matrix12.rb

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

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 count(n)
	
	c = 0
	n1 = n
	l = [n]
	c2 = nil
	begin
		n = f2(n) 
		l << n
		c += 1
		c2 = c if (c2.nil? && n <= n1)
	end while n != 1
	j = (0...l.size).max_by { |x| l[x] }
	
	return {'c' => c, 'c2' => c2, 'n' => n1, 'j' => j, 'l' => l}
end

def dist(c)
		
	return (0...c).map { |i| count(dense(100, i.to_f / (c - 1))) }

end
	
def sample(n)

	s = {}
	n.times \
	{
		l = dist(500)
		l.each { |x| s[x['n']] = x }
	}
	l2 = s.values
	
	v = 'c2'
	l1 = l2.map { |x| x[v] }
	mn = l1.min
	mx = l1.max * 0.50
	$stderr.puts([l2.size, mn, mx].inspect)
	
	l2.each { |x| x['z'] = (x[v].to_f - mn) / (mx - mn) }
	
	l = []
	(0..100).each \
	{
		|i|
		d = 1.0 - i.to_f / 100
		d = i.to_f / 100
		j = (0...l2.size).min_by { |x| (l2[x]['z'] - d).abs }
		l << l2.delete_at(j)
	}
	
	return l.sort_by { |x| -x[v] }
	
end

def dot(x, z)

	t = z['c']
	
	(z.keys - ['c']).each { |v| t += z[v] * x[v] }
	return t
		
end

def detect(x0, a, l1, c)
	
	x1 = x0.dup
	i = 0
	x1['nl'] = 1
	loop \
	{
		x2 = {}
		(a['v'] + ['wr']).each \
		{
			|vy|
			
			x2[vy] = dot(x1, a[vy].select { |k, x| (a['v'] + ['c']).member?(k) }) 
			
			return c if (x2[vy].abs > 1e10)
		}
		x2['nl'] = x1['nl'] * x2['wr']
		x1 = x2
		l1 << x1
		i += 1
		break if (x1['nl'] < 1 || i == c)
	}
	x0.merge!({'i' => i})
end

def out(fn, l)
	
	f = File.open(fn, 'w')
	k = l[0].keys
	f.puts(k.join("\t"))
	l.each { |x| f.puts(x.values.join("\t")) }
	f.close

	l = []
	k.each { |x| l << "'#{fn}' using (column('#{x}')) with line title '#{x}',\\" }
	return l
end

def sum(l)

	t = 0.0
	l.each { |x| t += x }
	return t
end

def load()
	
	raise if (ARGV[0].nil?)

	d = "out/#{ARGV[0]}"
	l = Dir.glob("#{d}/*").select { |x| x =~ /out\d+.txt$/}
	n = l.size

	i = n - 1
	a = Kernel.eval(File.open("#{d}/out#{i}.txt").readlines[0])
		
	l = a['lb'].map { |x| x.size }

	raise if (sum(l) != 0)
	return a
end

def add(l, z, x)
	
	x.each \
	{
		|k, v|
		z[k] = z.fetch(k, 0) + v
	}
	l << z.dup
	
end

a = load()

l = sample(10)
l1 = []
l2 = []

z1 = {}
z2 = {}
p(l[0]['c2'])
l[0]['l'].each_with_index \
{
	|x, i|
	x1 = data(x).select { |k, | !['n', 'ns', 'nl', 'mx0', 'd'].member?(k) }
	
	x2 = {}
	(a['v'] + ['wr']).each \
	{
		|vy|
		
		x2[vy] = dot(x1, a[vy].select { |k, x| (a['v'] + ['c']).member?(k) }) 
		
#			return c if (x2[vy].abs > 1e10)
	}

	add(l1, z1, x1) if (i > 0)
	add(l2, z2, x2.select { |k, | !['wr'].member?(k) })
	
}

l3 = []
l1.size.times \
{
	|i|
	
	l3 << Hash[l1[i].keys.map { |k| [k, l1[i][k] - l2[i][k]] }]
}

lx = out('out1.txt', l1)
ly = out('out2.txt', l2)
lz = out('out3.txt', l3)

f = File.open('gnuplot.cmd', 'w')
f.puts("set title '12'; plot \\", lx + ly, '', 'pause -1')
f.puts('plot \\', lz)
f.close