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84
fractal_dimension/mcmullen_stuff/dodecanode.py
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84
fractal_dimension/mcmullen_stuff/dodecanode.py
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import numpy as np
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import math
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from random import sample
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class Node:
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def __init__(self, tuple, word, words, infertile):
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self.tuple = tuple
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self.children = []
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self.word = word
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self.infertile = infertile
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words[str(word)] = self
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def dc_not_too_big(self, g, generator, dual_curvature):
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temp = np.matmul(generator, self.tuple)
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if g == 0:
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temp = [temp[i] for i in (0,1,16,12,17)]
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elif g == 1:
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temp = [temp[i] for i in (0,1,13,12,14)]
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elif g == 2:
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temp = [temp[i] for i in (9,11,19,8,15)]
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elif g == 3:
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temp = [temp[i] for i in (3,7,19,17,12)]
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elif g == 4:
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temp = [temp[i] for i in (2,13,4,8,15)]
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elif g == 5:
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temp = [temp[i] for i in (4,13,1,16,18)]
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elif g == 6:
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temp = [temp[i] for i in (7,11,9,5,19)]
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elif g == 7:
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temp = [temp[i] for i in (3,7,11,10,6)]
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elif g == 8:
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temp = [temp[i] for i in (0,14,5,19,17)]
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elif g == 9:
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temp = [temp[i] for i in (3,6,18,16,12)]
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elif g == 10:
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temp = [temp[i] for i in (2,14,5,9,15)]
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elif g == 11:
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temp = [temp[i] for i in (4,8,10,6,18)]
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if temp[0] < 0:
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return math.sqrt(-((temp[0]*temp[1]*temp[2] + temp[0]*temp[1]*temp[3] + temp[0]*temp[2]*temp[3] - temp[1]*temp[2]*temp[3] + temp[0]*temp[1]*temp[4] +
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temp[0]*temp[2]*temp[4] - temp[1]*temp[2]*temp[4] + temp[0]*temp[3]*temp[4] - temp[1]*temp[3]*temp[4] - temp[2]*temp[3]*temp[4] -
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math.sqrt(-4*temp[0]*temp[1]*temp[2]*temp[3]*(temp[0] - temp[1] - temp[2] - temp[3] - temp[4])*temp[4] + (temp[2]*temp[3]*temp[4] +
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temp[1]*(temp[3]*temp[4] + temp[2]*(temp[3] + temp[4])) -
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temp[0]*(temp[3]*temp[4] + temp[2]*(temp[3] + temp[4]) + temp[1]*(temp[2] + temp[3] + temp[4])))**2))/(-temp[0] + temp[1] +
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temp[2] + temp[3] + temp[4])))/math.sqrt(2) < dual_curvature
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else:
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return (1/math.sqrt(2))*(math.sqrt(temp[0]*temp[1] + temp[0]*temp[2] + temp[1]*temp[2] + temp[0]*temp[3] + temp[1]*temp[3] + temp[2]*temp[3] +
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temp[0]*temp[4] + temp[1]*temp[4] + temp[2]*temp[4] + temp[3]*temp[4] -
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math.sqrt(-4*temp[0]*temp[1]*temp[2]*temp[3] - 4*temp[0]*temp[1]*temp[2]*temp[4] - 4*temp[0]*temp[1]*temp[3]*temp[4] -
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4*temp[0]*temp[2]*temp[3]*temp[4] -
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4*temp[1]*temp[2]*temp[3]*temp[4] + (temp[2]*temp[3] + temp[2]*temp[4] + temp[3]*temp[4] + temp[1]*(temp[2] + temp[3] + temp[4]) +
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temp[0]*(temp[1] + temp[2] + temp[3] + temp[4]))**2))) < dual_curvature
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def next_generation(self, words, dual_curvature, generators):
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if self.infertile:
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return [self]
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if self.children == []:
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for g,generator in enumerate(generators):
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if len(self.word) == 0 or g != self.word[-1]:
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if self.word + [g] == [1, 8, 15, 8, 0] or self.word + [g] == [8, 15, 8, 0]:
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print(self.tuple)
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self.children.append(Node(np.matmul(generator,self.tuple), self.word[:] + [g], words, not self.dc_not_too_big(g, generator, dual_curvature)))
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if self.children == []:
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return [self]
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else:
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return self.children
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def next(self):
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if self.children == []:
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return [self]
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else:
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return self.children
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def leaves(self):
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current_leaves = [self]
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while True:
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new_leaves = []
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for leaf in current_leaves:
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new_leaves += leaf.next()
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if current_leaves == new_leaves:
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break
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else:
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current_leaves = new_leaves
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return current_leaves
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563
fractal_dimension/mcmullen_stuff/dodecatree.py
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563
fractal_dimension/mcmullen_stuff/dodecatree.py
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from dodecanode import Node
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import math
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import numpy as np
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import time
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from scipy.sparse import csr_matrix
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from scipy.sparse.linalg import eigs
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def functions(n, z):
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if n == 0:
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return -1*np.conj(z)
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duals = [[], [2/(-1 + math.sqrt(5)) - 1j,
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2/(-1 + math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/22*(-1 + 3*math.sqrt(5))*1j,
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1/(9 + 5*math.sqrt(5))], [2/(5 *(1 + math.sqrt(5))) + 1j/math.sqrt(5), 2/(
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5 *(1 + math.sqrt(5)))], [1/22*(1 + 3*math.sqrt(5)) + 1/11*(-3 + 2*math.sqrt(5))*1j,
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2/(13 + 5*math.sqrt(5))], [1/(2 + 2*math.sqrt(5)), 1/(
