Programming Praxis

7 Responses to “Entropy”

1. Jussi Piitulainen said

   January 22, 2016 at 2:07 PM

   Python has more entropy!

   from math import log
   from math import fsum as fum
   from collections import Counter as C
   
   def H(S):
       F = C(S)
       N = sum(F[s] for s in F)
       return - fum(p * log(p) for s in F for p in [F[s]/N]) / log(2)
   
   for data in ("banana", "nanana", "phenomenon"):
       print("H({}) = {:.4f}".format(repr(data), H(data)))
   
   print("H(H) = {:.4f}".format(H(open("H.py").read())))
   
   # Output before adding either of these comments:                                                                                                                        
   # H('banana') = 1.4591                                                                                                                                                  
   # H('nanana') = 1.0000                                                                                                                                                  
   # H('phenomenon') = 2.4464                                                                                                                                              
   # H(H) = 4.6956                                                                                                                                                         
   
   # Output after adding the above comment:                                                                                                                                
   # H('banana') = 1.4591                                                                                                                                                  
   # H('nanana') = 1.0000                                                                                                                                                  
   # H('phenomenon') = 2.4464                                                                                                                                              
   # H(H) = 4.9039                                                                                                                                                         
   
   # Afterthought, on Praxis' entropy.ss:                                                                                                                                  
   # H(entropy) = 3.8012
   
2. Kooda said

   January 23, 2016 at 11:53 AM

   Other Scheme version over arbitrary sorted lists

   (define (count-occurences l)
   (define (count l last lastcount)
   (cond
   ((null? l) ‘())
   ((equal? (car l) last) (count (cdr l) last (add1 lastcount)))
   (else (cons lastcount (count (cdr l) (car l) 1)))))
   (if (null? l) ‘() (count (cdr l) (car l) 1)))

   (define (shannon-entropy l)
   (let ((len (length l)))
   (* -1
   (fold
   (lambda (occ last)
   (let ((pi (/ occ len)))
   (+ last (* pi
   (/ (log pi) (log 2))))))
   0
   (count-occurences l)))))

   (shannon-entropy (sort (string->list “Hello mine-turtle!”) char 3.29883055667735

   (shannon-entropy ‘(red red blue black yellow purple))
   ;; -> 1.8208020839343
3. bartek said

   January 23, 2016 at 5:17 PM

   My chicken-scheme slightly modified version

   (use vector-lib)

   (define (log2 x) (/ (log x) (log 2)))

   (define (filefreqs filename)
   (with-input-from-file filename (lambda ()
   (let ((freqs (make-vector 256 0)))
   (let loop ((c (read-char))
   (len 0))
   (if (eof-object? c)
   (vector-map (lambda (i x) (/ x len)) freqs)
   (let ((i (char->integer c)))
   (vector-set! freqs i (+ (vector-ref freqs i) 1))
   (loop (read-char) (+ 1 len)))))))))

   (define (entropy filename)
   (- (vector-fold (lambda (i prev x)
   (+ prev (* x (if (positive? x) (log2 x) 0))))
   0
   (filefreqs filename))))

   (display (entropy "entropy.scm"))
4. bartek said

   January 23, 2016 at 5:19 PM

   Does formatting work?

   
   (use vector-lib)
   
   (define (log2 x) (/ (log x) (log 2)))
   
   (define (filefreqs filename)
     (with-input-from-file filename (lambda ()
       (let ((freqs (make-vector 256 0)))
         (let loop ((c (read-char))
                    (len 0))
           (if (eof-object? c)
             (vector-map (lambda (i x) (/ x len)) freqs)
             (let ((i (char->integer c)))
               (vector-set! freqs i (+ (vector-ref freqs i) 1))
               (loop (read-char) (+ 1 len)))))))))
   
   
   (define (entropy filename)
       (- (vector-fold (lambda (i prev x)
                     (+ prev (* x (if (positive? x) (log2 x) 0))))
                  0
                  (filefreqs filename))))
   
   (display (entropy "entropy.scm"))
   
   
5. Jared Tobin said

   January 24, 2016 at 9:08 AM

   Haskell, using the nice little foldl library:

   import           Control.Foldl    (Fold (..))
   import qualified Control.Foldl    as L
   import           Data.Map.Strict  (Map)
   import qualified Data.Map.Strict  as Map
   
   count :: (Ord k, Num a) => Fold k (Map k a)
   count = Fold step mempty id where
     step m k = Map.insertWith (+) k 1 m
   
   distribution :: (Ord k, Fractional a) => Fold k (Map k a)
   distribution = divide <$> count <*> L.genericLength where
     divide m n = fmap (/ n) m
   
   entropize :: Floating a => a -> a
   entropize m = negate (m * logBase 2 m)
   
   entropy :: (Foldable f, Ord k, Floating a) => f k -> a
   entropy = L.fold (L.premap entropize L.sum) . L.fold distribution
   
6. Jussi Piitulainen said

   January 24, 2016 at 12:20 PM

   Haskell has slightly less entropy than Python. Computed from my Python when the file contained just the source code, Jared’s Haskell, and Praxis’ Scheme:

   H(python) = 4.6956
   H(haskell) = 4.6592
   H(scheme) = 3.8012
   
7. mcmillhj said

   February 24, 2016 at 4:03 PM

   Almost got by without using a variable:

   #!/usr/bin/env perl
   
   use strict;
   use warnings;
   
   use List::Util qw(sum pairmap);
   use List::UtilsBy qw(count_by);
   
   sub H {
      my ($s) = @_;
     
      my $total_count = 0;
      return - sum(
         map      { $_ * log $_            } 
         map      { $_ / $total_count      } 
         pairmap  { $total_count += $b; $b } 
         count_by { $_                     } split //, $s
      ) / log 2;
   }
   
   my $text = do {
      open my $fh, '<', $ARGV[0] or die "$!";
      local $/ = undef; # slurp mode
      <$fh>;
   };
   
   print H("banana"), "\n";
   print H($text), "\n";
   
   __END__
   [hunter@apollo: 02]$ perl entropy.pl entropy.pl 
   1.45914791702725
   4.53554363380707