Anonymous user
Entropy: Difference between revisions
m
→{{header|uBasic/4tH}}
(→{{header|Perl 6}}: style again, avoiding list comprehension) |
imported>Thebeez |
||
| (341 intermediate revisions by more than 100 users not shown) | |||
Line 1:
{{task|Mathematics}}
;Task:
Calculate the Shannon entropy H of a given input string.
Given the discrete random variable <math>X</math> that is a string of <math>N</math> "symbols" (total characters) consisting of <math>n</math> different characters (n=2 for binary), the Shannon entropy of X in '''bits/symbol''' is :
:<math>H_2(X) = -\sum_{i=1}^n \frac{count_i}{N} \log_2 \left(\frac{count_i}{N}\right)</math>
where <math>count_i</math> is the count of character <math>n_i</math>.
For this task, use X="<tt>1223334444</tt>" as an example. The result should be 1.84644... bits/symbol. This assumes X was a random variable, which may not be the case, or it may depend on the observer.
This coding problem calculates the "specific" or "[[wp:Intensive_and_extensive_properties|intensive]]" entropy that finds its parallel in physics with "specific entropy" S<sup>0</sup> which is entropy per kg or per mole, not like physical entropy S and therefore not the "information" content of a file. It comes from Boltzmann's H-theorem where <math>S=k_B N H</math> where N=number of molecules. Boltzmann's H is the same equation as Shannon's H, and it gives the specific entropy H on a "per molecule" basis.
The "total", "absolute", or "[[wp:Intensive_and_extensive_properties|extensive]]" information entropy is
:<math>S=H_2 N</math> bits
This is not the entropy being coded here, but it is the closest to physical entropy and a measure of the information content of a string. But it does not look for any patterns that might be available for compression, so it is a very restricted, basic, and certain measure of "information". Every binary file with an equal number of 1's and 0's will have S=N bits. All hex files with equal symbol frequencies will have <math>S=N \log_2(16)</math> bits of entropy. The total entropy in bits of the example above is S= 10*18.4644 = 18.4644 bits.
The H function does not look for any patterns in data or check if X was a random variable. For example, X=000000111111 gives the same calculated entropy in all senses as Y=010011100101. For most purposes it is usually more relevant to divide the gzip length by the length of the original data to get an informal measure of how much "order" was in the data.
Two other "entropies" are useful:
Normalized specific entropy:
:<math>H_n=\frac{H_2 * \log(2)}{\log(n)}</math>
which varies from 0 to 1 and it has units of "entropy/symbol" or just 1/symbol. For this example, H<sub>n<\sub>= 0.923.
Normalized total (extensive) entropy:
:<math>S_n = \frac{H_2 N * \log(2)}{\log(n)}</math>
which varies from 0 to N and does not have units. It is simply the "entropy", but it needs to be called "total normalized extensive entropy" so that it is not confused with Shannon's (specific) entropy or physical entropy. For this example, S<sub>n<\sub>= 9.23.
Shannon himself is the reason his "entropy/symbol" H function is very confusingly called "entropy". That's like calling a function that returns a speed a "meter". See section 1.7 of his classic [http://worrydream.com/refs/Shannon%20-%20A%20Mathematical%20Theory%20of%20Communication.pdf A Mathematical Theory of Communication] and search on "per symbol" and "units" to see he always stated his entropy H has units of "bits/symbol" or "entropy/symbol" or "information/symbol". So it is legitimate to say entropy NH is "information".
In keeping with Landauer's limit, the physics entropy generated from erasing N bits is <math>S = H_2 N k_B \ln(2)</math> if the bit storage device is perfectly efficient. This can be solved for H<sub>2</sub>*N to (arguably) get the number of bits of information that a physical entropy represents.
;Related tasks:
:* [[Fibonacci_word]]
:* [[Entropy/Narcissist]]
<br><br>
=={{header|11l}}==
<syntaxhighlight lang="11l">F entropy(source)
DefaultDict[Char, Int] hist
L(c) source
hist[c]++
V r = 0.0
L(v) hist.values()
V c = Float(v) / source.len
r -= c * log2(c)
R r
print(entropy(‘1223334444’))</syntaxhighlight>
{{out}}
<pre>
1.84644
</pre>
=={{header|Ada}}==
Uses Ada 2012.
<syntaxhighlight lang="ada">with Ada.Text_IO, Ada.Float_Text_IO, Ada.Numerics.Elementary_Functions;
procedure Count_Entropy is
package TIO renames Ada.Text_IO;
Count: array(Character) of Natural := (others => 0);
Sum: Natural := 0;
Line: String := "1223334444";
begin
for I in Line'Range loop -- count the characters
Count(Line(I)) := Count(Line(I))+1;
Sum := Sum + 1;
end loop;
declare -- compute the entropy and print it
function P(C: Character) return Float is (Float(Count(C)) / Float(Sum));
use Ada.Numerics.Elementary_Functions, Ada.Float_Text_IO;
Result: Float := 0.0;
begin
for Ch in Character loop
Result := Result -
(if P(Ch)=0.0 then 0.0 else P(Ch) * Log(P(Ch), Base => 2.0));
end loop;
Put(Result, Fore => 1, Aft => 5, Exp => 0);
end;
end Count_Entropy;</syntaxhighlight>
=={{header|Aime}}==
<syntaxhighlight lang="aime">integer c;
real h, v;
index x;
data s;
for (, c in (s = argv(1))) {
x[c] += 1r;
}
h = 0;
for (, v in x) {
v /= ~s;
h -= v * log2(v);
}
o_form("/d6/\n", h);</syntaxhighlight>
Examples:
<pre>$ aime -a tmp/entr 1223334444
1.846439
$ aime -a tmp/entr 'Rosetta Code is the best site in the world!'
3.646513
$ aime -a tmp/entr 1234567890abcdefghijklmnopqrstuvwxyz
5.169925</pre>
=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">BEGIN
# calculate the shannon entropy of a string #
PROC shannon entropy = ( STRING s )REAL:
BEGIN
INT string length = ( UPB s - LWB s ) + 1;
# count the occurences of each character #
[ 0 : max abs char ]INT char count;
FOR char pos FROM LWB char count TO UPB char count DO
char count[ char pos ] := 0
OD;
FOR char pos FROM LWB s TO UPB s DO
char count[ ABS s[ char pos ] ] +:= 1
OD;
# calculate the entropy, we use log base 10 and then convert #
# to log base 2 after calculating the sum #
REAL entropy := 0;
FOR char pos FROM LWB char count TO UPB char count DO
IF char count[ char pos ] /= 0
THEN
# have a character that occurs in the string #
REAL probability = char count[ char pos ] / string length;
entropy -:= probability * log( probability )
FI
OD;
entropy / log( 2 )
END; # shannon entropy #
# test the shannon entropy routine #
print( ( shannon entropy( "1223334444" ), newline ) )
END</syntaxhighlight>
{{out}}
<pre>
+1.84643934467102e +0
</pre>
=={{header|ALGOL W}}==
{{trans|ALGOL 68}}
<syntaxhighlight lang="algolw">begin
% calculates the shannon entropy of a string %
% strings are fixed length in algol W and the length is part of the %
% type, so we declare the string parameter to be the longest possible %
% string length (256 characters) and have a second parameter to %
% specify how much is actually used %
real procedure shannon_entropy ( string(256) value s
; integer value stringLength
);
begin
real probability, entropy;
% algol W assumes there are 256 possible characters %
integer MAX_CHAR;
MAX_CHAR := 256;
% declarations must preceed statements, so we start a new %
% block here so we can use MAX_CHAR as an array bound %
begin
% increment an integer variable %
procedure incI ( integer value result a ) ; a := a + 1;
integer array charCount( 1 :: MAX_CHAR );
% count the occurances of each character in s %
for charPos := 1 until MAX_CHAR do charCount( charPos ) := 0;
for sPos := 0 until stringLength - 1 do incI( charCount( decode( s( sPos | 1 ) ) ) );
% calculate the entropy, we use log base 10 and then convert %
% to log base 2 after calculating the sum %
entropy := 0.0;
for charPos := 1 until MAX_CHAR do
begin
if charCount( charPos ) not = 0
then begin
% have a character that occurs in the string %
probability := charCount( charPos ) / stringLength;
entropy := entropy - ( probability * log( probability ) )
end
end charPos
end;
entropy / log( 2 )
end shannon_entropy ;
% test the shannon entropy routine %
r_format := "A"; r_w := 12; r_d := 6; % set output to fixed format %
write( shannon_entropy( "1223334444", 10 ) )
end.</syntaxhighlight>
{{out}}
<pre>
1.846439
</pre>
=={{header|APL}}==
<syntaxhighlight lang="apl">
ENTROPY←{-+/R×2⍟R←(+⌿⍵∘.=∪⍵)÷⍴⍵}
⍝ How it works:
⎕←UNIQUE←∪X←'1223334444'
1234
⎕←TABLE_OF_OCCURENCES←X∘.=UNIQUE
1 0 0 0
0 1 0 0
0 1 0 0
0 0 1 0
0 0 1 0
0 0 1 0
0 0 0 1
0 0 0 1
0 0 0 1
0 0 0 1
⎕←COUNT←+⌿TABLE_OF_OCCURENCES
1 2 3 4
⎕←N←⍴X
10
⎕←RATIO←COUNT÷N
0.1 0.2 0.3 0.4
-+/RATIO×2⍟RATIO
1.846439345
</syntaxhighlight>
{{out}}
<pre>
ENTROPY X
1.846439345
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">entropy: function [s][
t: #[]
loop s 'c [
unless key? t c -> t\[c]: 0
t\[c]: t\[c] + 1
]
result: new 0
loop values t 'x ->
'result - (x//(size s)) * log x//(size s) 2
return result
]
print entropy "1223334444"</syntaxhighlight>
{{out}}
<pre>1.846439344671015</pre>
=={{header|AutoHotkey}}==
<syntaxhighlight lang="autohotkey">MsgBox, % Entropy(1223334444)
Entropy(n)
{
a := [], len := StrLen(n), m := n
while StrLen(m)
{
s := SubStr(m, 1, 1)
m := RegExReplace(m, s, "", c)
a[s] := c
}
for key, val in a
{
m := Log(p := val / len)
e -= p * m / Log(2)
}
return, e
}</syntaxhighlight>
{{out}}
<pre>1.846440</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">#!/usr/bin/awk -f
{
N = length
for (i = 1; i <= N; ++i)
++H[substr($0, i, 1)]
}
END {
for (i in H)
S += H[i] * log(H[i])
print (log(N) - S / N) / log(2)
}</syntaxhighlight>
{{out|Usage}}
<syntaxhighlight lang="sh"> echo 1223334444 |./entropy.awk
1.84644</syntaxhighlight>
=={{header|BASIC}}==
Works with older (unstructured) Microsoft-style BASIC.
<syntaxhighlight lang="basic">10 DEF FN L(X)=LOG(X)/LOG(2)
20 S$="1223334444"
30 U$=""
40 FOR I=1 TO LEN(S$)
50 K=0
60 FOR J=1 TO LEN(U$)
70 IF MID$(U$,J,1)=MID$(S$,I,1) THEN K=1
80 NEXT J
90 IF K=0 THEN U$=U$+MID$(S$,I,1)
100 NEXT I
110 DIM R(LEN(U$)-1)
120 FOR I=1 TO LEN(U$)
130 C=0
140 FOR J=1 TO LEN(S$)
150 IF MID$(U$,I,1)=MID$(S$,J,1) THEN C=C+1
160 NEXT J
170 R(I-1)=(C/LEN(S$))*FN L(C/LEN(S$))
180 NEXT I
190 E=0
200 FOR I=0 TO LEN(U$)-1
210 E=E-R(I)
220 NEXT I
230 PRINT E</syntaxhighlight>
{{out}}
<pre>1.84643935</pre>
==={{header|QBasic}}===
<syntaxhighlight lang="qbasic">FUNCTION L (X)
L = LOG(X) / LOG(2)
END FUNCTION
S$ = "1223334444"
U$ = ""
FOR I = 1 TO LEN(S$)
K = 0
FOR J = 1 TO LEN(U$)
IF MID$(U$, J, 1) = MID$(S$, I, 1) THEN K = 1
NEXT J
IF K = 0 THEN U$ = U$ + MID$(S$, I, 1)
NEXT I
DIM R(LEN(U$) - 1)
FOR I = 1 TO LEN(U$)
C = 0
FOR J = 1 TO LEN(S$)
IF MID$(U$, I, 1) = MID$(S$, J, 1) THEN C = C + 1
NEXT J
R(I - 1) = (C / LEN(S$)) * L(C / LEN(S$))
NEXT I
E = 0
FOR I = 0 TO LEN(U$) - 1
E = E - R(I)
NEXT I
PRINT E
END</syntaxhighlight>
==={{header|Sinclair ZX81 BASIC}}===
Works with 1k of RAM.
