405 lines
12 KiB
Python
405 lines
12 KiB
Python
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from cmath import isnan
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import numpy as np
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import random
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import hashlib
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import math
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def get_state_id(state):
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return ','.join([str(x) for x in sorted(state)])
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class Point():
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def __init__(self, x, y):
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self.x = x
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self.y = y
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def id(self):
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return ','.join([str(int(x)) for x in self.x])
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class Influence():
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def __init__(self, a, b):
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self.a = a
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self.b = b
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self.original_dof = set()
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self.dof = set()
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for i in range(0, len(a.x)):
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if a.x[i] != b.x[i]:
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self.original_dof.add(i)
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self.dof.add(i)
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def coherent(self):
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return self.a.y == self.b.y
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def id(self):
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return ','.join(sorted([self.a.id(), self.b.id()]))
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def encode(v):
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byte_values = []
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for i in range(0, math.ceil(len(v) / 8)):
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x = 0
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for j in range(0, 8):
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index = i * 8 + j
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if index >= len(v):
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continue
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x <<= 1
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x |= int(v[index])
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byte_values.append(x)
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return bytearray(byte_values)
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def decode(x, N):
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index = 0
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output = np.zeros((N))
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while x > 0 and index < N:
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output[index] = x & 0b1
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x >>= 1
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index += 1
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return output
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def sha(v):
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x = encode(v)
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m = hashlib.sha256()
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m.update(x)
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result = m.digest()
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return result[0] & 0b1
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def hamming_distance(a, b):
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return np.sum(np.logical_xor(a.x, b.x))
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def random_x(N):
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x = np.zeros((N))
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for i in range(0, N):
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x[i] = random.randint(0, 1)
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return x
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def xor(x):
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# return sum(x[:4]) % 2
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return sum(x) % 2
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def create_dof_map(influences):
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dof_map = {}
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for influence in influences:
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for i in influence.dof:
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if not i in dof_map:
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dof_map[i] = []
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dof_map[i].append(influence)
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return dof_map
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def flip(influences, i):
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for influence in influences:
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if i in influence.dof:
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influence.a.y = int(influence.a.y) ^ 1
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def remove_dof(dof_map, i, flip = False):
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for influence in dof_map[i]:
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influence.dof.remove(i)
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if flip:
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influence.a.y = int(influence.a.y) ^ 1
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# if len(influence.dof) == 0 and not influence.coherent():
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# raise Exception('Invalid')
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del dof_map[i]
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def solve(dof_map, all_influences, all_samples):
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eliminated = True
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while eliminated:
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eliminated = False
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for influence in all_influences:
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if len(influence.dof) == 1:
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i = next(iter(influence.dof))
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if influence.coherent:
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remove_dof(dof_map, i)
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eliminated = True
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else:
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print('Forced', i)
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remove_dof(dof_map, i, True)
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eliminated = True
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lowest_dof = None
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for influence in all_influences:
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if not influence.coherent and len(influence.dof) > 1:
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if lowest_dof is None or len(influence.dof) < len(lowest_dof.dof):
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lowest_dof = influence
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flip = None
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highest_score = -1
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for i in lowest_dof.dof:
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per_point_scores = {}
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i_influences = dof_map[i]
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left = 0
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right = 0
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for influence in i_influences:
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if not influence.a in per_point_scores:
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per_point_scores[influence.a] = [0, 0]
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if not influence.b in per_point_scores:
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per_point_scores[influence.b] = [0, 0]
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if influence.coherent:
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per_point_scores[influence.a][0] += 1
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per_point_scores[influence.b][0] += 1
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left += 1
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else:
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per_point_scores[influence.a][1] += 1
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per_point_scores[influence.b][1] += 1
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right += 1
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print(i, left / (left + right))
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num = 0
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denom = 0
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for _, score in per_point_scores.items():
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if score[0] == score[1]:
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continue
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print(i, score)
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num += score[1] / (score[0] + score[1])
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denom += 1
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score = num / denom if denom > 0 else 0
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print(score)
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return None
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# 1st row (n+1 choose k+1) * (1-(k mod 2))
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# psuedopascal to compute the follow-on rows
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# assuming solvability, we want to maximize the probability that our current state and our state with
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# a particular single flip are one order apart in the correct direction
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# 2, 0
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# 2, 2, 0
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# 2, 4, 2, 0
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# 2, 6, 6, 2, 0
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# 2, 8,12, 8, 2, 0
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# 2,10,20,20,10, 2, 0
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# 3,-9,19,-33,51,-73,99
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# 3,-6,10,-14,18,-22,26
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# 3,-3, 4, -4, 4, -4, 4
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# 3, 0, 1, 0, 0, 0, 0
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# 3, 3, 1, 1, 0, 0, 0
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# 3, 6, 4, 2, 1, 0, 0
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# 3, 9,10, 6, 3, 1, 0
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# 4, 0, 4, 0
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# 4, 4, 4, 4, 0
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# 4, 8, 8, 8, 4, 0
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# 4,12,16,16,12, 4, 0
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# 5, 0,10, 0, 1
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# 5, 5,10,10, 1, 1
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# 5,
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# 5,
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# 3
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#
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# @1 [1, 2, 1]
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# @2 [2, 2, 0]
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# @3 [3, 0, 1]
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# 5 [5, 10, 10, 5, 1] (5 choose 1, 5 choose 2, ...)
