hpNaff
Numerical Analysis of Fundamental Frequencies (NAFF)
A little command line tool (macOS, Linux, Windows1) to perform high-resolution frequency analysis of time series following the Laskar method.
Pre-compiled binaries are available here
For macOS: after download, copy 'hpnaff' to a location in your search path, and add execute permissions by 'chmod a+x ./hpnaff; cp hpnaff /usr/local/bin' Then try it on an example file that contains a weighted mix of Earth's orbital eccentricity, obliquity and climatic precession.
Usage:
% ./hpnaff -v
Welcome to hpNAFF Analysis. ©2015-2021 Heiko Pälike. 3rd party licenses: see --licenses option
Please provide exactly one file name argument
Usage: hpnaff [options] file
file format: tab separated columns, data must be equidistantly spaced. Instead of file can specify '-' for stdin.
-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
-fAL, --filterAbscissaLower:
filter on Abscissa (x-axis) data greater or equal than value specified.
-fAU, --filterAbscissaUpper:
filter on Abscissa (x-axis) data lesser or equal than value specified.
-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
-n, --decimate:
Specify decimation of input data. Default: 1 (take every value)
-a, --abscissaColumn:
Specify column number for abscissa (time or depth). Default: 1
-o, --ordinateColumn:
Specify column number for ordinate (data). Default: 2
-C, --complex:
Compute spectra for complex input. Default: false. If true, by default takes values from abscissa column + 1.
-Co, --ComplexOrdinateColumn:
Specify column number for ordinate (data), complex part. Default: 3 (if C option used)
-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.
Example: Try it on a sample file: etp_1kyr_36Ma.txt
user$ ./hpnaff etp_1kyr_36Ma.txt -d 1 -m 75
===================================================================================================================================================
# | chunk | t0 | points | frequency | amplitude | phase | significance | period | arcsec/yr | phase (deg)
0 | 0 | 0.0000 | 14001 | 0.000000000 | 0.00000000 | 0.000000000 | 0.000000000 | inf | 0.0000000 | 0.0000000
1 | 0 | 0.0000 | 14001 | 0.002472456 | 0.75721258 | 3.740563127 | 0.795224850 | 404.45610756 | 3.2043032 | 214.3184802
2 | 0 | 0.0000 | 14001 | 0.010522542 | 0.59639514 | -0.083030087 | 0.840326031 | 95.03406718 | 13.6372149 | -4.7572736
3 | 0 | 0.0000 | 14001 | 0.024999241 | 0.53877772 | 5.657761056 | 0.827374133 | 40.00121445 | 32.3990163 | 324.1658300
4 | 0 | 0.0000 | 14001 | 0.008040668 | 0.50803290 | 2.884638325 | 0.832167805 | 124.36778406 | 10.4207051 | 165.2776014
5 | 0 | 0.0000 | 14001 | 0.010102115 | 0.39766702 | 4.191460276 | 0.868275179 | 98.98917382 | 13.0923408 | 240.1529838
6 | 0 | 0.0000 | 14001 | 0.042828239 | 0.31115152 | 1.466354530 | 0.901608023 | 23.34908056 | 55.5053976 | 84.0159259
7 | 0 | 0.0000 | 14001 | 0.007627856 | 0.30706911 | 0.558756463 | 0.900168886 | 131.09844523 | 9.8857008 | 32.0143871
8 | 0 | 0.0000 | 14001 | 0.000407279 | 0.27097231 | 2.625060814 | 0.917986628 | 2455.31930796 | 0.5278336 | 150.4049056
9 | 0 | 0.0000 | 14001 | 0.045302069 | 0.26148887 | 5.142663822 | 0.908826103 | 22.07404698 | 58.7114815 | 294.6529325
