174 lines
6.4 KiB
Python
174 lines
6.4 KiB
Python
|
#https://www.desmos.com/calculator/vaskxmhoxh
|
||
|
|
|
||
|
|
from cubenode import Node
|
||
|
|
import math
|
||
|
|
import numpy as np
|
||
|
|
import time
|
||
|
|
from scipy.sparse import csr_matrix
|
||
|
|
|
||
|
|
def functions(n, z):
|
||
|
|
if n == 0:
|
||
|
|
return -1.732050808 + 1j + np.conj(3./(1.732050808 - 1.000000000j + z))
|
||
|
|
elif n == 1:
|
||
|
|
return -2.000000000j + np.conj(3./(2.000000000j + z))
|
||
|
|
elif n == 2:
|
||
|
|
return 1.732050808 + 1j + np.conj(3./(-1.732050808 - 1.000000000j + z))
|
||
|
|
elif n == 3:
|
||
|
|
return 0.202041j + np.conj(0.0306154/(-0.202041j + z))
|
||
|
|
elif n == 4:
|
||
|
|
return 0.174973 - 0.101021j + np.conj(0.0306154/(-0.174973 + 0.101021j + z))
|
||
|
|
elif n == 5:
|
||
|
|
return -0.174973 - 0.101021j + np.conj(0.0306154/(0.174973 + 0.101021j + z))
|
||
|
|
|
||
|
|
def derivatives(n, z):
|
||
|
|
if n == 0:
|
||
|
|
return abs(-0.333333*(1.732050808 - 1.000000000j + z)**2)
|
||
|
|
elif n == 1:
|
||
|
|
return abs(-0.333333*(2.000000000j + z)**2)
|
||
|
|
elif n == 2:
|
||
|
|
return abs(-0.333333*(-1.732050808 - 1.000000000j + z)**2)
|
||
|
|
elif n == 3:
|
||
|
|
return abs(-32.6633*(-0.202041j + z)**2)
|
||
|
|
elif n == 4:
|
||
|
|
return abs(-32.6633*(-0.174973 + 0.101021j + z)**2)
|
||
|
|
elif n == 5:
|
||
|
|
return abs(-32.6633*(0.174973 + 0.101021j + z)**2)
|
||
|
|
|
||
|
|
def samplePoint(word):
|
||
|
|
points = [-0.606218 + 0.35j, 0. - 0.7j, 0.606218 + 0.35j, 0. +
|
||
|
|
0.181837j, 0.157475 - 0.0909185j, -0.157475 - 0.0909185j]
|
||
|
|
p = points[word[-1]]
|
||
|
|
for letter in word[-2::-1]:
|
||
|
|
p = functions(letter, p)
|
||
|
|
return p
|
||
|
|
|
||
|
|
def sampleValue(word):
|
||
|
|
return derivatives(word[0], samplePoint(word))
|
||
|
|
|
||
|
|
def generateTree(words, dc):
|
||
|
|
|
||
|
|
generators = [np.array([[0., 1., 1., 0., -1., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0.,
|
||
|
|
0.], [0., 0., 1., 0., 0., 0., 0., 0.], [0., 3., 3., 0., 0., 0.,
|
||
|
|
0., -1.], [0., 0., 0., 0., 1., 0., 0., 0.], [0., 3., 2., 0., 1., 0.,
|
||
|
|
0., -1.], [0., 2., 3., 0., 1., 0., 0., -1.], [0., 2., 2., 0., 2.,
|
||
|
|
0., 0., -1.]]),
|
||
|
|
np.array([[1., 0., 0., 0., 0., 0., 0., 0.], [1., 0., 3., 2., -1., 0., 0.,
|
||
|
|
0.], [0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0.,
|
||
|
|
0.], [0., 0., 4., 2., -1., 0., 0., 0.], [0., 0., 3., 3., -1., 0.,
|
||
|
|
0., 0.], [-1., 0., 1., 1., 0., 0., 0., 0.], [-1., 0., 4., 3., -1.,
|
||
|
|
0., 0., 0.]]),
|
||
|
|
np.array([[1., 0., 0., 0., 0., 0., 0., 0.], [1., 0., 0., -1., 0., 1., 0.,
|
||
|
|
0.], [4., 0., 0., -1., -1., 3., 0., 0.], [0., 0., 0., 1., 0., 0.,
|
||
|
|
0., 0.], [4., 0., 0., -2., -1., 4., 0., 0.], [0., 0., 0., 0., 0.,
|
||
|
|
1., 0., 0.], [3., 0., 0., 0., -1., 3., 0., 0.], [3., 0.,
|
||
|
|
0., -1., -1., 4., 0., 0.]]),
|
||
|
|
np.array([[0., 0., 0., 0., 3., 3., -1., 0.], [0., 1., 0., 0., 0., 0., 0.,
|
||
|
|
0.], [0., -1., 0., 0., 4., 3., -1., 0.], [0., -1., 0., 0., 3.,
|
||
|
|
4., -1., 0.], [0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0.,
|
||
|
|
1., 0., 0.], [0., -2., 0., 0., 4., 4., -1., 0.], [0., -1., 0., 0.,
|
||
|
|
1., 1., 0., 0.]]),
|
||
|
|
np.array([[0., 0., 0., 0., -1., 3., 3., 0.], [0., 0., 0., -1., -1., 4., 3.,
|
||
|
|
0.], [0., 0., 0., -1., -1., 3., 4., 0.], [0., 0., 0., 1., 0., 0.,
|
||
|
|
0., 0.], [0., 0., 0., -2., -1., 4., 4., 0.], [0., 0., 0., 0., 0.,
|
||
|
|
1., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0.], [0., 0., 0., -1., 0.,
|
||
|
|
1., 1., 0.]]),
|
||
|
|
np.array([[0., -1., 0., 0., 4., 0., 3., -1.], [0., -1., 0., 0., 4., 0., 2.,
|
||
|
|
0.], [0., 0., 0., 0., 1., 0., 1., -1.], [0., -1., 0., 0., 3., 0.,
|
||
|
|
3., 0.], [0., 0., 0., 0., 1., 0., 0., 0.], [0., -1., 0., 0., 3., 0.,
|
||
|
|
2., 1.], [0., 0., 0., 0., 0., 0., 1., 0.], [0., 0., 0., 0., 0., 0.,
|
||
|
|
0., 1.]])]