<syntaxhighlight lang="basic"> 10 LET X$="1223334444"
20 LET U$=""
30 FOR I=1 TO LEN X$
40 LET K=0
50 FOR J=1 TO LEN U$
60 IF U$(J)=X$(I) THEN LET K=K+1
70 NEXT J
80 IF K=0 THEN LET U$=U$+X$(I)
90 NEXT I
100 DIM R(LEN U$)
110 FOR I=1 TO LEN U$
120 LET C=0
130 FOR J=1 TO LEN X$
140 IF U$(I)=X$(J) THEN LET C=C+1
150 NEXT J
160 LET R(I)=C/LEN X$*LN (C/LEN X$)/LN 2
170 NEXT I
180 LET E=0
190 FOR I=1 TO LEN U$
200 LET E=E-R(I)
210 NEXT I
220 PRINT E</syntaxhighlight>
{{out}}
<pre>1.8464393</pre>
==={{header|uBasic/4tH}}===
{{Trans|QBasic}}
uBasic/4tH is an integer BASIC only. So, fixed point arithmetic is required go fulfill this task. Some loss of precision is unavoidable.
<syntaxhighlight lang="basic">If Info("wordsize") < 64 Then Print "This program requires a 64-bit uBasic" : End
s := "1223334444"
u := ""
x := FUNC(_Fln(FUNC(_Ntof(2)))) ' calculate LN(2)
For i = 0 TO Len(s)-1
k = 0
For j = 0 TO Len(u)-1
If Peek(u, j) = Peek(s, i) Then k = 1
Next
If k = 0 THEN u = Join(u, Char (Peek (s, i)))
Next
Dim @r(Len(u)-1)
For i = 0 TO Len(u)-1
c = 0
For J = 0 TO Len(s)-1
If Peek(u, i) = Peek (s, j) Then c = c + 1
Next
q = FUNC(_Fdiv(c, Len(s)))
@r(i) = FUNC(_Fmul(q, FUNC(_Fdiv(FUNC(_Fln(q)), x))))
Next
e = 0
For i = 0 To Len(u) - 1
e = e - @r(i)
Next
Print Using "+?.####"; FUNC(_Ftoi(e))
End
_Fln Param (1) : Return (FUNC(_Ln(a@*4))/4)
_Fmul Param (2) : Return ((a@*b@)/16384)
_Fdiv Param (2) : Return ((a@*16384)/b@)
_Ntof Param (1) : Return (a@*16384)
_Ftoi Param (1) : Return ((10000*a@)/16384)
_Ln
Param (1)
Local (2)
c@=681391
If (a@<32768) Then a@=SHL(a@, 16) : c@=c@-726817
If (a@<8388608) Then a@=SHL(a@, 8) : c@=c@-363409
If (a@<134217728) Then a@=SHL(a@, 4) : c@=c@-181704
If (a@<536870912) Then a@=SHL(a@, 2) : c@=c@-90852
If (a@<1073741824) Then a@=SHL(a@, 1) : c@=c@-45426
b@=a@+SHL(a@, -1) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-26573
b@=a@+SHL(a@, -2) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-14624
b@=a@+SHL(a@, -3) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-7719
b@=a@+SHL(a@, -4) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-3973
b@=a@+SHL(a@, -5) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-2017
b@=a@+SHL(a@, -6) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-1016
b@=a@+SHL(a@, -7) : If (AND(b@, 2147483648)) = 0 Then a@=b@ : c@=c@-510
a@=2147483648-a@;
c@=c@-SHL(a@, -15)
Return (c@)</syntaxhighlight>
{{Out}}
<pre>1.8461
0 OK, 0:638</pre>
=={{header|BBC BASIC}}==
{{trans|APL}}
<syntaxhighlight lang="bbcbasic">REM >entropy
PRINT FNentropy("1223334444")
END
:
DEF FNentropy(x$)
LOCAL unique$, count%, n%, ratio(), u%, i%, j%
unique$ = ""
n% = LEN x$
FOR i% = 1 TO n%
IF INSTR(unique$, MID$(x$, i%, 1)) = 0 THEN unique$ += MID$(x$, i%, 1)
NEXT
u% = LEN unique$
DIM ratio(u% - 1)
FOR i% = 1 TO u%
count% = 0
FOR j% = 1 TO n%
IF MID$(unique$, i%, 1) = MID$(x$, j%, 1) THEN count% += 1
NEXT
ratio(i% - 1) = (count% / n%) * FNlogtwo(count% / n%)
NEXT
= -SUM(ratio())
:
DEF FNlogtwo(n)
= LN n / LN 2</syntaxhighlight>
{{out}}
<pre>1.84643934</pre>
=={{header|BQN}}==
<syntaxhighlight lang="bqn">H ← -∘(+´⊢×2⋆⁼⊢)∘((+˝⊢=⌜⍷)÷≠)
H "1223334444"</syntaxhighlight>
{{out}}
<pre>1.8464393446710154</pre>
=={{header|Burlesque}}==
<syntaxhighlight lang="burlesque">blsq ) "1223334444"F:u[vv^^{1\/?/2\/LG}m[?*++
1.8464393446710157</syntaxhighlight>
=={{header|C}}==
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#include <math.h>
#define MAXLEN 100 //maximum string length
int makehist(unsigned char *S,int *hist,int len){
int wherechar[256];
int i,histlen;
histlen=0;
for(i=0;i<256;i++)wherechar[i]=-1;
for(i=0;i<len;i++){
if(wherechar[(int)S[i]]==-1){
wherechar[(int)S[i]]=histlen;
histlen++;
}
hist[wherechar[(int)S[i]]]++;
}
return histlen;
}
double entropy(int *hist,int histlen,int len){
int i;
double H;
H=0;
for(i=0;i<histlen;i++){
H-=(double)hist[i]/len*log2((double)hist[i]/len);
}
return H;
}
int main(void){
unsigned char S[MAXLEN];
int len,*hist,histlen;
double H;
scanf("%[^\n]",S);
len=strlen(S);
hist=(int*)calloc(len,sizeof(int));
histlen=makehist(S,hist,len);
//hist now has no order (known to the program) but that doesn't matter
H=entropy(hist,histlen,len);
printf("%lf\n",H);
return 0;
}</syntaxhighlight>
Examples:
<syntaxhighlight lang="text">$ ./entropy
1223334444
1.846439
$ ./entropy
Rosetta Code is the best site in the world!
3.646513</syntaxhighlight>
=={{header|
Translation of C++.
<syntaxhighlight lang="csharp">
using System;
using System.Collections.Generic;
namespace Entropy
{
class Program
{
public static double logtwo(double num)
{
return Math.Log(num)/Math.Log(2);
}
public static void Main(string[] args)
{
label1:
string input = Console.ReadLine();
double infoC=0;
Dictionary<char,double> table = new Dictionary<char, double>();
foreach (char c in input)
{
if (table.ContainsKey(c))
table[c]++;
else
table.Add(c,1);
}
double freq;
foreach (KeyValuePair<char,double> letter in table)
{
freq=letter.Value/input.Length;
infoC+=freq*logtwo(freq);
}
infoC*=-1;
Console.WriteLine("The Entropy of {0} is {1}",input,infoC);
goto label1;
}
}
}
</syntaxhighlight>
{{out}}
<pre>The Entropy of 1223334444 is 1.84643934467102</pre>
Without using Hashtables or Dictionaries:
<syntaxhighlight lang="csharp">using System;
namespace Entropy
{
class Program
{
public static double logtwo(double num)
{
return Math.Log(num)/Math.Log(2);
}
static double Contain(string x,char k)
{
double count=0;
foreach (char Y in x)
{
if(Y.Equals(k))
count++;
}
return count;
}
public static void Main(string[] args)
{
label1:
string input = Console.ReadLine();
double infoC=0;
double freq;
string k="";
foreach (char c1 in input)
{
if (!(k.Contains(c1.ToString())))
k+=c1;
}
foreach (char c in k)
{
freq=Contain(input,c)/(double)input.Length;
infoC+=freq*logtwo(freq);
}
infoC/=-1;
Console.WriteLine("The Entropy of {0} is {1}",input,infoC);
goto label1;
}
}
}</syntaxhighlight>
=={{header|C++}}==
<syntaxhighlight lang="cpp">#include <string>
#include <map>
#include <iostream>
#include <algorithm>
#include <cmath>
double log2( double number ) {
return log( number ) / log( 2 ) ;
}
int main( int argc , char *argv[ ] ) {
std::string teststring( argv[ 1 ] ) ;
std::map<char , int> frequencies ;
for ( char c : teststring )
frequencies[ c ] ++ ;
int numlen = teststring.length( ) ;
double infocontent = 0 ;
for ( std::pair<char , int> p : frequencies ) {
double freq = static_cast<double>( p.second ) / numlen ;
infocontent -= freq * log2( freq ) ;
}
std::cout << "The information content of " << teststring
<< " is " << infocontent << std::endl ;
return 0 ;
}</syntaxhighlight>
{{out}}
<pre>(entropy "1223334444")
The information content of 1223334444 is 1.84644</pre>
=={{header|Clojure}}==
<syntaxhighlight lang="clojure">(defn entropy [s]
(let [len (count s), log-2 (Math/log 2)]
(->> (frequencies s)
(map (fn [[_ v]]
(let [rf (/ v len)]
(-> (Math/log rf) (/ log-2) (* rf) Math/abs))))
(reduce +))))</syntaxhighlight>
{{out}}
<syntaxhighlight lang="clojure">(entropy "1223334444")
1.8464393446710154</syntaxhighlight>
=={{header|CLU}}==
<syntaxhighlight lang="clu">% NOTE: when compiling with Portable CLU,
% this program needs to be merged with 'useful.lib' to get log()
%
% pclu -merge $CLUHOME/lib/useful.lib -compile entropy.clu
shannon = proc (s: string) returns (real)
% find the frequency of each character
freq: array[int] := array[int]$fill(0, 256, 0)
for c: char in string$chars(s) do
i: int := char$c2i(c)
freq[i] := freq[i] + 1
end
% calculate the component for each character
h: real := 0.0
rlen: real := real$i2r(string$size(s))
for i: int in array[int]$indexes(freq) do
if freq[i] ~= 0 then
f: real := real$i2r(freq[i]) / rlen
h := h - f * log(f) / log(2.0)
end
end
return (h)
end shannon
start_up = proc ()
po: stream := stream$primary_output()
stream$putl(po, f_form(shannon("1223334444"), 1, 6))
end start_up </syntaxhighlight>
{{out}}
<pre>1.846439</pre>
=={{header|CoffeeScript}}==
<syntaxhighlight lang="coffeescript">entropy = (s) ->
freq = (s) ->
result = {}
for ch in s.split ""
result[ch] ?= 0
result[ch]++
return result
frq = freq s
n = s.length
((frq[f]/n for f of frq).reduce ((e, p) -> e - p * Math.log(p)), 0) * Math.LOG2E
console.log "The entropy of the string '1223334444' is #{entropy '1223334444'}"</syntaxhighlight>
{{out}}
<pre>The entropy of the string '1223334444' is 1.8464393446710157</pre>
=={{header|Common Lisp}}==
Not very Common Lisp-y version:
<syntaxhighlight lang="lisp">(defun entropy (string)
(let ((table (make-hash-table :test 'equal))
(entropy 0))
(mapc (lambda (c) (setf (gethash c table) (+ (gethash c table 0) 1)))
(coerce string 'list))
(maphash (lambda (k v)
(decf entropy (* (/ v (length input-string))
(log (/ v (length input-string)) 2))))
table)
entropy))</syntaxhighlight>
More like Common Lisp version:
<syntaxhighlight lang="lisp">(defun entropy (string &aux (length (length string)))
(declare (type string string))
(let ((table (make-hash-table)))
(loop for char across string
do (incf (gethash char table 0)))
(- (loop for freq being each hash-value in table
for freq/length = (/ freq length)
sum (* freq/length (log freq/length 2))))))</syntaxhighlight>
=={{header|Crystal}}==
<syntaxhighlight lang="ruby"># Method to calculate sum of Float64 array
def sum(array : Array(Float64))
res = 0
array.each do |n|
res += n
end
res
end
# Method to calculate which char appears how often
def histogram(source : String)
hist = {} of Char => Int32
l = 0
source.each_char do |e|
if !hist.has_key? e
hist[e] = 0
end
hist[e] += 1
end
return Tuple.new(source.size, hist)
end
# Method to calculate entropy from histogram
def entropy(hist : Hash(Char, Int32), l : Int32)
elist = [] of Float64
hist.each do |el|
v = el[1]
c = v / l
elist << (-c * Math.log(c, 2))
end
return sum elist
end
source = "1223334444"
hist_res = histogram source
l = hist_res[0]
h = hist_res[1]
puts ".[Results]."
puts "Length: " + l.to_s
puts "Entropy: " + (entropy h, l).to_s</syntaxhighlight>
=={{header|D}}==
<syntaxhighlight lang="d">import std.stdio, std.algorithm, std.math;
double entropy(T)(T[] s)
immutable sLen = s.length;
return s
.sort()
.group
.map!(g => g[1] /
.map!(p => -p *
.
}
void main() {
"1223334444"d.dup.entropy.writeln;
}</
{{out}}
=={{header|
{{libheader| StrUtils}}
{{libheader| Math}}
{{Trans|Pascal}}
Just fix Pascal code to run in Delphi.
