rand() * 2 * np.pi
P = T.find_P(np.pi / 2, a0, a1, b0, b1)
# print(P)
tlm = T.TLM(P)
# Sp, Sm = St.SPlusTemp(P)
# print(Sp)
# print(Sm)
# theta = np.random.rand()*np.pi/2
# thetaB = np.arcsin(T.hypoTreshold(a0,a1,b0,b1))
# print(thetaB)
thetaGr = np.arcsin(T.hypoTresholdImproved(a0, a1, b0, b1))
print(thetaGr)
Theta = np.linspace(0, np.pi / 2, N)
for theta in Theta:
# print(theta)
# if i%100 == 0:
# print(i)
P = T.find_P(theta, a0, a1, b0, b1)
stlm = St.STLM(P, theta)
c1, thetan = St.SPlusCondition(P)
if theta >= thetaGr:
c2 = 1
else:
c2 = 0
# sat = St.satoshiTest(P)
# ex = T.is_exposed(theta,a0,a1,b0,b1, 0.001)
if c1 and (not stlm):
stlm2 = St.STLMComment(P, theta)
print(tlm, stlm, c1, c2)
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()