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2 + 2*math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/2*(3 - math.sqrt(5))*1j, 1/(
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7 + 3*math.sqrt(5))], [1/22*(7 - math.sqrt(5)) + 1/11*(10 - 3*math.sqrt(5))*1j, 2/(
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19 + 9*math.sqrt(5))], [2/(1 + math.sqrt(5)) + 1j, 2/(
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1 + math.sqrt(5))], [2/(11 + 5*math.sqrt(5)) + (-2 + math.sqrt(5))*1j, 2/(
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11 + 5*math.sqrt(5))], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j,
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2/(7 + 5*math.sqrt(5))], [1/58*(11 + math.sqrt(5)) + 1/29*(-10 + 7*math.sqrt(5))*1j,
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2/(17 + 9*math.sqrt(5))]]
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return duals[n][0] + np.conj((duals[n][1])**2 / (z-duals[n][0]))
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def derivatives(n, z):
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if n == 0:
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return 1
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duals = [[], [2/(-1 + math.sqrt(5)) - 1j,
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2/(-1 + math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/22*(-1 + 3*math.sqrt(5))*1j,
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1/(9 + 5*math.sqrt(5))], [2/(5 *(1 + math.sqrt(5))) + 1j/math.sqrt(5), 2/(
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5 *(1 + math.sqrt(5)))], [1/22*(1 + 3*math.sqrt(5)) + 1/11*(-3 + 2*math.sqrt(5))*1j,
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2/(13 + 5*math.sqrt(5))], [1/(2 + 2*math.sqrt(5)), 1/(
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2 + 2*math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/2*(3 - math.sqrt(5))*1j, 1/(
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7 + 3*math.sqrt(5))], [1/22*(7 - math.sqrt(5)) + 1/11*(10 - 3*math.sqrt(5))*1j, 2/(
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19 + 9*math.sqrt(5))], [2/(1 + math.sqrt(5)) + 1j, 2/(
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1 + math.sqrt(5))], [2/(11 + 5*math.sqrt(5)) + (-2 + math.sqrt(5))*1j, 2/(
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11 + 5*math.sqrt(5))], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j,
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2/(7 + 5*math.sqrt(5))], [1/58*(11 + math.sqrt(5)) + 1/29*(-10 + 7*math.sqrt(5))*1j,
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2/(17 + 9*math.sqrt(5))]]
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return abs(-1*((z-duals[n][0])**2) / ((duals[n][1])**2))
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def samplePoint(word):
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points = [-(1/2), 1/5 + 1/math.sqrt(5) - (2j)/5,
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1/4*(-1 + math.sqrt(5)) + 1/22*(-1 + 3*math.sqrt(5))*1j, 2/(
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5*(1 + math.sqrt(5))) + 1j/math.sqrt(5),
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1/22*(1 + 3*math.sqrt(5)) + 1/11*(-3 + 2*math.sqrt(5))*1j, 1/(2 + 2*math.sqrt(5)),
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1/4*(-1 + math.sqrt(5)) + 1/2*(3 - math.sqrt(5))*1j,
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1/22*(7 - math.sqrt(5)) + 1/11*(10 - 3*math.sqrt(5))*1j,
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2/5*(-1 + math.sqrt(5)) + (4j)/5, 2/(11 + 5*math.sqrt(5)) + (-2 + math.sqrt(5))*1j,
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1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j,
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1/58*(11 + math.sqrt(5)) + 1/29*(-10 + 7*math.sqrt(5))*1j]
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p = points[word[-1]]
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for letter in word[-2::-1]:
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p = functions(letter, p)
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return p
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def sampleValue(word):
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return derivatives(word[0], samplePoint(word))
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def generateTree(words, dc):
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tt = time.time()
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generators = [np.array([[0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, -(2/(1 + math.sqrt(5))), 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3 + math.sqrt(5), 0, 0, -1,
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0, 0, 0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0,
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1/2*(1 + math.sqrt(5)), 0, 0], [0, math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0,
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0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0], [0,
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3 + math.sqrt(5), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1 + math.sqrt(5), 0, 0, 0, 0,
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0, 0, 0], [0, 2 + math.sqrt(5), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0,
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1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0], [0,
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2 + math.sqrt(5), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
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0, 0, 0], [0, 1/2*(5 + math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0,
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1 + math.sqrt(5), 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0], [0,
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3 + 2*math.sqrt(5), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0,
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1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 1, 0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0,
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0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0,
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0, 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0, 0,
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1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 1,
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0, 0], [0, 2*(1 + math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0,
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0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1/2*(1 + 3*math.sqrt(5)),
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0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(5 - math.sqrt(5)), 0,
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0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0], [0, 1 + math.sqrt(5), 0, 0,
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1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0, 0,
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0, 2, 0, 0], [0, 3 + 2*math.sqrt(5), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0,
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0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 2, 0, 0], [0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
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1/2*(1 - math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 1, 0, 0], [0, 1 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0,
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0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0], [0, math.sqrt(5),
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0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(5 - math.sqrt(5)), 0,
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0, 0, 0, 2, 0, 0]]), np.array([[1, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0], [1/2*(-1 - math.sqrt(5)), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0], [1/2*(-5 - 3*math.sqrt(5)),
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1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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3/2*(3 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
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0], [-(3/2)*(1 + math.sqrt(5)), 4 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-math.sqrt(5),
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1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 + math.sqrt(5),
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0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-3 - 2*math.sqrt(5),
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1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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2*(2 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