<syntaxhighlight lang="delphi">
program Entropytest;
uses
StrUtils,
Math;
type
FArray = array of CARDINAL;
var
strng: string = '1223334444';
// list unique characters in a string
function uniquechars(str: string): string;
var
n: CARDINAL;
begin
Result := '';
for n := 1 to length(str) do
if (PosEx(str[n], str, n) > 0) and (PosEx(str[n], Result, 1) = 0) then
Result := Result + str[n];
end;
// obtain a list of character-frequencies for a string
// given a string containing its unique characters
function frequencies(str, ustr: string): FArray;
var
u, s, p, o: CARDINAL;
begin
SetLength(Result, Length(ustr) + 1);
p := 0;
for u := 1 to length(ustr) do
for s := 1 to length(str) do
begin
o := p;
p := PosEx(ustr[u], str, s);
if (p > o) then
INC(Result[u]);
end;
end;
// Obtain the Shannon entropy of a string
function entropy(s: string): EXTENDED;
var
pf: FArray;
us: string;
i, l: CARDINAL;
begin
us := uniquechars(s);
pf := frequencies(s, us);
l := length(s);
Result := 0.0;
for i := 1 to length(us) do
Result := Result - pf[i] / l * log2(pf[i] / l);
end;
begin
Writeln('Entropy of "', strng, '" is ', entropy(strng): 2: 5, ' bits.');
readln;
end.</syntaxhighlight>
=={{header|EasyLang}}==
<syntaxhighlight>
func entropy s$ .
len d[] 255
for c$ in strchars s$
d[strcode c$] += 1
.
for cnt in d[]
if cnt > 0
prop = cnt / len s$
entr -= (prop * log10 prop / log10 2)
.
.
return entr
.
print entropy "1223334444"
</syntaxhighlight>
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">
(lib 'hash)
;; counter: hash-table[key]++
(define (count++ ht k )
(hash-set ht k (1+ (hash-ref! ht k 0))))
(define (hi count n )
(define pi (// count n))
(- (* pi (log2 pi))))
;; (H [string|list]) → entropy (bits)
(define (H info)
(define S (if(string? info) (string->list info) info))
(define ht (make-hash))
(define n (length S))
(for ((s S)) (count++ ht s))
(for/sum ((s (make-set S))) (hi (hash-ref ht s) n)))
</syntaxhighlight>
{{out}}
<syntaxhighlight lang="scheme">
;; by increasing entropy
(H "🔴") → 0
(H "🔵🔴") → 1
(H "1223334444") → 1.8464393446710154
(H "♖♘♗♕♔♗♘♖♙♙♙♙♙♙♙♙♙") → 2.05632607578088
(H "EchoLisp") → 3
(H "Longtemps je me suis couché de bonne heure") → 3.860828877124944
(H "azertyuiopmlkjhgfdsqwxcvbn") → 4.700439718141092
(H (for/list ((i 1000)) (random 1000))) → 9.13772704467521
(H (for/list ((i 100_000)) (random 100_000))) → 15.777516877140766
(H (for/list ((i 1000_000)) (random 1000_000))) → 19.104028424596976
</syntaxhighlight>
=={{header|Elena}}==
{{trans|C#}}
ELENA 6.x :
<syntaxhighlight lang="elena">import system'math;
import system'collections;
import system'routines;
import extensions;
extension op
{
logTwo()
= self.ln() / 2.ln();
}
public program()
{
var input := console.readLine();
var infoC := 0.0r;
var table := Dictionary.new();
input.forEach::(ch)
{
var n := table[ch];
if (nil == n)
{
table[ch] := 1
}
else
{
table[ch] := n + 1
}
};
var freq := 0;
table.forEach::(letter)
{
freq := letter.toInt().realDiv(input.Length);
infoC += (freq * freq.logTwo())
};
infoC *= -1;
console.printLine("The Entropy of ", input, " is ", infoC)
}</syntaxhighlight>
{{out}}
<pre>
The Entropy of 1223334444 is 1.846439344671
</pre>
=={{header|Elixir}}==
{{works with|Erlang/OTP|18}}
<code>:math.log2</code> was added in OTP 18.
<syntaxhighlight lang="elixir">defmodule RC do
def entropy(str) do
leng = String.length(str)
String.graphemes(str)
|> Enum.group_by(&(&1))
|> Enum.map(fn{_,value} -> length(value) end)
|> Enum.reduce(0, fn count, entropy ->
freq = count / leng
entropy - freq * :math.log2(freq)
end)
end
end
IO.inspect RC.entropy("1223334444")</syntaxhighlight>
{{out}}
<pre>
1.8464393446710154
</pre>
=={{header|Emacs Lisp}}==
<syntaxhighlight lang="lisp">(defun shannon-entropy (input)
(let ((freq-table (make-hash-table))
(entropy 0)
(length (+ (length input) 0.0)))
(mapcar (lambda (x)
(puthash x
(+ 1 (gethash x freq-table 0))
freq-table))
input)
(maphash (lambda (k v)
(set 'entropy (+ entropy
(* (/ v length)
(log (/ v length) 2)))))
freq-table)
(- entropy)))</syntaxhighlight>
{{out}}
After adding the above to the emacs runtime, you can run
the function interactively in the scratch buffer
as shown below (type ctrl-j at the end of the first line
and the output will be placed by emacs on the second line).
<syntaxhighlight lang="lisp">(shannon-entropy "1223334444")
1.8464393446710154</syntaxhighlight>
=={{header|Erlang}}==
<syntaxhighlight lang="erlang">
-module( entropy ).
-export( [shannon/1, task/0] ).
shannon( String ) -> shannon_information_content( lists:foldl(fun count/2, dict:new(), String), erlang:length(String) ).
task() -> shannon( "1223334444" ).
count( Character, Dict ) -> dict:update_counter( Character, 1, Dict ).
shannon_information_content( Dict, String_length ) ->
{_String_length, Acc} = dict:fold( fun shannon_information_content/3, {String_length, 0.0}, Dict ),
Acc / math:log( 2 ).
shannon_information_content( _Character, How_many, {String_length, Acc} ) ->
Frequency = How_many / String_length,
{String_length, Acc - (Frequency * math:log(Frequency))}.
</syntaxhighlight>
{{out}}
<pre>
24> entropy:task().
1.8464393446710157
</pre>
=={{header|Euler Math Toolbox}}==
<syntaxhighlight lang="eulermathtoolbox">>function entropy (s) ...
$ v=strtochar(s);
$ m=getmultiplicities(unique(v),v);
$ m=m/sum(m);
$ return sum(-m*logbase(m,2))
$endfunction
>entropy("1223334444")
1.84643934467</syntaxhighlight>
=={{header|Excel}}==
This solution uses the <code>LAMBDA</code>, <code>LET</code>, and <code>MAP</code> functions introduced into the Microsoft 365 version of Excel in 2021. The <code>LET</code> function is able to use functions as first class citizens. Taking advantage of this makes the solution much simpler. The solution below looks for the string in cell <code>A1</code>.
<syntaxhighlight lang="excel">
=LET(
_MainS,A1,
_N,LEN(_MainS),
_Chars,UNIQUE(MID(_MainS,SEQUENCE(LEN(_MainS),1,1,1),1)),
calcH,LAMBDA(_c,(_c/_N)*LOG(_c/_N,2)),
getCount,LAMBDA(_i,LEN(_MainS)-LEN(SUBSTITUTE(_MainS,_i,""))),
_CharMap,MAP(_Chars,LAMBDA(a, calcH(getCount(a)))),
-SUM(_CharMap)
)
</syntaxhighlight>
_Chars uses the <code>SEQUENCE</code> function to split the text into an array. The <code>UNIQUE</code> function then returns a list of unique characters in the string.
<code>calcH</code> applies the calculation described at the top of the page that will then be summed for each character
<code>getCount</code> uses the <code>SUBSTITUTE</code> method to count the occurrences of a character within the string.
If you needed to re-use this calculation then you could wrap it in a <code>LAMBDA</code> function within the name manager, changing <code>A1</code> to a variable name (e.g. <code>String</code>):
<syntaxhighlight lang="excel">
ShannonEntropyH2=LAMBDA(String,LET(_MainS,String,_N,LEN(_MainS),_Chars,UNIQUE(MID(_MainS,SEQUENCE(LEN(_MainS),1,1,1),1)),calcH,LAMBDA(_c,(_c/_N)*LOG(_c/_N,2)),getCount,LAMBDA(_i,LEN(_MainS)-LEN(SUBSTITUTE(_MainS,_i,""))),_CharMap,MAP(_Chars,LAMBDA(a, calcH(getCount(a)))),-SUM(_CharMap)))
</syntaxhighlight>
Then you can just use the named lambda. E.g. If A1 = 1223334444 then:
<syntaxhighlight lang="excel">
=ShannonEntropyH2(A1)
</syntaxhighlight>
Returns 1.846439345
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">open System
let ld x = Math.Log x / Math.Log 2.
let entropy (s : string) =
let n = float s.Length
Seq.groupBy id s
|> Seq.map (fun (_, vals) -> float (Seq.length vals) / n)
|> Seq.fold (fun e p -> e - p * ld p) 0.
printfn "%f" (entropy "1223334444")</syntaxhighlight>
{{out}}
<pre>1.846439</pre>
=={{header|Factor}}==
<syntaxhighlight lang="factor">USING: assocs kernel math math.functions math.statistics
prettyprint sequences ;
IN: rosetta-code.entropy
: shannon-entropy ( str -- entropy )
[ length ] [ histogram >alist [ second ] map ] bi
[ swap / ] with map
[ dup log 2 log / * ] map-sum neg ;
"1223334444" shannon-entropy .
"Factor is my favorite programming language." shannon-entropy .</syntaxhighlight>
{{out}}
<pre>
1.846439344671015
4.04291723248433
</pre>
=={{header|Forth}}==
<syntaxhighlight lang="forth">: flog2 ( f -- f ) fln 2e fln f/ ;
create freq 256 cells allot
: entropy ( str len -- f )
freq 256 cells erase
tuck
bounds do
i c@ cells freq +
1 swap +!
loop
0e
256 0 do
i cells freq + @ ?dup if
s>f dup s>f f/
fdup flog2 f* f-
then
loop
drop ;
s" 1223334444" entropy f. \ 1.84643934467102 ok
</syntaxhighlight>
=={{header|Fortran}}==
Please find the GNU/linux compilation instructions along with sample run among the comments at the start of the FORTRAN 2008 source. This program acquires input from the command line argument, thereby demonstrating the fairly new get_command_argument intrinsic subroutine. The expression of the algorithm is a rough translated of the j solution. Thank you.
<syntaxhighlight lang="fortran">
!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Tue May 21 21:43:12
!
!a=./f && make $a && OMP_NUM_THREADS=2 $a 1223334444
!gfortran -std=f2008 -Wall -ffree-form -fall-intrinsics f.f08 -o f
! Shannon entropy of 1223334444 is 1.84643936
!
!Compilation finished at Tue May 21 21:43:12
program shannonEntropy
implicit none
integer :: num, L, status
character(len=2048) :: s
num = 1
call get_command_argument(num, s, L, status)
if ((0 /= status) .or. (L .eq. 0)) then
write(0,*)'Expected a command line argument with some length.'
else
write(6,*)'Shannon entropy of '//(s(1:L))//' is ', se(s(1:L))
endif
contains
! algebra
!
! 2**x = y
! x*log(2) = log(y)
! x = log(y)/log(2)
! NB. The j solution
! entropy=: +/@:-@(* 2&^.)@(#/.~ % #)
! entropy '1223334444'
!1.84644
real function se(s)
implicit none
character(len=*), intent(in) :: s
integer, dimension(256) :: tallies
real, dimension(256) :: norm
tallies = 0
call TallyKey(s, tallies)
! J's #/. works with the set of items in the input.
! TallyKey is sufficiently close that, with the merge, gets the correct result.
norm = tallies / real(len(s))
se = sum(-(norm*log(merge(1.0, norm, norm .eq. 0))/log(2.0)))
end function se
subroutine TallyKey(s, counts)
character(len=*), intent(in) :: s
integer, dimension(256), intent(out) :: counts
integer :: i, j
counts = 0
do i=1,len(s)
j = iachar(s(i:i))
counts(j) = counts(j) + 1
end do
end subroutine TallyKey
end program shannonEntropy
</syntaxhighlight>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">' version 25-06-2015
' compile with: fbc -s console
Sub calc_entropy(source As String, base_ As Integer)
Dim As Integer i, sourcelen = Len(source), totalchar(255)
Dim As Double prop, entropy
For i = 0 To sourcelen -1
totalchar(source[i]) += 1
Next
Print "Char count"
For i = 0 To 255
If totalchar(i) = 0 Then Continue For
Print " "; Chr(i); Using " ######"; totalchar(i)
prop = totalchar(i) / sourcelen
entropy = entropy - (prop * Log (prop) / Log(base_))
Next
Print : Print "The Entropy of "; Chr(34); source; Chr(34); " is"; entropy
End Sub
' ------=< MAIN >=------
calc_entropy("1223334444", 2)
Print
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}
<pre>Char count
1 1
2 2
3 3
4 4
The Entropy of "1223334444" is 1.846439344671015</pre>
=={{header|friendly interactive shell}}==
Sort of hacky, but friendly interactive shell isn't really optimized for mathematic tasks (in fact, it doesn't even have associative arrays).
