def randomPairing(n, w=None, seed=None):
'''generates a (uniformly) random non-crossing pairing of length 2n
If w != None, then generates a pairing from a Galton-Watson tree
with weight sequence w'''
if w == None:
path = dp.randomDyckPath(n, seed=seed)
else:
tree = ut.randomTree(n + 1, w, seed=seed)
path = ut.treeToDyckPath(tree)
prng = Pairing(path)
return prng
def main():
print('OrderedTree methods are used')
w = np.array([1] * 3)
#rw = tu.rescale(w) #This rescaling is done in function that generates Lukasiewicz path
#print(rw)
n = 10
seed = 12345
#seed = 0 #(random - changing from one execution to another)
tr = randomTree(n, w, SEED=seed)
#tr = randomBTree(n, SEED = seed)
print(tr)
tr.draw(drawLabels=True)
heights, sizes = tr.calcHeightsSizes(0)
print("heights = " + str(heights))
print("sizes = " + str(sizes))
'''
These are some drawings and calculations associated with Slim Trees
'''
n = 400
#n = 20
seed = 12345
seed = 0
k = 10
tr = randomSlimTree(k, n, SEED=seed)
#print(tr)
#fig, ax = tr.draw(drawLabels = True, block = False)
#fig, ax = tr.draw(drawLabels = False, block = False)
#fig1, (ax1, ax2) = plt.subplots(nrows=1, ncols=2)
_, ax = tr.draw(drawLabels=False, block=False)
H, v = tr.height()
dist = tr.heightVertex(v)
print("Height of vertex " + str(v) + " is " + str(dist))
tr.drawPathToVertex(ax, v)
print("Height of the tree is " + str(H))
v = 1
S = tr.sizeVertex(v)
print("size of vertex " + str(v) + " is " + str(S))
n = 5
seed = 3
path = dp.randomDyckPath(n, seed=seed)
print("path = ", path)
tr = fromDyck(path)
_, ax = tr.draw(drawLabels=True, block=False)
plt.show()
def main():
'''
#Generate and prints a random tree (weighted)
n = 100
w = [1, 1, 1]
tree = randomTree(n, w)
print(tree)
tree.draw(drawLabels = True)
#Creates a random Dyck path and plot it
#path = randomDyckPath(n)
path = treeToDyckPath(tree)
#print(path)
S = np.cumsum([0] + path)
fig1, ax1 = plt.subplots(nrows=1, ncols=1)
ax1.plot(S)
ax1.grid(True)
ax1.xaxis.set_ticks(np.arange(0,S.shape[0]))
ax1.yaxis.set_ticks(np.arange(0, np.max(S) + 1))
#Generates a random meander, finds a random cluster cycle (all
#point in the cycle are near each other and prints them.
n = 100
mndr = mr.randomMeander(n)
fig, ax = mndr.draw()
clusters = findQuasiClusters(mndr)
print("clusters = \n", clusters)
#here it looks for the largest quasi cluster cycle -- some gaps are allowed.
mgs = 9
cycle = largestCluster(mndr, max_gap_size = mgs)
print("Largest quasi cluster cycle is ", cycle)
print("Its length is ", largestClusterLength(mndr, max_gap_size= mgs))
mndr.drawCycle(cycle, ax = ax)
'''
#let us generate all non-crossing pairings of length n
n = 6
A = allPairings(n)
print(len(A))
'''
p = [3, 2, 1, 0, 5, 4]
q = [1, 0, 3, 2, 5, 4]
mndr = Meander(p, q)
mndr.draw()
x = dot(p, q)
print(x)
'''
M = dotMatrix(n)
print(type(M))
print(M)
path = "/Users/vladislavkargin/Dropbox/Programs/forPapers/Meanders/"
print(os.path.isdir(path))
np.savetxt(path + "Matrix" + str(n) + ".csv", M.astype(int), delimiter=',')
w = la.eigvalsh(M)
print(w)
q = 0.5
#q = 7/8
Mq = q**(n - M)
print(Mq)
w = la.eigvalsh(Mq)
print("Eigenvalues: ", w)
print("Maximum eigenvalue: ", max(w))
print("Minimal Eigenvalue: ", min(w))
print("Minimal Eigenvalue * C_n^2: ", min(w) * (Mq.shape[0]**2))
print("Number of Negative Eigenvalues: ", (w[w < 0]).shape[0])
print("Index: ", (w[w > 0]).shape[0] - (w[w < 0]).shape[0])
plt.plot(w)
plt.grid()
''' I used this for an example in my Math 447 class.
plotRandomProperMeander(5)
plt.grid(True)
'''
'''This is for paper. It is now available as a notebook in Colab'''
'''
seed = 3
n = 5
path1 = randomDyckPath(n, seed = seed)
plotDyckPath(path1)
prng1 = pg.Pairing(path = path1)
prng1.draw()
area = areaDyckPath(path1)
print("Area of path1 is ", area)
path2 = randomDyckPath(n, seed = seed + 2)
#plotDyckPath(path2, method = "lowerLatticePath")
area = areaDyckPath(path2)
print("Area of path2 is ", area)
prng2 = pg.Pairing(path = path2)
mndr = Meander(prng1, prng2)
mndr.draw(drawCycles=True)
mr.drawAsPolygon(mndr)
'''
seed = 3
n = 10
path1 = dp.randomDyckPath(n, seed=seed)
dp.plotDyckPath(path1)
area = dp.areaDyckPath(path1)
print("Area of path1 is ", area)
nvalleys = len(dp.valleys(path1))
print("Number of valleys is ", nvalleys)
n = 4
np.random.seed()
perm = np.random.permutation(n)
print(perm)
cycles = cmb.cyclesOfPerm(perm)
print(cycles)
plt.show()
def random231perm(n):
''' generates a random 231 permutation of n objects, like 3 0 2 1 for n = 4'''
path = dp.randomDyckPath(n)
p = dp.pathTo231perm(path)
return p