492 lines
31 KiB
Python
492 lines
31 KiB
Python
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from icosanode 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 == 1:
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return -1*np.conj(z)
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duals = [[1/2*(-1 + math.sqrt(5)) - 1j, 1/2*(-1 + math.sqrt(5))], [],
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[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,
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2/(11 + 7*math.sqrt(5))], [1/22*(1 + 3*math.sqrt(5)) +
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1/11*(-3 + 2*math.sqrt(5))*1j, 2/(
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13 + 5*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(-4 + math.sqrt(5))*1j, 2/(
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17 + 7*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(4 - math.sqrt(5))*1j, 2/(
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17 + 7*math.sqrt(5))], [3/(2*math.sqrt(5)), 1/(
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10 + 4*math.sqrt(5))], [1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(2/5) + 1/
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math.sqrt(5)], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(-8 + 3*math.sqrt(5))*1j, 2/(
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23 + 11*math.sqrt(5))], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(8 - 3*math.sqrt(5))*1j,
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2/(23 + 11*math.sqrt(5))], [1/6*(-1 + 2*math.sqrt(5)),
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1/6*(-2 + math.sqrt(5))], [1 + (-2 + math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/(
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2 + 2*math.sqrt(5)), 1/(
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2 + 2*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/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, -(2/5) + 1/
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math.sqrt(5)], [2/(1 + math.sqrt(5)) + 1j, 2/(
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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/(
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7 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(-6 + math.sqrt(5))*1j,
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2/(11 + 7*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 == 1:
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return 1
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duals = [[1/2*(-1 + math.sqrt(5)) - 1j, 1/2*(-1 + math.sqrt(5))], [],
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[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,
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2/(11 + 7*math.sqrt(5))], [1/22*(1 + 3*math.sqrt(5)) +
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1/11*(-3 + 2*math.sqrt(5))*1j, 2/(
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13 + 5*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(-4 + math.sqrt(5))*1j, 2/(
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17 + 7*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(4 - math.sqrt(5))*1j, 2/(
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17 + 7*math.sqrt(5))], [3/(2*math.sqrt(5)), 1/(
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10 + 4*math.sqrt(5))], [1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(2/5) + 1/
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math.sqrt(5)], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(-8 + 3*math.sqrt(5))*1j, 2/(
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23 + 11*math.sqrt(5))], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(8 - 3*math.sqrt(5))*1j,
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2/(23 + 11*math.sqrt(5))], [1/6*(-1 + 2*math.sqrt(5)),
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1/6*(-2 + math.sqrt(5))], [1 + (-2 + math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/(
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2 + 2*math.sqrt(5)), 1/(
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2 + 2*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/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, -(2/5) + 1/
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math.sqrt(5)], [2/(1 + math.sqrt(5)) + 1j, 2/(
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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/(
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7 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(-6 + math.sqrt(5))*1j,
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2/(11 + 7*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 = [2/5*(-1 + math.sqrt(5)) - (4j)/5, -(1/
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2), 1/22*(1 + 3*math.sqrt(5)) + (1/100 + 1/11*(3 - 2*math.sqrt(5)))*1j, 1/
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62*(15 + 13*math.sqrt(5)) +
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1/31*(6 - math.sqrt(5))*1j, 1/
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22*(1 + 3*math.sqrt(5)) + (-(1/100) + 1/11*(-3 + 2*math.sqrt(5)))*1j, 1/
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22*(15 - math.sqrt(5)) +
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1/11*(-4 + math.sqrt(5))*1j, 1/22*(15 - math.sqrt(5)) +
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1/11*(4 - math.sqrt(5))*1j, 3/(
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2*math.sqrt(5)), 1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(3/38)*(-9 + math.sqrt(5)) +
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1/19*(-8 + 3*math.sqrt(5))*1j, -(3/38)*(-9 + math.sqrt(5)) +
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1/19*(8 - 3*math.sqrt(5))*1j, 1/6*(-1 + 2*math.sqrt(5)), 9/10 +
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9/10*(-2 + math.sqrt(5))*1j, 1/(
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2 + 2*math.sqrt(5)), 1/38*(11 + 3*math.sqrt(5)) +
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1/19*(-1 - 2*math.sqrt(5))*1j, 1/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, 8/(
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5*(1 + math.sqrt(5))) + (4j)/5, 9/10 +
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9/10*(2 - math.sqrt(5))*1j, 1/38*(11 + 3*math.sqrt(5)) +
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1/19*(1 + 2*math.sqrt(5))*1j, 1/62*(15 + 13*math.sqrt(5)) +
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1/31*(-6 + 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([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0], [5 + 2*math.sqrt(5), 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -1,
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2*(3 + math.sqrt(5)), 0, 0, 0], [1/2*(7 + math.sqrt(5)), 1/2*(3 + math.sqrt(5)),
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0, 0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0,
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0], [1/2*(5 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
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1/2*(1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0,
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0], [1/2*(7 + math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
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1/2*(-3 + math.sqrt(5)), 3, 0, 0, 0], [1/2*(5 + 3*math.sqrt(5)), 3 + math.sqrt(5),
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0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0,
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0], [2*(3 + math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, -1,
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2*(3 + math.sqrt(5)), 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
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0], [3 + 2*math.sqrt(5), 3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)),
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1/2*(5 + 3*math.sqrt(5)), 0, 0, 0], [3, 2 + math.sqrt(5), 0, 0, 0, 0, 0,
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1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0], [2*(3 + math.sqrt(5)),
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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,
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0, 0], [2*(2 + math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
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5 + 2*math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
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0], [1/2*(7 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5),
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0, 0, 0, 0, -1, 0], [1/2*(3 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0,