<syntaxhighlight lang="fishshell">function entropy
for arg in $argv
set name count_$arg
if not count $$name > /dev/null
set $name 0
set values $values $arg
end
set $name (math $$name + 1)
end
set entropy 0
for value in $values
set name count_$value
set entropy (echo "
scale = 50
p = "$$name" / "(count $argv)"
$entropy - p * l(p)
" | bc -l)
end
echo "$entropy / l(2)" | bc -l
end
entropy (echo 1223334444 | fold -w1)</syntaxhighlight>
{{out}}
<pre>1.84643934467101549345</pre>
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Entropy}}
'''Solution'''
[[File:Fōrmulæ - Entropy 01.png]]
'''Test case'''
[[File:Fōrmulæ - Entropy 02.png]]
[[File:Fōrmulæ - Entropy 03.png]]
[[File:Fōrmulæ - Entropy 04.png]]
[[File:Fōrmulæ - Entropy 05.png]]
=={{header|Go}}==
===Go: Slice version===
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
"strings"
)
func main(){
fmt.Println(H("1223334444"))
}
// for ASCII strings
func H(data string) (entropy float64) {
if data == "" {
return 0
}
for i := 0; i < 256; i++ {
px := float64(strings.Count(data, string(byte(i)))) / float64(len(data))
if px > 0 {
entropy += -px * math.Log2(px)
}
}
return entropy
}</syntaxhighlight>
{{out}}
<pre>
1.8464393446710154
</pre>
===Go: Map version===
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
)
func main() {
const s = "1223334444"
l := float64(0)
m := map[rune]float64{}
for _, r := range s {
m[r]++
l++
}
var hm float64
for _, c := range m {
hm += c * math.Log2(c)
}
fmt.Println(math.Log2(l) - hm/l)
}</syntaxhighlight>
{{out}}
<pre>
1.8464393446710152
</pre>
=={{header|Groovy}}==
<syntaxhighlight lang="groovy">String.metaClass.getShannonEntrophy = {
-delegate.inject([:]) { map, v -> map[v] = (map[v] ?: 0) + 1; map }.values().inject(0.0) { sum, v ->
def p = (BigDecimal)v / delegate.size()
sum + p * Math.log(p) / Math.log(2)
}
}</syntaxhighlight>
Testing
<syntaxhighlight lang="groovy">[ '1223334444': '1.846439344671',
'1223334444555555555': '1.969811065121',
'122333': '1.459147917061',
'1227774444': '1.846439344671',
aaBBcccDDDD: '1.936260027482',
'1234567890abcdefghijklmnopqrstuvwxyz': '5.169925004424',
'Rosetta Code': '3.084962500407' ].each { s, expected ->
println "Checking $s has a shannon entrophy of $expected"
assert sprintf('%.12f', s.shannonEntrophy) == expected
}</syntaxhighlight>
{{out}}
<pre>Checking 1223334444 has a shannon entrophy of 1.846439344671
Checking 1223334444555555555 has a shannon entrophy of 1.969811065121
Checking 122333 has a shannon entrophy of 1.459147917061
Checking 1227774444 has a shannon entrophy of 1.846439344671
Checking aaBBcccDDDD has a shannon entrophy of 1.936260027482
Checking 1234567890abcdefghijklmnopqrstuvwxyz has a shannon entrophy of 5.169925004424
Checking Rosetta Code has a shannon entrophy of 3.084962500407</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Data.List
main = print $ entropy "1223334444"
entropy
where lg
fq
Or, inlining with an applicative expression (turns out to be fractionally faster):
<syntaxhighlight lang="haskell">import Data.List (genericLength, group, sort)
entropy
:: (Ord a, Floating c)
=> [a] -> c
entropy =
sum .
map (negate . ((*) <*> logBase 2)) .
(map =<< flip (/) . sum) . map genericLength . group . sort
main :: IO ()
main = print $ entropy "1223334444"</syntaxhighlight>
{{out}}
<pre>1.8464393446710154</pre>
=={{header|Icon}} and {{header|Unicon}}==
Hmmm, the 2nd equation sums across the length of the string (for the
example, that would be the sum of 10 terms). However, the answer cited
is for summing across the <i>different</i> characters in the string
(sum of 4 terms). The code shown here assumes the latter and works
in Icon and Unicon. This assumption is consistent with the Wikipedia
description.
<syntaxhighlight lang="unicon">procedure main(a)
s := !a | "1223334444"
write(H(s))
end
procedure H(s)
P := table(0.0)
every P[!s] +:= 1.0/*s
every (h := 0.0) -:= P[c := key(P)] * log(P[c],2)
return h
end</syntaxhighlight>
{{out}}
<pre>
->en
1.846439344671015
->
</pre>
=={{header|J}}==
'''Solution''':<
{{out|Example}}
<syntaxhighlight lang="j"> entropy '1223334444'
1.84644
entropy i.256
8
entropy 256$9
0
entropy 256$0 1
1
entropy 256$0 1 2 3
2</syntaxhighlight>
So it looks like entropy is roughly the number of bits which would be needed to ''distinguish between'' each item in the argument (for example, with perfect compression). Note that in some contexts this might not be the same thing as information because the choice of the items themselves might matter. But it's good enough in contexts with a fixed set of symbols.
=={{header|Java}}==
{{trans|NetRexx}}
{{trans|REXX}}
{{works with|Java|7+}}
<syntaxhighlight lang="java5">import java.lang.Math;
import java.util.Map;
import java.util.HashMap;
public class REntropy {
@SuppressWarnings("boxing")
public static double getShannonEntropy(String s) {
int n = 0;
Map<Character, Integer> occ = new HashMap<>();
for (int c_ = 0; c_ < s.length(); ++c_) {
char cx = s.charAt(c_);
if (occ.containsKey(cx)) {
occ.put(cx, occ.get(cx) + 1);
} else {
occ.put(cx, 1);
}
++n;
}
double e = 0.0;
for (Map.Entry<Character, Integer> entry : occ.entrySet()) {
char cx = entry.getKey();
double p = (double) entry.getValue() / n;
e += p * log2(p);
}
return -e;
}
private static double log2(double a) {
return Math.log(a) / Math.log(2);
}
public static void main(String[] args) {
String[] sstr = {
"1223334444",
"1223334444555555555",
"122333",
"1227774444",
"aaBBcccDDDD",
"1234567890abcdefghijklmnopqrstuvwxyz",
"Rosetta Code",
};
for (String ss : sstr) {
double entropy = REntropy.getShannonEntropy(ss);
System.out.printf("Shannon entropy of %40s: %.12f%n", "\"" + ss + "\"", entropy);
}
return;
}
}</syntaxhighlight>
{{out}}
<pre>
Shannon entropy of "1223334444": 1.846439344671
Shannon entropy of "1223334444555555555": 1.969811065278
Shannon entropy of "122333": 1.459147917027
Shannon entropy of "1227774444": 1.846439344671
Shannon entropy of "aaBBcccDDDD": 1.936260027532
Shannon entropy of "1234567890abcdefghijklmnopqrstuvwxyz": 5.169925001442
Shannon entropy of "Rosetta Code": 3.084962500721
</pre>
=={{header|JavaScript}}==
{{works with|ECMAScript 2015}}
Calculate the entropy of a string by determining the frequency of each character, then summing each character's probability multiplied by the log base 2 of that same probability, taking the negative of the sum.
<syntaxhighlight lang="javascript">// 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</syntaxhighlight>
{{out}}
<pre>1.8464393446710154
0
1
2
3
4</pre>
;Another variant
<syntaxhighlight lang="javascript">const entropy = (s) => {
const split = s.split('');
const counter = {};
split.forEach(ch => {
if (!counter[ch]) counter[ch] = 1;
else counter[ch]++;
});
const lengthf = s.length * 1.0;
const counts = Object.values(counter);
return -1 * counts
.map(count => count / lengthf * Math.log2(count / lengthf))
.reduce((a, b) => a + b);
};</syntaxhighlight>
{{out}}
<pre>console.log(entropy("1223334444")); // 1.8464393446710154</pre>
=={{header|jq}}==
For efficiency with long strings, we use a hash (a JSON object)
to compute the frequencies.
The helper function, ''counter'', could be defined as an inner function of ''entropy'', but for the sake of clarity and because it is independently useful,
it is defined separately.
<syntaxhighlight lang="jq"># Input: an array of strings.
# Output: an object with the strings as keys, the values of which are the corresponding frequencies.
def counter:
reduce .[] as $item ( {}; .[$item] += 1 ) ;
# entropy in bits of the input string
def entropy:
(explode | map( [.] | implode ) | counter
| [ .[] | . * log ] | add) as $sum
| ((length|log) - ($sum / length)) / (2|log) ;</syntaxhighlight>
{{out|Example}}
<syntaxhighlight lang="jq">"1223334444" | entropy # => 1.8464393446710154</syntaxhighlight>
=={{header|Jsish}}==
From Javascript entry.
<syntaxhighlight lang="javascript">/* Shannon entropy, in Jsish */
function values(obj:object):array {
var vals = [];
for (var key in obj) vals.push(obj[key]);
return vals;
}
function entropy(s) {
var split = s.split('');
var counter = {};
split.forEach(function(ch) {
if (!counter[ch]) counter[ch] = 1;
else counter[ch]++;
});
var lengthf = s.length * 1.0;
var counts = values(counter);
return -1 * counts.map(function(count) {
return count / lengthf * (Math.log(count / lengthf) / Math.log(2));
})
.reduce(function(a, b) { return a + b; }
);
};
if (Interp.conf('unitTest')) {
; entropy('1223334444');
; entropy('Rosetta Code');
; entropy('password');
}</syntaxhighlight>
{{out}}
<pre>prompt$ jsish --U entropy.jsi
entropy('1223334444') ==> 1.84643934467102
entropy('Rosetta Code') ==> 3.08496250072116
entropy('password') ==> 2.75</pre>
=={{header|Julia}}==
{{works with|Julia|0.6}}
<syntaxhighlight lang="julia">entropy(s) = -sum(x -> x * log(2, x), count(x -> x == c, s) / length(s) for c in unique(s))
@show entropy("1223334444")
@show entropy([1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 5])</syntaxhighlight>
{{out}}
<pre>entropy("1223334444") = 1.8464393446710154
entropy([1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 5]) = 2.103909910282364</pre>
=={{header|K}}==
{{works with|ngn/k}}
<syntaxhighlight lang="k">entropy: {(`ln[#x]-(+/{x*`ln@x}@+/{x=\:?x}x)%#x)%`ln@2}
entropy "1223334444"</syntaxhighlight>
{{out}}
<pre>1.8464393446710161</pre>
=={{header|Kotlin}}==
<syntaxhighlight lang="kotlin">// version 1.0.6
fun log2(d: Double) = Math.log(d) / Math.log(2.0)
fun shannon(s: String): Double {
val counters = mutableMapOf<Char, Int>()
for (c in s) {
if (counters.containsKey(c)) counters[c] = counters[c]!! + 1
else counters.put(c, 1)
}
val nn = s.length.toDouble()
var sum = 0.0
for (key in counters.keys) {
val term = counters[key]!! / nn
sum += term * log2(term)
}
return -sum
}
fun main(args: Array<String>) {
val samples = arrayOf(
"1223334444",
"1223334444555555555",
"122333",
"1227774444",
"aaBBcccDDDD",
"1234567890abcdefghijklmnopqrstuvwxyz",
"Rosetta Code"
)
println(" String Entropy")
println("------------------------------------ ------------------")
for (sample in samples) println("${sample.padEnd(36)} -> ${"%18.16f".format(shannon(sample))}")
}</syntaxhighlight>
{{out}}
<pre>
String Entropy
------------------------------------ ------------------
1223334444 -> 1.8464393446710154
1223334444555555555 -> 1.9698110652780971
122333 -> 1.4591479170272448
1227774444 -> 1.8464393446710154
aaBBcccDDDD -> 1.9362600275315274
1234567890abcdefghijklmnopqrstuvwxyz -> 5.1699250014423095
Rosetta Code -> 3.0849625007211556
</pre>
=={{header|Ksh}}==
{{works with|ksh93}}
<syntaxhighlight lang="ksh">function entropy {
typeset -i i len=${#1}
typeset -X13 r=0
typeset -Ai counts
for ((i = 0; i < len; ++i))
do
counts[${1:i:1}]+=1
done
for i in "${counts[@]}"
do
r+='i * log2(i)'
done
r='log2(len) - r / len'
print -r -- "$r"
}
printf '%g\n' "$(entropy '1223334444')"</syntaxhighlight>
{{out}}
<pre>1.84644</pre>
=={{header|Lambdatalk}}==
<syntaxhighlight lang="scheme">
{def entropy
{def entropy.count
{lambda {:s :c :i}
{let { {:c {/ {A.get :i :c} {A.length :s}}}
} {* :c {log2 :c}}}}}
{def entropy.sum
{lambda {:s :c}
{- {+ {S.map {entropy.count :s :c}
{S.serie 0 {- {A.length :c} 1}}}}}}}
{lambda {:s}
{entropy.sum {A.split :s} {cdr {W.frequency :s}}}}}
-> entropy
The W.frequency function is explained in rosettacode.org/wiki/Letter_frequency#Lambdatalk
{def txt 1223334444}
-> txt
{def F {W.frequency {txt}}}
-> F
characters: {car {F}} -> [1,2,3,4]
frequencies: {cdr {F}} -> [1,2,3,4]
{entropy {txt}}
-> 1.8464393446710154
{entropy 0}
-> 0
{entropy 00000000000000}
-> 0
{entropy 11111111111111}
-> 0
{entropy 01}
-> 1
{entropy Lambdatalk}
-> 2.8464393446710154
{entropy entropy}
-> 2.807354922057604
{entropy abcdefgh}
-> 3
{entropy Rosetta Code}
-> 3.084962500721156
{entropy Longtemps je me suis couché de bonne heure}
-> 3.8608288771249444
{entropy abcdefghijklmnopqrstuvwxyz}
-> 4.70043971814109
{entropy abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz}
-> 4.70043971814109
</syntaxhighlight>
=={{header|Lang5}}==
<syntaxhighlight lang="lang5">: -rot rot rot ; [] '__A set : dip swap __A swap 1 compress append '__A
set execute __A -1 extract nip ; : nip swap drop ; : sum '+ reduce ;
: 2array 2 compress ; : comb "" split ; : lensize length nip ;
: <group> #( a -- 'a )
grade subscript dup 's dress distinct strip
length 1 2array reshape swap
'A set
: `filter(*) A in A swap select ;
'`filter apply
;
: elements(*) lensize ;
: entropy #( s -- n )
length "<group> 'elements apply" dip /
dup neg swap log * 2 log / sum ;
"1223334444" comb entropy . # 1.84643934467102</syntaxhighlight>
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">
dim countOfChar( 255) ' all possible one-byte ASCII chars
source$ ="1223334444"
charCount =len( source$)
usedChar$ =""
for i =1 to len( source$) ' count which chars are used in source
ch$ =mid$( source$, i, 1)
if not( instr( usedChar$, ch$)) then usedChar$ =usedChar$ +ch$
'currentCh$ =mid$(
j =instr( usedChar$, ch$)
countOfChar( j) =countOfChar( j) +1
next i
l =len( usedChar$)
for i =1 to l
probability =countOfChar( i) /charCount
entropy =entropy -( probability *logBase( probability, 2))
next i
print " Characters used and the number of occurrences of each "
for i =1 to l
print " '"; mid$( usedChar$, i, 1); "'", countOfChar( i)
next i
print " Entropy of '"; source$; "' is "; entropy; " bits."
