Equars People - Hiraedd (Marco's blog)

Non-negative Matrix Factorization

2008-07-08T15:00:00Z

Here it is a small ruby script that calculate the non-negative matrix factorization of a given matrix. I tried to mantain the notation consistent with the one used in the paper of Lee and Seung.

The script requires the GSL library.


#!/usr/bin/ruby


require("gsl")



def nmf(v, col, thresh)
   r, c = v.shape

   # w * h = v
   w = GSL::Matrix.alloc(r, col)
   h = GSL::Matrix.alloc(col, c)
   initrand(w)
   initrand(h)
   dist = thresh
   iter = 0
   while(dist >= thresh)
      # multiplicative update rule
      dist, w, h = update(v, w, h)
      puts dist if (iter%50 == 0)
      iter += 1
   end   
   puts "Ended in #{iter} iteration(s) with dist=#{dist}"
   return w, h
end


def initrand(m)
   r, c = m.shape
   0.upto(r-1) { |i|
       0.upto(c-1) { |j|
          m[i,j] = rand()
       }
   }
end

def update(v, w, h)
   # choose an update rule
   # v, w, h are GSL::Matrix objects
   dist, w, h = update_eu(v, w, h)
   return dist, w, h
end

def update_eu(v, w, h)
   # multiplicative update rule
   # for minimizing euclidean distance
   # v, w, h are GSL::Matrix objects
   dist = dist_eu(v, w*h)
   wt = w.transpose
   ht =  h.transpose
   h = h.mul_elements(wt * v).div_elements(wt * w * h)
   w = w.mul_elements(v * ht).div_elements(w * h * ht)
   return dist, w, h
end


def update_kl(v, w, h)
   # multiplicative update rule
   # for minimizing divergence
   # v, w, h are GSL::Matrix objects
   dist = dist_kl(v, w*h)
   wt = w.transpose
   ht =  h.transpose
   num = v.div_elements(w * h)
   rh, ch = h.shape
   rw, cw = w.shape
   0.upto(rh-1) { |i|
       0.upto(ch-1) { |j|
          h[i, j] *= w.col(i).mul(num.col(j)).sum / w.col(i).sum
       }
   }
   0.upto(rw-1) { |i|
       0.upto(cw-1) { |j|
          w[i, j] *= h.row(j).mul(num.row(i)).sum / h.row(j).sum
       }
   }
   return dist, w, h
end



# Euclidean distance
def dist_eu(a, b)
   # a,b are GSL::Matrix objects
   dist = 0
   (a-b).collect { |d| dist += d * d }
   dist
end

# Kullback-Leibler divergence
def dist_kl(a, b)
   # a, b are GSL::Matrix objects
   dist = 0
   r, c = a.shape
   0.upto(r-1) { |i|
       0.upto(c-1) { |j|
          if (b[i,j] == 0) 
             dist = 2**32
             break
          end
          dist += a[i,j] * Math::log(a[i,j]/b[i,j]) - a[i,j] + b[i,j]
       }
   }
   dist
end

v = GSL::Matrix[[29, 31], [37, 41]]
w, h = nmf(v, 3, 10**(-10))
puts w
puts h
puts w*h

Tanimoto Coefficient

2008-07-02T14:40:00Z

A small Ruby snippet to calculate the Tanimoto coefficient (aka extended Jaccard coefficient) of two real vectors.


#!/usr/bin/ruby

class Array
   def sum
      inject( 0 ) { |sum,x| sum+x }
   end
   def sum_square
      inject( 0 ) { |sum,x| sum+x*x }
   end
   def *(other) # dot_product
      ret = []
      return nil if !other.is_a? Array || size != other.size
      self.each_with_index {|x, i| ret << x * other[i]}
      ret.sum
   end
end

def tanimoto(a, b)
   dot = (a*b)
   den = a.sum_square + b.sum_square - dot
   dot.to_f/den.to_f
end

# puts tanimoto([1,2,2],[3,3,1])

Pearson Correlation Coefficient

2008-07-01T10:26:00Z

A small Ruby snippet to calculate the Pearson product-moment correlation coefficient:


#!/usr/bin/ruby

class Array 
   def sum
      inject( 0 ) { |sum,x| sum+x }
   end
   def sum_square
      inject( 0 ) { |sum,x| sum+x*x }
   end
   def mean
      sum / size
   end
   def *(other)
      ret = []
      return nil if !other.is_a? Array || size != other.size
      self.each_with_index {|x, i| ret << x * other[i]}
      ret
   end
end


x = Array.new(100) {|i| rand(10) }
y = Array.new(100) {|i| rand(20) }


sumx = x.sum
sumy  = y.sum
num = (x.size * (x*y).sum) - (sumx * sumy)
den = Math.sqrt((x.size * x.sum_square) - sumx * sumx) * Math.sqrt((y.size * y.sum_square) - sumy * sumy)
r = num /den

puts "X= [#{x.join(', ')}]"
puts "Y= [#{y.join(', ')}]"
puts "r= #{r}"

ζ(s)

2008-06-18T11:19:00Z

Such a terse and strong abstract, and a really short paper, for an hypothesis that lasts unproved for a century. We shall see if the proof is correct.

Ruby Fiber Ring Benchmark

2008-05-22T15:51:00Z

I stole an exercise from the Erlang world: the ring benchmark

I used the exercise as a way to get acquainted with a new class in Ruby, Fiber (starting from the version 1.9). Fibers are a way to implement asymmetric coroutines in Ruby,


#!/usr/bin/ruby1.9

require 'fiber'
require 'benchmark'

class Ring
   attr_reader :id
   attr_accessor :attach 

   def initialize(id)
      @id = id
      @fiber = Fiber.new do
         pass_message
      end
   end

   def |(other)
      other.attach = self if !other.nil?
      other
   end

   def resume
      @fiber.resume
    end

   def pass_message
      while message = message_in
         message_out(message)      
      end
   end

   def message_in
      @attach.resume if !@attach.nil?
   end

   def message_out(message)
      Fiber.yield(message)
   end

end

class RingStart < Ring
   attr_accessor :message
   def initialize(n, m, message)
      @m = m
      @message = message
      super(n)
   end
   
   def pass_message 
      loop { message_out(@message) }
   end

end


def create_chain_r(i, chain)
   # recursive version
   return chain if i<=0
   r = chain.nil? ? Ring.new(i) :  chain | Ring.new(i)
   create_chain(i-1, r)
end

def create_chain(n, chain)
   # loop version
   # needed to avoid stack overflow for high n
   n.downto(0) {
      chain = chain | Ring.new(n)
   }
   chain
end



n=ARGV[0].to_i
m=ARGV[1].to_i
mess=:hello
tm  = Benchmark.measure {
   ringu = RingStart.new(0, m, mess)
   chain = create_chain(n, ringu)
   m.times { ringu.message = chain.resume }
}.format("%10.6r\n").gsub!(/\(|\)/, "")

puts "#{n}, #{m}, #{tm}"

The comparison with the equivalent Erlang program is of course unfair, for one of the Erlang specialty is the spawning of cooperative processes. Anyway, here are the results:

N	M	Execution Time
Ruby [ms]	Erlang [ms]
10	10	1	0
10	20	2	0
10	50	4	10
10	100	10	0
10	200	18	0
10	500	42	0
10	1000	82	10
100	10	15	0
100	20	23	10
100	50	60	0
100	100	99	10
100	200	186	20
100	500	433	50
100	1000	805	90
1000	10	320	10
1000	20	423	20
1000	50	809	60
1000	100	1479	130
1000	200	2803	250
1000	500	6914	600
1000	1000	15410	1190
10000	10	16168	190
10000	20	17491	320
10000	50	21348	710
10000	100	28314	1480
10000	200	41547	2860
10000	500	81166	7200
10000	1000	147570	14190

Oil price

2008-05-21T22:13:00Z

I’d like to reiterate a past meme. This time I restrict the meme to one single prediction: please tell me wether you think the crude oil price will pass the 150$ per barrell in the very near future, and, if you think that of it’s only matter of weeks, dare to say the exact day. I venture myself to bespeak the 30th of June, 2008.

Carlo, Alx, what do you think?

Caching Mephisto with lighttpd and mod_magnet

2008-05-14T22:15:00Z

This blog uses Mephisto, a rails application, and Thin as backend webserver. The frontend webserver is Lighttpd.

While Mephisto has a good caching system, producing a static html file for every visited page, the file is still served via Thin, reducing the speed and the scalability of the system and introducing an unnecessary step.

Lighttpd is very good at serving static files, thus I searched a way to serve a file from the cache directory of Mephisto, if present; I found a hack using mod_magnet.

Hereafter I wrote the relevant snippets of configuration files and how to put every piece in the right position.

