ENTROPY(1)ENTROPY(1)NAMEentropy - calculate data entropySYNOPSISentropy [ -sv ] [ -tstring ]
DESCRIPTION
This manual describes the operating procedure for the entropy program.
This program will calculate the specific entropy for a given chunk of
binary or ascii data that was previously read from stdin or supplied on
the command line via -t.
The most common use for this program is to gauge the efficiency of a
compression algorithm. In theory, based on the data's entropy, the max‐
imum theoretical compression rate can be calculated.
To understand how compression works, we must understand that all data
can be characterized by informational content, called its entropy (the
term is borrowed from Thermo-Dynamics). Compression is possible
because most data is represented with more bits then its entropy sug‐
gests is optimal.
OPTIONS-tstring Rather then read the data from the stdin input stream, use
the string string as the source of the data. This is useful
when you would like to calculate for a specific word or sen‐
tence.
-s Sorted output based on symbol frequencies
-v Print entropy version.
THEORY
A data set's entropy is the sum of each distinct symbol's entropies. A
symbol is a distinct set of contiguous bits. For the sake of simplic‐
ity, I use 8 (number of bits making up a byte). It is important to note
that a symbol does NOT have to consist of 8 bits. A distinct symbols
entropy `S' of symbol 'z' can be defined as:
Sz = -log2(Pz)
Where `Pz' is the probability of symbol 'z' being found in the set. By
storing each distinct symbol as a node in a list, we can calculate
exactly how many times the symbol occurs in the set. This is also known
as solving for the symbol's frequency.
In order to calculate the overall entropy of the data; we sum the total
entropies contributed by each distinct symbol and divide that by a
coefficient known as the data size. This coefficient is calculated by
taking the number of bits per symbol and multiplying it by the total
quantity of symbols.
DIAGNOSTICS
The entropy utility exits 0 on success, and non-zero if an error
occurs.
SEE ALSOgzip(1), bzip2(1), tar(1), minigzip(1), gzexe(1), kgzip(8)compress(1), zcmp(1), zdiff(1), zlib(3)AUTHOR
o Chris S.J. Peron
BUGS
None known. This does not mean they do not exist though. Please send
bug reports and source code patches to (bugs@sqrt.ca).
entropy version 1.0.0 9 Aug 2002 ENTROPY(1)
