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December 25, 2020 01:29
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require 'statsample' | |
def f2(n) | |
return n.odd? ? (n * 3 + 1) / 2 : n / 2 | |
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["#{vy}_y"] = dot(x, z) } | |
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 = "#{y1}_y") | |
ye = "#{y1}_e" | |
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 | |
z[ye] = (x - y) | |
e1 = z[ye] | |
e += e1.abs | |
} | |
d = Math.sqrt(tx) * Math.sqrt(ty) | |
r = txy / (d.abs < $z ? $z : d) | |
e /= l.size | |
return r | |
end | |
def fit(l, vx, vy) | |
a = {} | |
(vx + [vy]).each { |v| a[v] = l.map { |x| x[v] }.to_vector() } | |
begin | |
r = Statsample::Regression.multiple(a.to_dataset(), vy) | |
# rescue Statsample::Regression::LinearDependency | |
# return nil | |
end | |
# $stderr.puts(r.summary) | |
z = r.coeffs.merge({'c' => r.constant}) | |
predict(l, vy, z) | |
r = corr(l, vy) | |
return r, z | |
end | |
def read(fn) | |
l = (f = File.open(fn)).readlines.map { |x| Kernel.eval(x) } | |
f.close | |
$stderr.puts(['read', fn, l.size].inspect) | |
return l | |
end | |
def stat(k, l) | |
t = l.inject { |a, x| a + x } | |
t2 = l.inject(0) { |a, x| a + (x ** 2) } | |
c = l.size | |
a = t.to_f / c | |
z = t2.to_f / c - a ** 2 | |
sd = Math.sqrt(z < 0 ? 0 : z) | |
raise [k, l].inspect if (sd.nan?) | |
return {"#{k}_a" => a, "#{k}_s" => sd, | |
"#{k}_mn" => l.min, "#{k}_mx" => l.max} | |
end | |
def outd(f, l) | |
f.puts('$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 plot(f, d, k, a, t = nil) | |
f.puts("# #{t}") if (!t.nil?) | |
f.puts("set colors classic; set title '#{t}'; ") | |
# f.puts("set key top right opaque; ") | |
f.puts("set ytics nomirror; set y2tics;") | |
f.puts("plot \\") | |
k.each \ | |
{ | |
|x| | |
next if (hide(a, x)) | |
opt = a.fetch(x, '') | |
opt = ' with line ' + opt if (!opt.include?('with') && !opt.include?('pt')) | |
opt += ' lw 2 ' if (!opt.include?('lw') && !opt.include?('pt')) | |
f.puts("#{d} using (column('#{x}')) #{opt} title '#{x}',\\") | |
} | |
f.puts | |
# f.puts("reset; pause -1;") | |
end | |
def outa(f, l, a = {}, t = nil) | |
k = outd(f, l) | |
plot(f, '$dat', k, a, t) | |
end | |
def outafn(l, a = {}, fno = nil, t = '') | |
outa(f = File.open(fn = "gnuplot#{fno}.cmd", 'w'), l, a, t) | |
f.close | |
$stderr.puts([fn, l.size, t, l[0].keys].inspect) | |
end | |
def streamafn(a = nil, a1 = {}, fno = nil, t = nil) | |
$f, $n = [{}, 1] if ($f.nil?) | |
fno = $n if (fno.nil?) | |
if (a.nil?) then | |
$f[$f.keys.last]['f'].close | |
$n += 1 | |
return | |
end | |
if (!$f.member?(fno)) then | |
$f[fno] = {'fn' => (fn2 = "out#{fno}.txt"), | |
'f' => File.open(fn2, 'w')} | |
$f[fno]['f'].puts(a.keys.join("\t")) | |
plot(f = File.open(fn = "gnuplot#{fno}.cmd", 'w'), "'#{fn2}'", a.keys, a1, t) | |
f.close | |
$stderr.puts([fn, fn2, t, a.keys].inspect) | |
end | |
$f[fno]['f'].puts(a.values.join("\t")) | |
$f[fno]['f'].flush | |
end | |
def keys(l, ks) | |
return l.map { |x| Hash[[ks, x.values_at(*ks)].transpose] } | |
end | |
def seq(n) | |
l = [n] | |
while (n != 1) | |
n = f2(n) | |
l << n | |
end | |
return l | |
end | |
def sum(l) | |
return l.inject(0) { |t, x| t + x } | |
end | |
def avg(l) | |
return sum(l).to_f / l.size | |
end | |
def runavg(l, k, c, ka = "#{k}_a") | |
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 | |
l.each_with_index { |x, i| x[ka] = l2[i] } | |
