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OpenTSTOOL User Manual - Third Institute of Physics

1. e n number of nearest neighbour to compute e past a nearest neighbour is only valid if it is as least past timesteps away from the reference point past 1 means use all points but ref_point itself n nearest neighbour algorithm Find n nearest neighbours in order of increasing distances to each point in signal s uses accelerated searching distances are calculated with euclidian norm 6 20 3 47 normi Syntax e rs normi s gt low 0 upp 1 e rs normi s low gt upp 1 e rs normi s low upp Scale and move signal values to be within low upp 6 20 3 48 norm2 Syntax e rs norm2 s Normalize signal by removing it s mean and dividing by the standard deviation 6 20 3 49 pca Syntax e rs eigvals eigvecs e rs eigvals eigvecs e rs eigvals eigvecs Input arguments pca s pca s pca s gt mode normalized maxpercent 95 mode gt maxpercent 95 mode maxpercent e each row of data is one observation e g the sample values of all channels in a multichannel measurement at one point in time e mode can be one of the following normalized default mean raw 61 in mode normalized each column of data is centered by removing its mean and then normalized by dividing through its standard deviation before the covariance matrix is cal culated in mode mean only the mean of every column of data is removed
2. Int J Bifurcation and Chaos 2 pp 155 165 Kadtke J B J Brush J Holzfuss 1993 Global dynamical equations and Lyapunov expo nents from noisy chaotic time series Int J Bifurcation Chaos 3 pp 607 616 Gencay R W D Dechert 1992 An algorithm for the n Lyapunov exponents of an n dimensional unknown dynamical system Physica D 59 pp 142 157 Eckmann J P D Ruelle 1992 Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems Physica D 56 pp 185 187 106 109 Ellner S A R Gallant D McCaffrey D Nychka 1991 Convergence rates and data require ments for Jacobian based estimates of Lyapunov exponents from data Phys Lett A 153 pp 357 363 110 Fell J J R schke P Beckmann 1993 Deterministic chaos and the first positive Lyapunov exponent a nonlinear analysis of the human electroencephalogram during sleep Biol Cybern 69 pp 139 146 111 Fell J P Beckmann 1994 Resonance like phenomena in Lyapunov calculations from data reconstructed by the time delay method Phys Lett A 190 pp 172 176 112 Sato S M Sano Y Sawada 1987 Practical methods of measuring the generalized dimension and largest Lyapunov exponent in high dimensional chaotic systems Prog Theor Phys 77 pp 1 5 113 Kurths J H Herzel 1987 An attractor in solar time series Physica D 25 pp 165 172 114 D
3. Syntax ex largelyap pointset query_indices taumax k exclude e x largelyap atria pointset query_indices taumax k exclude Input arguments e atria output of nn prepare for pointset optional cf Section 6 13 e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N e taumax maximal time shift e k number of nearest neighbors to compute e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments e x vector of length taumax 1 x tau 1 Nref sum log2 dist reference point tau nearest neighbor tau dist reference point nearest neighbor 146 42 6 13 nn prepare Do nearest neighbor preprocessing The intention of this mex file was to reduce the computational overhead of preprocessing for nearest neighbor or range searching With nn_prepare it is possible to do the preprocessing for a given point set only once and save the created tree structure into a Matlab variable This Matlab variable us
4. e a setdelta a f 6 23 3 15 setfirst Syntax e a setfirst a f 6 23 3 16 setname Syntax e a setname a newname 6 23 3 17 setunit Syntax e a setunit a u 87 6 23 3 18 setvalues Syntax e a setvalues a v 6 23 3 19 spacing Syntax e v values a len Returns spacing values for linear logarithmic or arbitary spacing in case of lin or log spacing len values are returned In case of arbitary spacing all stored values are returned 6 23 3 20 unit 6 24 Class unit 6 24 1 Overview Objects of class unit try to model physical units It s is possible to multiply or divide objects of this type A small database is used to find the right label for compound units See also directory unit private file units mat 6 24 2 Attributes e label string e name string e quantity structure holding two strings e factor double value e exponents vector e dBScale double value e dBRef double value e opt cell array may be used to store optional information 6 24 3 Member functions 6 24 3 1 char gives the unit s label e g V for Volt back 6 24 3 2 dbref returns reference value for 0 dB when calculating decibel values from data of this unit 88 6 24 3 3 dbscale returns scaling value when calculating decibel values from data of this unit dpscale returns either 10 for power or energy units e g Watt or 20 for all other units e g Volt 6 24 3 4