10 | 0 | 0.0000 | 14001 | 0.025832617 | 0.23907704 | 3.749692849 | 0.917331368 | 38.71075060 | 33.4790718 | 214.8415747
11 | 0 | 0.0000 | 14001 | 0.001034652 | 0.22887920 | 0.316263467 | 0.926607014 | 966.50814962 | 1.3409095 | 18.1205619
12 | 0 | 0.0000 | 14001 | 0.053350844 | 0.23311864 | 1.355155680 | 0.912974999 | 18.74384580 | 69.1426943 | 77.6447010
13 | 0 | 0.0000 | 14001 | 0.009911387 | 0.18079485 | 5.692179885 | 0.941223401 | 100.89404923 | 12.8451580 | 326.1378837
14 | 0 | 0.0000 | 14001 | 0.019210470 | 0.15673509 | -0.475810951 | 0.949106113 | 52.05494759 | 24.8967689 | -27.2619593
15 | 0 | 0.0000 | 14001 | 0.052929481 | 0.14841497 | 5.755575872 | 0.947991689 | 18.89306257 | 68.5966076 | 329.7702061
16 | 0 | 0.0000 | 14001 | 0.009488271 | 0.15112041 | -0.166596764 | 0.960411285 | 105.39327551 | 12.2967997 | -9.5452915
17 | 0 | 0.0000 | 14001 | 0.025098798 | 0.17311913 | 2.629896209 | 0.958954086 | 39.84254538 | 32.5280423 | 150.6819533
18 | 0 | 0.0000 | 14001 | 0.025414340 | 0.14355863 | 4.818018103 | 0.948646430 | 39.34786366 | 32.9369851 | 276.0521029
19 | 0 | 0.0000 | 14001 | 0.024888808 | 0.14098312 | 5.710170222 | 0.964800625 | 40.17870229 | 32.2558949 | 327.1686540
20 | 0 | 0.0000 | 14001 | 0.010323185 | 0.13699989 | -1.010239654 | 0.950068676 | 96.86932826 | 13.3788478 | -57.8824685
21 | 0 | 0.0000 | 14001 | 0.007440236 | 0.12986997 | 2.040413354 | 0.952028440 | 134.40433245 | 9.6425463 | 116.9070736
22 | 0 | 0.0000 | 14001 | 0.001455303 | 0.12708837 | 2.315320953 | 0.947284449 | 687.14223688 | 1.8860724 | 132.6581188
23 | 0 | 0.0000 | 14001 | 0.010925100 | 0.11817448 | -0.359553604 | 0.955088752 | 91.53234018 | 14.1589300 | -20.6009040
24 | 0 | 0.0000 | 14001 | 0.009667251 | 0.11874251 | 2.622499903 | 0.954076811 | 103.44202802 | 12.5287567 | 150.2581762
25 | 0 | 0.0000 | 14001 | 0.010413463 | 0.09715315 | 2.916722459 | 0.980490597 | 96.02953115 | 13.4958485 | 167.1158869
26 | 0 | 0.0000 | 14001 | 0.000901134 | 0.09569726 | 1.601650029 | 0.968540900 | 1109.71245232 | 1.1678701 | 91.7677869
27 | 0 | 0.0000 | 14001 | 0.012994167 | 0.10086003 | 0.611296497 | 0.967944111 | 76.95760564 | 16.8404408 | 35.0247093
28 | 0 | 0.0000 | 14001 | 0.042724400 | 0.09486676 | 1.049712893 | 0.980633322 | 23.40582906 | 55.3708222 | 60.1441185
29 | 0 | 0.0000 | 14001 | 0.000231340 | 0.09813349 | 0.120421080 | 0.967044518 | 4322.64694648 | 0.2998163 | 6.8996196
30 | 0 | 0.0000 | 14001 | 0.005563540 | 0.10009924 | 2.397732816 | 0.967425007 | 179.74168484 | 7.2103475 | 137.3799708
31 | 0 | 0.0000 | 14001 | 0.010638958 | 0.09688648 | -0.508419978 | 0.964555303 | 93.99417100 | 13.7880891 | -29.1303190
32 | 0 | 0.0000 | 14001 | 0.008918727 | 0.08741944 | 2.593049312 | 0.963917464 | 112.12362149 | 11.5586705 | 148.5707817
33 | 0 | 0.0000 | 14001 | 0.007853668 | 0.09431921 | 1.158980960 | 0.966015093 | 127.32903632 | 10.1783540 | 66.4047175
34 | 0 | 0.0000 | 14001 | 0.024592220 | 0.08828171 | 3.104291584 | 0.962948350 | 40.66326600 | 31.8715176 | 177.8628061
35 | 0 | 0.0000 | 14001 | 0.008385587 | 0.08641115 | 2.992612020 | 0.964466604 | 119.25223732 | 10.8677206 | 171.4640385