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0], [1/2*(-5 - 3*math.sqrt(5)), 2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
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0], [1/2*(-7 - 3*math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0], [-3 - math.sqrt(5),
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1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0], [-2*(2 + math.sqrt(5)),
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1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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5 + 2*math.sqrt(5), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [-3 - 2*math.sqrt(5),
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1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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5 + 2*math.sqrt(5), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
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0], [1/2*(-3 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, -1, 0], [1/2*(-1 - math.sqrt(5)),
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1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
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0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
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0], [-(3/2)*(1 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-math.sqrt(5),
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3 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(3 + math.sqrt(5)),
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0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [1/2*(1 - math.sqrt(5)),
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1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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1/2*(3 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-3 - math.sqrt(5),
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2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 + math.sqrt(5),
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0, 0, 0, -1, 0], [1/2*(-3 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, -1, 0]]), np.array([[0, 0,
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0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 2*(3 + math.sqrt(5)), 7 + 3*math.sqrt(5),
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0, 0, 0, 0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0,
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0, 0, 1/2*(-3 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 5/2*(3 + math.sqrt(5)),
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0, 0, 0, 0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0,
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0, 0, -1, 1/2*(5 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0,
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0, -math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
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2*(2 + math.sqrt(5)), 1/2*(9 + 5*math.sqrt(5)), 0, 0, 0, 0,
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0, -5 - 2*math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1,
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3 + math.sqrt(5), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0,
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1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1,
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1/2*(5 + math.sqrt(5)), 4 + math.sqrt(5), 0, 0, 0, 0, 0,
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1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1,
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4 + math.sqrt(5), 4 + math.sqrt(5), 0, 0, 0, 0, 0, -2*(1 + math.sqrt(5)), 0, 0, 0,
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0], [0, 0, 0, 0, 0, 0, 0, -1, 3 + math.sqrt(5), 5 + math.sqrt(5), 0, 0, 0,
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0, 0, -2*(1 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(1 + math.sqrt(5)), 1, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0,
|
||||
0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 8 + 3*math.sqrt(5), 0, 0, 0,
|
||||
0, 0, -3*(2 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0, 0, 0,
|
||||
0, -3 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0,
|
||||
0, 0, -3 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 7 + 3*math.sqrt(5), 0, 0, 0,
|
||||
0, 0, -5 - 3*math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 8 + 3*math.sqrt(5), 0, 0, 0,
|
||||
0, 0, -5 - 3*math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 2*(2 + math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, -(3/2)*(3 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 1/2*(9 + 5*math.sqrt(5)), 0, 0,
|
||||
0, 0, 0, -(3/2)*(3 + math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0, 0, 0, 0, -1,
|
||||
0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1/2*(3 - math.sqrt(5)), 0,
|
||||
1/2*(5 + math.sqrt(5))], [0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 2 + math.sqrt(5), 0, 0, 0, 0, -1, 0, 1/2*(5 + 3*math.sqrt(5))], [0, 0,
|
||||
0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 4 + math.sqrt(5), 0, 0,
|
||||
0, 0, -1 - math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0, 1], [0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, -(3/2)*(1 + math.sqrt(5)), 0,
|
||||
1/2*(11 + 5*math.sqrt(5))], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0,
|
||||
0, 0, 0, 1 - math.sqrt(5), 0, 3 + math.sqrt(5)], [0, 0, 0, 0, 0, -1, 0, 0, 0,
|
||||
0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0,
|
||||
3 + math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 1/2*(1 + math.sqrt(5))], [0, 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0,
|
||||
0, 1/2*(-5 - 3*math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5))], [0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
|
||||
1/2*(-5 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5))], [0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
0, -3 - math.sqrt(5), 0, 2*(2 + math.sqrt(5))], [0, 0, 0, 0, 0, -1, 0, 0, 0,
|
||||
0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0,
|
||||
4 + math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
|
||||
0, 0, 0], [0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, -1 - math.sqrt(5), 0,
|
||||
2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 1 + math.sqrt(5), 0, 0, 0, 0, -1, 0, 1/2*(7 + 3*math.sqrt(5))], [0, 0,
|
||||
0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
0, 0, 0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5))], [0, 0,
|
||||
0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
1 - math.sqrt(5), 0, 1/2*(5 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0,
|
||||
1/2*(-5 - math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 0, -1, 0, 0, 0, 0, 0,
|
||||
0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1 - math.sqrt(5), 0, 0, 0, 0,
|
||||
0, 0, -1, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 1/2*(5 + math.sqrt(5)), 0, 0,
|
||||
0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 0, 0, 0, 3/2*(3 + math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 1, 0, 0, 0, 0], [0,
|
||||
0, -1, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 1 + math.sqrt(5),
|
||||
0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, -3 - math.sqrt(5), 0, 0, 0,
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0,
|
||||
2*(2 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0,
|
||||
0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0], [0,
|
||||
0, 1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 3 + math.sqrt(5),
|
||||
0, 0, 0, 0], [0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, -1, 0,
|
||||
0, 0, 1/2*(5 + math.sqrt(5)), 0, 4 + math.sqrt(5), 0, 0, 0, 0], [0, 0,
|
||||
1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0,
|
||||
2 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0], [0,
|
||||
0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0,
|
||||
0, 0, 3/2*(3 + math.sqrt(5)), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0], [0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0,
|
||||
1/2*(3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, -1 - math.sqrt(5), 0, 0, 0, 0,
|
||||
0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
2*(3 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0,
|
||||
0, 0, 0, -1, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0,
|
||||
0], [0, 0, -1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0,
|
||||
0, 0, 4 + math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0,
|
||||
0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 4 + math.sqrt(5), 0,
|
||||
0, 0, 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0,
|
||||
0, 0, 0, 1, 0], [0, 0, 0, 0, -1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 0], [0,