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 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 d1(s) | |
c = s.split('').select { |x| x == '1' }.size | |
return c | |
end | |
def midpt2(ns) | |
w2 = d1(ns) / 2 | |
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 log2(x) | |
return Math.log(x) / Math.log(2.0) | |
end | |
def features(ns) | |
d = d(ns) - 0.5 | |
e = e(ns) - 0.5 | |
nw = ns.length | |
nw2 = nw / 2 | |
nshi = ns[0...nw2] | |
nslo = ns[nw2..-1] | |
dlo = d(nslo) - 0.5 | |
dhi = d(nshi) - 0.5 | |
elo = e(nslo) - 0.5 | |
ehi = e(nshi) - 0.5 | |
mp1 = midpt(ns) - 0.5 | |
mp2 = midpt2(ns) - 0.5 | |
l0 = len0(ns) | |
mx0 = l0.empty? ? 0 : l0.max | |
mx1 = len1(ns).max | |
mx01 = [mx0, mx1].max | |
mx = log2(log2(ns.to_i(2).to_f)) | |
a0 = l0.empty? ? 0 : avg(l0) | |
a1 = avg(len1(ns)) | |
a01 = avg(len01(ns).flatten) | |
return { | |
"d" => d, | |
"e" => e, | |
"ea" => e.abs, | |
"da" => d.abs, | |
"dlo" => dlo, | |
"dhi" => dhi, | |
"elo" => elo, | |
"ehi" => ehi, | |
'mp1' => mp1, | |
"mp2" => mp2, | |
'mx0' => mx0.to_f / ns.length, | |
'mx1' => mx1.to_f / ns.length, | |
'mx01' => mx01.to_f / ns.length, | |
'a0' => a0 / ns.length, | |
'a1' => a1 / ns.length, | |
'a01' => a01 / ns.length, | |
'a1m' => a1 / (mx == 0 ? 1 : mx), | |
# 'c0' => l0.size, | |
# 'c1' => l1.size, | |
"nw" => ns.length | |
} | |
end | |
def smooth(l2) | |
l = l2.map { |x| features(x.to_s(2)) } | |
c = 50 | |
(ks = l[0].keys).each { |k| runavg(l, k, c) } | |
return (c...l.size).map { |x| Hash[[ks + ['nw1'], l[x].values_at(*(ks.map { |x1| "#{x1}_a" } + ['nw']))].transpose] } | |
end | |
def dataset(l) | |
return l.map { |x| smooth(x) } | |
end | |
def adj(l, z, ks, wt) | |
ks.each \ | |
{ | |
|k| | |
l.each { |x| x[k] = (x[k] - z["#{k}_a"]) * wt[k] } | |
} | |
end | |
def model(l1, ks, k, wt, s) | |
ks.each \ | |
{ | |
|k| | |
s.merge!(stat(k, l1.map { |x| x[k] })) | |
wt[k] = 1.0 / s["#{k}_s"] | |
} | |
adj(l1, s, ks, wt) | |
r, z = fit(l1, ks, k) | |
$stderr.puts([r, z].inspect) | |
return z | |
end | |
def cg(l2) | |
cg = l2.index { |x| x < l2[0] } | |
return cg | |
end | |
def sample2(l, n) | |
d = (l.size - 1).to_f / (n - 1) | |
l2 = [] | |
n.times \ | |
{ | |
|i| | |
j = (i * d).to_i | |
l2 << l[j] | |
} | |
return l2 | |
end | |
def apply(n1, k, ky, n, s, ks, wt, z) | |
l2 = smooth(l = seq(n1)) | |
l2.each_with_index { |x, j| x['hc'] = (l2.size - j - 1).to_f / x['nw1']; x['j'] = (l2.size - j - 1); x['nw2'] = 1.0 / x['nw1']; } | |
l2.pop | |
adj(l2, s, ks, wt) | |
predict(l2, k, z) | |
outafn(keys(l2, [k, ky, 'nw1']), {'nw1' => 'axes x1y2'}, n) | |
end | |
def linear(fn, n) | |
l1 = read(fn) | |
k = 'hc' | |
l1.each \ | |
{ | |
|x| | |
c = (l = seq(x['ns'].to_i(2))).size | |
x[k] = c.to_f / x['ns'].length | |
x['c'] = c | |
x['cg'] = cg(l) | |
} | |
ks = [ | |
'a0', 'a1', 'a01', | |
'a1m', | |
# 'd', | |
# 'e', | |
'da', 'ea', | |
# 'dlo', | |
'dhi', 'elo', 'ehi', 'mp1', 'mp2', 'mx0', 'mx1', 'mx01', | |
# 'c0', 'c1' | |
] | |
z = model(l1, ks, k, wt = {}, s = {}) | |
ky = "#{k}_y" | |
l1.sort_by! { |x| x[k] } | |
outafn(keys(l1, [k, ky]), {}) | |
x = l1.max_by { |x| x['cg'] } | |
$stderr.puts(keys([x], ['cg', 'c', 'nw'])[0].inspect) | |
apply(x['ns'].to_i(2), k, ky, 1, s, ks, wt, z) | |
apply(n, k, ky, 2, s, ks, wt, z) | |
end | |
$z = 1e-4 | |
n = 20678096139828932684255824799921978289932242905629473048320332 | |
linear('outline2.txt', n) | |
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