matrix2.rb

require 'matrix'


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 pair2(n, m)
	n1 = n
	
	m.times { n = f2(n) }
	x = {0 => data(n1), 1 => data(n)}

	x[1]['wr'] = x[1]['nl'].to_f / x[0]['nl'].to_f
	return x
end

def pair(d, m)
	w = 100
	return(pair2(dense(w, d), m))
end


def dist(m, c)
		
	w = 100
	d = 0.0
	l = []
	c.times \
	{
		|i|
		
		l << pair(i.to_f / (c - 1), m)
	}
#	$stderr.puts("#{l.size} pts")
	return l
end

def dot(x, z)

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

def detect(x1, a, l1, xe = nil)
	
	x1 = x1.dup
	i = 0
	c = $c
	x1['nl'] = 1
	loop \
	{
		x2 = {}
		(a['v'] + ['wr']).each \
		{
			|vy|
			
			x2[vy] = dot(x1, a[vy].select { |k, x| (a['v'] + ['c']).member?(k) }) 
			
			x2[vy] += xe["#{vy}_e"] if (!xe.nil?)
			
			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)
	}
	return i

end

def sum(l)

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

def detect2(x, v, d, vi, xz, vx, l2, c)
	x = x.dup
	x['wr'] = 1.0
	x0 = Matrix[vx.map { |k| x[k] }].transpose - xz
	nl = 1.0
	
	(1..c).each \
	{
		|t|
	
		at = v * (d ** t) * vi
		y = at * x0 + xz
		
		x1 = Hash[[vx, y.transpose.to_a[0]].transpose]
		
		nl *= x1['wr']
		x1['nl'] = nl
		l2 << x1
	}
	
end

def out(fn, a)
	
	f = File.open(fn, 'a')
	f.puts(a.keys.join("\t")) if (f.size == 0)
	f.puts(a.values.join("\t"))
	f.close
end


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)

vx = a['v'] + ['wr']
vxn = Hash[[vx + ['c'], (0..vx.size).to_a].transpose]

am = (1..vx.size).map { [0] * vx.size }

vx.each \
{
	|x|
	(vx + ['c']).each \
	{
		|y|
		am[vxn[x]][vxn[y]] = a[x][y] if (!a[x][y].nil?)
	}
}
am = am.transpose
b = am.pop
am = am.transpose
$stderr.puts(['vx', vx].inspect)
$stderr.puts(['am', am].inspect)
$stderr.puts(['b', b].inspect)

v, d, vi = Matrix[*am].eigen

xz = (Matrix.identity(vx.size) - Matrix[*am]).inverse * Matrix[b].transpose

p(['d', d])

l = dist(1, 100)
$c = 500
l0 = []

l.each_with_index \
{
	|x, i|
	
	c = detect(x[0], a, l1 = [])
	detect2(x[0], v, d, vi, xz, vx, l2 = [], c)
	l0 << [i, l1, l2]
}

x = l0.max_by { |x| x[1].size }
$stderr.puts([x[0], x[1].size, x[2].size].inspect)

File.open(fn = 'out.txt', 'w').close

x[1].size.times \
{
	|i|
	a = {'wr1' => x[1][i]['wr'], 'wr2' => x[2][i]['wr'], 
		'nl1' => x[1][i]['nl'], 'nl2' => x[2][i]['nl']}
	a['wrd'] = a['wr2'] - a['wr1']
	a['nld'] = a['nl2'] - a['nl1']
	out(fn, a)
	
}