|
||||
0, 0, 0, 1/2*(-7 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0,
|
||||
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0,
|
||||
1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 0], [0, 0, 0,
|
||||
0, -1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0,
|
||||
0, 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0,
|
||||
1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0], [0, 0, 0,
|
||||
0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(1 - math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 0], [0, 0, 0,
|
||||
0, -2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2*(3 + math.sqrt(5)), 0], [0, 0, 0,
|
||||
0, -2 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0,
|
||||
0, -1, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 0, 0, 0, -2*(2 + math.sqrt(5)), 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
1/2*(11 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)),
|
||||
4 + math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
|
||||
0, 0, 0, 0], [0, 0, 0, 0, 1/2*(-7 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, -1, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 0,
|
||||
0, 0, -2 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
0, 0, 0, -1, 1/2*(5 + 3*math.sqrt(5)), 0], [0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
|
||||
1/2*(1 + math.sqrt(5)), 0], [0, 0, 0, 0, -2*(2 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, -1, 2*(2 + math.sqrt(5)), 0], [0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0,
|
||||
0, 1/2*(-11 - 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
1/2*(13 + 5*math.sqrt(5)), 0]]), np.array([[0, 0, 0, 0, 1/2*(1 - math.sqrt(5)),
|
||||
1 + math.sqrt(5), 0, 1 + math.sqrt(5), 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1/2*(5 + math.sqrt(5)), 0, 3 + math.sqrt(5),
|
||||
0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), math.sqrt(5), 0, 1/2*(3 + math.sqrt(5)), 0, 1 + math.sqrt(5),
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)),
|
||||
3 - math.sqrt(5), 0, 1 + math.sqrt(5), 0, 1/2*(5 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 2, 0, 3 + math.sqrt(5), 0, 3 + math.sqrt(5),
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(-1 + math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 1 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0], [0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 1/2*(-1 + math.sqrt(5)), 0,
|
||||
1 + math.sqrt(5), 0, 2 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 2 - math.sqrt(5), 0, 1/2*(3 + math.sqrt(5)), 0, 3, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0,
|
||||
1/2*(-1 + math.sqrt(5)), 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0,
|
||||
0, 1/2*(1 - math.sqrt(5)), math.sqrt(5), 0, 2 + math.sqrt(5), 0,
|
||||
1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1,
|
||||
3, 0, 3/2*(1 + math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 1/2*(7 - math.sqrt(5)), 0,
|
||||
1/2*(1 + math.sqrt(5)), 0, 1/2*(5 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 3 - math.sqrt(5), 0,
|
||||
1/2*(1 + math.sqrt(5)), 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0,
|
||||
0, -1, 3, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)),
|
||||
1/2*(7 - math.sqrt(5)), 0, 1/2*(3 + math.sqrt(5)), 0, 1/2*(3 - math.sqrt(5)), 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 2, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0], [0, 0, 0, 0, 0, 1, 0, 1/2*(-1 + math.sqrt(5)), 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]), np.array([[0, 0, 0, 1, 0,
|
||||
0, 4 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 4 + math.sqrt(5), 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0,
|
||||
3/2*(3 + math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 2 + math.sqrt(5),
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, -math.sqrt(5), 0, 0, 1/2*(7 + math.sqrt(5)), 1/2*(5 + math.sqrt(5)),
|
||||
0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -math.sqrt(5), 0, 0,
|
||||
1/2*(5 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, -1, 0, 0, 0, 0,
|
||||
0, 0, 0], [0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 1/2*(1 + math.sqrt(5)), 1,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0, 0, 1, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3/2*(3 + math.sqrt(5)),
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 0], [0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 0], [0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)),
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 0], [0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5),
|
||||
1 + math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 1 + math.sqrt(5), 2 + math.sqrt(5), 0,
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0], [0, 0, 0,
|
||||
1/2*(3 - math.sqrt(5)), 0, 0, 1/2*(5 + math.sqrt(5)), 2, 0, 0, 0, 0, -1, 0,
|
||||
0, 0, 0, 0, 0, 0], [0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0, 2,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0]]), np.array([[0, 0,
|
||||
0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
|
||||
1/2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 1/2*(7 - 3*math.sqrt(5)), 0,
|
||||
0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 5 - math.sqrt(5), 0, 0,
|
||||
2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, -(3/2)*(-3 + math.sqrt(5)), 0,
|
||||
0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 5 - math.sqrt(5), 0,
|
||||
0, -3 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 1/2*(-1 + 3*math.sqrt(5)), 0,
|
||||
0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, -1 + math.sqrt(5), 0, 0, 4, 0,
|
||||
0], [0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)),
|
||||
0, 0, 3/2*(1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0,
|
||||
0, 0, 3, 0, 0, 1 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 5 - math.sqrt(5),
|
||||
0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(7 - 3*math.sqrt(5)), 0, 0,
|
||||
2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0, 0,
|
||||
0, 4, 0, 0, 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 5 - math.sqrt(5), 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, -(3/2)*(-3 + math.sqrt(5)), 0,
|
||||
0, -3 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0,
|
||||
0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 3/2*(1 + math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
0, 0, 1/2*(1 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, -1 + math.sqrt(5), 0, 0, 3, 0, 0], [0, 0, 0, 0,
|
||||
0, -(3/2)*(-3 + math.sqrt(5)), 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, -(3/2)*(-3 + math.sqrt(5)), 0, 0, 5/2*(-1 + math.sqrt(5)), 0, 0], [0, 0,
|
||||
0, 0, 0, -1 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(1 + 3*math.sqrt(5)), 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0,
|
||||
1/2*(-1 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-1 + 3*math.sqrt(5)), 0, 0, 1/2*(7 - math.sqrt(5)), 0, 0], [0, 0, 0, 0,
|
||||
0, -1 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-1 + 3*math.sqrt(5)), 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, -1, 0,
|
||||
0, 0, 0, 0, 4, 0, 0, 1 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 1, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(-1 + math.sqrt(5)), 0,
|
||||
0]]), np.array([[0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1 + math.sqrt(5), 0, -1 + math.sqrt(5),
|
||||
0], [0, 0, 0, 3/2*(-1 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(7 - math.sqrt(5)),
|
||||
0, -(3/2)*(-3 + math.sqrt(5)), 0], [0, 0, 0, 1 + 2*math.sqrt(5), 0, 0, 0, 0,
|
||||
0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3/2*(-1 + math.sqrt(5)), 0,
|
||||
0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 3 - math.sqrt(5), 0,
|
||||
5 - math.sqrt(5), 0], [0, 0, 0, 2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, -1, 0,
|
||||
0, 0, 0, 0, 0, 3, 0, 3, 0], [0, 0, 0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, -(2/(1 + math.sqrt(5))), 0, 1, 0], [0, 0,
|
||||
0, -1 + 2*math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 3 - math.sqrt(5), 0, -(3/2)*(-3 + math.sqrt(5)), 0], [0, 0, 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 1/2*(-1 + math.sqrt(5)), 0, 1/2*(1 + 3*math.sqrt(5)), 0], [0, 0, 0,
|
||||
2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 4,
|
||||
0], [0, 0, 0, 1/2*(-1 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 2 - math.sqrt(5), 0, 5 - math.sqrt(5),
|
||||
0], [0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 0, 1/2*(-1 + math.sqrt(5)), 0, 1/2*(-1 + 3*math.sqrt(5)),
|
||||
0], [0, 0, 0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1, 0, 1/2*(1 - math.sqrt(5)), 0], [0, 0, 0, 3, 0, 0, 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, math.sqrt(5), 0,
|
||||
1/2*(-1 + 3*math.sqrt(5)), 0], [0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
