def getNextRational(element, fareyList, d, k):
n = element * fareyList[-1].num + fareyList[-2].num
m = element * fareyList[-1].den + fareyList[-2].den
return rational(n, m, d, k)
def plotLine(CF,axisoffset=0., d = 0.15,k = 2.,
cmap = matplotlib.cm.ScalarMappable(cmap=cmaps.viridis), axisLog = False):
def getNextRational(element, fareyList, d, k):
n = element * fareyList[-1].num + fareyList[-2].num
m = element * fareyList[-1].den + fareyList[-2].den
return rational(n, m, d, k)
CF = [float(c) for c in CF]
farey = [rational(1,0,d,k), rational(0,1,d,k)] # initiate
if (CF[-1] != 1.0):
CF[-1] = float(CF[-1])-1
CF.append(1.)
neighbors = []
for i in range(len(CF)):
a = getNextRational(int(CF[i]),farey,d,k)
farey.append(a)
farey = farey[1:]
# for i in range(len(farey)-1):
# level = 0
# while True:
# fareySequence = fareySequences[level]
# fareyNum = [x[0] for x in fareySequence]
# fareyDen = [x[1] for x in fareySequence]
# ind = []
# for f in [farey[i],farey[i+1]]:
# indNum = np.where(np.asarray(fareyNum) == f.num)[0]
# indDen = np.where(np.asarray(fareyDen) == f.den)[0]
# if (len(list(np.intersect1d(indNum, indDen))) == 0):
# level += 1
# continue
# else:
# ind.append(list(np.intersect1d(indNum, indDen))[0])
# if len(ind) == 2:
# neighboring = True if abs(ind[0]-ind[1]) == 1 else False
# neighbors.append(neighboring)
# break
plt.plot([d-axisoffset,-d-axisoffset],
[farey[0].den]*2, color = cmap.to_rgba(1), linewidth=4)
for j in range(len(farey)-1):
changed = False
if CF[0] > 1:
CF[0] -= 1
changed = True
maxBound = max(CF[:j]) if j > 0 else 1
if changed:
CF[0] += 1
color = cmap.to_rgba(maxBound) # if cmap.norm == None else cmap(maxBound/10)
# plot line only if partners are Farey neighbors
# if neighbors[j]:
plt.plot([i.val-axisoffset for i in farey[j:j+2]],
[i.den for i in farey[j:j+2]],color=color,linewidth=1)
(diophantineMin, diophantineMax) = farey[j+1].diophantine
plt.plot([diophantineMin-axisoffset,diophantineMax-axisoffset],
[farey[j+1].den]*2,
color = color, linewidth=4)
# print(CF, farey, neighbors)
# print(Brjuno(farey,1), Brjuno(farey,2), Brjuno(farey,3))
return farey
