184 lines
8 KiB
Python
184 lines
8 KiB
Python
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from fournode 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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def functions(n, z):
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if n == 0:
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#return 3 - 2*math.sqrt(2) + (3 - 2*math.sqrt(2))*1j + np.conj((-1 + math.sqrt(2))**2 / ((-3 + 2*math.sqrt(2) - (3 - 2*math.sqrt(2))*1j + z)))
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return 3-2*math.sqrt(2) + (3-2*math.sqrt(2))*1j + np.conj((1 / (17+12*math.sqrt(2))) / (z - (3-2*math.sqrt(2) + (3-2*math.sqrt(2))*1j)))
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elif n == 1:
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#return -3 + 2*math.sqrt(2) + (3 - 2*math.sqrt(2))*1j + np.conj((-1 + math.sqrt(2))**2 / ((3 - 2*math.sqrt(2) - (3 - 2*math.sqrt(2))*1j + z)))
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return -3+2*math.sqrt(2) + (3-2*math.sqrt(2))*1j + np.conj((1 / (17+12*math.sqrt(2))) / (z - (-3+2*math.sqrt(2) + (3-2*math.sqrt(2))*1j)))
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elif n == 2:
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#return -3 + 2*math.sqrt(2) + (-3 + 2*math.sqrt(2))*1j + np.conj((-1 + math.sqrt(2))**2 / ((3 - 2*math.sqrt(2) - (-3 + 2*math.sqrt(2))*1j + z)))
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return -3+2*math.sqrt(2) + (-3+2*math.sqrt(2))*1j + np.conj((1 / (17+12*math.sqrt(2))) / (z - (-3+2*math.sqrt(2) + (-3+2*math.sqrt(2))*1j)))
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elif n == 3:
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#return 3 - 2*math.sqrt(2) + (-3 + 2*math.sqrt(2))*1j + np.conj((-1 + math.sqrt(2))**2 / ((-3 + 2*math.sqrt(2) - (-3 + 2*math.sqrt(2))*1j + z)))
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return 3-2*math.sqrt(2) + (-3+2*math.sqrt(2))*1j + np.conj((1 / (17+12*math.sqrt(2))) / (z - (3-2*math.sqrt(2) + (-3+2*math.sqrt(2))*1j)))
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elif n == 4:
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#return 1 + 1j + np.conj((-1 + math.sqrt(2))**2 / (-1 - 1j + z))
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return 1 + 1j + np.conj(1 / (z - 1 - 1j))
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elif n == 5:
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#return -1 + 1j + np.conj((-1 + math.sqrt(2))**2 / (1 - 1j + z))
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return -1 + 1j + np.conj(1 / (z + 1 - 1j))
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elif n == 6:
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#return -1 - 1j + np.conj((-1 + math.sqrt(2))**2 / (1 + 1j + z))
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return -1 - 1j + np.conj(1 / (z + 1 + 1j))
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elif n == 7:
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#return 1 - 1j + np.conj((-1 + math.sqrt(2))**2 / (-1 + 1j + z))
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return 1 - 1j + np.conj(1 / (z - 1 + 1j))
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def derivatives(n, z):
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if n == 0:
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#return abs(-((-3 + 2*math.sqrt(2) - (3 - 2*math.sqrt(2))*1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((17+12*math.sqrt(2))*(-3+2*math.sqrt(2)-(3-2*math.sqrt(2))*1j + z)**2)
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elif n == 1:
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#return abs(-((3 - 2*math.sqrt(2) - (3 - 2*math.sqrt(2))*1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((17+12*math.sqrt(2))*(3-2*math.sqrt(2)-(3-2*math.sqrt(2))*1j + z)**2)
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elif n == 2:
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#return abs(-((3 - 2*math.sqrt(2) - (-3 + 2*math.sqrt(2))*1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((17+12*math.sqrt(2))*(3-2*math.sqrt(2)-(-3+2*math.sqrt(2))*1j + z)**2)
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elif n == 3:
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#return abs(-((-3 + 2*math.sqrt(2) - (-3 + 2*math.sqrt(2))*1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((17+12*math.sqrt(2))*(-3+2*math.sqrt(2)-(-3+2*math.sqrt(2))*1j + z)**2)
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elif n == 4:
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#return abs(-((-1 - 1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((-1-1j+z)**2)
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elif n == 5:
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#return abs(-((1 - 1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((1-1j+z)**2)
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elif n == 6:
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#return abs(-((1 + 1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((1+1j+z)**2)
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elif n == 7:
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#return abs(-((-1 + 1j + z)**2 / (-1 + math.sqrt(2))**2))
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return abs((-1+1j+z)**2)
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def samplePoint(word):
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if word[-1] == 4:
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p = 1/2 + 1j/2
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elif word[-1] == 5:
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p = -1/2 + 1j/2
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elif word[-1] == 7:
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p = 1/2 - 1j/2
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elif word[-1] == 6:
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p = -1/2 - 1j/2
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elif word[-1] == 1:
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p = -3+2*math.sqrt(2) + (3-2*math.sqrt(2))*1j
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elif word[-1] == 0:
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p = 3-2*math.sqrt(2) + (3-2*math.sqrt(2))*1j
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elif word[-1] == 2:
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p = -3+2*math.sqrt(2) + (-3+2*math.sqrt(2))*1j
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elif word[-1] == 3:
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p = 3-2*math.sqrt(2) + (-3+2*math.sqrt(2))*1j
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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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generators = [np.array([[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [3, 3, 0, -1, 4, 0], [4, 2, 0, -1, 4, 0], [0, 0, 0, 0, 1, 0], [4, 3, 0, -1, 3, 0]]),
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np.array([[1, 0, 0, 0, 0, 0], [3, 0, -1, 3, 4, 0], [2, 0, -1, 4, 4, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [3, 0, -1, 4, 3, 0]]),
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np.array([[0, 0, 3, 4, 3, -1], [0, 0, 4, 3, 3, -1], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 4, 4, 2, -1]]),
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np.array([[0, 3, 3, -1, 4, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 2, 4, -1, 4, 0], [0, 0, 0, 0, 1, 0], [0, 3, 4, -1, 3, 0]]),
