Created
May 9, 2017 01:25
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def f2(n, o2, e) | |
while (n.odd?) | |
n = (n * 3 + 1) / 2 | |
break if (o2) | |
end | |
while (n.even?) do | |
n /= 2 if (n.even?) | |
break if (e) | |
end | |
return n | |
end | |
def adv(x) | |
n1 = n = x['n'] | |
x['t'].times { n = f2(n, x['o2'], x['e']) } | |
return d(n.to_s(2)) | |
end | |
def ratio(x) | |
n1 = n = x['n'] | |
x['t'].times { n = f2(n, x['o2'], x['e']) } | |
return n.to_s(2).length.to_f / n1.to_s(2).length | |
end | |
def coef(x, y) | |
x1 = x2 = y1 = y2 = xy = 0.0 | |
n = x.size | |
n.times \ | |
{ | |
|i| | |
x1 += x[i] | |
y1 += y[i] | |
xy += x[i] * y[i] | |
x2 += x[i] ** 2 | |
y2 += y[i] ** 2 | |
} | |
d = n * x2 - x1 ** 2 | |
b = (y1 * x2 - x1 * xy) / d | |
m = (n * xy - x1 * y1) / d | |
b = 1 if (b.nan?) | |
m = 1 if (m.nan?) | |
return b, m | |
end | |
def sum(l) | |
t = 0.0 | |
l.each { |x| t += x } | |
return t | |
end | |
def av(l) | |
return nil if (l.empty?) | |
return sum(l) / l.size | |
end | |
def corr(l, y1, yp) | |
xav = av(l.map { |x| x[y1] }) | |
yav = av(l.map { |x| x[yp] }) | |
tx = ty = txy = e = 0.0 | |
l.each \ | |
{ | |
|z| | |
x = z[y1] | |
y = z[yp] | |
txy += (x - xav) * (y - yav) | |
tx += (x - xav) ** 2 | |
ty += (y - yav) ** 2 | |
e += (x - y) ** 2 | |
} | |
r = txy / (Math.sqrt(tx) * Math.sqrt(ty)) | |
e /= l.size | |
return r | |
end | |
def dense(x) | |
w, d, o = x.values_at('w', 'd', 'o') | |
w2 = w - (o ? 2 : 1) | |
a = (0...w2).to_a | |
s = '0' * w2 | |
(1..(d * w - (o ? 2 : 1))).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' } | |
return ('1' + s + (o ? '1' : '')).to_i(2) | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def test(t, o, o2, e) | |
w = 100 | |
c = 500 | |
l = [] | |
(c + 1).times \ | |
{ | |
|i| | |
d = i.to_f / c | |
n = dense({'d' => d, 'w' => w, 'o' => o}) | |
a = {'n' => n, 'o2' => o2, 'e' => e, 't' => t} | |
d2 = adv(a) | |
r = ratio(a) | |
l << {'d' => d, 'd2' => d2, 'wr' => r} | |
} | |
return l | |
end | |
def out(fn, a) | |
return if (a.nil?) | |
f = File.open(fn, 'a') | |
f.puts(a.keys.join("\t")) if (f.size == 0) | |
f.puts(a.values.join("\t")) | |
f.close | |
end | |
def out2(fn, l, t) | |
f = File.open(fn, 'a') | |
l.each { |x| x.merge!({'t' => t}) } | |
f.puts(l[0].keys.join("\t")) if (f.size == 0) | |
l.each { |x| f.puts(x.values.join("\t")) } | |
f.puts | |
f.close | |
end | |
def fit(l, k, t, a) | |
b, m = coef(l.map { |x| x['d'] }, l.map { |x| x[k]}) | |
l.each { |x| x['y'] = m * x['d'] + b } | |
r = corr(l, k, 'y') | |
a.merge!(k => {'t' => t, 'm' => m, 'b' => b, 'r' => r}) | |
end | |
def model(t) | |
tf = [false, true] | |
z= (0...8).map { |x| (1..3).map { |y| tf[x.to_s(2)[-y, 1].to_i] } } | |
l = test(t, *z[6]) | |
a = {} | |
fit(l, 'd2', t, a) | |
fit(l, 'wr', t, a) | |
return a | |
end | |
def adv2(x) | |
n1 = n = x['n'] | |
l = [n] | |
while (n != 1) | |
n = (n * 3 + 1) / 2 while (n.odd?) | |
n /= 2 while (n.even?) | |
l << n | |
end | |
x['ls'] = l.size | |
x['ns'] = n1.to_s(2).length | |
return x | |
end | |
def next2(z) | |
l = [z] | |
p = z['p'] + 1 | |
l << adv2({'n'=>z['n'] + 2**p, 'p'=>p}) | |
l << z.merge({'p'=>p}) | |
return l | |
end | |
def rank(l) | |
l.sort_by! { |x| x[1]['ls'] } | |
l.reverse! | |
end | |
def opt(c) | |
l = [next2({'n'=>1, 'p'=>0})] | |
c.times \ | |
{ | |
rank(l) | |
z = l.delete_at(rand([l.size, 50].min)) | |
l.pop if (l.size > 1000) | |
l << next2(z[1]) | |
l << next2(z[2]) | |
} | |
return l.map { |x| x[1] } | |
end | |
def detect(n, a) | |
d = d(n.to_s(2)) | |
w = n.to_s(2).length | |
c = 1000 | |
i = 0 | |
c.times \ | |
{ | |
break if (w < 1.0) | |
n = (n * 3 + 1) / 2 while (n.odd?) | |
n /= 2 while (n.even?) | |
d = d * a['d2']['m'] + a['d2']['b'] | |
w *= d * a['wr']['m'] + a['wr']['b'] | |
# puts([d, w].join("\t")) | |
i += 1 | |
} | |
return i == c ? 0 : i | |
end | |
l = opt(2e3.to_i) | |
n = l[0]['n'] | |
a = model(1) | |
$stderr.puts(a.inspect) | |
l.each \ | |
{ | |
|x| | |
c = detect(x['n'], a) | |
puts([x['ls'], c, d(x['n'].to_s(2))].join("\t")) | |
} |
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