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Numerical Analysis of Fundamental Frequencies (NAFF)
A little command line tool (macOS only) to perform high-resolution frequency analysis of time series following the Laskar method.
Usage: hpnaff [options] file
file format: tab separated columns, data must be equidistantly spaced.
-h, --help:
Displays help message.
-r, --fracRMSChangeLimit:
fracRMSChangeLimit. Default: 0.000002
-f, --fracFreqAccuracyLimit:
fracFreqAccuracyLimit. Default: 0.00000001
-m, --maxFrequencies:
maxFrequencies. Default: 30
-c, --freqCycleLimit:
freqCycleLimit. Default: 100
-l, --lowerFreqLimit:
lowerFreqLimit. Default: 0.0
-u, --upperFreqLimit:
upperFreqLimit. Default: 0.5 (NYQUIST)
-d, --detrendingOrder:
Order for polynomial detrending. 0 removes DC only. >0 removes a polynomial fit. Default: not set
-dC, --detrendChunks:
Option to apply detrending (-d) to individual chunks. Default: false
-s, --chunkSize:
Split the input file into chunks of this size. Default: not set, no chunking
-w, --window_offsets:
Specify windowing offset for evolutive analysis. Default: chunkSize if set, or None.
-z, --columnSeparator:
Use this as columns separtor for input file instead of default tab \t. Default: \t
-k, --skipHeaderLines:
Specify number of (header)lines to be skipped. Default: 0
-a, --abscissaColumn:
Specify column number for abscissa (time or depth). Default: 1
-o, --ordinateColumn:
Specify column number for ordinate (data). Default: 2
-t, --deltaT:
Specify time/depth offset between data. Default: 1.0
-x, --ratios:
Compute and output frequency ratio matrix. Default: false.
--ratio_list:
If ratio_option is set, provides comma separated list of frequency ratios to highlight in output.
--output_detrended_data:
Output detrended data to this filename. Not implemented yet.
--version:
Shows current version and build of this software
-v, --verbose:
Print verbose messages. Specify multiple times to increase verbosity.
--references:
Shows references to papers and sources.
--licenses:
Shows licenses of code components used in this software.
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Binary download:
hpnaff
after download, add execute permissions by 'chmod a+x ./hpnaff'
Then try it on a sample file etp_1kyr_36Ma.txt:
"Evolutive" outputs can be obtained with the -s option, e.g. -s 1000 computes an analysis for every 1000 points.
Notes:
This is a Swift implementation of https://ops.aps.anl.gov/manuals/SDDStoolkit/SDDStoolkitsu61.html
Related efforts:
https://github.com/MichaelEhrlichman/FortNAFF
https://github.com/adrn/SuperFreq
https://github.com/nkarast/PyNAFF
References:
1. Laskar, J., 1990, The chaotic motion of the Solar System. A numerical estimate of the size of the chaotic zones, Icarus, 88, 266-291.
2. Laskar, J., 1993, Frequency analysis for multi-dimensional systems. Global dynamics and diffusion, Physica D, 67, 257-281.
3. Dumas, S., Laskar, J., 1993, Global Dynamics and Long-Time Stability in Hamiltonian Systems Via Numerical Frequency Analysis, Phys. Rev. Letters, 70 (20), 2975-2979.
4. Laskar, J. : 1999, Introduction to frequency map analysis, in proc. of NATO ASI 533 3DHAM95, S'Agaro, Spain, 134150.
5. Papaphilippou, Y., Frequency maps for LHC models, PAC99.
6. Papahilippou, Y. Zimmermann, F., Weak-strong beam-beam simulations for the Large Hadron Collider, Phys. Rev. ST Accel.
Beams 2, 104001 (1999).
7. Robin, D., Steir, C., Laskar, J., Nadolski, L. : 2000, Global dynamics of the ALS revealed through experimental Frequency Map Analysis, Phys. Rev. Let., 85, pp. 558-561.
8. Laskar, J., Frequency map analysis and quasiperiodic decompositions. preprint (https://arxiv.org/pdf/math/0305364.pdf) (2003).
9. Valluri & Merritt, 1998