print " The result should be around 1.84644 bits."
end
function logBase( x, b) ' in LB log() is base 'e'.
logBase =log( x) /log( 2)
end function
</syntaxhighlight>
{{Out}}
<pre> Characters used and the number of occurrences of each
'1' 1
'2' 2
'3' 3
'4' 4
Entropy of '1223334444' is 1.84643934 bits.
The result should be around 1.84644 bits.</pre>
=={{header|Lua}}==
<syntaxhighlight lang="lua">function log2 (x) return math.log(x) / math.log(2) end
function entropy (X)
local N, count, sum, i = X:len(), {}, 0
for char = 1, N do
i = X:sub(char, char)
if count[i] then
count[i] = count[i] + 1
else
count[i] = 1
end
end
for n_i, count_i in pairs(count) do
sum = sum + count_i / N * log2(count_i / N)
end
return -sum
end
print(entropy("1223334444"))</syntaxhighlight>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">shE[s_String] := -Plus @@ ((# Log[2., #]) & /@ ((Length /@ Gather[#])/
Length[#]) &[Characters[s]])</syntaxhighlight>
{{out|Example}}<syntaxhighlight lang="mathematica"> shE["1223334444"]
1.84644
shE["Rosetta Code"]
3.08496</syntaxhighlight>
=={{header|MATLAB}} / {{header|Octave}}==
This version allows for any input vectors,
including strings, floats, negative integers, etc.
<syntaxhighlight lang="matlab">function E = entropy(d)
if ischar(d), d=abs(d); end;
[Y,I,J] = unique(d);
H = sparse(J,1,1);
p = full(H(H>0))/length(d);
E = -sum(p.*log2(p));
end; </syntaxhighlight>
{{out|Usage}}
<syntaxhighlight lang="matlab">> entropy('1223334444')
ans = 1.8464</syntaxhighlight>
=={{header|MiniScript}}==
<syntaxhighlight lang="miniscript">entropy = function(s)
count = {}
for c in s
if count.hasIndex(c) then count[c] = count[c]+1 else count[c] = 1
end for
sum = 0
for x in count.values
countOverN = x / s.len
sum = sum + countOverN * log(countOverN, 2)
end for
return -sum
end function
print entropy("1223334444")</syntaxhighlight>
{{out}}
<pre>1.846439</pre>
=={{header|Modula-2}}==
<syntaxhighlight lang="modula2">MODULE Entropy;
FROM InOut IMPORT WriteString, WriteLn;
FROM RealInOut IMPORT WriteReal;
FROM Strings IMPORT Length;
FROM MathLib IMPORT ln;
PROCEDURE entropy(s: ARRAY OF CHAR): REAL;
VAR freq: ARRAY [0..255] OF CARDINAL;
i, length: CARDINAL;
h, f: REAL;
BEGIN
(* the entropy of the empty string is zero *)
length := Length(s);
IF length = 0 THEN RETURN 0.0; END;
(* find the frequency of each character *)
FOR i := 0 TO 255 DO freq[i] := 0; END;
FOR i := 0 TO length-1 DO
INC(freq[ORD(s[i])]);
END;
(* calculate the component for each character *)
h := 0.0;
FOR i := 0 TO 255 DO
IF freq[i] # 0 THEN
f := FLOAT(freq[i]) / FLOAT(length);
h := h - f * (ln(f) / ln(2.0));
END;
END;
RETURN h;
END entropy;
BEGIN
WriteReal(entropy("1223334444"), 14);
WriteLn;
END Entropy.</syntaxhighlight>
{{out}}
<pre> 1.8464394E+00</pre>
=={{header|NetRexx}}==
{{trans|REXX}}
<syntaxhighlight lang="netrexx">/* NetRexx */
options replace format comments java crossref savelog symbols
runSample(Arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/* REXX ***************************************************************
* 28.02.2013 Walter Pachl
**********************************************************************/
method getShannonEntropy(s = "1223334444") public static
--trace var occ c chars n cn i e p pl
Numeric Digits 30
occ = 0
chars = ''
n = 0
cn = 0
Loop i = 1 To s.length()
c = s.substr(i, 1)
If chars.pos(c) = 0 Then Do
cn = cn + 1
chars = chars || c
End
occ[c] = occ[c] + 1
n = n + 1
End i
p = ''
Loop ci = 1 To cn
c = chars.substr(ci, 1)
p[c] = occ[c] / n
End ci
e = 0
Loop ci = 1 To cn
c = chars.substr(ci, 1)
pl = log2(p[c])
e = e + p[c] * pl
End ci
Return -e
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method log2(a = double) public static binary returns double
return Math.log(a) / Math.log(2)
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(Arg) public static
parse Arg sstr
if sstr = '' then
sstr = '1223334444' -
'1223334444555555555' -
'122333' -
'1227774444' -
'aaBBcccDDDD' -
'1234567890abcdefghijklmnopqrstuvwxyz' -
'Rosetta_Code'
say 'Calculating Shannon''s entropy for the following list:'
say '['(sstr.space(1, ',')).changestr(',', ', ')']'
say
entropies = 0
ssMax = 0
-- This crude sample substitutes a '_' character for a space in the input strings
loop w_ = 1 to sstr.words()
ss = sstr.word(w_)
ssMax = ssMax.max(ss.length())
ss_ = ss.changestr('_', ' ')
entropy = getShannonEntropy(ss_)
entropies[ss] = entropy
end w_
loop report = 1 to sstr.words()
ss = sstr.word(report)
ss_ = ss.changestr('_', ' ')
Say 'Shannon entropy of' ('"'ss_'"').right(ssMax + 2)':' entropies[ss].format(null, 12)
end report
return
</syntaxhighlight>
{{out}}
<pre>
Calculating Shannon's entropy for the following list:
[1223334444, 1223334444555555555, 122333, 1227774444, aaBBcccDDDD, 1234567890abcdefghijklmnopqrstuvwxyz, Rosetta_Code]
Shannon entropy of "1223334444": 1.846439344671
Shannon entropy of "1223334444555555555": 1.969811065278
Shannon entropy of "122333": 1.459147917027
Shannon entropy of "1227774444": 1.846439344671
Shannon entropy of "aaBBcccDDDD": 1.936260027532
Shannon entropy of "1234567890abcdefghijklmnopqrstuvwxyz": 5.169925001442
Shannon entropy of "Rosetta Code": 3.084962500721
</pre>
=={{header|Nim}}==
<syntaxhighlight lang="nim">import tables, math
proc entropy(s: string): float =
var t = initCountTable[char]()
for c in s: t.inc(c)
for x in t.values: result -= x/s.len * log2(x/s.len)
echo entropy("1223334444")</syntaxhighlight>
=={{header|Objeck}}==
<syntaxhighlight lang="objeck">use Collection;
class Entropy {
function : native : GetShannonEntropy(result : String) ~ Float {
frequencies := IntMap->New();
each(i : result) {
c := result->Get(i);
if(frequencies->Has(c)) {
count := frequencies->Find(c)->As(IntHolder);
count->Set(count->Get() + 1);
}
else {
frequencies->Insert(c, IntHolder->New(1));
};
};
length := result->Size();
entropy := 0.0;
counts := frequencies->GetValues();
each(i : counts) {
count := counts->Get(i)->As(IntHolder)->Get();
freq := count->As(Float) / length;
entropy += freq * (freq->Log() / 2.0->Log());
};
return -1 * entropy;
}
function : Main(args : String[]) ~ Nil {
inputs := [
"1223334444",
"1223334444555555555",
"122333",
"1227774444",
"aaBBcccDDDD",
"1234567890abcdefghijklmnopqrstuvwxyz",
"Rosetta Code"];
each(i : inputs) {
input := inputs[i];
"Shannon entropy of '{$input}': "->Print();
GetShannonEntropy(inputs[i])->PrintLine();
};
}
}</syntaxhighlight>
Output:
<pre>
Shannon entropy of '1223334444': 1.84644
Shannon entropy of '1223334444555555555': 1.96981
Shannon entropy of '122333': 1.45915
Shannon entropy of '1227774444': 1.84644
Shannon entropy of 'aaBBcccDDDD': 1.93626
Shannon entropy of '1234567890abcdefghijklmnopqrstuvwxyz': 5.16993
Shannon entropy of 'Rosetta Code': 3.08496
</pre>
=={{header|OCaml}}==
;By using a map, purely functional
<syntaxhighlight lang="ocaml">module CharMap = Map.Make(Char)
let entropy s =
let count map c =
CharMap.update c (function Some n -> Some (n +. 1.) | None -> Some 1.) map
and calc _ n sum =
sum +. n *. Float.log2 n
in
let sum = CharMap.fold calc (String.fold_left count CharMap.empty s) 0.
and len = float (String.length s) in
Float.log2 len -. sum /. len
let () =
entropy "1223334444" |> string_of_float |> print_endline</syntaxhighlight>
;By using a mutable Hashtbl
<syntaxhighlight lang="ocaml">
(* pre-bake & return an inner-loop function to bin & assemble a character frequency map *)
let get_fproc (m: (char, int) Hashtbl.t) :(char -> unit) =
(fun (c:char) -> try
Hashtbl.replace m c ( (Hashtbl.find m c) + 1)
with Not_found -> Hashtbl.add m c 1)
(* pre-bake and return an inner-loop function to do the actual entropy calculation *)
let get_calc (slen:int) :(float -> float) =
let slen_float = float_of_int slen in
let log_2 = log 2.0 in
(fun v -> let pt = v /. slen_float in
pt *. ((log pt) /. log_2) )
(* main function, given a string argument it:
builds a (mutable) frequency map (initial alphabet size of 255, but it's auto-expanding),
extracts the relative probability values into a list,
folds-in the basic entropy calculation and returns the result. *)
let shannon (s:string) :float =
let freq_hash = Hashtbl.create 255 in
String.iter (get_fproc freq_hash) s;
let relative_probs = Hashtbl.fold (fun k v b -> (float v)::b) freq_hash [] in
let calc = get_calc (String.length s) in
-1.0 *. List.fold_left (fun b x -> b +. calc x) 0.0 relative_probs
</syntaxhighlight>
{{out}}
<pre>1.84643934467</pre>
=={{header|Oforth}}==
<syntaxhighlight lang="oforth">: entropy(s) -- f
| freq sz |
s size dup ifZero: [ return ] asFloat ->sz
ListBuffer initValue(255, 0) ->freq
s apply( #[ dup freq at 1+ freq put ] )
0.0 freq applyIf( #[ 0 <> ], #[ sz / dup ln * - ] ) Ln2 / ;
entropy("1223334444") .</syntaxhighlight>
{{out}}
<pre>1.84643934467102</pre>
=={{header|ooRexx}}==
{{trans|REXX}}
<syntaxhighlight lang="oorexx">/* REXX */
Numeric Digits 16
Parse Arg s
If s='' Then
s="1223334444"
occ.=0
chars=''
n=0
cn=0
Do i=1 To length(s)
c=substr(s,i,1)
If pos(c,chars)=0 Then Do
cn=cn+1
chars=chars||c
End
occ.c=occ.c+1
n=n+1
End
do ci=1 To cn
c=substr(chars,ci,1)
p.c=occ.c/n
/* say c p.c */
End
e=0
Do ci=1 To cn
c=substr(chars,ci,1)
e=e+p.c*rxcalclog(p.c)/rxcalclog(2)
End
Say s 'Entropy' format(-e,,12)
Exit
::requires 'rxmath' LIBRARY </syntaxhighlight>
{{out}}
<pre>1223334444 Entropy 1.846439344671</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">entropy(s)=s=Vec(s);my(v=vecsort(s,,8));-sum(i=1,#v,(x->x*log(x))(sum(j=1,#s,v[i]==s[j])/#s))/log(2)</syntaxhighlight>
<pre>>entropy("1223334444")
%1 = 1.8464393446710154934341977463050452232</pre>
=={{header|Pascal}}==
Free Pascal (http://freepascal.org).