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#
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# @1 [1, 4, 6, 4, 1], [4, 6, 4, 1, 0] - 16, 15 - binomial (4 choose 0, 4 choose 1, 4 choose 2),
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# @2 [2, 6, 6, 2, 0], [3, 4, 4, 3, 1] - 16, 15 - (4 choose 1) + (2 choose -1) - (2 choose 1)
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# @3 [3, 6, 4, 2, 1], [2, 4, 6, 3, 0] - 16, 15 - (4 choose 2) + (2 choose -2) - (2 choose 2) + (2 choose -1) - (2 choose 1)
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# @4 [4, 4, 4, 4, 0], [1, 6, 6, 1, 1] - 16, 15 -
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# @5 [5, 0, 10, 0, 1], [0, 10, 0, 5, 0] - 16, 15 -
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# @0 [0.0, 0.0, 0.0, 0.0, 0.0]
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# @1 [0.2, 0.4, 0.6, 0.8, 1.0]
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# @2 [0.4, 0.6, 0.6, 0.4, 0.0]
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# @3 [0.6, 0.6, 0.4, 0.4, 1.0]
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# @4 [0.8, 0.4, 0.4, 0.8, 0.0]
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# @5 [1.0, 0.0, 1.0, 0.0, 1.0]
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# 6
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#
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# @1 [1, 5, 10, 10, 5, 1]
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# @2 [2, 8, 12, 8, 2, 0]
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# @3 [3, 9, 10, 6, 3, 1]
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# @4 [4, 8, 8, 8, 4, 0]
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# @5 [5, 5, 10, 10, 1, 1]
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# @6 [6, 0, 20, 0, 6, 0]
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# last row, 1 if odd, 0 if even
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# second to last, subtract 2 on odds, add 2 on evens
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def compute_distributions(N):
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dist = np.zeros((N, N))
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for j in range(0, N):
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dist[0][j] = math.comb(N - 1, j)
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dist[-1][j] = math.comb(N, j + 1) * (1 - (j % 2))
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for i in range(1, N):
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for j in range(0, i + 1):
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dist[i][j] = math.comb(i + 1, j + 1) * (1 - (j % 2))
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for k in range(i + 1, N):
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for j in reversed(range(0, k)):
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dist[i][j+1] = dist[i][j] + dist[i][j+1]
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print(dist)
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for i in range(0, N):
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for j in range(0, N):
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denom = math.comb(N, j+1)
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dist[i][j] /= denom
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return dist
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def raised_cosine(x, u, s):
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if x < (u - s):
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return 0
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if x > (u + s):
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return 0
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return 1.0 / (2.0 * s) * (1 + math.cos(math.pi * (x - u) / s))
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def average_index(x):
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total = 0
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for k in range(0, len(x)):
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total += k * x[k]
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return total / np.sum(x)
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# 8, 32, 2^5
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# 10, 64, 2^6
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# 12, 128, 2^7
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# 14, 256, 2^8
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# 16, 512, 2^9
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# 18, 1024, 2^10
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# 20, 2048, 2^11
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# 22, 4096, 2^12
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def main():
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N = 16
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sample_size = 128
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sample_ids = set()
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samples = []
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dist = compute_distributions(N)
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print(dist)
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for i in range(0, sample_size):
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x = random_x(N)
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y = int(xor(x))
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p = Point(x, y)
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p_id = p.id()
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if p_id in sample_ids:
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continue
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sample_ids.add(p_id)
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samples.append(p)
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total_sample_count = len(samples)
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# for i in range(0, 2**N):
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# x = decode(i, N)
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# y = int(xor(x))
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# samples.append(Point(x,y))
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base = np.zeros(N)
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current = np.zeros(N)
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cumulative_probability = np.ones(N)
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for _ in range(0, N):
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lowest_err = -1
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use_flip = -1
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for flip in range(-1, N):
