Created
May 20, 2017 01:10
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def f2(n, o2, e) | |
while (n.odd?) | |
n = (n * 3 + 1) / 2 | |
break if (o2) | |
end | |
while (n.even?) do | |
n /= 2 if (n.even?) | |
break if (e) | |
end | |
return n | |
end | |
def adv(x) | |
n1 = n = x['n'] | |
x['t'].times { n = f2(n, x['o2'], x['e']) } | |
return d(n.to_s(2)) | |
end | |
def ratio(x) | |
n1 = n = x['n'] | |
x['t'].times { n = f2(n, x['o2'], x['e']) } | |
return n.to_s(2).length.to_f / n1.to_s(2).length | |
end | |
def coef(x, y) | |
x1 = x2 = y1 = y2 = xy = 0.0 | |
n = x.size | |
n.times \ | |
{ | |
|i| | |
x1 += x[i] | |
y1 += y[i] | |
xy += x[i] * y[i] | |
x2 += x[i] ** 2 | |
y2 += y[i] ** 2 | |
} | |
d = n * x2 - x1 ** 2 | |
b = (y1 * x2 - x1 * xy) / d | |
m = (n * xy - x1 * y1) / d | |
b = 1 if (b.nan?) | |
m = 1 if (m.nan?) | |
return b, m | |
end | |
def sum(l) | |
t = 0.0 | |
l.each { |x| t += x } | |
return t | |
end | |
def av(l) | |
return nil if (l.empty?) | |
return sum(l) / 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 | |
e += (x - y).abs | |
m = [m, (x - y).abs].compact.max | |
} | |
r = txy / (Math.sqrt(tx) * Math.sqrt(ty)) | |
e /= l.size | |
return {'r' => r, 'e_a' => e, 'e_m' => m} | |
end | |
def dense(x) | |
w, d, o = x.values_at('w', 'd', 'o') | |
w2 = w - (o ? 2 : 1) | |
a = (0...w2).to_a | |
s = '0' * w2 | |
(1..(d * w - (o ? 2 : 1))).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' } | |
return ('1' + s + (o ? '1' : '')).to_i(2) | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def test(t, w, o, o2, e) | |
c = 500 | |
l = [] | |
(c + 1).times \ | |
{ | |
|i| | |
d = i.to_f / c | |
n = dense({'d' => d, 'w' => w, 'o' => o}) | |
a = {'n' => n, 'o2' => o2, 'e' => e, 't' => t} | |
d2 = adv(a) | |
r = ratio(a) | |
l << {'d' => d, 'd2' => d2, 'wr' => r} | |
} | |
return l | |
end | |
def fit(l, k, a) | |
b, m = coef(l.map { |x| x['d'] }, l.map { |x| x[k]}) | |
l.each { |x| x['y'] = m * x['d'] + b } | |
a.merge!(k => {'m' => m, 'b' => b}.merge!(corr(l, k, 'y'))) | |
end | |
def model(w) | |
l = test(1, w, *[false, true, true]) | |
a = {} | |
fit(l, 'd2', a) | |
fit(l, 'wr', a) | |
return a.merge!({ 'w' => w }) | |
end | |
f = File.open('out.txt', 'w') | |
(20..100).each \ | |
{ | |
|w| | |
a = model(w) | |
f.puts([w, a['d2']['e_a'], a['d2']['e_m'], a['wr']['e_a'], a['wr']['e_m']].join("\t")) | |
} | |
f.close | |
f = File.open('plot.cmd', 'w') | |
f.puts("set ytics nomirror; set y2tics;") | |
f.puts("plot 'out.txt' using 1:2 with line title 'd2 e_a',\\") | |
f.puts("'' using 1:4 with line title 'wr e_a',\\") | |
f.puts("'' using 1:3 with line title 'd2 e_m' axes x1y2,\\") | |
f.puts("'' using 1:5 with line title 'wr e_m' axes x1y2") | |
f.close |
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