Note: the same procedure should apply if you use Mongrel instead of Thin, for the relevant point is to bypass the backend rails webserver and serve all files (whether they exist) from the Mephisto cache.

First I configure Lighttpd to proxy to Thin for the rails application. I assume Thin (or Mongrel) is listening on port 3000 on two hosts.

  HTTP[''host"] == "virtualhost.example.org" {
        magnet.attract-physical-path-to = ( "/var/www/cache_mephisto.lua" ) 
        proxy.balance = "hash"
        proxy.server  = ( "" => ( ( "host" => "10.0.0.1", "port" =>  3000 ),
                                ( "host" => "10.0.0.2", "port" =>  3000 ) ) )
  }

The magnet.attract-physical-path-to = ( "/var/www/cache_mephisto.lua" ) is the magic trick. cache_mephisto.lua is a script written in lua programming language. The whole script is:

  local dir =  "/path/to/mephisto/public/cache/" .. lighty.request["Host"]

  if ( lighty.env["request.uri"] == nil or lighty.env["request.uri"] == "/") then
    file = dir .. "/index.html"
  else
    file = dir .. lighty.env["request.uri"] ..  ".html"
  end

  if lighty.stat(file) then
  lighty.header["Content-Type"] = "text/html"
  lighty.content = { { filename = file } }
  return 200
  end

 return lighty.RESTART_REQUEST

Inside the script you should adapt the variable dir to your Mephisto installation path. I need to append the virtual host name lighty.request["Host"] to the directory, for I run a multisite Mephisto installation; if you use a single site mephisto installation, probably you need to remove this append.

Now for some benchmarks:

serving the file via Thin:

   Requests per second:    1.40 [#/sec] (mean)
   Time per request:       716.007 [ms] (mean)

serving the file from the cache

   Requests per second:    11.46 [#/sec] (mean)
   Time per request:       87.247 [ms] (mean)

Almost a tenfold improvement!

Future works: serve from the cache the image files.

US Economy

2008-04-20T20:06:00Z

A thoughtful article: why Us economy is collapsing

A really interesting movie: money as debt

Postgresql Graph

2008-03-13T11:19:00Z

I wrote a small tool, postgresqlgraph, to monitor and plot the statistics of a postgresql database, using rrdtool.

The tool is able to monitor every database created inside a postgresql installation.

The parameters plotted for each database in the graph are:

numbackends: number of backends:
xact_commit: transactions committed;
xact_rollback: transactions rolled back;
blks_read: blocks read from the disk;:
blks_hit: blocks hit in the cache;
tup_returned: tuples returned (only in postgresql 8.3)
tup_fetched: tuples fetched (only in postgresql 8.3)
tup_inserted: tuples inserted (only in postgresql 8.3)
tup_updated: tuples updated (only in postgresql 8.3)
tup_deleted: deleted (only in postgresql 8.3)

For each parameter the graph shows the maximum and average values, and plots the derivative (rate change).

The software is published under GPLv3 .

A demo is available here.

Please feel free to submit me bugs, critics, improvements, or tell me if you find the tool of any worthwhileness.

SNAFU

2007-11-27T16:00:00Z

I spent a frustrating week of problem solving (or at least trying to…) of obscure integration issues among different programs, like trying to get zabbix to talk with a jabber server (the solution was found in IPV6), reading unuseful logs to debug problems (what the hell do you mean with “connection failed”? To what?) , recompiling software with arcane options, rebooting servers with the swap space full (apache, what are you doing?), or trying to stop a server that continues to reboot itself at boot (Xen, please tell me why…), or fighting with buggy PHP frontend, and, last but not least, investigate why a monitoring software just stopped working.

So I come to wonder if it exists a software that “just works”. If you ever happen to read this rambling and know such a software, please, please tell me. In the meanwhile I coined a law:

Dela’s Law of software: there is no software that “just works”
Corollary to the Dela’s Law of software: if a software seems to “just work”, after some times it will stop to work for an obscure, unknown and very difficult to find reason.

Universal Turing Machine

2007-10-25T21:43:00Z

So, it seems that the simplest universal turing machine has been demonstrated.

The simplest universal turing machine (T. M.) is, well, the simplest: 2 states and 3 symbols (or colors, as they are called by Stephen Wolfram), since a 2-states 2-symbols T.M. can not be universal.