0, 0, -1, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 3, 0], [0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 1, 0, 0, 0], [0, 0, 0, 1/2*(-1 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(7 - math.sqrt(5)), 0,
|
||||
1/2*(7 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 1, 0], [0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, math.sqrt(5), 0, -1 + math.sqrt(5),
|
||||
0]]), np.array([[0, 0, 5, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
|
||||
0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 2*(1 + math.sqrt(5)), 0, 0,
|
||||
0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, -1,
|
||||
0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0,
|
||||
0], [0, 0, 3/2*(1 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0,
|
||||
2 + math.sqrt(5), 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0,
|
||||
0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0,
|
||||
0], [0, 0, 5 + math.sqrt(5), 0, 0, 0, -1, 0, 0, 2*(2 + math.sqrt(5)), 0, 0,
|
||||
0, 0, 0, -1 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 3/2*(1 + math.sqrt(5)), 0, 0,
|
||||
0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(7 - math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(3 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1/2*(1 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, -1, 0, 0, 0,
|
||||
0], [0, 0, 1/2*(7 - math.sqrt(5)), 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0,
|
||||
2 + math.sqrt(5), 0, 0, 0, 0, 0, 1 - math.sqrt(5), 0, 0, 0, 0], [0, 0,
|
||||
1/2*(11 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0,
|
||||
0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 4, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
0, 1, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0,
|
||||
1/2*(11 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0,
|
||||
0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 2*(1 + math.sqrt(5)), 0,
|
||||
0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, -3 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, -1,
|
||||
0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, -1 - math.sqrt(5), 0, 0, 0,
|
||||
0], [0, 0, 4, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 0,
|
||||
0, 0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0, 0, 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 2*(3 + math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 0, 0, 0, -2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, -2 - math.sqrt(5), 0], [0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-7 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0,
|
||||
3 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0,
|
||||
0, -1 - math.sqrt(5), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 1/2*(-11 - 5*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
2*(2 + math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-7 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 1, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [0, 0, 0, 0,
|
||||
2*(2 + math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, -2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 1/2*(1 + math.sqrt(5)), 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [0, 0, 0, 0,
|
||||
3 + math.sqrt(5), 0, 4 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0], [0, 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, -2 - math.sqrt(5), 0], [0, 0, 0, 0, 3 + math.sqrt(5), 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0,
|
||||
0, -1 - math.sqrt(5), 0], [0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0], [0, 0, 0, 0, 4 + math.sqrt(5), 0,
|
||||
3 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-5 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0], [0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
0, 0, -2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0]])]
|
||||
|
||||
root = Node([-1, 2, 1/2*(11 + 5*math.sqrt(5)), 1/2*(23 + 9*math.sqrt(5)), 3/2*(7 +
|
||||
3*math.sqrt(5)), 3*(2 + math.sqrt(5)), 1/2*(27 + 13*math.sqrt(5)), 12 +
|
||||
5*math.sqrt(5), 1/2*(29 + 13*math.sqrt(5)), 13 + 5*math.sqrt(5), 18 +
|
||||
7*math.sqrt(5), 15 + 7*math.sqrt(5), 5 + 2*math.sqrt(5), 5 +
|
||||
2*math.sqrt(5), 1/2*(7 + math.sqrt(5)), 12 +
|
||||
5*math.sqrt(5), 2*(2 + math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 11 +
|
||||
4*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5))], [], words, False)
|
||||
|
||||
#print(root.tuple)
|
||||
#print(np.matmul(generators[0],root.tuple))
|
||||
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")
|
||||
print("tree construction (s): %f\ntree construction (m): %f" % (time.time()-tt, (time.time()-tt)/60))
|
||||
return current_leaves
|
||||
|
||||
def constructMatrix(words, dc):
|
||||
leave = generateTree(words, dc)
|
||||
row = []
|
||||
col = []
|
||||
data = []
|
||||
for i,leaf in enumerate(leave):
|
||||
print(leaf.word)
|
||||
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):
|
||||
#return np.real(eigs(matrix.power(a),k=1)[0][0])
|
||||
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-10:
|
||||
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)
|
||||
#y2 = testFunction(k2)
|
||||
count += 1
|
||||
print(count,k1,y1)
|
||||
|
||||
def main():
|
||||
start = time.time()
|
||||
|
||||
words = {}
|
||||
m = 600
|
||||
print("maximum:",m)
|
||||
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])*11)
|
||||
secantMethod(matrix,matrix.shape[0],1,1.55,1.59,10**(-10),1000)
|
||||
|
||||
print("total (s): %f\ntotal (m): %f" % (time.time()-start, (time.time()-start)/60))
|
||||
|
||||
main()
|
||||
84
fractal_dimension/mcmullen_stuff/icosanode.py
Normal file
84
fractal_dimension/mcmullen_stuff/icosanode.py
Normal file
|
|
@ -0,0 +1,84 @@
|
|||
import numpy as np
|
||||
import math
|
||||
|
||||
class Node:
|
||||
def __init__(self, tuple, word, words, infertile):
|
||||
self.tuple = tuple
|
||||
self.children = []
|
||||
self.word = word
|
||||
self.infertile = infertile
|
||||
words[str(word)] = self
|
||||
|
||||
def dc_not_too_big(self, g, generator, dual_curvature):
|
||||
temp = np.matmul(generator, self.tuple)
|
||||
if g == 0:
|
||||
temp = [temp[i] for i in (0,1,8)]
|
||||
elif g == 1:
|
||||
temp = [temp[i] for i in (0,1,5)]
|
||||
elif g == 2:
|
||||
temp = [temp[i] for i in (1,4,10)]
|
||||
elif g == 3:
|
||||
temp = [temp[i] for i in (3,7,9)]
|
||||
elif g == 4:
|
||||
temp = [temp[i] for i in (4,5,11)]
|
||||
elif g == 5:
|
||||
temp = [temp[i] for i in (6,8,10)]
|
||||
elif g == 6:
|
||||
temp = [temp[i] for i in (7,9,11)]
|
||||
elif g == 7:
|
||||
temp = [temp[i] for i in (3,6,7)]
|
||||
elif g == 8:
|
||||
temp = [temp[i] for i in (2,4,11)]
|
||||
elif g == 9:
|
||||
temp = [temp[i] for i in (2,6,10)]
|
||||
elif g == 10:
|
||||
temp = [temp[i] for i in (2,7,11)]
|
||||
elif g == 11:
|
||||
temp = [temp[i] for i in (2,6,7)]
|
||||
elif g == 12:
|
||||
temp = [temp[i] for i in (0,3,9)]
|
||||
elif g == 13:
|
||||
temp = [temp[i] for i in (1,4,5)]
|
||||
elif g == 14:
|
||||
temp = [temp[i] for i in (1,8,10)]
|
||||
elif g == 15:
|
||||
temp = [temp[i] for i in (2,4,10)]
|
||||
elif g == 16:
|
||||
temp = [temp[i] for i in (0,5,9)]
|
||||
elif g == 17:
|
||||
temp = [temp[i] for i in (0,3,8)]
|
||||
elif g == 18:
|
||||
temp = [temp[i] for i in (5,9,11)]
|
||||
elif g == 19:
|
||||
temp = [temp[i] for i in (3,6,8)]
|
||||
return math.sqrt(temp[0]*temp[1] + temp[0]*temp[2] + temp[1]*temp[2]) < dual_curvature
|
||||
|
||||
def next_generation(self, words, dual_curvature, generators):
|
||||
if self.infertile:
|
||||
return [self]
|
||||
if self.children == []:
|
||||
for g,generator in enumerate(generators):
|
||||
if len(self.word) == 0 or g != self.word[-1]:
|
||||
self.children.append(Node(np.matmul(generator,self.tuple), self.word[:] + [g], words, not self.dc_not_too_big(g, generator, dual_curvature)))
|
||||
if self.children == []:
|
||||
return [self]
|
||||
else:
|
||||
return self.children
|
||||
|
||||
def next(self):
|
||||
if self.children == []:
|
||||
return [self]
|
||||
else:
|
||||
return self.children
|
||||
|
||||
def leaves(self):
|
||||
current_leaves = [self]
|
||||
while True:
|
||||
new_leaves = []
|
||||
for leaf in current_leaves:
|
||||
new_leaves += leaf.next()
|
||||
if current_leaves == new_leaves:
|
||||
break
|
||||
else:
|
||||
current_leaves = new_leaves
|
||||
return current_leaves
|
||||
492
fractal_dimension/mcmullen_stuff/icosatree.py
Normal file
492
fractal_dimension/mcmullen_stuff/icosatree.py
Normal file
|
|
@ -0,0 +1,492 @@
|
|||
from icosanode import Node
|
||||
import math
|
||||
import numpy as np
|
||||
import time
|
||||
from scipy.sparse import csr_matrix
|
||||
from scipy.sparse.linalg import eigs
|
||||
|
||||
def functions(n, z):
|
||||
if n == 1:
|
||||
return -1*np.conj(z)
|
||||
duals = [[1/2*(-1 + math.sqrt(5)) - 1j, 1/2*(-1 + math.sqrt(5))], [],
|
||||
[1/22*(1 + 3*math.sqrt(5)) + 1/11*(3 - 2*math.sqrt(5))*1j, 2/(13 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(6 - math.sqrt(5))*1j,
