Created
September 25, 2019 01:41
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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 lenx(ns, p) | |
l = ns.split(p) | |
l = [] if (l.nil?) | |
l.shift if (l[0] == '') | |
return l.map { |x| x.length } | |
end | |
def len01x(ns) | |
return lenx(ns, /0+/), lenx(ns, /1+/) | |
end | |
def e(ns) | |
return len01x(ns).flatten.size.to_f / ns.length | |
end | |
def seq(n) | |
n1 = n | |
l = [] | |
begin | |
l << n | |
n = f2(n) | |
end while (n != 1) | |
return l | |
end | |
def mx01x(ns) | |
l1, l0 = len01x(ns) | |
return (l1 + l0).max.to_f | |
end | |
def measure(l) | |
cm1 = (0...l.size).max_by { |x| l[x] } | |
cg = l.index { |x| x < l[0] } | |
cg = l.size - 1 if (cg.nil?) | |
cg1 = l.rindex { |x| x >= l[0] } | |
cm = (0..cg).max_by { |x| l[x] } | |
c = l.size | |
n = l[0] | |
ns = n.to_s(2) | |
mx01 = mx01x(ns) | |
mx01s = mx01.to_f / ns.length | |
a = {'n' => n, | |
'nl' => Math.log(n), | |
'cg' => cg, | |
'cg1' => cg1, | |
'c' => c, | |
'cm1' => cm1, | |
'cm' => cm, | |
'mx01' => mx01 * 10, | |
'mx01s' => mx01s, | |
'd' => d(ns), | |
'e' => e(ns)} | |
$i = 0 if ($i.nil?) | |
$i += 1 | |
$l << a.dup if ($i % 100 == 0) | |
return a | |
end | |
def stat(l) | |
return 0, 0, 0 if (l.empty?) | |
t = l.inject { |a, x| a + x } | |
t2 = l.inject { |a, x| a + x ** 2 } | |
c = l.size | |
a = t.to_f / c | |
z = t2.to_f / c - a ** 2 | |
sd = Math.sqrt(z < 0 ? 0 : z) | |
raise if (sd.nan?) | |
return a, sd, l.max | |
end | |
def z(x, s) | |
z = 0 | |
ks = x.keys - ['z', 'f', 'n'] | |
ks.each { |k| z += ((x[k] - s["#{k}_a"]) / s["#{k}_s"]) ** 2 } | |
x['z'] = z | |
end | |
def stats(a) | |
s = {} | |
ks = a.first[1].keys - ['z', 'f', 'n'] | |
ks.each \ | |
{ | |
|k| | |
av, sd = stat(a.select { |x, x1| x1['f'] == 'b' }.map { |x| x[1][k] }) | |
s["#{k}_a"] = av | |
s["#{k}_s"] = sd | |
} | |
a.each \ | |
{ | |
|k, x| | |
z(x, s) | |
} | |
$s = s | |
return s | |
end | |
def count(a, n, x = 'a') | |
m = a.member?(n) | |
a[n] = measure(seq(n)) if (!m) | |
a[n]['f'] = x | |
if (x == 'a') then | |
$n = 1 if ($n.nil?) | |
$n += 1 while (a.fetch($n, {}))['f'] == 'a' | |
end | |
return a[n] | |
end | |
def node(a, n) | |
count(a, n) | |
count(a, n * 2, 'b') | |
n2 = nil | |
count(a, n2, 'b') if (n % 3 == 1 && (n2 = (n - 1) / 3).odd? && n2 != 1) | |
end | |
def adv(a, x, s, f, d = nil) | |
n = x['n'] | |
f.puts([s, n, x['z'], d].join("\t")) | |
node(a, n) | |
end | |
def outa(f, l, a = {}, t = '') | |
f.puts('$dat << eof') | |
k = l[0].keys | |
f.puts(k.join("\t")) | |
l.each { |x| f.puts(x.values.join("\t")) } | |
f.puts('eof') | |
f.puts("set colors classic; set ytics nomirror; set y2tics; set title '#{t}'; plot \\") | |
k.each \ | |
{ | |
|x| | |
next if (a.member?(x) && a[x].nil?) | |
f.puts("'$dat' using (column('#{x}')) with line #{a.fetch(x, '')},\\") | |
} | |
f.puts | |
# f.puts("reset; pause -1;") | |
end | |
def axes2(x2) | |
return x2.inject({}) { |h, x| h.merge({x => 'axes x1y2' }) } | |
end | |
def asd(l) | |
l.map { |x| ["#{x}_a", "#{x}_s"] }.flatten | |
end | |
a = {} | |
n = 0 | |
c = 100 | |
$l = [] | |
c.times { node(a, n += 1) } | |
f = File.open('gnuplot.cmd', 'w') | |
f.puts('$dat << eof') | |
f.puts(['s', 'n', 'x_z', 'd'].join("\t")) | |
l1 = [] | |
n2 = 0 | |
200.times \ | |
{ | |
|i| | |
s = stats(a) | |
l1 << s | |
l2 = a.values.select { |x| x['f'] == 'b' } | |
$stderr.puts({'i' => i, 'l2s' => l2.size, 'n' => $n}.inspect) if (i % 10 == 0) | |
x1 = {'n' => $n, 'f' => 'a'} | |
x1 = count(a, $n) | |
z(x1, $s) | |
adv(a, x1, 1, f, x1['n'] - n2) | |
n2 = x1['n'] | |
l = l2.sort_by { |x| x['z'] }.reverse | |
(c / 2).times \ | |
{ | |
raise if (l.empty?) | |
x = l.shift | |
adv(a, x, 2, f) | |
} | |
} | |
f.puts('eof') | |
f.puts("plot $dat using x:(log(column('n'))):(column('s')) with point linecolor variable pt 5 ps 0.5; pause -1;") | |
f.puts("plot $dat using x:(log(column('x_z'))):(column('s')) with point linecolor variable pt 5 ps 0.5; pause -1;") | |
outa(f = File.open('gnuplot1.cmd', 'w'), l1, | |
axes2(asd(['d', 'e', 'mx01s'])).merge({'n_a' => nil, 'n_sd' => nil})) | |
f.close | |
outa(f = File.open('gnuplot2.cmd', 'w'), $l, | |
axes2(['d', 'e', 'mx01s']).merge({'n' => nil})) | |
f.close | |
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