Output

Genuine frequencies are assigned identifiers f#index#, where #index# denotes an integer number starting at $1$. According to the number of significant signals present in the file <infile>, COMBINE chooses a constant number of digits. For example, if the input file contains from $1$ to $9$ frequencies, the identifiers for genuine frequencies are f1, f2, ... If the input file contains from $10$ to $99$ frequencies, COMBINE enumerates the genuine components f01, f02, ..., and so on. This format convention applies to the indexing of rows also.

Linear combinations are denoted by the frequency identifiers of the genuine components and appear as a formula: if the frequency under consideration is, e.g., $f_1+3f_3-2f_{10}-f_{14}-0.00214$, COMBINE displays it as f01+3f02-2f10-f14-0.00214 both on the screen and in the output file. In this context, $-0.00214$ is the frequency accuracy.

The screen output consists of a single line for each signal (i.e., for each row in the input file). COMBINE displays

1. the row index,
2. the linear combination including the frequency accuracy, and
3. the reliability $R$ (Eq.6).

For genuine frequencies, COMBINE displays only the row index and the frequency identifier. At runtime, the most reliable linear combination identified so far is displayed. If COMBINE finds a ``better'' solution, the line on the screen is updated.

By default, COMBINE generates an output file <infile>.cmb. It contains a row index in the first column, then all information of the input file in the further columns, plus three additional columns at the end:

1. reliability $R$ (Eq.6),
2. total number of linear combinations within the frequency resolution,
3. the linear combination itself, plus the frequency accuracy. If a frequency is considered genuine, only the frequency identifier is displayed.

For convenience, a second output file <infile>.gen is produced by COMBINE. It is truncated to the genuine frequencies only and contains the row index in the first column, then all the information provided in the input file, plus the frequency identifier in the last column. The columns for the reliability and the number of linear combinations within the frequency resolution are omitted. This file provides the opportunity to have all the genuine frequencies available at a glance.

Example. The sample project CombineNative contains a list of significant frequencies found in the MOST (Microvariability & Oscillations of STars) photometry of $\zeta$ Oph (Walker et al. 2003, 2004, 2005). According to the input file result.dat, altogether 294 formally significant signal components (sig $>$ 5) were identified.

The file result.dat.ini contains five keywords:

order 0.2
dt 26
decay 1.5
cdamp 10
sens 0.2

The dataset is 26 days long, and the frequencies are provided in cycles per day. Thus COMBINE will assume a Rayleigh frequency resolution of 0.03846 cycles per day. There is no specification for the frequency tolerance parameter (keyword tol). Thus the default setting 0 is used.

Running COMBINE by typing the command line Combine result.dat yields a welcome message on the screen.

 CCCCCC                   bb      ii                 
CC    CC                  bb                         
CC        ooooo  m mm mm  bb bbb  ii n nnnn   eeeee  
CC       oo   oo mm mm mm bbb  bb ii nn   nn ee   ee 
CC       oo   oo mm mm mm bb   bb ii nn   nn ee   ee 
CC       oo   oo mm mm mm bb   bb ii nn   nn eeeeeee 
CC       oo   oo mm mm mm bb   bb ii nn   nn ee      
CC    CC oo   oo mm mm mm bb   bb ii nn   nn ee   ee 
 CCCCCC   ooooo  mm mm mm b bbbb  ii nn   nn  eeeee  


Version 1.0
************************************************************
by Piet Reegen
Institute of Astronomy
University of Vienna
Tuerkenschanzstrasse 17
1180 Vienna, Austria
Release date: August 18, 2009

The program finds out that the input file is a seven-column SIGSPEC result file, determines the number of rows and reads the input data. Note that 295 rows correspond to 294 significant signal components, because the last row in the SIGSPEC result file contains information on the residuals (see SIGSPEC manual, p.).

*** start **************************************************

File result.dat: SigSpec format
rows                                    295
read input file

Then the search for linear combinations starts. For each row in the input file, COMBINE displays the most reliable combination detected so far.

The first four signal components are found to be genuine. Since the number of signal components is 294, COMBINE uses a three-digit format for the row indices and frequency identifiers.

row 001: f001
row 002: f002
row 003: f003
row 004: f004

For rows 5 and 6 in the input data, the screen output contains the most reliable linear combination (including the frequency accuracy) and the reliability.

row 005: 3f001-f002-2f003-f004+0.0284306 0.236585
row 006: 3f001+2f002-f004+0.0136421 0.35803

An examination of the output file result.dat.cmb shows that rows 005 and 006 end with

0.2365853347754522  1 3f001-f002-2f003-f004+0.0284306168856169
0.3580304203945811  2 3f001+2f002-f004+0.0136420746028509

These entries refer to the columns added by COMBINE. The first value is the reliability, the second one is the number of examined linear combinations, and the last column represents the linear combination itself. For row 005, there is only one linear combination available within the frequency resolution, for row 006 the number of linear combinations taken into account is 2.

Subsequently, the screen output indicates a fifth genuine frequency.

row 007: f005

The frequency in row number 8 is 0.02783 cycles per day, which is below the frequency resolution. Thus the component is considered to refer to zero frequency, and in this case, no reliability is evaluated.

row 008: 0+0.0278395

In the further rows of the input files, no more genuine frequencies are detected.

row 009: -f002+f005-0.025485 0.759005
row 010: f001-f002-f004+f005+0.0313392 0.490535
row 011: -f001+f004-0.00275538 1.26888
row 012: f001-f002-f004+f005-0.0295542 0.680494
row 013: -2f001+2f003+f004-0.00567519 0.523911
row 014: -f001+f005+0.024731 1.72772
row 015: 2f002+0.0249392 1.47442
row 016: 2f001-f004-0.0100088 1.70761
row 017: -f001+2f002-0.00217389 1.55951
row 018: f001-f002+0.00824894 3.95466
row 019: f002+f005-0.00668728 1.64167
row 020: 2f002+f003-f005-0.00199182 0.779607

It is a remarkable matter of fact that COMBINE is able to compose all 294 frequencies contained by the input file as linear combinations of no more than five genuine frequencies. However, a different parameter constellation in the configuration file result.dat.ini can produce completely different output. Note that the time consumption by COMBINE dramatically increases with the number of genuine frequencies identified. This is because more genuine frequencies increase the number of possible linear combinations over-proportionally. A list of genuine frequencies only is found in the output file result.dat.gen.

5 genuine frequencies found.


Finished.

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Thank you for using Combine!
Questions or comments?
Please contact Piet Reegen ([email protected])
Bye!