Created
January 17, 2019 03:42
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def f2(n) | |
return n.odd? ? (n * 3 + 1) / 2 : n / 2 | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def len01(ns) | |
nl = ns.length | |
l1 = ns.split(/0+/).map { |x| x.length } | |
l2 = ns.split(/1+/)[1..-1] | |
l2 = [''] if (l2.nil?) | |
l0 = l2.map { |x| x.length } | |
return l0, l1 | |
end | |
def e(ns) | |
return len01(ns).flatten.size.to_f / ns.length | |
end | |
def av(l) | |
return l.inject(0.0) { |t, x| t + x } / 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 | |
m = nil | |
l.each \ | |
{ | |
|z| | |
x = z[y1] | |
y = z[yp] | |
txy += (x - xav) * (y - yav) | |
tx += (x - xav) ** 2 | |
ty += (y - yav) ** 2 | |
e1 = (x - y).abs | |
e += e1 | |
m = [m, e1].compact.max | |
} | |
r = txy / (Math.sqrt(tx) * Math.sqrt(ty)) | |
e /= l.size | |
return {'r' => r, 'e_a' => e, 'e_m' => m} | |
end | |
def slopecorr(l, l2) | |
return 0 if (l.nil? || l.empty?) | |
l = l.map { |x| Math.log(x) } | |
a, b = [l[0], l[-1]] | |
l2.replace((0...l.size).map \ | |
{ | |
|x| | |
y1 = a + x.to_f / (l.size - 1) * (b - a) | |
y2 = l[x] | |
{'y1' => y1, 'y2' => y2} | |
}) | |
return corr(l2, 'y1', 'y2')['r'] | |
end | |
def count(x, l2 = []) | |
n = n1 = x['n'] | |
l = [n1] | |
while (n != 1) | |
n = f2(n) | |
l << n | |
end | |
d = d(ns = n1.to_s(2)) | |
cg = l.index { |x| x < n1 } | |
cg = 0 if (cg.nil?) | |
cm = (0..cg).max_by { |x| l[x] } | |
cg1 = l.rindex { |x| x >= n1 } | |
cm1 = (0...l.size).max_by { |x| l[x] } | |
nl = ns.length | |
sc = slopecorr(l[nl..-1], l2) | |
return x.merge({'da' => (d - 0.5).abs, | |
'ns' => ns, | |
'cm' => cm, | |
'cg' => cg, | |
'cm1' => cm, | |
'cg1' => cg, | |
'c' => l.size, | |
'nl' => nl, | |
'd' => d, | |
'e' => e(ns), | |
'sc' => sc | |
}) | |
end | |
def out(a, a2 = {}, t = nil) | |
fn = 'out.txt' | |
k = a.keys | |
if ($f1.nil?) then | |
$f1 = File.open(fn, 'w') | |
$f1.puts(k.join("\t")) | |
f2 = File.open('gnuplot.cmd', 'w') | |
st = t.nil? ? 'unset title; ' : "set title '#{t}'; " | |
f2.puts("set ytics nomirror; set y2tics; set colors classic; set key top left box opaque; #{st}; plot \\") | |
(a.keys - ['t']).each \ | |
{ | |
|x| | |
f2.puts("'#{fn}' using (column('t')):(column('#{x}')) with line title '#{x}' #{a2[x]}, \\") | |
} | |
f2.puts | |
f2.close | |
end | |
$f1.puts(a.values_at(*k).join("\t")) | |
$f1.flush | |
end | |
def fmt(ks = []) | |
fmt = {} | |
ks.each { |x| fmt[x] = 'lw 2' } | |
['da', 'd', 'e', 'sc'].each { |x| fmt[x] = fmt.fetch(x, '') + ' dt 3 axes x1y2' } | |
return fmt | |
end | |
def next2(z, l, ks, t) | |
out(z.select { |k, v| !['n', 'ns', 'p'].member?(k) }, | |
fmt(ks), t.inspect) if (z['t'] % 10 == 0) | |
p = z['p'] + 1 | |
l << [z, count({'n'=>z['n'] + 2 ** p, 'p'=>p, 't' => z['t']}), z.merge({'p'=>p})] | |
return | |
end | |
def maxs(l) | |
l.map { |x| x[-1, 1] == '-' ? x.dup.chop : x } | |
end | |
def hard(ks) | |
$stderr.puts(ks.inspect) | |
$f1 = nil | |
l = [] | |
mx = maxs(ks) | |
next2(count({'n' => 1, 'p' => 0, 't' => 0}), l, mx, ks) | |
add = nil | |
seen = {} | |
f = File.open($fn, 'w') | |
c = 20 | |
5e3.to_i.times \ | |
{ | |
|t| | |
l2 = (0...l.size).map { {} } | |
mx.each \ | |
{ | |
|k2| | |
l1 = (0...l.size).map { |x| {k2 => l[x][1][k2], 'i' => x} } | |
l1.sort_by! { |x| x[k2] } | |
l1 = l1.reverse if (ks.member?(k2)) | |
(0...l1.size).each { |x| l2[l1[x]['i']][k2] = x } | |
} | |
l2.each { |x| x['z'] = x.values.inject(0) { |t, x| t + x } } | |
l1 = (0...l2.size).sort_by { |x| l2[x]['z'] } | |
a = {'t1' => t, 'l1' => l.size, 'cs' => seen.size}.merge(l[l1[0]][1]) | |
if (!seen.member?(a['n'])) then | |
seen[a['n']] = nil | |
f.puts(a) | |
f.flush | |
end | |
$stderr.puts(a.select { |k, | !['n'].member?(k)}) if ((t + 1) % 500 == 0) | |
i = l1[rand([l1.size, c].min)] | |
z = l.delete_at(i) | |
[z[1], z[2]].each { |x| next2(x.merge({'t' => t}), l, mx, ks) } | |
l.delete_at(l1[-1]) if (l.size > 2000) | |
} | |
f.close | |
end | |
def out2(fn, l, a2 = {}) | |
f = File.open(fn, 'w') | |
f.puts('$dat << eof') | |
f.puts(l[0].keys.join("\t")) | |
l.each { |x| f.puts(x.values.join("\t")) } | |
f.puts('eof') | |
f.puts('plot \\') | |
l[0].keys.each \ | |
{ | |
|x| | |
next if (a2.member?(x) && a2[x] == nil) | |
f.puts("$dat using (column('#{x}')) with line #{a2[x]},\\") | |
} | |
f.close | |
end | |
def review() | |
l = File.open($fn).readlines.map { |x| Kernel.eval(x) } | |
x = l.min_by { |x| x['sc'] } | |
$stderr.puts(x.inspect) | |
count({'n' => x['n']}, l2 = []) | |
out2('gnuplot2.cmd', l2) | |
out2('gnuplot3.cmd', l.sort_by { |x| x['nl'] }, | |
fmt().merge(Hash[[['n', 'ns', 'p', 't', 't1', 'l1', 'cs'], [nil] * 7].transpose] | |
).merge({'sc' => 'axes x1y2 dt 3 lw 2'})) | |
exit | |
end | |
review() if (File.exist?($fn = 'mixdb.txt')) | |
hard(['sc-']) | |
#hard(['sc-', 'nl', 'cm', 'cg', 'c']) |
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