|
||||
2/(11 + 7*math.sqrt(5))], [1/22*(1 + 3*math.sqrt(5)) +
|
||||
1/11*(-3 + 2*math.sqrt(5))*1j, 2/(
|
||||
13 + 5*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(-4 + math.sqrt(5))*1j, 2/(
|
||||
17 + 7*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(4 - math.sqrt(5))*1j, 2/(
|
||||
17 + 7*math.sqrt(5))], [3/(2*math.sqrt(5)), 1/(
|
||||
10 + 4*math.sqrt(5))], [1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(2/5) + 1/
|
||||
math.sqrt(5)], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(-8 + 3*math.sqrt(5))*1j, 2/(
|
||||
23 + 11*math.sqrt(5))], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(8 - 3*math.sqrt(5))*1j,
|
||||
2/(23 + 11*math.sqrt(5))], [1/6*(-1 + 2*math.sqrt(5)),
|
||||
1/6*(-2 + math.sqrt(5))], [1 + (-2 + math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/(
|
||||
2 + 2*math.sqrt(5)), 1/(
|
||||
2 + 2*math.sqrt(5))], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(-1 - 2*math.sqrt(5))*1j,
|
||||
2/(7 + 5*math.sqrt(5))], [1/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, -(2/5) + 1/
|
||||
math.sqrt(5)], [2/(1 + math.sqrt(5)) + 1j, 2/(
|
||||
1 + math.sqrt(5))], [1 + (2 - math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 2/(
|
||||
7 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(-6 + math.sqrt(5))*1j,
|
||||
2/(11 + 7*math.sqrt(5))]]
|
||||
return duals[n][0] + np.conj((duals[n][1])**2 / (z-duals[n][0]))
|
||||
|
||||
def derivatives(n, z):
|
||||
if n == 1:
|
||||
return 1
|
||||
duals = [[1/2*(-1 + math.sqrt(5)) - 1j, 1/2*(-1 + math.sqrt(5))], [],
|
||||
[1/22*(1 + 3*math.sqrt(5)) + 1/11*(3 - 2*math.sqrt(5))*1j, 2/(13 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(6 - math.sqrt(5))*1j,
|
||||
2/(11 + 7*math.sqrt(5))], [1/22*(1 + 3*math.sqrt(5)) +
|
||||
1/11*(-3 + 2*math.sqrt(5))*1j, 2/(
|
||||
13 + 5*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(-4 + math.sqrt(5))*1j, 2/(
|
||||
17 + 7*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(4 - math.sqrt(5))*1j, 2/(
|
||||
17 + 7*math.sqrt(5))], [3/(2*math.sqrt(5)), 1/(
|
||||
10 + 4*math.sqrt(5))], [1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(2/5) + 1/
|
||||
math.sqrt(5)], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(-8 + 3*math.sqrt(5))*1j, 2/(
|
||||
23 + 11*math.sqrt(5))], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(8 - 3*math.sqrt(5))*1j,
|
||||
2/(23 + 11*math.sqrt(5))], [1/6*(-1 + 2*math.sqrt(5)),
|
||||
1/6*(-2 + math.sqrt(5))], [1 + (-2 + math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/(
|
||||
2 + 2*math.sqrt(5)), 1/(
|
||||
2 + 2*math.sqrt(5))], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(-1 - 2*math.sqrt(5))*1j,
|
||||
2/(7 + 5*math.sqrt(5))], [1/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, -(2/5) + 1/
|
||||
math.sqrt(5)], [2/(1 + math.sqrt(5)) + 1j, 2/(
|
||||
1 + math.sqrt(5))], [1 + (2 - math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 2/(
|
||||
7 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(-6 + math.sqrt(5))*1j,
|
||||
2/(11 + 7*math.sqrt(5))]]
|
||||
return abs(-1*((z-duals[n][0])**2) / ((duals[n][1])**2))
|
||||
|
||||
def samplePoint(word):
|
||||
points = [2/5*(-1 + math.sqrt(5)) - (4j)/5, -(1/
|
||||
2), 1/22*(1 + 3*math.sqrt(5)) + (1/100 + 1/11*(3 - 2*math.sqrt(5)))*1j, 1/
|
||||
62*(15 + 13*math.sqrt(5)) +
|
||||
1/31*(6 - math.sqrt(5))*1j, 1/
|
||||
22*(1 + 3*math.sqrt(5)) + (-(1/100) + 1/11*(-3 + 2*math.sqrt(5)))*1j, 1/
|
||||
22*(15 - math.sqrt(5)) +
|
||||
1/11*(-4 + math.sqrt(5))*1j, 1/22*(15 - math.sqrt(5)) +
|
||||
1/11*(4 - math.sqrt(5))*1j, 3/(
|
||||
2*math.sqrt(5)), 1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(3/38)*(-9 + math.sqrt(5)) +
|
||||
1/19*(-8 + 3*math.sqrt(5))*1j, -(3/38)*(-9 + math.sqrt(5)) +
|
||||
1/19*(8 - 3*math.sqrt(5))*1j, 1/6*(-1 + 2*math.sqrt(5)), 9/10 +
|
||||
9/10*(-2 + math.sqrt(5))*1j, 1/(
|
||||
2 + 2*math.sqrt(5)), 1/38*(11 + 3*math.sqrt(5)) +
|
||||
1/19*(-1 - 2*math.sqrt(5))*1j, 1/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, 8/(
|
||||
5*(1 + math.sqrt(5))) + (4j)/5, 9/10 +
|
||||
9/10*(2 - math.sqrt(5))*1j, 1/38*(11 + 3*math.sqrt(5)) +
|
||||
1/19*(1 + 2*math.sqrt(5))*1j, 1/62*(15 + 13*math.sqrt(5)) +
|
||||
1/31*(-6 + math.sqrt(5))*1j]
|
||||
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):
|
||||
tt = time.time()
|
||||
generators = [np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0], [5 + 2*math.sqrt(5), 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -1,
|
||||
2*(3 + math.sqrt(5)), 0, 0, 0], [1/2*(7 + math.sqrt(5)), 1/2*(3 + math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0,
|
||||
0], [1/2*(5 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0,
|
||||
0], [1/2*(7 + math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 3, 0, 0, 0], [1/2*(5 + 3*math.sqrt(5)), 3 + math.sqrt(5),
|
||||
0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0,
|
||||
0], [2*(3 + math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, -1,
|
||||
2*(3 + math.sqrt(5)), 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
|
||||
0], [3 + 2*math.sqrt(5), 3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0], [3, 2 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0], [2*(3 + math.sqrt(5)),
|
||||
5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -1, 5 + 2*math.sqrt(5), 0, 0, 0]]), np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0], [2*(2 + math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
5 + 2*math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0], [1/2*(7 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5),
|
||||
0, 0, 0, 0, -1, 0], [1/2*(3 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0,
|
||||
2 + math.sqrt(5), 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [0, 0, 0, 0, 0, 1,
|
||||
0, 0, 0, 0, 0, 0], [5 + 2*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
2*(2 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [5 + 2*math.sqrt(5),
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0], [2 + math.sqrt(5), 3 + math.sqrt(5), 0, 0, 0,
|
||||
1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [2 + math.sqrt(5),
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0], [3 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0, 0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 0, -1, 0], [3 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, -1, 0]]), np.array([[0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0], [0, 1, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0], [0, 1/2*(3 + math.sqrt(5)), 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0], [0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0,
|
||||
0, -1, 0, 0, 2*(3 + math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 2 + math.sqrt(5), 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 3, 0], [0, 3 + math.sqrt(5), 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + 2*math.sqrt(5),
|
||||
0], [0, 2*(2 + math.sqrt(5)), 0, 0, 2*(3 + math.sqrt(5)), 0, 0, -1, 0, 0,
|
||||
2*(3 + math.sqrt(5)), 0], [0, 2 + math.sqrt(5), 0, 0, 3, 0, 0,
|
||||
1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(7 + math.sqrt(5)), 0], [0, 5 + 2*math.sqrt(5),
|
||||
0, 0, 2*(3 + math.sqrt(5)), 0, 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0], [0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 3 + math.sqrt(5), 0, 0,
|
||||
3 + 2*math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)),
|
||||
0]]), np.array([[0, 0, 0, 2 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0,
|
||||
1/2*(3 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0], [0, 0, 0, 5 + 2*math.sqrt(5),
|
||||
0, 1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5)),
|
||||
0, 0], [0, 0, 0, 3 + math.sqrt(5), 0, -1, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 2*(2 + math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5)), 0,
|
||||
5 + 2*math.sqrt(5), 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
3 + math.sqrt(5), 0, -1, 0, 3 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0], [0,
|
||||
0, 0, 2 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0,
|
||||
0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, -1, 0, 3 + math.sqrt(5), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
|
||||
0], [0, 0, 0, 5 + 2*math.sqrt(5), 0, 1/2*(-1 - math.sqrt(5)), 0,
|
||||
5 + 2*math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
1/2*(3 + math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0,
|
||||
3 + math.sqrt(5), 0, 0]]), np.array([[0, 0, 1/2*(-1 - math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5))], [0, 0, -1, 0, 3 + math.sqrt(5), 1/2*(5 + math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0, -1, 0, 3 + math.sqrt(5), 2,
|
||||
0, 0, 0, 0, 0, 3 + math.sqrt(5)], [0, 0, 1/2*(-3 - math.sqrt(5)), 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5))], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0,
|
||||