<syntaxhighlight lang="pascal">
PROGRAM entropytest;
USES StrUtils, Math;
TYPE FArray = ARRAY of CARDINAL;
VAR strng: STRING = '1223334444';
// list unique characters in a string
FUNCTION uniquechars(str: STRING): STRING;
VAR n: CARDINAL;
BEGIN
uniquechars := '';
FOR n := 1 TO length(str) DO
IF (PosEx(str[n],str,n)>0)
AND (PosEx(str[n],uniquechars,1)=0)
THEN uniquechars += str[n];
END;
// obtain a list of character-frequencies for a string
// given a string containing its unique characters
FUNCTION frequencies(str,ustr: STRING): FArray;
VAR u,s,p,o: CARDINAL;
BEGIN
SetLength(frequencies, Length(ustr)+1);
p := 0;
FOR u := 1 TO length(ustr) DO
FOR s := 1 TO length(str) DO BEGIN
o := p; p := PosEx(ustr[u],str,s);
IF (p>o) THEN INC(frequencies[u]);
END;
END;
// Obtain the Shannon entropy of a string
FUNCTION entropy(s: STRING): EXTENDED;
VAR pf : FArray;
us : STRING;
i,l: CARDINAL;
BEGIN
us := uniquechars(s);
pf := frequencies(s,us);
l := length(s);
entropy := 0.0;
FOR i := 1 TO length(us) DO
entropy -= pf[i]/l * log2(pf[i]/l);
END;
BEGIN
Writeln('Entropy of "',strng,'" is ',entropy(strng):2:5, ' bits.');
END.
</syntaxhighlight>
{{out}}
<pre>
Entropy of "1223334444" is 1.84644 bits.
</pre>
=={{header|Perl}}==
<syntaxhighlight lang="perl">sub entropy {
my %count; $count{$_}++ for @_;
my $entropy = 0;
for (values %count) {
my $p = $_/@_;
$entropy -= $p * log $p;
}
$entropy / log 2
}
print entropy split //, "1223334444";</syntaxhighlight>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">entropy</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">symbols</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">si</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">,</span><span style="color: #000000;">symbols</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">symbols</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">symbols</span><span style="color: #0000FF;">,</span><span style="color: #000000;">si</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">H</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">N</span>
<span style="color: #000000;">H</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">ci</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">log2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ci</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">H</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">entropy</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1223334444"</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
1.846439345
</pre>
=={{header|
<syntaxhighlight lang="php"><?php
function shannonEntropy($string) {
$h = 0.0;
$len = strlen($string);
foreach (count_chars($string, 1) as $count) {
$h -= (double) ($count / $len) * log((double) ($count / $len), 2);
}
return $h;
}
$strings = array(
'1223334444',
'1225554444',
'aaBBcccDDDD',
'122333444455555',
'Rosetta Code',
'1234567890abcdefghijklmnopqrstuvwxyz',
);
foreach ($strings AS $string) {
printf(
'%36s : %s' . PHP_EOL,
$string,
number_format(shannonEntropy($string), 6)
);
}</syntaxhighlight>
{{out}}
<pre> 1223334444 : 1.846439
1225554444 : 1.846439
aaBBcccDDDD : 1.936260
122333444455555 : 2.149255
Rosetta Code : 3.084963
1234567890abcdefghijklmnopqrstuvwxyz : 5.169925</pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">go =>
["1223334444",
"Rosetta Code is the best site in the world!",
"1234567890abcdefghijklmnopqrstuvwxyz",
"Picat is fun"].map(entropy).println(),
nl.
% probabilities of each element/character in L
entropy(L) = Entropy =>
Len = L.length,
Occ = new_map(), % # of occurrences
foreach(E in L)
Occ.put(E, Occ.get(E,0) + 1)
end,
Entropy = -sum([P2*log2(P2) : _C=P in Occ, P2 = P/Len]).</syntaxhighlight>
{{out}}
<pre>[1.846439344671016,3.646513010214172,5.169925001442309,3.251629167387823]</pre>
=={{header|PicoLisp}}==
PicoLisp only supports fixed point arithmetic, but it does have the ability to call libc transcendental functions (for log)
<syntaxhighlight lang="picolisp">
(scl 8)
(load "@lib/math.l")
(setq LN2 0.693147180559945309417)
(de tabulate-chars (Str)
(let Map NIL
(for Ch (chop Str)
(if (assoc Ch Map)
(con @ (inc (cdr @)))
(setq Map (cons (cons Ch 1) Map))))
Map))
(de entropy (Str)
(let (
Sz (length Str)
Hist (tabulate-chars Str)
)
(*/
(sum
'((Pair)
(let R (*/ (cdr Pair) 1. Sz)
(- (*/ R (log R) 1.))))
Hist)
1. LN2)))
</syntaxhighlight>
{{Out}}
<pre>
: (format (entropy "1223334444") *Scl)
-> "1.84643934"
</pre>
=={{header|PL/I}}==
<syntaxhighlight lang="pli">*process source xref attributes or(!);
/*--------------------------------------------------------------------
* 08.08.2014 Walter Pachl translated from REXX version 1
*-------------------------------------------------------------------*/
ent: Proc Options(main);
Dcl (index,length,log2,substr) Builtin;
Dcl sysprint Print;
Dcl occ(100) Bin fixed(31) Init((100)0);
Dcl (n,cn,ci,i,pos) Bin fixed(31) Init(0);
Dcl chars Char(100) Var Init('');
Dcl s Char(100) Var Init('1223334444');
Dcl c Char(1);
Dcl (occf,p(100)) Dec Float(18);
Dcl e Dec Float(18) Init(0);
Do i=1 To length(s);
c=substr(s,i,1);
pos=index(chars,c);
If pos=0 Then Do;
pos=length(chars)+1;
cn+=1;
chars=chars!!c;
End;
occ(pos)+=1;
n+=1;
End;
do ci=1 To cn;
occf=occ(ci);
p(ci)=occf/n;
End;
Do ci=1 To cn;
e=e+p(ci)*log2(p(ci));
End;
Put Edit('s='''!!s!!''' Entropy=',-e)(Skip,a,f(15,12));
End;</syntaxhighlight>
{{out}}
<pre>s='1223334444' Entropy= 1.846439344671</pre>
=={{header|PowerShell}}==
<syntaxhighlight lang="powershell">
function entropy ($string) {
$n = $string.Length
$string.ToCharArray() | group | foreach{
$p = $_.Count/$n
$i = [Math]::Log($p,2)
-$p*$i
} | measure -Sum | foreach Sum
}
entropy "1223334444"
</syntaxhighlight>
<b>Output:</b>
<pre>
1.84643934467102
</pre>
=={{header|Prolog}}==
{{works with|Swi-Prolog|7.3.3}}
This solution calculates the run-length encoding of the input string to get the relative frequencies of its characters.
<syntaxhighlight lang="prolog">:-module(shannon_entropy, [shannon_entropy/2]).
%! shannon_entropy(+String, -Entropy) is det.
%
% Calculate the Shannon Entropy of String.
%
% Example query:
% ==
% ?- shannon_entropy(1223334444, H).
% H = 1.8464393446710154.
% ==
%
shannon_entropy(String, Entropy):-
atom_chars(String, Cs)
,relative_frequencies(Cs, Frequencies)
,findall(CI
,(member(_C-F, Frequencies)
,log2(F, L)
,CI is F * L
)
,CIs)
,foldl(sum, CIs, 0, E)
,Entropy is -E.
%! frequencies(+Characters,-Frequencies) is det.
%
% Calculates the relative frequencies of elements in the list of
% Characters.
%
% Frequencies is a key-value list with elements of the form:
% C-F, where C a character in the list and F its relative
% frequency in the list.
%
% Example query:
% ==
% ?- relative_frequencies([a,a,a,b,b,b,b,b,b,c,c,c,a,a,f], Fs).
% Fs = [a-0.3333333333333333, b-0.4, c-0.2,f-0.06666666666666667].
% ==
%
relative_frequencies(List, Frequencies):-
run_length_encoding(List, Rle)
% Sort Run-length encoded list and aggregate lengths by element
,keysort(Rle, Sorted_Rle)
,group_pairs_by_key(Sorted_Rle, Elements_Run_lengths)
,length(List, Elements_in_list)
,findall(E-Frequency_of_E
,(member(E-RLs, Elements_Run_lengths)
% Sum the list of lengths of runs of E
,foldl(plus, RLs, 0, Occurences_of_E)
,Frequency_of_E is Occurences_of_E / Elements_in_list
)
,Frequencies).
%! run_length_encoding(+List, -Run_length_encoding) is det.
%
% Converts a list to its run-length encoded form where each "run"
% of contiguous repeats of the same element is replaced by that
% element and the length of the run.
%
% Run_length_encoding is a key-value list, where each element is a
% term:
%
% Element:term-Repetitions:number.
%
% Example query:
% ==
% ?- run_length_encoding([a,a,a,b,b,b,b,b,b,c,c,c,a,a,f], RLE).
% RLE = [a-3, b-6, c-3, a-2, f-1].
% ==
%
run_length_encoding([], []-0):-
!. % No more results needed.
run_length_encoding([Head|List], Run_length_encoded_list):-
run_length_encoding(List, [Head-1], Reversed_list)
% The resulting list is in reverse order due to the head-to-tail processing
,reverse(Reversed_list, Run_length_encoded_list).
%! run_length_encoding(+List,+Initialiser,-Accumulator) is det.
%
% Business end of run_length_encoding/3. Calculates the run-length
% encoded form of a list and binds the result to the Accumulator.
% Initialiser is a list [H-1] where H is the first element of the
% input list.
%
run_length_encoding([], Fs, Fs).
% Run of F consecutive occurrences of C
run_length_encoding([C|Cs],[C-F|Fs], Acc):-
% Backtracking would produce successive counts
% of runs of C at different indices in the list.
!
,F_ is F + 1
,run_length_encoding(Cs, [C-F_| Fs], Acc).
% End of a run of consecutive identical elements.
run_length_encoding([C|Cs], Fs, Acc):-
run_length_encoding(Cs,[C-1|Fs], Acc).
/* Arithmetic helper predicates */
%! log2(N, L2_N) is det.
%
% L2_N is the logarithm with base 2 of N.
%
log2(N, L2_N):-
L_10 is log10(N)
,L_2 is log10(2)
,L2_N is L_10 / L_2.
%! sum(+A,+B,?Sum) is det.
%
% True when Sum is the sum of numbers A and B.
%
% Helper predicate to allow foldl/4 to do addition. The following
% call will raise an error (because there is no predicate +/3):
% ==
% foldl(+, [1,2,3], 0, Result).
% ==
%
% This will not raise an error:
% ==
% foldl(sum, [1,2,3], 0, Result).
% ==
%
sum(A, B, Sum):-
must_be(number, A)
,must_be(number, B)
,Sum is A + B.
</syntaxhighlight>
Example query:
<pre>
?- shannon_entropy(1223334444, H).
H = 1.8464393446710154.