36 | 0 | 0.0000 | 14001 | 0.018145511 | 0.08763660 | 3.810401603 | 0.965100179 | 55.11004768 | 23.5165828 | 218.3199301
37 | 0 | 0.0000 | 14001 | 0.024810831 | 0.08240291 | 4.521072773 | 0.982190253 | 40.30497880 | 32.1548364 | 259.0383888
38 | 0 | 0.0000 | 14001 | 0.042929640 | 0.09470460 | -1.714770886 | 0.974168391 | 23.29392958 | 55.6368128 | -98.2491346
39 | 0 | 0.0000 | 14001 | 0.001312871 | 0.08074684 | 0.777678607 | 0.975863805 | 761.68923898 | 1.7014813 | 44.5577020
40 | 0 | 0.0000 | 14001 | 0.002884917 | 0.08065197 | 2.947032331 | 0.969528197 | 346.63039200 | 3.7388528 | 168.8525146
41 | 0 | 0.0000 | 14001 | 0.009282092 | 0.07995912 | -0.902914836 | 0.959472393 | 107.73432964 | 12.0295917 | -51.7332094
42 | 0 | 0.0000 | 14001 | 0.002172887 | 0.07898195 | 1.985388299 | 0.966843584 | 460.21714558 | 2.8160620 | 113.7543702
43 | 0 | 0.0000 | 14001 | 0.025182288 | 0.07351399 | 1.270869502 | 0.989395181 | 39.71045117 | 32.6362447 | 72.8154588
44 | 0 | 0.0000 | 14001 | 0.002006049 | 0.07122474 | 1.007509645 | 0.970121706 | 498.49230512 | 2.5998395 | 57.7260505
45 | 0 | 0.0000 | 14001 | 0.008233354 | 0.07018462 | 4.902075131 | 0.962605563 | 121.45718541 | 10.6704267 | 280.8682159
46 | 0 | 0.0000 | 14001 | 0.043838032 | 0.06715352 | 3.232504867 | 0.965810782 | 22.81124276 | 56.8140900 | 185.2088861
47 | 0 | 0.0000 | 14001 | 0.007224019 | 0.06531452 | 4.276908703 | 0.978785703 | 138.42710917 | 9.3623280 | 245.0488180
48 | 0 | 0.0000 | 14001 | 0.045402169 | 0.07436495 | 2.063108445 | 0.977076727 | 22.02537938 | 58.8412112 | 118.2074066
49 | 0 | 0.0000 | 14001 | 0.002344771 | 0.06402237 | 1.101819579 | 0.974716549 | 426.48086343 | 3.0388233 | 63.1296117
50 | 0 | 0.0000 | 14001 | 0.034012471 | 0.06632261 | 0.311286623 | 0.964879805 | 29.40098080 | 44.0801621 | 17.8354097
51 | 0 | 0.0000 | 14001 | 0.000615717 | 0.06955959 | 0.324652566 | 0.966238480 | 1624.12260860 | 0.7979693 | 18.6012218
52 | 0 | 0.0000 | 14001 | 0.024999132 | 0.06125458 | 3.871230190 | 0.987944595 | 40.00138890 | 32.3988750 | 221.8051514
53 | 0 | 0.0000 | 14001 | 0.012584554 | 0.06352103 | 4.354136361 | 0.970616108 | 79.46248859 | 16.3095823 | 249.4736369
54 | 0 | 0.0000 | 14001 | 0.007042302 | 0.05954369 | 3.178070923 | 0.967975779 | 141.99901671 | 9.1268238 | 182.0900509
55 | 0 | 0.0000 | 14001 | 0.053168977 | 0.06126971 | -0.361831203 | 0.974607869 | 18.80796025 | 68.9069938 | -20.7314008
56 | 0 | 0.0000 | 14001 | 0.018476857 | 0.05675901 | 1.358226583 | 0.977498040 | 54.12175935 | 23.9460065 | 77.8206508
57 | 0 | 0.0000 | 14001 | 0.025289765 | 0.06621217 | -0.908124254 | 0.973848255 | 39.54168736 | 32.7755361 | -52.0316871
58 | 0 | 0.0000 | 14001 | 0.045202487 | 0.05979910 | 4.539755712 | 0.986931113 | 22.12267664 | 58.5824230 | 260.1088423
59 | 0 | 0.0000 | 14001 | 0.001552070 | 0.05459046 | 3.384103161 | 0.981459103 | 644.30080647 | 2.0114828 | 193.8948286
60 | 0 | 0.0000 | 14001 | 0.010774958 | 0.06013873 | -0.920994981 | 0.970525666 | 92.80778711 | 13.9643455 | -52.7691253
61 | 0 | 0.0000 | 14001 | 0.035180014 | 0.05381168 | 6.108664303 | 0.971837152 | 28.42523015 | 45.5932984 | 350.0006830
62 | 0 | 0.0000 | 14001 | 0.025932854 | 0.05497186 | 0.528441367 | 0.981080756 | 38.56112370 | 33.6089791 | 30.2774600