0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1/2*(-3 - math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5))], [0, 0, 1/2*(-1 - math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
2*(2 + math.sqrt(5))], [0, 0, 1/2*(-3 - math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(11 + 5*math.sqrt(5))], [0, 0, -1, 0, 1/2*(5 + math.sqrt(5)),
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5)], [0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0,
|
||||
0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 3 + 2*math.sqrt(5),
|
||||
1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 3, 0,
|
||||
1/2*(7 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)), 2 + math.sqrt(5), 0], [0, 0, 0,
|
||||
0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 3, 1/2*(-3 + math.sqrt(5)), 2 + math.sqrt(5),
|
||||
0], [0, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)),
|
||||
1/2*(-3 + math.sqrt(5)), 1/2*(3 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(5 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(7 + 3*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 5 + 2*math.sqrt(5), 0,
|
||||
2*(3 + math.sqrt(5)), -1, 5 + 2*math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0,
|
||||
0, 0, 0], [0, 0, 0, 0, 0, 0, 3 + 2*math.sqrt(5), 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0,
|
||||
0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
|
||||
2*(3 + math.sqrt(5)), -1, 2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
|
||||
5 + 2*math.sqrt(5), -1, 5 + 2*math.sqrt(5), 0]]), np.array([[0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 5 + 2*math.sqrt(5), 0,
|
||||
5 + 2*math.sqrt(5), -1, 2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0, 1/2*(3 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)),
|
||||
1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0,
|
||||
2 + math.sqrt(5), 1/2*(-3 + math.sqrt(5)), 3], [0, 0, 0, 0, 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)),
|
||||
3 + 2*math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 3, 0, 2 + math.sqrt(5),
|
||||
1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
|
||||
3 + 2*math.sqrt(5), 0, 3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0,
|
||||
0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 5 + 2*math.sqrt(5), -1,
|
||||
5 + 2*math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0,
|
||||
0, 0, 0, 2*(3 + math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), -1,
|
||||
2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 0, 0,
|
||||
2*(2 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0], [0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0,
|
||||
3/2*(3 + math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 0, 1/2*(-3 - math.sqrt(5)), 0,
|
||||
0], [0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 1/2*(5 + math.sqrt(5)),
|
||||
3 + math.sqrt(5), 0, -1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 3/2*(3 + math.sqrt(5)),
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-3 - math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-3 - math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0,
|
||||
0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0,
|
||||
0, 3 + math.sqrt(5), 0, 0, 1/2*(5 + math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 0, -1,
|
||||
0, 0], [0, 0, 0, 3 + math.sqrt(5), 0, 0, 2, 3 + math.sqrt(5), 0, -1, 0,
|
||||
0], [0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)),
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0]]), np.array([[0, 0, 1/2*(11 + 5*math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)),
|
||||
3/2*(3 + math.sqrt(5))], [0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 2*(2 + math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2 + math.sqrt(5)], [0, 0, 1, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)),
|
||||
3/2*(3 + math.sqrt(5))], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, -1,
|
||||
1/2*(5 + math.sqrt(5))], [0, 0, 2*(2 + math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2 + math.sqrt(5)], [0, 0,
|
||||
3 + math.sqrt(5), 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, -1,
|
||||
1/2*(5 + math.sqrt(5))], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)),
|
||||
1/2*(7 + 3*math.sqrt(5))], [0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
1/2*(5 + 3*math.sqrt(5))], [0, 0, 3 + math.sqrt(5), 0, 3 + math.sqrt(5), 0, 0, 0,
|
||||
0, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0,
|
||||
1/2*(-1 - math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0,
|
||||
0, 1/2*(13 + 5*math.sqrt(5)), 0], [0, -1, 3 + math.sqrt(5), 0, 0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 2*(2 + math.sqrt(5)), 0], [0, 0, 1, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0], [0, -1, 3 + math.sqrt(5), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
0, 0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 1/2*(1 - math.sqrt(5)), 2 + math.sqrt(5),
|
||||
0, 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5), 0], [0,
|
||||
1/2*(-1 - math.sqrt(5)), 5 + 2*math.sqrt(5), 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 0,
|
||||
0, 1/2*(13 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
|
||||
0], [0, 1/2*(1 - math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 2 + math.sqrt(5), 0, 0,
|
||||
0, 1/2*(5 + math.sqrt(5)), 0], [0, 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(3 + math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 3 + math.sqrt(5),
|
||||
0], [0, 1/2*(-1 - math.sqrt(5)), 5 + 2*math.sqrt(5), 0, 0, 0, 5 + 2*math.sqrt(5),
|
||||
0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1, 0], [0, -1, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0]]), np.array([[0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
3/2*(3 + math.sqrt(5))], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
3/2*(3 + math.sqrt(5))], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2*(2 + math.sqrt(5)),
|
||||
0, 0, 0, 2 + math.sqrt(5)], [0, 0, 3 + math.sqrt(5), 0, 0, 0, -1,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5))], [0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, -1, 3 + math.sqrt(5), 0, 0, 0, 2], [0, 0, 0, 0, 0,
|
||||
0, 0, 1, 0, 0, 0, 0], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5))], [0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, -1,
|
||||
3 + math.sqrt(5), 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0, 2*(2 + math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
2 + math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[-1, 0,
|
||||
2*(2 + math.sqrt(5)), 0, 0, 0, 2*(3 + math.sqrt(5)), 2*(3 + math.sqrt(5)), 0, 0,
|
||||
0, 0], [-1, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 2*(3 + math.sqrt(5)),
|
||||
5 + 2*math.sqrt(5), 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [1/2*(-3 + math.sqrt(5)), 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0,
|
||||
0], [1/2*(1 - math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0], [-1, 0,
|
||||
5 + 2*math.sqrt(5), 0, 0, 0, 5 + 2*math.sqrt(5), 2*(3 + math.sqrt(5)), 0, 0, 0,
|
||||
0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1,
|
||||
0, 0, 0, 0], [1/2*(1 - math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0,
|
||||
3 + 2*math.sqrt(5), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
0], [1/2*(1 - math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0, 0,
|
||||
0], [1/2*(-3 + math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 3, 0, 0, 0, 0], [1/2*(-3 + math.sqrt(5)), 0,
|
||||
2 + math.sqrt(5), 0, 0, 0, 3, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0]]), np.array([[1, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1/2*(7 + 3*math.sqrt(5)), 0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
0, -1], [2*(2 + math.sqrt(5)), 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5))], [0, 0, 0, 1, 0, 0, 0,
|
||||
0, 0, 0, 0, 0], [5 + 2*math.sqrt(5), 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5))], [2 + math.sqrt(5), 0,
|
||||
0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0,
|
||||
1/2*(1 - math.sqrt(5))], [3 + math.sqrt(5), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0,
|
||||
0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, -1], [1/2*(3 + math.sqrt(5)), 0, 0,
|
||||
2 + math.sqrt(5), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0,
|
||||
1/2*(1 - math.sqrt(5))], [2 + math.sqrt(5), 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 1, 0, 0], [5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5))], [3 + math.sqrt(5), 0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, -1]]), np.array([[0,
|
||||
2 + math.sqrt(5), 0, 0, 1/2*(3 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0,
|
||||
3 + math.sqrt(5), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0,
|
||||
0, -1, 0, 0], [0, 5 + 2*math.sqrt(5), 0, 0, 2*(2 + math.sqrt(5)),
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
|
||||