This particular machine has however a subtle issue, for it requires an infinite memory (or ”tape” in the original definition of Turing), not satisfying perfectly the definition of universality given by Davis and Minsky.

The answer to the issue is that the pattern of bits in the memory can be set up without an universal T.M., so the universality is independent from the encoding of the pattern. I wonder if a (2,3) universal T.M. can be built with finite memory.

Asterisk Username Mismatch Workaround

2007-10-24T22:10:00Z

I installed recently AsteriskNow beta6, that is a rpath based Linux distribution, which contains Asterisk 1.4.9 and AsteriskGUI.

While I was trying to use with a SNOM phone (which, by the way, is a great product) with two identies configured on it, say 101 and 103, I stumbled on a problem well known on the web.

If I try to use an identity calling out, everything is working fine; while if I try to use the other identity, I obtain the following error:

   WARNING[32233]: chan_sip.c:8126 check_auth: username mismatch, have <101>, digest has <103>

The users 101 and 103 are created with the GUI. If you look in /etc/asterisk/users.conf you will find something like this:

   [101]
   callwaiting = yes
   cid_number = 
   context = numberplan-custom-1
   fullname = 101
   hasagent = no
   hasdirectory = no
   hasiax = no
   hasmanager = no
   hassip = yes
   hasvoicemail = yes
   host = dynamic
   mailbox = 101
   secret = xxx
   threewaycalling = yes
   vmsecret = xxx
   registersip = yes 
   canreinvite = yes
   nat = no
   dtmfmode = rfc2833
   disallow = all
   allow = ulaw,alaw

   [103]
   callwaiting = yesWorkaround
   cid_number = 
   context = numberplan-custom-1
   fullname = 103
   hasagent = no
   hasdirectory = no
   hasiax = no
   hasmanager = no
   hassip = yes
   hasvoicemail = yes
   host = dynamic
   mailbox = 103
   secret = xxx
   threewaycalling = yes
   vmsecret = xxx
   registersip = yes 
   canreinvite = yes
   nat = no
   dtmfmode = rfc2833
   disallow = all
   allow = ulaw,alaw

Workaround

I solved the problem, at least in my installation, using a workaround. I just copied and adapted the above definitions in the file /etc/asterik/sip.conf. This file is not touched by the GUI, so you can edit it safely. Just remember to modify it if you modify the users definition with the GUI, in order to reflect the variations of users.conf. The relevant part of sip.conf looks like:

  [101]
  type = friend;
  context = numberplan-custom-1;
  secret = xxx
  host = dynamic ;
  dtmfmode = rfc2833;
  disallow = all
  allow = ulaw,alaw;
  canreinvite = yes

  [103]
  type = friend;
  context = numberplan-custom-1;
  secret = xxx
  host = dynamic ;
  dtmfmode = rfc2833;
  disallow = all
  allow = ulaw,alaw;
  canreinvite = yes

Well, it seems to work.

Unicode

2007-10-14T21:32:00Z

Inspired by http://www.inference.phy.cam.ac.uk/cjb/codepoints.html I write some of my favourite Unicode Codepoints:

U+0488 ҈ COMBINING CYRILLIC HUNDRED THOUSANDS SIGN

U+0489 ҉ COMBINING CYRILLIC MILLIONS SIGN

U+0F17 ༗ TIBETAN ASTROLOGICAL SIGN GRA GCAN -CHAR RTAGS

U+0FCA ࿊ TIBETAN SYMBOL NOR BU NYIS -KHYIL

U+1697 ᚗ OGHAM LETTER UILLEANN

U+2121 ℡ TELEPHONE SIGN

U+2618 ☘ SHAMROCK

U+2620 ☠ SKULL AND CROSSBONES

U+2623 ☣ BIOHAZARD SIGN

U+20AC ⨌ QUADRUPLE INTEGRAL OPERATOR

U+260F ☏ WHITE TELEPHONE

U+2709 ✉ ENVELOPE

𐌌𐌀𐌓𐌂𐌏

P.s. Does your browser support idn: http://☠.equars.com ?

Lost

2007-10-04T11:17:00Z

Lost: is a game, an experiment in social networking, or just bright marketing? (Well, just in case you’d like to try it www.lost.eu/6674b ;) )

Bandaloop: wow.

2007-10-04T10:06:00Z

Yesterday I saw in Turin a performance of the Bandaloop. It was absolutely speechless and breathtaking to see the dancers performing their aerial choreography and vertical dance at 70m of height in the air.