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December 27, 2016 23:15
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require 'statsample' | |
def f2(n) | |
n = (n * 3 + 1) / 2 while (n.odd?) | |
n /= 2 while (n.even?) | |
return n | |
end | |
def adv(x) | |
n1 = n = x['n'] | |
l = [n] | |
while (n >= n1 && n != 1) | |
n = f2(n) | |
l << n | |
end | |
x['l'] = l | |
x['ls'] = l.size | |
x['ns'] = x['n'].to_s(2).length | |
x['h'] = x['ls'].to_f / x['ns'] | |
x['h2'] = (x['h'] * $g).to_i | |
return x | |
end | |
def next2(z) | |
l = [z] | |
p = z['p'] + 1 | |
l << adv({'n'=>z['n'] + 2**p, 'p'=>p}) | |
l << z.merge({'p'=>p}) | |
return l | |
end | |
def insert(l, x) | |
l << x | |
end | |
def delete(l, j) | |
z = l.delete_at(j) | |
return z | |
end | |
def sum(l) | |
t = 0 | |
l.each { |x| t += x } | |
return t | |
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 | |
end | |
def dist(l) | |
l2 = [] | |
l.each_with_index \ | |
{ | |
|x, i| | |
h = x[1]['h2'] | |
l2[h] = [] if (l2[h].nil?) | |
l2[h] << i | |
} | |
l1 = (0...l2.size).sort_by { |i| l2[i].nil? ? 0 : l2[i].size } | |
return l2, l1 | |
end | |
def rank(l1, l2) | |
l1h, l1s = dist(l1) | |
l2h, l2s = dist(l2) | |
j = l1s.find { |x| !l2h[x].nil? && (l1h[x].nil? || l1h[x].size < $n) } | |
j = l2h.size - 1 if (j.nil?) | |
k = l2s.find { |x| !l2h[x].nil? } | |
l = (0...l2.size).to_a | |
l.sort_by! { |x| l2[x][1]['ls'] } | |
k = l.find { |x| x != j } | |
return l2h[j][rand(l2h[j].size)], k | |
end | |
def opt(c) | |
l = [] | |
l1 = [] | |
insert(l, next2({'n'=>1, 'p'=>0})) | |
puts('# ' + Time.now.to_s) | |
t = Time.now.to_i | |
c.times \ | |
{ | |
|i| | |
$stderr.puts([i, sprintf('%.1fm', (Time.now.to_i - t) / 60.0), Time.now.to_s].join("\t")) if (i % 100 == 0) | |
j, k = rank(l1, l) | |
if (l.size > 1000) then | |
z2 = delete(l, [j, k].max) | |
z1 = delete(l, [j, k].min) | |
l1 += [z1, z2] | |
z = j < k ? z1 : z2 | |
else | |
z = delete(l, j) | |
l1 += [z] | |
end | |
insert(l, next2(z[1])) | |
insert(l, next2(z[2])) | |
$stdout.flush | |
} | |
puts('# ' + Time.now.to_s) | |
return l1.map { |x| x[1] } | |
end | |
def stat2(l, t) | |
return stat(l).map { |x| x / t } | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def fit(l1, c) | |
l1 = l1.transpose | |
a = {} | |
a['y'] = l1[c].to_vector() | |
($c...l1.size).each \ | |
{ | |
|i| | |
a["d#{i}"] = l1[i].to_vector() | |
} | |
ds = a.to_dataset() | |
r = Statsample::Regression.multiple(ds, 'y') | |
# $stderr.puts(r.summary) | |
return [r.constant] + r.coeffs.values_at(*(a.keys - ['y'])) | |
end | |
def err(z, l1, fn) | |
z = z.dup | |
c1 = z.shift | |
l = [] | |
l1.each_with_index \ | |
{ | |
|l2, j| | |
nl, = l2 | |
t = c1 | |
z.size.times { |i| t += z[i] * l2[i + $c] } | |
b = fn.call(t, nl) | |
l << [l2[0...$c], t, b].flatten | |
} | |
return l | |
end | |
def data(x) | |
n = x['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) | |
l1 = ns.split(/1+/) | |
l1.shift | |
asdm0 = stat2(l1.map { |x| x.length }, nl) | |
return [nl, x['ls'], x['h2'], d(ns), d(nsh), d(nsl), asdm1].flatten | |
end | |
def out(fn, l) | |
f = File.open("#{fn}.txt", 'w') | |
l.each { |x| f.puts(x.join("\t")) } | |
f.close | |
end | |
def out2(fn, l) | |
out("#{fn}e", l) | |
out("#{fn}e2", l.sort_by { |x| x[1] }) | |
end | |
def samplefit(c) | |
l = opt(c) | |
a = {} | |
h = {} | |
l.each \ | |
{ | |
|x| | |
n = x['n'] | |
h2 = x['h2'] | |
h[h2] = h.fetch(h2, {}).merge!({ n => nil }) | |
a[n] = x | |
} | |
# h.sort.each { |k, v| p([k, v.size]) }; exit; | |
l2 = [] | |
l3 = [] | |
c1 = 10 | |
h1 = h.select { |k, v| v.size >= c1 }.sort | |
h1.each_with_index \ | |
{ | |
|kv, n| | |
k, v = kv | |
l1 = v.keys.sort | |
l0 = [] | |
c1.times \ | |
{ | |
|i| | |
n = l1[(i.to_f / (c1 - 1) * (l1.size - 1)).to_i] | |
l0 << n | |
l2 << data(a[n]) | |
l3 << a[n] | |
} | |
} | |
$stderr.puts("#{l2.size} pts") | |
$c = 3 | |
z = fit(l2, $c - 1) | |
out('out', l2) | |
out2('out', err(z, l2, lambda { |x, nl| x / $g * nl })) | |
return z, l3 | |
end | |
def adv2(l) | |
l2 = [] | |
l.each_with_index \ | |
{ | |
|n, i| | |
x = {'n' => n} | |
l2 << data(x) | |
} | |
return l2 | |
end | |
def avg(l) | |
return nil if (l.empty?) | |
return sum(l) / l.size | |
end | |
def improve(z, l) | |
$stderr.puts("#{l.size} pts2") | |
l4 = [] | |
l.each \ | |
{ | |
|x| | |
c = x['l'].size | |
c2 = c.to_f / 2 | |
l2 = adv2(x['l']) | |
l3 = l2.transpose.map { |x| avg(x.compact) } | |
l1 = err(z, [l3], lambda { |x, nl| x / $g * nl }) | |
nl = x['n'].to_s(2).length | |
nl2 = l3[0][0] | |
l4 << [nl, x['ls'], x['h2']] + [l1[0][3] + c2 / nl2, l1[0][4] + c2] | |
} | |
out2('out2', l4) | |
end | |
def compare() | |
$n = 40 | |
$g = 50 | |
z, l = samplefit(5000) | |
# $stderr.puts(z.inspect) | |
improve(z, l) | |
end | |
l2 = compare() | |
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