Created
November 16, 2017 02:27
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require 'matrix' | |
def f2(n) | |
return n.odd? ? (n * 3 + 1) / 2 : n / 2 | |
end | |
def dense(w, d) | |
w2 = w - 1 | |
a = (0...w2).to_a | |
s = '0' * w2 | |
(1..(d * w - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' } | |
return ('1' + s).to_i(2) | |
end | |
def stat(l) | |
l = [0] if (l.empty?) | |
t = t2 = 0 | |
l.each \ | |
{ | |
|x| | |
t += x | |
t2 += x ** 2 | |
} | |
c = l.size | |
a = t.to_f / c | |
z = t2.to_f / c - a ** 2 | |
sd = Math.sqrt(z < 0 ? 0 : z) | |
return a, sd, l.max.to_f, l.min.to_f | |
end | |
def stat2(l, t, n) | |
return Hash[[["a#{n}", "sd#{n}", "mx#{n}"], stat(l)[0..2].map { |x| x / t }].transpose] | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def count(n) | |
c = 0 | |
n1 = n | |
l = [n] | |
begin | |
n = f2(n) | |
l << n | |
c += 1 | |
end while n >= n1 | |
return {'c' => c, 'l' => l} | |
end | |
def data(n) | |
ns = n.to_s(2) | |
nl = ns.length | |
m = nl / 2 | |
nsh = ns[0..m] | |
nsl = ns[m..-1] | |
asdm1 = stat2(ns.split(/0+/).map { |x| x.length }, nl, 1) | |
l1 = ns.split(/1+/) | |
l1.shift | |
asdm0 = stat2(l1.map { |x| x.length }, nl, 0) | |
return {'n' => n, 'ns' => ns, 'nl' => nl, 'd' => d(ns), 'dh' => d(nsh), 'dl' => d(nsl)}.merge(asdm1).merge(asdm0) | |
end | |
def data2(n) | |
return data(n).merge(count(n)) | |
end | |
def dist(c) | |
return (0...c).map { |i| data2(dense(200, i.to_f / (c - 1))) } | |
end | |
def sum(l) | |
t = 0.0 | |
l.each { |x| t += x } | |
return t | |
end | |
def real(x) | |
raise x.imag.to_s if (x.imag > 1e-15) | |
return x.real | |
end | |
def fmt(n) | |
n.real? ? sprintf("%.3g", n) : sprintf("(%.3g %.3gi)", n.real, n.imag) | |
end | |
def detect2(z, v, d, vi, xz, vx, i) | |
$stderr.puts(z['ns']) | |
$stderr.puts(z['c']) | |
z['l'].each_with_index \ | |
{ | |
|x, j| | |
x1 = data(x) | |
x1['wr'] = 1.0 | |
y0 = Matrix[vx.map { |k| x1[k] }].transpose - xz | |
puts([j, i, y0.column(0).norm, x1['d']].join("\t")) | |
} | |
puts | |
end | |
def out(fn, a) | |
f = File.open(fn, 'a') | |
f.puts(a.keys.join("\t")) if (f.size == 0) | |
f.puts(a.values.join("\t")) | |
f.close | |
end | |
raise if (ARGV[0].nil?) | |
d = "out/#{ARGV[0]}" | |
l = Dir.glob("#{d}/*").select { |x| x =~ /out\d+.txt$/} | |
n = l.size | |
i = n - 1 | |
a = Kernel.eval(File.open("#{d}/out#{i}.txt").readlines[0]) | |
l = a['lb'].map { |x| x.size } | |
raise if (sum(l) != 0) | |
vx = a['v'] + ['wr'] | |
$vxn = Hash[[vx + ['c'], (0..vx.size).to_a].transpose] | |
am = (1..vx.size).map { [0] * vx.size } | |
vx.each { |x| (vx + ['c']).each { |y| am[$vxn[x]][$vxn[y]] = a[x][y] if (!a[x][y].nil?) } } | |
am = am.transpose | |
b = am.pop | |
am = am.transpose | |
#$stderr.puts(['vx', vx].inspect) | |
#$stderr.puts(['am', am].inspect) | |
#$stderr.puts(['b', b].inspect) | |
v, d, vi = Matrix[*am].eigen | |
xz = (Matrix.identity(vx.size) - Matrix[*am]).inverse * Matrix[b].transpose | |
l = dist(500) | |
l.sort_by! { |x| -x['c'] } | |
l[0..10].each_with_index \ | |
{ | |
|x, i| | |
detect2(x, v, d, vi, xz, vx, i) | |
} | |
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