matrix9b.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 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 , 'l' => l, 'j' => j}
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 data2(n)
	
	return data(n).merge(count(n))
end

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

end

def out(fn, l)
	
	k = l[0].keys
	f = File.open(fn, 'w')
	f.puts(k.join("\t"))
	l.each { |x| f.puts(x.values.join("\t")) }
	f.close
	
	f = File.open('gnuplot.cmd', 'a')
	f.puts("set title '#{fn}'; plot \\")
	l = []
	(k - ['t']).each { |x| l << "'#{fn}' using (column('t')):(column('#{x}')) with line title '#{x}',\\" }
	f.puts(l)
	f.puts
	f.puts("pause -1")
	f.close
	return l
end

def sum(l)

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

def int(x0, am2, vx, c, h)
	yt = x0
	t = 0
	l = []
	while (t < c)
		l << Hash[[vx, yt.transpose.to_a[0]].transpose].merge({'t' => t})
		yt = (h * Matrix[*am2] + Matrix.identity(vx.size)) * yt
		t += h
	end
	return l
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

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

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



x1 = dist(500).max_by { |x| x['c'] }
p(x1['c'])

x = data(x1['l'][0]).merge({'wr' => 1.0})


x0 = Matrix[vx.map { |k| x[k] }].transpose - xz




am2 = (Matrix[*am] - Matrix.identity(vx.size)).to_a

v2, d2, vi2 = (Matrix[*am2]).eigen

ei = (0...d2.to_a.size).map { |i| d2.row(i)[i] }
c0 = (vi2 * x0).column(0).to_a



l1 = []
l3 = []


c = 20
c.times \
{
	|t|
	n = x1['l'][t]
	x = data(n).merge({'wr' => 1.0})

	y = Vector[*vx.map { |k| x[k] }]

	at = v * (d ** t) * vi
	y = at * x0

#	y += xz

	l1 << Hash[[vx, y.transpose.to_a[0]].transpose].merge({'t' => t})
		
	e = Matrix[(0...ei.size).map { |i| c0[i] * Math.exp(ei[i] * t.to_f) }].transpose
	
	l3 << Hash[[vx, (v2 * e).to_a].transpose].merge({'t' => t})
}

l2 = int(x0, am2, vx, c, 1.0)
l4 = int(x0, am2, vx, c, 0.05)

File.open('gnuplot.cmd', 'w').close

l1p = out('out1.txt', l1)
l2p = out('out2.txt', l2)
l3p = out('out3.txt', l3)
l4p = out('out4.txt', l4)


f = File.open('gnuplot.cmd', 'a')

[l1p + l2p, l3p + l4p].each_with_index \
{
	|l, i|

	f.puts("set title '#{['l1/l2', 'l3/l4'][i]}'; plot \\")
	f.puts(l)
	f.puts
	f.puts("pause -1")
	f.puts
}

f.close