</pre>
=={{header|PureBasic}}==
<syntaxhighlight lang="purebasic">#TESTSTR="1223334444"
NewMap uchar.i() : Define.d e
Procedure.d nlog2(x.d) : ProcedureReturn Log(x)/Log(2) : EndProcedure
Procedure countchar(s$, Map uchar())
If Len(s$)
uchar(Left(s$,1))=CountString(s$,Left(s$,1))
s$=RemoveString(s$,Left(s$,1))
ProcedureReturn countchar(s$, uchar())
EndIf
EndProcedure
countchar(#TESTSTR,uchar())
ForEach uchar()
e-uchar()/Len(#TESTSTR)*nlog2(uchar()/Len(#TESTSTR))
Next
OpenConsole()
Print("Entropy of ["+#TESTSTR+"] = "+StrD(e,15))
Input()</syntaxhighlight>
{{out}}
<pre>Entropy of [1223334444] = 1.846439344671015</pre>
=={{header|Python}}==
===Python: Longer version===
<syntaxhighlight lang="python">from __future__ import division
import math
def hist(source):
hist = {}; l = 0;
for e in source:
l += 1
if e not in hist:
hist[e] = 0
hist[e] += 1
return (l,hist)
def entropy(hist,l):
elist = []
for v in hist.values():
c = v / l
elist.append(-c * math.log(c ,2))
return sum(elist)
def printHist(h):
flip = lambda (k,v) : (v,k)
h = sorted(h.iteritems(), key = flip)
print 'Sym\thi\tfi\tInf'
for (k,v) in h:
print '%s\t%f\t%f\t%f'%(k,v,v/l,-math.log(v/l, 2))
source = "1223334444"
(l,h) = hist(source);
print '.[Results].'
print 'Length',l
print 'Entropy:', entropy(h, l)
printHist(h)</syntaxhighlight>
{{out}}
<pre>
.[Results].
Length 10
Entropy: 1.84643934467
Sym hi fi Inf
1 1.000000 0.100000 3.321928
2 2.000000 0.200000 2.321928
3 3.000000 0.300000 1.736966
4 4.000000 0.400000 1.321928
</pre>
===Python: More succinct version===
The <tt>Counter</tt> module is only available in Python >= 2.7.
<syntaxhighlight lang="python">from math import log2
from collections import Counter
def entropy(s):
p, lns = Counter(s), float(len(s))
return log2(lns) - sum(count * log2(count) for count in p.values()) / lns
print(entropy("1223334444"))</syntaxhighlight>
{{out}}
<pre>1.8464393446710154</pre>
===Uses Python 2===
<syntaxhighlight lang="python">def Entropy(text):
import math
log2=lambda x:math.log(x)/math.log(2)
exr={}
infoc=0
for each in text:
try:
exr[each]+=1
except:
exr[each]=1
textlen=len(text)
for k,v in exr.items():
freq = 1.0*v/textlen
infoc+=freq*log2(freq)
infoc*=-1
return infoc
while True:
print Entropy(raw_input('>>>'))</syntaxhighlight>
=={{header|R}}==
<syntaxhighlight lang="rsplus">
entropy <- function(str) {
vec <- strsplit(str, "")[[1]]
N <- length(vec)
p_xi <- table(vec) / N
-sum(p_xi * log(p_xi, 2))
}
</syntaxhighlight>
{{out}}
<pre>
> entropy("1223334444")
[1] 1.846439
</pre>
=={{header|Racket}}==
<syntaxhighlight lang="racket">#lang racket
(require math)
(provide entropy hash-entropy list-entropy digital-entropy)
(define (hash-entropy h)
(define (log2 x) (/ (log x) (log 2)))
(define n (for/sum [(c (in-hash-values h))] c))
(- (for/sum ([c (in-hash-values h)] #:unless (zero? c))
(* (/ c n) (log2 (/ c n))))))
(define (list-entropy x) (hash-entropy (samples->hash x)))
(define entropy (compose list-entropy string->list))
(define digital-entropy (compose entropy number->string))
(module+ test
(require rackunit)
(check-= (entropy "1223334444") 1.8464393446710154 1E-8)
(check-= (digital-entropy 1223334444) (entropy "1223334444") 1E-8)
(check-= (digital-entropy 1223334444) 1.8464393446710154 1E-8)
(check-= (entropy "xggooopppp") 1.8464393446710154 1E-8))
(module+ main (entropy "1223334444"))</syntaxhighlight>
{{out}}
<pre> 1.8464393446710154</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|rakudo|2015-09-09}}
<syntaxhighlight lang="raku" line>sub entropy(@a) {
[+] map -> \p { p * -log p }, bag(@a).values »/» +@a;
}
say log(2) R/ entropy '1223334444'.comb;</syntaxhighlight>
{{out}}
<pre>1.84643934467102</pre>
In case we would like to add this function to Raku's core, here is one way it could be done:
<syntaxhighlight lang="raku" line>use MONKEY-TYPING;
augment class Bag {
method entropy {
[+] map -> \p { - p * log p },
self.values »/» +self;
}
}
say '1223334444'.comb.Bag.entropy / log 2;</syntaxhighlight>
=={{header|REXX}}==
===version 1===
<syntaxhighlight lang="rexx">/* REXX ***************************************************************
* 28.02.2013 Walter Pachl
* 12.03.2013 Walter Pachl typo in log corrected. thanx for testing
* 22.05.2013 -"- extended the logic to accept other strings
* 25.05.2013 -"- 'my' log routine is apparently incorrect
* 25.05.2013 -"- problem identified & corrected
**********************************************************************/
Numeric Digits 30
Parse Arg s
If s='' Then
s="1223334444"
occ.=0
chars=''
n=0
cn=0
Do i=1 To length(s)
c=substr(s,i,1)
If pos(c,chars)=0 Then Do
cn=cn+1
chars=chars||c
End
occ.c=occ.c+1
n=n+1
End
do ci=1 To cn
c=substr(chars,ci,1)
p.c=occ.c/n
/* say c p.c */
End
e=0
Do ci=1 To cn
c=substr(chars,ci,1)
e=e+p.c*log(p.c,30,2)
End
Say 'Version 1:' s 'Entropy' format(-e,,12)
Exit
log: Procedure
/***********************************************************************
* Return log(x) -- with specified precision and a specified base
* Three different series are used for the ranges 0 to 0.5
* 0.5 to 1.5
* 1.5 to infinity
* 03.09.1992 Walter Pachl
* 25.05.2013 -"- 'my' log routine is apparently incorrect
* 25.05.2013 -"- problem identified & corrected
***********************************************************************/
Parse Arg x,prec,b
If prec='' Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz 3
Select
When x<=0 Then r='*** invalid argument ***'
When x<0.5 Then Do
z=(x-1)/(x+1)
o=z
r=z
k=1
Do i=3 By 2
ra=r
k=k+1
o=o*z*z
r=r+o/i
If r=ra Then Leave
End
r=2*r
End
When x<1.5 Then Do
z=(x-1)
o=z
r=z
k=1
Do i=2 By 1
ra=r
k=k+1
o=-o*z
r=r+o/i
If r=ra Then Leave
End
End
Otherwise /* 1.5<=x */ Do
z=(x+1)/(x-1)
o=1/z
r=o
k=1
Do i=3 By 2
ra=r
k=k+1
o=o/(z*z)
r=r+o/i
If r=ra Then Leave
End
r=2*r
End
End
If b<>'' Then
r=r/log(b,prec)
Numeric Digits (prec)
r=r+0
Return r </syntaxhighlight>
<!-- these types of comparisons are not part of this Rosetta Code task, and
since the results are identical, why post them?
<syntaxhighlight lang="rexx">/* REXX ***************************************************************
* Test program to compare Versions 1 and 2
* (the latter tweaked to be acceptable by my (oo)Rexx
* and to give the same output.)
* version 1 was extended to accept the strings of the incorrect flag
* 22.05.2013 Walter Pachl (I won't analyze the minor differences)
* 25.05.2013 I did now analyze and had to discover that
* 'my' log routine is apparently incorrect
* 25.05.2013 problem identified & corrected
*********************************************************************/
Call both '1223334444'
Call both '1223334444555555555'
Call both '122333'
Call both '1227774444'
Call both 'aaBBcccDDDD'
Call both '1234567890abcdefghijklmnopqrstuvwxyz'
Exit
both:
Parse Arg s
Call entropy s
Call entropy2 s
Say ' '
Return
</syntaxhighlight>
{{out}}
<pre>Version 1: 1223334444 Entropy 1.846439344671
Version 2: 1223334444 Entropy 1.846439344671
Version 1: 1223334444555555555 Entropy 1.969811065278
Version 2: 1223334444555555555 Entropy 1.969811065278
Version 1: 122333 Entropy 1.459147917027
Version 2: 122333 Entropy 1.459147917027
Version 1: 1227774444 Entropy 1.846439344671
Version 2: 1227774444 Entropy 1.846439344671
Version 1: 1234567890abcdefghijklmnopqrstuvwxyz Entropy 5.169925001442
Version 2: 1234567890abcdefghijklmnopqrstuvwxyz Entropy 5.169925001442</pre> !-->
===version 2===
REXX doesn't have a BIF for '''LOG''' or '''LN''', so the subroutine (function) '''LOG2''' is included herein.
The '''LOG2''' subroutine is only included here for functionality, not to document how to calculate LOG<sub>2</sub> using REXX.
<syntaxhighlight lang="rexx">/*REXX program calculates the information entropy for a specified character string. */
numeric digits length( e() ) % 2 - length(.) /*use 1/2 of the decimal digits of E. */
parse arg $; if $='' then $= 1223334444 /*obtain the optional input from the CL*/
#=0; @.= 0; L= length($) /*define handy-dandy REXX variables. */
$$= /*initialize the $$ list. */
do j=1 for L; _= substr($, j, 1) /*process each character in $ string.*/
if @._==0 then do; #= # + 1 /*Unique? Yes, bump character counter.*/
$$= $$ || _ /*add this character to the $$ list. */
end
@._= @._ + 1 /*keep track of this character's count.*/
end /*j*/
sum= 0 /*calculate info entropy for each char.*/
do i=1 for #; _= substr($$, i, 1) /*obtain a character from unique list. */
sum= sum - @._/L * log2(@._/L) /*add (negatively) the char entropies. */
end /*i*/
say ' input string: ' $
say 'string length: ' L
say ' unique chars: ' #; say
say 'the information entropy of the string ──► ' format(sum,,12) " bits."
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
e: e= 2.718281828459045235360287471352662497757247093699959574966967627724076630; return e
/*──────────────────────────────────────────────────────────────────────────────────────*/
log2: procedure; parse arg x 1 ox; ig= x>1.5; ii= 0; is= 1 - 2 * (ig\==1)
numeric digits digits()+5; call e /*the precision of E must be≥digits(). */
do while ig & ox>1.5 | \ig&ox<.5; _= e; do j=-1; iz= ox * _ ** -is
if j>=0 & (ig & iz<1 | \ig&iz>.5) then leave; _= _ * _; izz= iz; end /*j*/
ox=izz; ii=ii+is*2**j; end /*while*/; x= x * e** -ii -1; z= 0; _= -1; p= z
do k=1; _= -_ * x; z= z+_/k; if z=p then leave; p= z; end /*k*/
r= z + ii; if arg()==2 then return r; return r / log2(2, .)</syntaxhighlight>
{{out|output|text= when using the default input of: <tt> 1223334444 </tt>}}
<pre>
input string: 1223334444
string length: 10
unique chars: 4
the information entropy of the string ──► 1.846439344671 bits.
</pre>
{{out|output|text= when using the input of: <tt> Rosetta Code </tt>}}
<pre>
input string: Rosetta Code
string length: 12
unique chars: 9
the information entropy of the string ──► 3.084962500721 bits.
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
decimals(8)
entropy = 0
countOfChar = list(255)
source="1223334444"
charCount =len( source)
usedChar =""
for i =1 to len( source)
ch =substr(source, i, 1)
if not(substr( usedChar, ch)) usedChar =usedChar +ch ok
j =substr( usedChar, ch)
countOfChar[j] =countOfChar[j] +1
next
l =len(usedChar)
for i =1 to l
probability =countOfChar[i] /charCount
entropy =entropy - (probability *logBase(probability, 2))
next
see "Characters used and the number of occurrences of each " + nl
for i =1 to l
see "'" + substr(usedChar, i, 1) + "' " + countOfChar[i] + nl
next
see " Entropy of " + source + " is " + entropy + " bits." + nl
see " The result should be around 1.84644 bits." + nl
func logBase (x, b)
logBase =log( x) /log( 2)
return logBase
</syntaxhighlight>
Output:
<pre>
Characters used and the number of occurrences of each
'1' 1
'2' 2
'3' 3
'4' 4
Entropy of 1223334444 is 1.84643934 bits.
The result should be around 1.84644 bits.
</pre>
=={{header|RPL}}==
{{works with|Halcyon Calc|4.2.7}}
{| class="wikitable"
! Code
! Comments
|-
|
≪
DUP SIZE 2 LN → str len log2
≪ { 255 } 0 CON
1 len '''FOR''' j
str j DUP SUB
NUM DUP2 GET 1 + PUT
'''NEXT'''
0 1 255 '''FOR''' j
'''IF''' OVER j GET
'''THEN''' LAST len / DUP LN log2 / * + '''END'''
'''NEXT'''
NEG SWAP DROP
≫ ≫ '<span style="color:blue">NTROP</span>' STO
|
<span style="color:blue">NTROP</span> ''( "string" -- entropy )''
Initialize local variables
Initialize a vector with 255 counters
For each character in the string...
