Created
May 31, 2017 01:48
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require 'statsample' | |
def f2(n) | |
return n.odd? ? (n * 3 + 1) / 2 : n / 2 | |
end | |
def f1(n) | |
n = (n * 3 + 1) / 2 if (n.odd?) | |
n /= 2 if (n.even?) | |
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).to_i(2) | |
end | |
def stat(l) | |
l = [0] if (l.empty?) | |
t = t2 = 0 | |
l.each \ | |
{ | |
|x| | |
t += x | |
t2 += x ** 2 | |
} | |
c = l.size | |
a = t.to_f / c | |
z = t2.to_f / c - a ** 2 | |
sd = Math.sqrt(z < 0 ? 0 : z) | |
return a, sd, l.max.to_f, l.min.to_f | |
end | |
def stat2(l, t, n) | |
return Hash[[["a#{n}", "sd#{n}", "mx#{n}"], stat(l)[0..2].map { |x| x / t }].transpose] | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = c.to_f / s.length | |
return d | |
end | |
def data(n) | |
ns = n.to_s(2) | |
nl = ns.length | |
m = nl / 2 | |
nsh = ns[0..m] | |
nsl = ns[m..-1] | |
asdm1 = stat2(ns.split(/0+/).map { |x| x.length }, nl, 1) | |
l1 = ns.split(/1+/) | |
l1.shift | |
asdm0 = stat2(l1.map { |x| x.length }, nl, 0) | |
return {'n' => n, 'ns' => ns, 'nl' => nl, 'd' => d(ns), 'dh' => d(nsh), 'dl' => d(nsl)}.merge(asdm1).merge(asdm0) | |
end | |
def dist() | |
w = 100 | |
d = 0.0 | |
c = 250 | |
l = [] | |
(c + 1).times \ | |
{ | |
|x| | |
d = x.to_f / c | |
n = dense(w, d) | |
x = {0 => data(n), 1 => data(f2(n))} | |
x[1]['wr'] = x[1]['nl'].to_f / x[0]['nl'].to_f | |
l << x | |
} | |
return l | |
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 | |
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 dot(x, z) | |
t = z['c'] | |
(z.keys - ['c']).each { |v| t += z[v] * x[v] } | |
return t | |
end | |
def predict(l, vy, z) | |
l.each \ | |
{ | |
|x| | |
x[1]["#{vy}_p"] = dot(x[0], z) | |
} | |
end | |
def fit(l, vx, vy) | |
a = {} | |
vx.each { |v| a[v] = l.map { |x| x[0][v] }.to_vector() } | |
a[vy] = l.map { |x| x[1][vy] }.to_vector() | |
ds = a.to_dataset() | |
r = Statsample::Regression.multiple(ds, vy) | |
# $stderr.puts(r.summary) | |
z = r.coeffs.merge({'c' => r.constant}) | |
predict(l, vy, z) | |
a = corr(l.map { |x| x[1] }, vy, "#{vy}_p") | |
return z.merge!(a) | |
end | |
def model(v) | |
l = dist() | |
a = {} | |
(v + ['wr']).each \ | |
{ | |
|x| | |
a[x] = fit(l, v, x) | |
l1 = l.map { |y| y[1][x] } | |
a[x].merge!({'mn' => l1.min, 'mx' => l1.max}) | |
p([x, a[x]['r'], a[x]['e_m'], a[x]['mn'], a[x]['mx']]) | |
} | |
return a | |
end | |
def out(fn, a) | |
f = File.open(fn, 'a') | |
f.puts(a.keys.join("\t")) if (f.size == 0) | |
if (a.nil?) | |
f.puts | |
else | |
f.puts(a.values.join("\t")) | |
end | |
f.close | |
end | |
def detect(a, v, n, e) | |
x1 = data(n) | |
i = 0 | |
c = 500 | |
fn = 'out.txt' | |
x1['nl'] = 2 | |
loop \ | |
{ | |
x2 = {} | |
(v + ['wr']).each \ | |
{ | |
|vy| | |
r = [1, rand() * [-1, 1][rand(2)]][a['i']] | |
x2[vy] = dot(x1, a[vy].select { |k, x| (v + ['c']).member?(k) }) + e * a[vy]['e_m'] * r | |
x2[vy] = a[vy]['mn'] if (x2[vy] < a[vy]['mn']) | |
x2[vy] = a[vy]['mx'] if (x2[vy] > a[vy]['mx']) | |
} | |
x2['nl'] = x1['nl'] * x2['wr'] | |
x1 = x2 | |
# out(fn, x1) | |
i += 1 | |
break if (x1['nl'] < 1 || i == c) | |
} | |
# out(fn, nil) | |
return i == c ? nil : i | |
end | |
def scan(a, v, d) | |
c = 50 | |
j = k = 0 | |
# File.open(fn = 'out.txt', 'w').close | |
(c + 1).times \ | |
{ | |
|i| | |
x = detect(a, v, dense(100, i.to_f / c), d) | |
if (x.nil?) | |
j += 1 | |
else | |
k += x | |
end | |
} | |
j = j.to_f / (c + 1) | |
k = k.to_f / (c + 1) | |
# $stderr.puts([d, j, k].inspect) | |
return j, k | |
end | |
def trans(a, v, lo, hi, fn) | |
c = 100 | |
File.open(fn, 'w').close | |
(c + 1).times \ | |
{ | |
|i| | |
d = lo + (i.to_f / c) * (hi - lo) | |
x = scan(a, v, d) | |
out(fn, {'d' => d, 'x0' => x[0], 'x1' => x[1] }) | |
$stderr.puts([i, d].inspect) | |
} | |
end | |
def adj(a, b, f, d) | |
if (f) then | |
a = d | |
else | |
b = d | |
end | |
return a, b | |
end | |
def trans2(a, v, lo, hi, z) | |
g = (hi - lo) / 20 | |
i = 0 | |
d = nil | |
loop \ | |
{ | |
d = lo + 0.5 * (hi - lo) | |
x = scan(a, v, d) | |
$stderr.puts([i, d, x].inspect) | |
lo, hi = adj(lo, hi, z == 0 ? (x[0] == 0) : (x[0] != 1), d) | |
break if (hi - lo < g) | |
i += 1 | |
} | |
return d | |
end | |
srand(0) | |
v = ['a1', 'a0', 'dh', 'dl', 'sd0', 'sd1', 'mx1'] | |
#v = ['a1', 'a0', 'd', 'dl', 'sd0', 'sd1', 'mx1'] | |
#v = ['a1', 'a0', 'd', 'dh', 'sd0', 'sd1', 'mx1'] | |
a = model(v) | |
#scan(a, v, 0) | |
[0, 1].each \ | |
{ | |
|i| | |
a['i'] = i | |
mx = [0.1, 3.0][i] | |
lo = trans2(a, v, 0, mx, 0) | |
hi = trans2(a, v, 0, mx, 1) | |
d = [0.05, 0.10][i] | |
trans(a, v, lo - d * lo, hi + d * hi, "out#{i}.txt") | |
} |
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