induct.rb

def f2(n)
	return n.odd? ? (n * 3 + 1) / 2 : n / 2

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 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 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 = midpt2(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].round(3)
		a["#{k}2"] = l1[-1].round(3)
	}
	a['nw21'] = (a['nw2'].to_f / a['nw']).round(3)
	return a
end

def dataset(c1)
	w = 200
	c2 = 5
	a = 0.0
	b = 1.0
	l1 = []
	
	c1.times \
	{
		|j|

		d = a + (b - a) * rand()
		ns = dense(w, d)
		n = ns.to_i(2)
		
		l = seq(n, c2)
		
		a1 = data(l).merge({'j' => j})
		l1 << a1
	}
	return l1
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 out(a, fno = 1, a2 = {}, t = nil)

	$f = {} if ($f.nil?)
	if (!$f.member?(fno)) then
		$f[fno] = {'fn' => "out#{fno}.txt", 'c' => 0} 
		$f[fno]['f'] = File.open($f[fno]['fn'], 'w')
	end

	f = $f[fno]
	f['f'].puts(a.keys.join("\t")) if (f['c'] == 0)
	f['f'].puts(a.values.join("\t"))
	f['c'] += 1
	f['f'].flush
	
	return if ((f['c'] - 1) % 1000 != 0)
	
	d = (f['c'] / 2000).to_i
	d = 1 if (d == 0)
	
	f2 = File.open("gnuplot#{fno}.cmd", 'w')
	fn = f['fn']
	st = t.nil? ? 'unset title; ' : "set title '#{t}'; "
	k = "key top left box opaque"
	f2.puts("set ytics nomirror; set y2tics; set colors classic; set #{k}; #{st}; plot \\")
	c1, c2 = ":(column('w'))", 'linecolor palette' if (a.key?('w'))
	
	ct = "(column('t')):"
	(a.keys - ['t']).each \
	{
		|x|
		next if (a2.member?(x) && a2[x].nil?)
		f2.puts("'#{fn}' using (column('#{x}'))#{c1} every #{d} with line lw 2 #{c2} #{a2[x]} title '#{x}', \\")
	}
	f2.puts
	f2.close
	
end


c1 = 100


l1 = dataset(c1)
l1.each { |x| x['y'] = rand() }

(0...c1).to_a.shuffle[0...(c1 / 2)].each { |x| l1[x]['x'] = nil }

500.times \
{

	a = {}
	(l2 = l1.select { |x| !x.member?('x') }).each \
	{
		|x|
		x1 = near(x, l1)[0]
		x2 = near(x, l1, '2')[0]
		j = x1['j']
		a[j] = a.fetch(j, 0) + 1 if (j == x2['j'])
	}
	mx = a.max_by { |x| x[1] }
	
	out({'a' => a.size, 'mx' => mx[1], 'v' => sum(a.values)})
	j = mx[0]
	l1[j].delete('x')
	l2[rand(l2.size)]['x'] = nil

}