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PENT

PENT

## Purpose

Return the information entropy of a time series

## Explanation

This function will return S, the information entropy of a time series
for a set of trial periods

## Category

Time series analysis, period finding, astronomical utilities.

## Calling Sequence

Result = PENT(P, T, X, [N, M ] )

## Inputs

P - array of trial period values.
T - array of observation times (same units as P).
X - array of observations.

## Optional Inputs

N - If four parameters are given then the 4th parameter is assumed
to be N. Then NxN boxes are used to calculate S.
M,N - If five parameters are given then parameter 4 is M and parameter
5 is N. S is then calculated using MxN boxes - M partitions for the
phase and N partitions for the data.

## Outputs

This function returns S, the information entropy of the time series for
the periods given in P as defined by Cincotta, Me'ndez & Nu'n~ez
(Astrophysical Journal 449, 231-235, 1995). The minima of S occur at
values of P where X shows periodicity.

## Procedure

The procedure involves dividing the phase space into N^2 partitions
(NxN boxes) and then calculating:

__ N^2
S = - \ mu_i . ln(mu_i) for all mu_i <> 0
/_
i = 1
where mu_i is the number of data points in partition i normalised by
the number of partitions.
The option of using MxN boxes is an additional feature of this routine.

## Example

To generate a similar synthetic data set to Cincotta et al. we
do the following:
IDL> P0 = 173.015 ; Fundamental period
IDL> T = randomu(seed,400)*15000 ; 400 random observation times
IDL> A0 = 14.0 ; Mean magnitude
IDL> M0 = -0.5 * sin(2*!pi*T/P0) ; Fundamental mode
IDL> M1 = -0.15 * sin(4*!pi*T/P0) ; 1st harmonic
IDL> M2 = -0.05 * sin(6*!pi*T/P0) ; 2nd harmonic
IDL> sig = randomu(seed,400)*0.03 ; noise
IDL> U = A0 + M0 + M1 + M2 + sig ; Synthetic data
IDL> Ptest = 100. + findgen(2000)/2. ; Trial periods
IDL> S = pent(Ptest,T,U) ; Calculate S
... this takes a few seconds ...
IDL> plot,Ptest,S,xtitle="P",ytitle="S" ; plot S v. P
IDL> print,Ptest(where(S eq min(S))) ; Print best period (+/- 0.5)
The plot produced should be similar to Fig. 2 of Cincotta et al.

## Restrictions

My own (limited) experience with this routine suggests that it is not
as good as other techniques for finding weak, multi-periodic signals in
poorly sampled data, but is good for establishing periods of eclipsing
binary stars when M is quite large (try MxN = 64x16, 128x16 or even
256x16). This suggests it may be good for other periodic light curves
(Cepheids, RR Lyrae etc.).
I would be glad to receive reports of other peoples experience with
this technique (e-mail pflm@bro730.astro.ku.dk).

## Modification History

Written by: Pierre Maxted, 14Sep95
Modifications:
Normalisation of S corrected, T-min(T) taken out of loop.
- Pierre Maxted, 15Sep95
Converted to IDL V5.0 W. Landsman September 1997

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