Created
October 28, 2020 05:01
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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 seq(n, c) | |
l = [n] | |
while (n != 1 && l.size < c) | |
n = f2(n) | |
l << n | |
end | |
raise if (l.size != c) | |
return l | |
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 sum(l) | |
return l.inject { |t, x| t + x } | |
end | |
def avg(l) | |
return (l.nil? || l.empty?) ? 0 : sum(l).to_f / l.size | |
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 len1(ns) | |
return len(ns, /0+/) | |
end | |
def len0(ns) | |
return len(ns, /1+/) | |
end | |
def len01(ns) | |
return len1(ns), len0(ns) | |
end | |
def e(ns) | |
return 0 if (ns.empty?) | |
return len01(ns).flatten.size.to_f / ns.length | |
end | |
def d(s) | |
return 0 if (s.empty?) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def runavg(l, k, c) | |
l1 = l.map { |x| x[k] } | |
t = sum(l1[0...c]) | |
l2 = (['-'] * (c - 1)) + [t.to_f / c] | |
while (l1.size > c) | |
t -= l1.shift | |
t += l1[c - 1] | |
l2 << (t.to_f / c) | |
end | |
return l2 | |
end | |
def midpt(ns) | |
w2 = ns.length / 4 | |
l = ns.split('') | |
i = j = 0 | |
while (i < w2 && j < l.size) | |
i += l[j].to_i | |
j += 1 | |
end | |
return j.to_f / ns.length | |
end | |
def features(ns) | |
d = d(ns) | |
e = e(ns) | |
nw = ns.length | |
nw2 = nw / 2 | |
nshi = ns[0...nw2] | |
nslo = ns[nw2..-1] | |
dlo = d(nslo) | |
dhi = d(nshi) | |
elo = e(nslo) | |
ehi = e(nshi) | |
mp = midpt(ns) | |
return { | |
"d" => d, | |
"e" => e, | |
"ea" => (0.5 - e).abs, | |
"da" => (0.5 -d).abs, | |
"dlo" => dlo, | |
"dhi" => dhi, | |
"elo" => elo, | |
"ehi" => ehi, | |
"mp" => mp, | |
"nw" => ns.length | |
} | |
end | |
def data(l) | |
l2 = l.map { |x| features(x.to_s(2)) } | |
a = {} | |
l2[0].keys.each \ | |
{ | |
|k| | |
l1 = runavg(l2, k, l2.size - 1) | |
a[k] = l1[-2] | |
a["#{k}2"] = l1[-1] | |
} | |
a['nw21'] = a['nw2'].to_f / a['nw'] | |
return a | |
end | |
def outd(f, l) | |
f.puts('$dat << eof') | |
k = l[0].keys | |
f.puts(k.join("\t")) | |
l.each { |x| f.puts(x.values.join("\t")) } | |
f.puts('eof') | |
return k | |
end | |
def hide(a, x) | |
return (a.member?(x) && a[x].nil?) | |
end | |
def outa(f, l, a = {}, t = '') | |
k = outd(f, l) | |
f.puts("set colors classic; set key top right opaque; set title '#{t}'; ") | |
f.puts("set ytics nomirror; set y2tics;") | |
f.puts("plot \\") | |
ct = '' | |
k, ct = [k - ['t'], "(column('t')):"] if (k.member?('t') && !hide(a, 't')) | |
k.each \ | |
{ | |
|x| | |
next if (hide(a, x)) | |
opt = a.fetch(x, '') | |
opt = ' with line lw 2 ' + opt if (!opt.include?('with')) | |
f.puts("'$dat' using #{ct}(column('#{x}')) #{opt} title '#{x}',\\") | |
} | |
f.puts | |
# f.puts("reset; pause -1;") | |
end | |
def outafn(l, a = {}, fn = nil, t = '') | |
fn = 'gnuplot.cmd' if (fn.nil?) | |
outa(f = File.open(fn, 'w'), l, a, t) | |
f.close | |
$stderr.puts([fn, l.size, t].inspect) | |
end | |
def near(x, l, k2 = '', l1 = []) | |
l.each_with_index \ | |
{ | |
|x1, j| | |
next if (x == x1) | |
# next if (x1.member?('x')) | |
z = 0 | |
['d', 'e', 'da', 'ea', 'dlo', 'dhi', 'elo', 'ehi', 'mp'].each \ | |
{ | |
|k1| | |
k = "#{k1}#{k2}" | |
z += (x[k] - x1[k1]) ** 2 | |
} | |
l1 << [z, j] | |
} | |
l1.sort_by! { |x| x[0] } | |
i = 0 | |
i += 1 while (i + 1 < l1.size && l1[i][0] == l1[i + 1][0]) | |
return (0..i).map { |x| l[l1[x][1]].merge({'z' => l1[x][0]}) } | |
end | |
def predict(l2, l1) | |
e1 = 0 | |
l2.each { |x| x['nn'] = []; x.delete('er2') } | |
l2.each \ | |
{ | |
|x| | |
l = near(x, l1, '2') | |
j = x['j'] | |
et = 0 | |
l.each \ | |
{ | |
|x1| | |
e = (x1['nw21'] - x['nw21']).abs | |
x1['nn'] << {'er' => e, 'j' => j, 'z' => x1['z']} | |
et += e | |
} | |
x['er1'] = et / l.size | |
e1 += x['er1'] | |
} | |
ea = e1 / l2.size | |
return ea | |
end | |
def opt(l2) | |
l1 = l2.select { |x| !x.member?('x') } | |
ea = predict(l2, l1) | |
l1.each \ | |
{ | |
|x| | |
# next if (x.member?('x')) | |
next if (x['nn'].empty?) | |
l = x['nn'].map { |x1| x1['er'] } | |
x['er2'] = avg(l) | |
} | |
x = l1.max_by { |x1| x1.fetch('er2', 0) } | |
l2[x['j']]['x'] = nil | |
a = {'ea' => ea, 'er2max' => x['er2']} | |
return a | |
end | |
def dataset(l1, c1) | |
w = 200 | |
c2 = 10 | |
c1.times \ | |
{ | |
|j| | |
ns = dense(w, j.to_f / (c1 - 1)) | |
n = ns.to_i(2) | |
# n = terras121(ns) | |
l = seq(n, c2) | |
a = data(l).merge({'j' => j}) | |
l1 << a | |
} | |
end | |
c1 = 250 | |
dataset(l1 = [], c1) | |
dataset(l2 = [], 250) | |
l = [] | |
(c1 * 3.0 / 5).to_i.times \ | |
{ | |
|i| | |
x = opt(l1) | |
x['ea2'] = predict(l2, l1.select { |x| !x.member?('x') }) | |
l << x | |
$stderr.puts({'i' => i}.merge(x).inspect) | |
} | |
l.each { |x| x['r'] = x['ea'] / l[0]['ea']; x['r2'] = x['ea2'] / l[0]['ea2'] } | |
outafn(l, {'r' => 'dt 3 axes x1y2', 'r2' => 'dt 3 axes x1y2'}) | |
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