entropy

Functions

int main(int argc, char *argv[])

entropy [ option ] [ infile ]

-l int
- number of elements \((1 \le N)\)
-o int
- output format \(O\)
  - 0 bit
  - 1 nat
  - 2 dit
-f bool
- output entropy frame by frame
infile str
- double-type probability sequence
stdout
- double-type entropy

The input is a set of probabilities:

\[ \begin{array}{ccc} \underbrace{p_0(1),\,p_0(2),\,\ldots,\,p_0(N)}_{\boldsymbol{p}(0)}, & \underbrace{p_1(1),\,p_1(2),\,\ldots,\,p_1(N)}_{\boldsymbol{p}(1)}, & \ldots, \end{array} \]

If -f option is given, the output sequence is

\[ \begin{array}{cccc} H(0), & H(1), & H(2), & \ldots, \end{array} \]

where \(H(t)\) is the entropy at \(t\)-th frame:

\[ H(t) = -\sum_{n=1}^{N} p_t(n) \log_b p_t(n) = -\boldsymbol{p}(t)^\mathsf{T} \log_b \boldsymbol{p}(t). \]

The base \(b\) depends on the value of \(O\):

\[\begin{split} b = \left\{\begin{array}{ll} 2,\quad & O = 0 \\ e, & O = 1 \\ 10. & O = 2 \\ \end{array}\right. \end{split}\]

If -f option is not given, only the average of the entropies, \(\bar{H}\), is sent to the standard output:

\[ \bar{H} = \frac{1}{T} \sum_{t=0}^{T-1} H(t), \]

where \(T\) is the number of the set of probabilities.

The below example calculates maximum value of entropy:

step -l 4 | sopr -d 4 | entropy -l 4 | x2x +da

Parameters

argc – [in] Number of arguments.
argv – [in] Argument vector.

Returns

0 on success, 1 on failure.