0], [0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 1/2*(11 + 5*math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0], [0, 2*(2 + math.sqrt(5)), 0, 0,
|
||||
5 + 2*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
|
||||
0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 3 + math.sqrt(5),
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0], [0, 3 + math.sqrt(5), 0, 0,
|
||||
3 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0, 0, 0, -1, 0, 0], [0, 2 + math.sqrt(5),
|
||||
0, 0, 2 + math.sqrt(5), 1/2*(5 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)),
|
||||
0, 0], [0, 1/2*(3 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 3 + math.sqrt(5), 0, 0,
|
||||
0, 1/2*(1 - math.sqrt(5)), 0, 0]]), np.array([[0, 3 + math.sqrt(5), 0, 0, 0,
|
||||
1/2*(1 - math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 0, 1/2*(3 + math.sqrt(5)), 0], [0,
|
||||
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0, 0,
|
||||
0, -1, 0, 0, 3 + math.sqrt(5), 0, 1/2*(7 + 3*math.sqrt(5)), 0], [0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
3 + math.sqrt(5), 0], [0, 3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0,
|
||||
1/2*(3 + math.sqrt(5)), 0, 2 + math.sqrt(5), 0], [0, 2*(2 + math.sqrt(5)), 0, 0,
|
||||
0, -1, 0, 0, 3 + math.sqrt(5), 0, 3 + math.sqrt(5), 0], [0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 2 + math.sqrt(5),
|
||||
0, 2 + math.sqrt(5), 0], [0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0, 5 + 2*math.sqrt(5), 0, 5 + 2*math.sqrt(5), 0], [0,
|
||||
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1/2*(13 + 5*math.sqrt(5)), 0, 0,
|
||||
0, 1/2*(-1 - math.sqrt(5)), 0, 0, 5 + 2*math.sqrt(5), 0, 2*(2 + math.sqrt(5)),
|
||||
0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1/2*(13 + 5*math.sqrt(5)),
|
||||
0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 2*(2 + math.sqrt(5)), 0,
|
||||
5 + 2*math.sqrt(5), 0]]), np.array([[0, 1/2*(-3 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)),
|
||||
0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)),
|
||||
0], [0, -1, 2, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0], [0,
|
||||
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/2*(-3 - math.sqrt(5)),
|
||||
3/2*(3 + math.sqrt(5)), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0,
|
||||
1/2*(-1 - math.sqrt(5)), 2 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, -1, 1/2*(5 + math.sqrt(5)), 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0], [0,
|
||||
1/2*(-1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 1/2*(-1 - math.sqrt(5)),
|
||||
2 + math.sqrt(5), 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
|
||||
2*(2 + math.sqrt(5)), 0], [0, 1/2*(-3 - math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0], [0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, -1, 1/2*(5 + math.sqrt(5)), 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0]]), np.array([[1, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0], [2 + math.sqrt(5), 0, 1/2*(-3 + math.sqrt(5)), 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0, 0, 0, 3, 0, 0], [2*(2 + math.sqrt(5)), 0, -1, 0,
|
||||
0, 2*(3 + math.sqrt(5)), 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 0], [2 + math.sqrt(5),
|
||||
0, 1/2*(-3 + math.sqrt(5)), 0, 0, 3, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0,
|
||||
0], [3 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + 2*math.sqrt(5), 0, 0,
|
||||
0, 1/2*(5 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
|
||||
0], [5 + 2*math.sqrt(5), 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0,
|
||||
2*(3 + math.sqrt(5)), 0, 0], [3 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 3 + 2*math.sqrt(5), 0,
|
||||
0], [1/2*(7 + 3*math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5)), 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0], [0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 1, 0, 0], [5 + 2*math.sqrt(5), 0, -1, 0, 0,
|
||||
2*(3 + math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0], [1/2*(3 + math.sqrt(5)),
|
||||
0, 1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0, 0]]), np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [3 + math.sqrt(5), 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0,
|
||||
1/2*(5 + math.sqrt(5)), -1, 0, 0], [1/2*(11 + 5*math.sqrt(5)), 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 3/2*(3 + math.sqrt(5)),
|
||||
1/2*(-3 - math.sqrt(5)), 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0,
|
||||
3/2*(3 + math.sqrt(5)), 1/2*(-3 - math.sqrt(5)), 0, 0], [2*(2 + math.sqrt(5)), 0,
|
||||
0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 2 + math.sqrt(5),
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0], [1/2*(5 + math.sqrt(5)), 0, 0, 3 + math.sqrt(5),
|
||||
0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), -1, 0, 0], [1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 2 + math.sqrt(5), 1/2*(-1 - math.sqrt(5)), 0,
|
||||
0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [3 + math.sqrt(5), 0, 0,
|
||||
3 + math.sqrt(5), 0, 0, 0, 0, 2, -1, 0, 0], [1/2*(7 + 3*math.sqrt(5)), 0, 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)),
|
||||
1/2*(-1 - math.sqrt(5)), 0, 0], [1/2*(13 + 5*math.sqrt(5)), 0, 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
1/2*(-3 - math.sqrt(5)), 0, 0]]), np.array([[0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0,
|
||||
0, 0, 2 + math.sqrt(5), 1/2*(-3 + math.sqrt(5)), 3], [0, 0, 0, 0, 0,
|
||||
3 + 2*math.sqrt(5), 0, 0, 0, 3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)),
|
||||
1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
|
||||
3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)), 3 + 2*math.sqrt(5)], [0, 0, 0, 0, 0,
|
||||
1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)),
|
||||
1/2*(1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0,
|
||||
1/2*(7 + math.sqrt(5)), 0, 0, 0, 1/2*(3 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)),
|
||||
1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0,
|
||||
0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 5 + 2*math.sqrt(5), -1,
|
||||
2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 3, 0, 0, 0, 2 + math.sqrt(5),
|
||||
1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0,
|
||||
2*(3 + math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), -1, 5 + 2*math.sqrt(5)], [0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
|
||||
0, 0, 2*(2 + math.sqrt(5)), -1, 2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 1]]), np.array([[0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 0,
|
||||
1/2*(3 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0], [0, -1, 0,
|
||||
3 + math.sqrt(5), 0, 0, 3 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0,
|
||||
0], [0, -1, 0, 3 + math.sqrt(5), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
|
||||
0], [0, 1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 0,
|
||||
5 + 2*math.sqrt(5), 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0], [0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 5 + 2*math.sqrt(5), 0, 0, 2*(2 + math.sqrt(5)), 0,
|
||||
1/2*(13 + 5*math.sqrt(5)), 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
|
||||
0], [0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 0, 2 + math.sqrt(5), 0,
|
||||
1/2*(5 + math.sqrt(5)), 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
|
||||
0], [0, -1, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0,
|
||||
1/2*(7 + 3*math.sqrt(5)), 0, 0, 0], [0, 1/2*(1 - math.sqrt(5)), 0,
|
||||
1/2*(3 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 0, 3 + math.sqrt(5), 0, 0, 0], [0,
|
||||
1/2*(-1 - math.sqrt(5)), 0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0,
|
||||
1/2*(11 + 5*math.sqrt(5)), 0, 0, 0]])]
|
||||
|
||||
root = Node([-1, 2, 10 + 3*math.sqrt(5), 4 + math.sqrt(5), 1/(1 - 2/math.sqrt(5)), 2, 7 +
|
||||
3*math.sqrt(5), 7 +
|
||||
3*math.sqrt(5), 1/2*(7 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 1/2*(11 +
|
||||
5*math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5))], [], 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")
|
||||
print("tree construction (s): %f\ntree construction (m): %f" % (time.time()-tt, (time.time()-tt)/60))
|
||||
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):
|
||||
#return np.real(eigs(matrix.power(a),k=1)[0][0])
|
||||
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-10:
|
||||
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)
|
||||
#y2 = testFunction(k2)
|
||||
count += 1
|
||||
print(count,k1,y1)
|
||||
|
||||
def main():
|
||||
start = time.time()
|
||||
|
||||
words = {}
|
||||
m = 1500
|
||||
print("maximum:",m)
|
||||
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])*19)
|
||||
secantMethod(matrix,matrix.shape[0],1,1.33,1.34,10**(-10),1000)
|
||||
|
||||
print("total (s): %f\ntotal (m): %f" % (time.time()-start, (time.time()-start)/60))
|
||||
|
||||
main()
|
||||
Loading…
Reference in a new issue