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np.array([[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [3, 4, 0, 0, -1, 3], [4, 3, 0, 0, -1, 3], [4, 4, 0, 0, -1, 2], [0, 0, 0, 0, 0, 1]]),
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np.array([[1, 0, 0, 0, 0, 0], [3, 0, -1, 3, 0, 4], [2, 0, -1, 4, 0, 4], [0, 0, 0, 1, 0, 0], [3, 0, -1, 4, 0, 3], [0, 0, 0, 0, 0, 1]]),
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np.array([[0, 0, 3, 4, -1, 3], [0, 0, 4, 3, -1, 3], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 4, 4, -1, 2], [0, 0, 0, 0, 0, 1]]),
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np.array([[0, 3, 3, -1, 0, 4], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 2, 4, -1, 0, 4], [0, 3, 4, -1, 0, 3], [0, 0, 0, 0, 0, 1]])]
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root = Node([1 + math.sqrt(2), 1 + math.sqrt(2), 1 + math.sqrt(2), 1 + math.sqrt(2), 3 + 2*math.sqrt(2), -1], [], words, False)
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current_leaves = [root]
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nodes = 1
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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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next_gen = leaf.next_generation(words, dc, generators)
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new_leaves += next_gen
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nodes += len(next_gen) if len(next_gen) > 1 else 0
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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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for i,leaf in enumerate(current_leaves):
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words[str(leaf.word)] = i
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print(len(current_leaves), "partitions")
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print(nodes,"nodes")
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return current_leaves
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def constructMatrix(words, dc):
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leave = generateTree(words, dc)
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row = []
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col = []
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data = []
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for i,leaf in enumerate(leave):
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thing = words[str(leaf.word[1:])]
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if isinstance(thing,int):
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row.append(i)
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col.append(thing)
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data.append(sampleValue(leaf.word))
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else:
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sample = sampleValue(leaf.word)
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for wor in thing.leaves():
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row.append(i)
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col.append(words[str(wor.word)])
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data.append(sample)
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return csr_matrix((data,(row,col)),shape=(len(leave),len(leave)))
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def secant(x0,y0,x1,y1,z):
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return x0 - (y0-z) * ((x1-x0)/(y1-y0))
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def matrixFunction(matrix,l,a):
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matrix = matrix.power(a)
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vec = np.ones(l)
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previous_entry = vec[0]
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previous_val = 0
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current = matrix * vec
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current_val = current[0] / previous_entry
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count = 0
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while count < 10000000000 and abs(current_val - previous_val) > 1e-15:
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previous_val = current_val
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previous_entry = current[0]
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current = matrix * current
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#print(current[0],previous_entry)
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current_val = current[0] / previous_entry
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count += 1
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print("power method:", count)
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return current_val
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def secantMethod(matrix,l,z,x1,x2,e,its):
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k1 = x1
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k2 = x2
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y1 = matrixFunction(matrix,l,k1)
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y2 = matrixFunction(matrix,l,k2)
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#y1 = testFunction(k1)
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#y2 = testFunction(k2)
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count = 1
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print(count,k1,y1)
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while abs(y1-z)>e and count<its:
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k3 = secant(k1,y1,k2,y2,z)
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k1 = k2
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y1 = y2
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k2 = k3
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y2 = matrixFunction(matrix,l,k2)
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#y2 = testFunction(k2)
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count += 1
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print(count,k1,y1)
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def main():
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start = time.time()
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words = {}
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matrix = constructMatrix(words,5000)
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#print(matrix)
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print("construction (s): %f\nconstruction (m): %f" % (time.time()-start, (time.time()-start)/60))
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#print(csr_matrix.transpose(matrix))
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print(csr_matrix.count_nonzero(matrix), (matrix.shape[0])*7)
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secantMethod(matrix,matrix.shape[0],1,1.33,1.34,10**(-10),1000)
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print("total (s): %f\ntotal (m): %f" % (time.time()-start, (time.time()-start)/60))
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main()
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