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coherent_distances = np.zeros(N+1)
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incoherent_distances = np.zeros(N+1)
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all_coherent = True
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for i in range(0, len(samples)):
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a = samples[i]
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for j in range(0, len(samples)):
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b = samples[j]
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distance = hamming_distance(a, b)
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is_coherent = ((flip < 0 or a.x[flip] == b.x[flip]) and a.y == b.y) or ((flip >= 0 and a.x[flip] != b.x[flip]) and a.y != b.y)
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if is_coherent:
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coherent_distances[distance] += 1
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else:
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incoherent_distances[distance] += 1
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all_coherent = False
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if all_coherent:
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print('Flip and halt', flip)
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return
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# print(coherent_distances, incoherent_distances)
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# print(coherent_distances, incoherent_distances)
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est_incoherence = np.divide(incoherent_distances, np.add(coherent_distances, incoherent_distances))
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# print(est_incoherence)
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for k in range(0, N):
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known_incoherence_at_k = dist[k]
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err = 0
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# denom = 0
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probability = 1.0
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for i in range(1, N + 1):
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if isnan(est_incoherence[i]):
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continue
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sample_size = coherent_distances[i] + incoherent_distances[i]
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full_size = math.comb(N, i) * (2 ** N)
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num_unknowns = full_size - sample_size
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min_true_value = incoherent_distances[i] / full_size
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max_true_value = (incoherent_distances[i] + num_unknowns) / full_size
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s = max(abs(est_incoherence[i] - min_true_value), abs(est_incoherence[i] - max_true_value))
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u = est_incoherence[i]
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known_incoherence = known_incoherence_at_k[i - 1]
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err = raised_cosine(known_incoherence, u, s)
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probability *= err
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# print(k, i, min_true_value, max_true_value)
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# confidence = (coherent_distances[i] + incoherent_distances[i]) / math.comb(N, i) # probability that the sample is representative
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# err += abs(est_incoherence[i] - known_incoherence_at_k[i-1]) * confidence
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# denom += 1
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# print(flip, k, err)
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# err /= denom
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if flip < 0:
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base[k] = probability
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else:
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current[k] = probability
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if flip >= 0:
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if np.sum(current) == 0:
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continue
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np.divide(current, np.sum(current), current)
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# print(current)
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# temp = np.roll(cumulative_probability, -1)
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# temp[-1] = 1.0
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# np.multiply(current, temp, current)
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# np.divide(current, np.sum(current), current)
|
||
|
|
p_forward = 0
|
||
|
|
p_backward = 0
|
||
|
|
for i in range(1, N):
|
||
|
|
p_forward += cumulative_probability[i] * current[i - 1]
|
||
|
|
for i in range(0, N - 1):
|
||
|
|
p_backward += cumulative_probability[i] * current[i + 1]
|
||
|
|
|
||
|
|
# base_index = average_index(cumulative_probability)
|
||
|
|
# new_index = average_index(current)
|
||
|
|
# if isnan(new_index):
|
||
|
|
# continue
|
||
|
|
# np.divide(current, np.sum(current), current)
|
||
|
|
# np.subtract(1, current, current)
|
||
|
|
print(flip,p_forward,p_backward,current)
|
||
|
|
delta = p_forward - p_backward
|
||
|
|
if use_flip < 0 or delta > lowest_err:
|
||
|
|
use_flip = flip
|
||
|
|
lowest_err = delta
|
||
|
|
|
||
|
|
# for k in range(0, N - 1):
|
||
|
|
# value = current[k] * cumulative_probability[k + 1]
|
||
|
|
# if use_flip < 0 or value > lowest_err:
|
||
|
|
# use_flip = flip
|
||
|
|
# lowest_err = value
|
||
|
|
# print(flip, highest_value)
|
||
|
|
else:
|
||
|
|
np.divide(base, np.sum(base), base)
|
||
|
|
# np.subtract(1, base, base)
|
||
|
|
# print(cumulative_probability)
|
||
|
|
cumulative_probability = np.roll(cumulative_probability, -1)
|
||
|
|
cumulative_probability[-1] = 1.0
|
||
|
|
# print(cumulative_probability)
|
||
|
|
# print(base)
|
||
|
|
np.multiply(base, cumulative_probability, cumulative_probability)
|
||
|
|
np.divide(cumulative_probability, np.sum(cumulative_probability), cumulative_probability)
|
||
|
|
print(cumulative_probability)
|
||
|
|
|
||
|
|
if use_flip < 0:
|
||
|
|
return
|
||
|
|
|
||
|
|
print('Flip', use_flip, lowest_err)
|
||
|
|
for p in samples:
|
||
|
|
if p.x[use_flip]:
|
||
|
|
p.y ^= 1
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
main()
|