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2 + math.sqrt(5), 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [0, 0, 0, 0, 0, 1,
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0, 0, 0, 0, 0, 0], [5 + 2*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0,
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2*(2 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [5 + 2*math.sqrt(5),
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1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0,
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1/2*(-1 - math.sqrt(5)), 0], [2 + math.sqrt(5), 3 + math.sqrt(5), 0, 0, 0,
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1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [2 + math.sqrt(5),
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1/2*(5 + math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
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1/2*(1 - math.sqrt(5)), 0], [3 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0, 0, 0,
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3 + math.sqrt(5), 0, 0, 0, 0, -1, 0], [3 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)),
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0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, -1, 0]]), np.array([[0,
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1/2*(7 + 3*math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0,
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1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0], [0, 1, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0], [0, 1/2*(3 + math.sqrt(5)), 0, 0,
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1/2*(7 + math.sqrt(5)), 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0,
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1/2*(7 + math.sqrt(5)), 0], [0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0,
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0, -1, 0, 0, 2*(3 + math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
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0], [0, 2 + math.sqrt(5), 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0,
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1/2*(-3 + math.sqrt(5)), 0, 0, 3, 0], [0, 3 + math.sqrt(5), 0, 0,
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1/2*(5 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + 2*math.sqrt(5),
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0], [0, 2*(2 + math.sqrt(5)), 0, 0, 2*(3 + math.sqrt(5)), 0, 0, -1, 0, 0,
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2*(3 + math.sqrt(5)), 0], [0, 2 + math.sqrt(5), 0, 0, 3, 0, 0,
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1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(7 + math.sqrt(5)), 0], [0, 5 + 2*math.sqrt(5),
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0, 0, 2*(3 + math.sqrt(5)), 0, 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0], [0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 3 + math.sqrt(5), 0, 0,
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3 + 2*math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)),
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0]]), np.array([[0, 0, 0, 2 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0,
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1/2*(3 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0], [0, 0, 0, 5 + 2*math.sqrt(5),
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0, 1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5)),
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0, 0], [0, 0, 0, 3 + math.sqrt(5), 0, -1, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
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1/2*(7 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
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0], [0, 0, 0, 2*(2 + math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5)), 0,
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5 + 2*math.sqrt(5), 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0], [0, 0, 0,
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3 + math.sqrt(5), 0, -1, 0, 3 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0], [0,
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0, 0, 2 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0,
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1/2*(5 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0,
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0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, -1, 0, 3 + math.sqrt(5), 0,
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1/2*(7 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
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0], [0, 0, 0, 5 + 2*math.sqrt(5), 0, 1/2*(-1 - math.sqrt(5)), 0,
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5 + 2*math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0], [0, 0, 0,
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1/2*(3 + math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0,
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3 + math.sqrt(5), 0, 0]]), np.array([[0, 0, 1/2*(-1 - math.sqrt(5)), 0,
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1/2*(7 + 3*math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
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1/2*(7 + 3*math.sqrt(5))], [0, 0, -1, 0, 3 + math.sqrt(5), 1/2*(5 + math.sqrt(5)),
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0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0, -1, 0, 3 + math.sqrt(5), 2,
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0, 0, 0, 0, 0, 3 + math.sqrt(5)], [0, 0, 1/2*(-3 - math.sqrt(5)), 0,
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1/2*(11 + 5*math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0,
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1/2*(13 + 5*math.sqrt(5))], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0,
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0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1/2*(-3 - math.sqrt(5)), 0,
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1/2*(13 + 5*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0,
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1/2*(13 + 5*math.sqrt(5))], [0, 0, 1/2*(-1 - math.sqrt(5)), 0,
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1/2*(7 + 3*math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
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2*(2 + math.sqrt(5))], [0, 0, 1/2*(-3 - math.sqrt(5)), 0,
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1/2*(13 + 5*math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0,
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1/2*(11 + 5*math.sqrt(5))], [0, 0, -1, 0, 1/2*(5 + math.sqrt(5)),
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1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5)], [0, 0,
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1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
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1/2*(7 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0,
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0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 3 + 2*math.sqrt(5),
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1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 3, 0,
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1/2*(7 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)), 2 + math.sqrt(5), 0], [0, 0, 0,
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0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 3, 1/2*(-3 + math.sqrt(5)), 2 + math.sqrt(5),
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0], [0, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)),
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1/2*(-3 + math.sqrt(5)), 1/2*(3 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0,
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1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(5 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)),
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1/2*(7 + 3*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 5 + 2*math.sqrt(5), 0,
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2*(3 + math.sqrt(5)), -1, 5 + 2*math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0,
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0, 0, 0], [0, 0, 0, 0, 0, 0, 3 + 2*math.sqrt(5), 0,
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1/2*(5 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0,
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0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
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2*(3 + math.sqrt(5)), -1, 2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
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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()
|