... increase the counter according to ASCII code
For each non-zero counter
calculate term
Change sign and forget the vector
|}
The following line of code delivers what is required:
"1223334444" <span style="color:blue">NTROP</span>
{{out}}
<pre>
1: 1.84643934467
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">def entropy(s)
counts = s.chars.tally
leng = s.length.to_f
counts.values.reduce(0) do |entropy, count|
freq = count / leng
entropy - freq * Math.log2(freq)
end
end
p entropy("1223334444")</syntaxhighlight>
{{out}}
<pre>
1.8464393446710154
</pre>
=={{header|Run BASIC}}==
<syntaxhighlight lang="runbasic">dim chrCnt( 255) ' possible ASCII chars
source$ = "1223334444"
numChar = len(source$)
for i = 1 to len(source$) ' count which chars are used in source
ch$ = mid$(source$,i,1)
if not( instr(chrUsed$, ch$)) then chrUsed$ = chrUsed$ + ch$
j = instr(chrUsed$, ch$)
chrCnt(j) =chrCnt(j) +1
next i
lc = len(chrUsed$)
for i = 1 to lc
odds = chrCnt(i) /numChar
entropy = entropy - (odds * (log(odds) / log(2)))
next i
print " Characters used and times used of each "
for i = 1 to lc
print " '"; mid$(chrUsed$,i,1); "'";chr$(9);chrCnt(i)
next i
print " Entropy of '"; source$; "' is "; entropy; " bits."
end</syntaxhighlight><pre>
Characters used and times used of each
'1' 1
'2' 2
'3' 3
'4' 4
Entropy of '1223334444' is 1.84643939 bits.
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">fn entropy(s: &[u8]) -> f32 {
let mut histogram = [0u64; 256];
for &b in s {
histogram[b as usize] += 1;
}
histogram
.iter()
.cloned()
.filter(|&h| h != 0)
.map(|h| h as f32 / s.len() as f32)
.map(|ratio| -ratio * ratio.log2())
.sum()
}
fn main() {
let arg = std::env::args().nth(1).expect("Need a string.");
println!("Entropy of {} is {}.", arg, entropy(arg.as_bytes()));
}</syntaxhighlight>
{{out}}
<pre>$ ./entropy 1223334444
Entropy of 1223334444 is 1.8464394.
</pre>
=={{header|Scala}}==
<syntaxhighlight lang="scala">import scala.math._
def entropy( v:String ) = { v
.groupBy (a => a)
.values
.map( i => i.length.toDouble / v.length )
.map( p => -p * log10(p) / log10(2))
.sum
}
// Confirm that "1223334444" has an entropy of about 1.84644
assert( math.round( entropy("1223334444") * 100000 ) * 0.00001 == 1.84644 )</syntaxhighlight>
=={{header|scheme}}==
A version capable of calculating multidimensional entropy.
<syntaxhighlight lang="scheme">
(define (entropy input)
(define (close? a b)
(define (norm x y)
(define (infinite_norm m n)
(define (absminus p q)
(cond ((null? p) '())
(else (cons (abs (- (car p) (car q))) (absminus (cdr p) (cdr q))))))
(define (mm l)
(cond ((null? (cdr l)) (car l))
((> (car l) (cadr l)) (mm (cons (car l) (cddr l))))
(else (mm (cdr l)))))
(mm (absminus m n)))
(if (pair? x) (infinite_norm x y) (abs (- x y))))
(let ((epsilon 0.2))
(< (norm a b) epsilon)))
(define (freq-list x)
(define (f x)
(define (count a b)
(cond ((null? b) 1)
(else (+ (if (close? a (car b)) 1 0) (count a (cdr b))))))
(let ((t (car x)) (tt (cdr x)))
(count t tt)))
(define (g x)
(define (filter a b)
(cond ((null? b) '())
((close? a (car b)) (filter a (cdr b)))
(else (cons (car b) (filter a (cdr b))))))
(let ((t (car x)) (tt (cdr x)))
(filter t tt)))
(cond ((null? x) '())
(else (cons (f x) (freq-list (g x))))))
(define (scale x)
(define (sum x)
(if (null? x) 0.0 (+ (car x) (sum (cdr x)))))
(let ((z (sum x)))
(map (lambda(m) (/ m z)) x)))
(define (cal x)
(if (null? x) 0 (+ (* (car x) (/ (log (car x)) (log 2))) (cal (cdr x)))))
(- (cal (scale (freq-list input)))))
(entropy (list 1 2 2 3 3 3 4 4 4 4))
(entropy (list (list 1 1) (list 1.1 1.1) (list 1.2 1.2) (list 1.3 1.3) (list 1.5 1.5) (list 1.6 1.6)))
</syntaxhighlight>
{{out}}
<pre>
1.8464393446710154 bits
1.4591479170272448 bits
</pre>
=={{header|Scilab}}==
<syntaxhighlight lang="text">function E = entropy(d)
d=strsplit(d);
n=unique(string(d));
N=size(d,'r');
count=zeros(n);
n_size = size(n,'r');
for i = 1:n_size
count(i) = sum ( d == n(i) );
end
E=0;
for i=1:length(count)
E = E - count(i)/N * log(count(i)/N) / log(2);
end
endfunction
word ='1223334444';
E = entropy(word);
disp('The entropy of '+word+' is '+string(E)+'.');</syntaxhighlight>
{{out}}
<pre> The entropy of 1223334444 is 1.8464393.</pre>
=={{header|Seed7}}==
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";
include "float.s7i";
include "math.s7i";
const func float: entropy (in string: stri) is func
result
var float: entropy is 0.0;
local
var hash [char] integer: count is (hash [char] integer).value;
var char: ch is ' ';
var float: p is 0.0;
begin
for ch range stri do
if ch in count then
incr(count[ch]);
else
count @:= [ch] 1;
end if;
end for;
for key ch range count do
p := flt(count[ch]) / flt(length(stri));
entropy -:= p * log(p) / log(2.0);
end for;
end func ;
const proc: main is func
begin
writeln(entropy("1223334444") digits 5);
end func;</syntaxhighlight>
{{out}}
<pre>
1.84644
</pre>
=={{header|SETL}}==
<syntaxhighlight lang="setl">program shannon_entropy;
print(entropy "1223334444");
op entropy(symbols);
hist := {};
loop for symbol in symbols do
hist(symbol) +:= 1;
end loop;
h := 0.0;
loop for count = hist(symbol) do
f := count / #symbols;
h -:= f * log f / log 2;
end loop;
return h;
end op;
end program; </syntaxhighlight>
{{out}}
<pre>1.84643934467102</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func entropy(s) {
var counts = Hash.new;
s.each { |c| counts{c} := 0 ++ };
var len = s.len;
[0, counts.values.map {|count|
var freq = count/len; freq * freq.log2 }...
]«-»;
}
say entropy("1223334444");</syntaxhighlight>
{{out}}
<pre>1.846439344671015493434197746305045223237</pre>
=={{header|Standard ML}}==
<syntaxhighlight lang="standard ml">val Entropy = fn input =>
let
val N = Real.fromInt (String.size input) ;
val term = fn a => Math.ln (a/N) * a / ( Math.ln 2.0 * N ) ;
val v0 = Vector.tabulate (255,fn i=>0) ;
val freq = Vector.map Real.fromInt (* List.foldr: count occurrences *)
(List.foldr (fn (i,v) => Vector.update( v, ord i, Vector.sub(v,ord i) + 1) ) v0 (explode input) )
in
~ (Vector.foldr (fn (a,s) => if a > 0.0 then term a + s else s) 0.0 freq )
end ;</syntaxhighlight>
Entropy "1223334444" ;
val it = 1.846439345: real
=={{header|Swift}}==
<syntaxhighlight lang="swift">import Foundation
func entropy(of x: String) -> Double {
return x
.reduce(into: [String: Int](), {cur, char in
cur[String(char), default: 0] += 1
})
.values
.map({i in Double(i) / Double(x.count) } as (Int) -> Double)
.map({p in -p * log2(p) } as (Double) -> Double)
.reduce(0.0, +)
}
print(entropy(of: "1223334444"))</syntaxhighlight>
{{out}}
<pre>1.8464393446710154</pre>
=={{header|Tcl}}==
<syntaxhighlight lang="tcl">proc entropy {str} {
set log2 [expr log(2)]
foreach char [split $str ""] {dict incr counts $char}
set entropy 0.0
foreach count [dict values $counts] {
set freq [expr {$count / double([string length $str])}]
set entropy [expr {$entropy - $freq * log($freq)/$log2}]
}
return $entropy
}</syntaxhighlight>
Demonstration:
<syntaxhighlight lang="tcl">puts [format "entropy = %.5f" [entropy "1223334444"]]
puts [format "entropy = %.5f" [entropy "Rosetta Code"]]</syntaxhighlight>
{{out}}
<pre>
entropy = 1.84644
entropy = 3.08496
</pre>
=={{header|V (Vlang)}}==
===Vlang: Map version===
<syntaxhighlight lang="v (vlang)">import math
import arrays
fn hist(source string) map[string]int {
mut hist := map[string]int{}
for e in source.split('') {
if e !in hist {
hist[e] = 0
}
hist[e]+=1
}
return hist
}
fn entropy(hist map[string]int, l int) f64 {
mut elist := []f64{}
for _,v in hist {
c := f64(v) / f64(l)
elist << -c * math.log2(c)
}
return arrays.sum<f64>(elist) or {-1}
}
fn main(){
input := "1223334444"
h := hist(input)
e := entropy(h, input.len)
println(e)
}</syntaxhighlight>
{{out}}
<pre>
1.8464393446710152
</pre>
=={{header|Wren}}==
{{trans|Go}}
<syntaxhighlight lang="wren">var s = "1223334444"
var m = {}
for (c in s) {
var d = m[c]
m[c] = (d) ? d + 1 : 1
}
var hm = 0
for (k in m.keys) {
var c = m[k]
hm = hm + c * c.log2
}
var l = s.count
System.print(l.log2 - hm/l)</syntaxhighlight>
{{out}}
<pre>
1.846439344671
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">code real RlOut=48, Ln=54; \intrinsic routines
string 0; \use zero-terminated strings
func StrLen(A); \Return number of characters in an ASCIIZ string
char A;
int I;
for I:= 0, -1>>1-1 do
if A(I) = 0 then return I;
func real Entropy(Str); \Return Shannon entropy of string
char Str;
int Len, I, Count(128);
real Sum, Prob;
[Len:= StrLen(Str);
for I:= 0 to 127 do Count(I):= 0;
for I:= 0 to Len-1 do \count number of each character in string
Count(Str(I)):= Count(Str(I)) + 1;
Sum:= 0.0;
for I:= 0 to 127 do
if Count(I) # 0 then \(avoid Ln(0.0) error)
[Prob:= float(Count(I)) / float(Len); \probability of char in string
Sum:= Sum + Prob*Ln(Prob);
];
return -Sum/Ln(2.0);
];
RlOut(0, Entropy("1223334444"))</syntaxhighlight>
{{out}}
<pre>
1.84644
</pre>
=={{header|Zig}}==
<syntaxhighlight lang="zig">
const std = @import("std");
const math = std.math;
pub fn main() !void {
const stdout = std.io.getStdOut().outStream();
try stdout.print("{d:.12}\n", .{H("1223334444")});
}
fn H(s: []const u8) f64 {
var counts = [_]u16{0} ** 256;
for (s) |ch|
counts[ch] += 1;
var h: f64 = 0;
for (counts) |c|
if (c != 0) {
const p = @intToFloat(f64, c) / @intToFloat(f64, s.len);
h -= p * math.log2(p);
};
return h;
}
</syntaxhighlight>
{{Out}}
<pre>
1.846439344671
</pre>
=={{header|zkl}}==
{{trans|D}}
<syntaxhighlight lang="zkl">fcn entropy(text){
text.pump(Void,fcn(c,freq){ c=c.toAsc(); freq[c]+=1; freq }
.fp1( (0).pump(256,List,0.0).copy() )) // array[256] of 0.0
.filter() // remove all zero entries from array
.apply('/(text.len())) // (num of char)/len
.apply(fcn(p){-p*p.log()}) // |p*ln(p)|
.sum(0.0)/(2.0).log(); // sum * ln(e)/ln(2) to convert to log2
}
entropy("1223334444").println(" bits");</syntaxhighlight>
{{out}}
<pre>
1.84644 bits
</pre>
=={{header|ZX Spectrum Basic}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="zxbasic">10 LET s$="1223334444": LET base=2: LET entropy=0
20 LET sourcelen=LEN s$
30 DIM t(255)
40 FOR i=1 TO sourcelen
50 LET number= CODE s$(i)
60 LET t(number)=t(number)+1
70 NEXT i
80 PRINT "Char";TAB (6);"Count"
90 FOR i=1 TO 255
100 IF t(i)<>0 THEN PRINT CHR$ i;TAB (6);t(i): LET prop=t(i)/sourcelen: LET entropy=entropy-(prop*(LN prop)/(LN base))
110 NEXT i
120 PRINT '"The Entropy of """;s$;""" is ";entropy</syntaxhighlight>
| |||