77 lines
2.1 KiB
Python
77 lines
2.1 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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def flip(n, index):
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return n ^ (1 << index)
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def distance(i, j):
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return bin(i ^ j).count('1')
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def matrix_system_with_two_knowns(p, q, N):
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S = 2 ** N
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mat = np.zeros((S, S))
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val = np.zeros(S)
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for i in range(0, S):
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if i == p:
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mat[i][i] = 1.0
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val[i] = 1.0
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elif i == q:
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mat[i][i] = 1.0
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else:
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mat[i][i] = -1.0
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for j in range(0, N):
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mat[i][flip(i,j)] = 1.0 / N
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return (mat, val)
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def main():
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final_values = []
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final_x = []
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final_y = []
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for N in range(11, 12):
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print(N)
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S = 2 ** N
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distances = np.zeros((S, S))
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for i in range(0, S):
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for j in range(0, S):
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distances[i][j] = distance(i,j)
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# final_values = []
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# final_basis = []
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visited_distances = set()
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for p in range(0, S):
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for q in range(p + 1, S):
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pq_distance = distances[p, q]
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if pq_distance in visited_distances:
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continue
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visited_distances.add(pq_distance)
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(mat, val) = matrix_system_with_two_knowns(p, q, N)
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solution = np.linalg.inv(mat).dot(val)
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for i in range(0, len(solution)):
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final_x.append(distances[i, p] / N)
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final_y.append(distances[i, q] / N)
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final_values.append(solution[i])
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# values = list(set(solution))
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# values.sort()
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# if len(values) <= 1:
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# continue
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# basis = [1.0 * i / (len(values) - 1) for i in range(len(values))]
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# final_values.extend(values)
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# final_basis.extend(basis)
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# fig, ax = plt.subplots()
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# ax.scatter(final_values, final_basis)
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# print(np.linalg.lstsq((final_x, final_y), final_values))
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fig = plt.figure()
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ax = fig.add_subplot(projection='3d')
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ax.scatter(final_x, final_y, final_values)
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ax.grid(True)
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plt.show()
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if __name__ == "__main__":
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main()
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