|
||
|
|
|
||
|
|
root = Node([-1,2.632993161855454,2.632993161855454,2.632993161855454,6.265986323710909,6.265986323710909,6.265986323710909,9.898979485566363], [], words, False)
|
||
|
|
current_leaves = [root]
|
||
|
|
nodes = 1
|
||
|
|
while True:
|
||
|
|
new_leaves = []
|
||
|
|
for leaf in current_leaves:
|
||
|
|
next_gen = leaf.next_generation(words, dc, generators)
|
||
|
|
new_leaves += next_gen
|
||
|
|
nodes += len(next_gen) if len(next_gen) > 1 else 0
|
||
|
|
if current_leaves == new_leaves:
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
current_leaves = new_leaves
|
||
|
|
for i,leaf in enumerate(current_leaves):
|
||
|
|
words[str(leaf.word)] = i
|
||
|
|
print(len(current_leaves), "partitions")
|
||
|
|
print(nodes,"nodes")
|
||
|
|
return current_leaves
|
||
|
|
|
||
|
|
def constructMatrix(words, dc):
|
||
|
|
leave = generateTree(words, dc)
|
||
|
|
row = []
|
||
|
|
col = []
|
||
|
|
data = []
|
||
|
|
for i,leaf in enumerate(leave):
|
||
|
|
thing = words[str(leaf.word[1:])]
|
||
|
|
if isinstance(thing,int):
|
||
|
|
row.append(i)
|
||
|
|
col.append(thing)
|
||
|
|
data.append(sampleValue(leaf.word))
|
||
|
|
else:
|
||
|
|
sample = sampleValue(leaf.word)
|
||
|
|
for wor in thing.leaves():
|
||
|
|
row.append(i)
|
||
|
|
col.append(words[str(wor.word)])
|
||
|
|
data.append(sample)
|
||
|
|
return csr_matrix((data,(row,col)),shape=(len(leave),len(leave)))
|
||
|
|
|
||
|
|
def secant(x0,y0,x1,y1,z):
|
||
|
|
return x0 - (y0-z) * ((x1-x0)/(y1-y0))
|
||
|
|
|
||
|
|
def matrixFunction(matrix,l,a):
|
||
|
|
matrix = matrix.power(a)
|
||
|
|
vec = np.ones(l)
|
||
|
|
previous_entry = vec[0]
|
||
|
|
previous_val = 0
|
||
|
|
current = matrix * vec
|
||
|
|
current_val = current[0] / previous_entry
|
||
|
|
count = 0
|
||
|
|
while count < 10000000000 and abs(current_val - previous_val) > 1e-15:
|
||
|
|
previous_val = current_val
|
||
|
|
previous_entry = current[0]
|
||
|
|
current = matrix * current
|
||
|
|
#print(current[0],previous_entry)
|
||
|
|
current_val = current[0] / previous_entry
|
||
|
|
count += 1
|
||
|
|
print("power method:", count)
|
||
|
|
return current_val
|
||
|
|
|
||
|
|
def secantMethod(matrix,l,z,x1,x2,e,its):
|
||
|
|
k1 = x1
|
||
|
|
k2 = x2
|
||
|
|
y1 = matrixFunction(matrix,l,k1)
|
||
|
|
y2 = matrixFunction(matrix,l,k2)
|
||
|
|
#y1 = testFunction(k1)
|
||
|
|
#y2 = testFunction(k2)
|
||
|
|
count = 1
|
||
|
|
print(count,k1,y1)
|
||
|
|
while abs(y1-z)>e and count<its:
|
||
|
|
k3 = secant(k1,y1,k2,y2,z)
|
||
|
|
k1 = k2
|
||
|
|
y1 = y2
|
||
|
|
k2 = k3
|
||
|
|
y2 = matrixFunction(matrix,l,k2)
|
||
|
|
count += 1
|
||
|
|
print(count,k1,y1)
|
||
|
|
|
||
|
|
def main():
|
||
|
|
start = time.time()
|
||
|
|
|
||
|
|
m = 10
|
||
|
|
print("maximum:",m)
|
||
|
|
words = {}
|
||
|
|
matrix = constructMatrix(words,m)
|
||
|
|
#print(matrix)
|
||
|
|
|
||
|
|
print("construction (s): %f\nconstruction (m): %f" % (time.time()-start, (time.time()-start)/60))
|
||
|
|
#print(csr_matrix.transpose(matrix))
|
||
|
|
print(csr_matrix.count_nonzero(matrix), (matrix.shape[0])*5)
|
||
|
|
secantMethod(matrix,matrix.shape[0],1,1.47,1.49,10**(-10),1000)
|
||
|
|
|
||
|
|
print("total (s): %f\ntotal (m): %f" % (time.time()-start, (time.time()-start)/60))
|
||
|
|
|
||
|
|
main()
|