Created
February 23, 2019 04:46
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def f2(n) | |
return n.odd? ? (n * 3 + 1) / 2 : n / 2 | |
end | |
def adj(x, m, n, s2, p2, p, x3) | |
s2.replace(p[0...x] + (x3 % 2).to_s) | |
m = (s2[x, 1] == p[x, 1]) | |
n = p2.reverse.to_i(2) | |
p2[x, 1] = m ? '11' : '01' | |
return m, n, x3 | |
end | |
def terras121(p) | |
p2 = ['01', '11'][p[0, 1].to_i] | |
n = 1 | |
n3 = 0 | |
m = p2 == '11' | |
x3 = (p2.reverse.to_i(2)) >> 1 | |
(1...p.length).each \ | |
{ | |
|x| | |
if (!m) | |
ns = n.to_s(2) | |
ns[0, 1] = '' | |
m1 = x3 - 3**n3 | |
n1 = f2(m1) | |
end | |
n3 = p[0...x].split('').select { |z| z == '1' }.size | |
s2 = '' | |
m, n, x3 = adj(x, m, n, s2, p2, p, m ? (f2(x3) + 3**n3) : (n1 + 3**n3)) | |
} | |
n = p2.reverse.to_i(2) | |
return n | |
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) | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def len(ns, p) | |
l = ns.split(p) | |
l = [] if (l.nil?) | |
l.shift if (l[0] == '') | |
return l.map { |x| x.length } | |
end | |
def len01(ns) | |
return len(ns, /0+/), len(ns, /1+/) | |
end | |
def e(ns) | |
return len01(ns).flatten.size.to_f / ns.length | |
end | |
def stat(l) | |
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 stat2(l, n) | |
return Hash[[["a#{n}", "sd#{n}", "mx#{n}"], stat(l)].transpose] | |
end | |
def avg(l) | |
l.inject { |t, x| t + x }.to_f / l.size | |
end | |
def avgs(l) | |
ks = l[0][0].keys | |
l1 = [] | |
l[0].size.times \ | |
{ | |
|i| | |
l1[i] = Hash[[ks, ks.map { |k| avg(l.map { |x| x[i][k] }) }].transpose] | |
} | |
return l1 | |
end | |
def seq(n, c) | |
l = [n] | |
while (n != 1) | |
n = f2(n) | |
l << n | |
return l if (l.size == c) | |
end | |
raise "#{l.size} != #{c}" | |
end | |
def dataset() | |
l = [] | |
t = 50 | |
w = 400 | |
t.times \ | |
{ | |
|c| | |
d = c.to_f / (t - 1) | |
ps = dense(w, d) | |
n = terras121(ps) | |
ns = seq(n, w)[w - 1].to_s(2) | |
nslo = ns[0..ns.length / 2] | |
nshi = ns[ns.length / 2 .. -1] | |
l1, l0 = len01(ns) | |
a = {'d1' => d, | |
'e' => e(ns), | |
'd' => d(ns), | |
'dlo' => d(nslo), | |
'dhi' => d(nshi), | |
'elo' => e(nslo), | |
'ehi' => e(nshi), | |
'da' => (d(ns) - 0.5).abs, | |
'ea' => (e(ns) - 0.5).abs, | |
}.merge(stat2(l0, '0')) | |
.merge(stat2(l1, '1')) | |
l << a | |
} | |
return l | |
end | |
def gp(l) | |
f = File.open('gnuplot.cmd', 'w') | |
f.puts('$dat << eof') | |
k = l[0].keys | |
f.puts(k.join("\t")) | |
l.each { |x| f.puts(x.values.join("\t")) } | |
f.puts('eof') | |
f.puts('set key top right; set ytics nomirror; set y2tics; plot \\') | |
(k - ['d1']).each \ | |
{ | |
|x| | |
m = '' | |
m = 'dt 3 axes x1y2' if (['e', 'd'].member?(x[0, 1])) | |
f.puts("$dat using (column('d1')):(column('#{x}')) title '#{x}' with line #{m},\\") | |
} | |
f.close | |
end | |
l = avgs((1..100).map { dataset() }) | |
gp(l) | |
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