Javascript implementation of a Shannon entropy calculation in bits per symbol

entropy.js

// entropy.js MIT License © 2014 James Abney http://github.com/jabney

/***************************************
 * ES2015
 ***************************************/

// Shannon entropy in bits per symbol.
function entropy(str) {
  const len = str.length
 
  // Build a frequency map from the string.
  const frequencies = Array.from(str)
    .reduce((freq, c) => (freq[c] = (freq[c] || 0) + 1) && freq, {})
 
  // Sum the frequency of each character.
  return Object.values(frequencies)
    .reduce((sum, f) => sum - f/len * Math.log2(f/len), 0)
}
 
console.log(entropy('1223334444'))        // 1.8464393446710154
console.log(entropy('0'))                 // 0
console.log(entropy('01'))                // 1
console.log(entropy('0123'))              // 2
console.log(entropy('01234567'))          // 3
console.log(entropy('0123456789abcdef'))  // 4


/***************************************
 * ES5
 ***************************************/

// Calculate the Shannon entropy of a string in bits per symbol.
(function(shannon) {
'use strict';

  // Create a dictionary of character frequencies and iterate over it.
  function process(s, evaluator) {
    var h = Object.create(null), k;
    s.split('').forEach(function(c) {
      h[c] && h[c]++ || (h[c] = 1); });
    if (evaluator) for (k in h) evaluator(k, h[k]);
    return h;
  };
  
  // Measure the entropy of a string in bits per symbol.
  shannon.entropy = function(s) {
    var sum = 0,len = s.length;
    process(s, function(k, f) {
      var p = f/len;
      sum -= p * Math.log(p) / Math.log(2);
    });
    return sum;
  };
  
  // Measure the entropy of a string in total bits.
  shannon.bits = function(s) {
    return shannon.entropy(s) * s.length;
  };
  
  // Log the entropy of a string to the console.
  shannon.log = function(s) {
    console.log('Entropy of "' + s + '" in bits per symbol:', shannon.entropy(s));
  };
})(window.shannon = window.shannon || Object.create(null));
 
shannon.log('1223334444');          // 1.8464393446710154
shannon.log('0');                   // 0
shannon.log('01');                  // 1
shannon.log('0123');                // 2
shannon.log('01234567');            // 3
shannon.log('0123456789abcdef');    // 4

Thank you very much, quite useful!

@tiagocesar,

Thank you very much, quite useful!

Glad you found it helpful. Here's an updated (and more concise) version for ECMAScript 2015:

// Shannon entropy in bits per symbol.
function entropy(str) {
  const len = str.length
 
  // Build a frequency map from the string.
  const frequencies = Array.from(str)
    .reduce((freq, c) => (freq[c] = (freq[c] || 0) + 1) && freq, {})
 
  // Sum the frequency of each character.
  return Object.values(frequencies)
    .reduce((sum, f) => sum - f/len * Math.log2(f/len), 0)
}
 
console.log(entropy('1223334444'))        // 1.8464393446710154
console.log(entropy('0'))                 // 0
console.log(entropy('01'))                // 1
console.log(entropy('0123'))              // 2
console.log(entropy('01234567'))          // 3
console.log(entropy('0123456789abcdef'))  // 4

And here's a version for people who don't have an exobrain and don't wear the Hubble telescope as glasses:

function entropy(text) {
    var textLength = text.length;

    // find symbolCount of all symbols
    var symbolCount = {};
    for (var i = 0; i < textLength; i++) {
        var symbol = text[i];
        if (symbolCount[symbol] === undefined) {
            symbolCount[symbol] = 1;
        }
        else {
            symbolCount[symbol]++;
        }
    }

    var complexity = 0;
    var allCounts = Object.values(symbolCount);
    var allCountsLength = allCounts.length;
    for (var i = 0; i < allCountsLength; i++) {
        complexity = complexity - allCounts[i]/textLength * Math.log2(allCounts[i]/textLength);
    }
    return complexity;
}

Thanks @pkrumins - I can actually read that code! 😀 Thanks @jabney for the original code too, very helpful!