63 | 0 | 0.0000 | 14001 | 0.019098347 | 0.05289607 | 5.666427635 | 0.977106362 | 52.36055271 | 24.7514576 | 324.6623884
64 | 0 | 0.0000 | 14001 | 0.052829237 | 0.05592637 | 4.622260192 | 0.978276065 | 18.92891225 | 68.4666917 | 264.8360008
65 | 0 | 0.0000 | 14001 | 0.011547573 | 0.05030718 | 3.661455364 | 0.969207741 | 86.59828253 | 14.9656548 | 209.7859392
66 | 0 | 0.0000 | 14001 | 0.052667555 | 0.04771644 | 4.565272429 | 0.975236135 | 18.98702155 | 68.2571512 | 261.5708425
67 | 0 | 0.0000 | 14001 | 0.008514638 | 0.04804064 | 4.938804770 | 0.978348985 | 117.44480713 | 11.0349707 | 282.9726692
68 | 0 | 0.0000 | 14001 | 0.017723966 | 0.04660213 | 1.785804511 | 0.976900743 | 56.42078067 | 22.9702600 | 102.3190615
69 | 0 | 0.0000 | 14001 | 0.013408861 | 0.04526629 | -0.218064195 | 0.976731996 | 74.57754915 | 17.3778840 | -12.4941580
70 | 0 | 0.0000 | 14001 | 0.004944881 | 0.04401069 | 3.792380702 | 0.977679719 | 202.22932980 | 6.4085660 | 217.2874085
71 | 0 | 0.0000 | 14001 | 0.024477668 | 0.04221972 | 2.795577253 | 0.982047896 | 40.85356574 | 31.7230571 | 160.1747779
72 | 0 | 0.0000 | 14001 | 0.025733760 | 0.04584982 | 3.159868039 | 0.992264403 | 38.85945885 | 33.3509534 | 181.0471025
73 | 0 | 0.0000 | 14001 | 0.044937430 | 0.04272239 | 0.214967789 | 0.979100871 | 22.25316390 | 58.2389096 | 12.3167471
74 | 0 | 0.0000 | 14001 | 0.018373301 | 0.04170326 | 4.267372537 | 0.976418419 | 54.42680232 | 23.8117976 | 244.5024360
75 | 0 | 0.0000 | 14001 | 0.016041231 | 0.04508949 | 2.028721000 | 0.980103195 | 62.33935561 | 20.7894353 | 116.2371511
Notes
"Evolutive" outputs can be obtained with the -s option, e.g. -s 1000 computes an analysis for every 1000 points.
Source code available at repository below. Note: There are three branches, "main" contains a new swift package manager version, which can also be compiled for Linux/Windows, and "Accelerate" whichh uses the LinearAlgebra system library. The Linux version is linked statically. The "Windows" branch is modified to enable compilation with the Windows Toolchain 1
https://paloz.marum.de/bitbucket/scm/essp/hpnaff.git
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
References:
- Laskar, J., 1990, The chaotic motion of the Solar System. A numerical estimate of the size of the chaotic zones, Icarus, 88, 266-291.
- Laskar, J., 1993, Frequency analysis for multi-dimensional systems. Global dynamics and diffusion, Physica D, 67, 257-281.
- 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.
- Laskar, J. : 1999, Introduction to frequency map analysis, in proc. of NATO ASI 533 3DHAM95, S'Agaro, Spain, 134150.
- Papaphilippou, Y., Frequency maps for LHC models, PAC99.
- Papahilippou, Y. Zimmermann, F., Weak-strong beam-beam simulations for the Large Hadron Collider, Phys. Rev. ST Accel. Beams 2, 104001 (1999).
- 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.
- Laskar, J., Frequency map analysis and quasiperiodic decompositions. preprint (https://arxiv.org/pdf/math/0305364.pdf) (2003).
- Valluri & Merritt, 1998
Footnotes
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Windows version requires installation of Windows Swift Toolchain
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