5. 79 80 81 82 83 84 85 86 87 88 Aguirre L A S A Billings 1995 Identification of models for chaotic systems from noisy data implications for performance and nonlinear filtering Physica D 85 pp 239 258 Aguirre L A E M A M Mendes 1996 Global nonlinear polynomial models structure term clustering and fixed points Int J Bifurc Chaos 6 2 pp 279 294 Allie S A Mees K Judd D Watson 1997 Reconstructing noisy dynamical systems by triangulation Phys Rev E 55 1 pp 87 93 Szpiro G G 1997 Forecasting chaotic time series with genetic algorithms Phys Rev E 55 3 pp 2557 2568 Jaeger L H Kantz 1997 Effective deterministic models for chaotic dynamics perturbed by noise Phys Rev E 55 5 pp 5234 5247 Farmer J D J J Sidorowich 1987 Predicting chaotic time series Phys Rev Lett 59 pp 845 848 Casdagli M 1989 Nonlinear Prediction of chaotic time series Physica D 35 pp 335 356 Brown R N F Rulkov E R Tracy 1994 Modeling and synchronizing chaotic systems from time series data Phys Rev E 49 pp 3784 3800 Grassberger P I Procaccia 1983 On the characterization of strange attractors Phys Rev Lett 50 pp 346 349 Theiler J 1986 Spurious dimension from correlation algorithms applied to limited time series data Phys Rev A 34 pp 2427 2431 Badii R
6. Some arithmetic can be done with units e units can be multiplied unit V unit A unit Watt e or taken to an integer or rational power unit m 6 25 Class list 6 25 1 Overview Simple list of strings used in class description cf Section 6 21 6 25 2 Attributes e data cellarray of strings e len double value counts number of strings in data 6 25 3 Member functions 6 25 3 1 append Syntax e list append list string e list append list list Add string s to existing list 6 25 3 2 cellstr cellstr return cell array of strings from list 1 90 6 25 3 3 char returns a char array from list 1 6 25 3 4 display 6 25 3 5 get Syntax es get l nr returns string number nr from list 1 6 25 3 6 length Syntax e len length 1 returns the number of strings in list 1 6 25 3 7 list Syntax e 1 list creates empty list e 1 list Hello world create list with one entry Hello world e 1 list Hello My World create list with three entries e 1 list Hello My World create list with three entries An object of type list contains a list of strings 6 25 3 8 sort sort list 1 in increasing order 91 Chapter 7 Frequently asked questions 7 1 Questions 1 Introduction and general information cf Section 7 2 1 What is TSTOOL cf Section 7 2 1 1 What software is required to run TSTOO
7. in mode raw no preprocessing is applied to data e maxpercent gives the limit of the accumulated percentage of the resulting eigenvalues default is 95 Principal component analysis of column orientated data set 6 20 3 50 plosivity Syntax e rs plosivity s blen gt flen 1 thresh 0 windowtype Rect e rs plosivity s blen flen gt thresh 0 windowtype Rect e rs plosivity s blen flen thresh gt windowtype Rect e rs plosivity s blen flen thresh windowtype Compute plosivity of a spectrogram See also window for list of possible window types 6 20 3 51 plus Syntax e rs plus s offset e rs plus s1 s2 Add two signals s1 and s2 or add a scalar value offset to s 6 20 3 52 poincare Syntax e rs poincare s ref Compute Poincare section of an embedded time series the result is a set of vector points with dimension DIM 1 when the input data set of vectors had dimension DIM The projection is done orthogonal to the tangential vector at the vector with index 6 20 3 53 power Syntax e power s Calculate squared magnitude of each sample 62 6 20 3 54 predict Syntax e rs predict s dim delay len gt nnr 1 e rs predict s dim delay len nnr gt mode 0 e rs predict s dim delay len nnr mode Input arguments e dim dimension for time delay reconstruction e delay delay time in samples for time delay reconstruction e len l
8. A Politi 1984 Hausdorff dimension and uniformity factor of strange attractors Phys Rev Lett 52 pp 1661 1664 Badii R A Politi 1985 Statistical description of chaotic attractors J Stat Phys 40 pp 725 750 Grassberger P 1985 Generalizations of the Hausdorff dimension of fractal measures Phys Lett A 107 pp 101 105 Schreiber T 1995 Efficient neighbor searching in nonlinear times series analysis Int J Bifurcation and Chaos 5 pp 349 358 Holzfuss J G Mayer Kress 1986 An approach to error estimation in the application of dimension algorithms in 82 pp 114 122 Mayer Kress G ed 1986 Dimensions and Entropies in Chaotic Systems Quantification of Complex Behavior Berlin Springer Theiler J 1990 Estimating fractal dimension J Opt Soc Am A 7 pp 1055 1073 Broggi G 1988 Evaluation of dimensions and entropies of chaotic systems J Opt Soc Am B 5 pp 1020 1028 Oseledec V I 1968 A multiplicative ergodic theorem Lyapunov characteristic numbers for dynamical systems Trans Moscow Math Soc 19 pp 197 231 Benettin G L Galgani A Giorgilli J M Strelcyn 1980 Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems a method for computing all of them Part II Numerical application Meccanica 15 pp 21 30 Shimada I T Nagashima 1979 A numerical approach
9. Attributes of data values Comment History 16 Aug 1999 19 15 01 Imported from MATLAB workspace Instead a row vector must be given to create the desired one dimensional signal 98 gt gt s signal sin 0 0 5 100 s signal object Dlens 201 X Axis 1 Name Type Attributes of data values Comment History 16 Aug 1999 19 16 58 Imported from MATLAB workspace 99 Bibliography 101 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Ott E 1993 Chaos in Dynamical Systems Cambridge Cambridge University Press Thompson J M T H B Stewart 1986 Nonlinear Dynamics and Chaos Chichester Wiley Schuster H G 1988 Deterministic Chaos 2nd ed Weinheim VHC Publishers Berg P Y Pomeau C Vidal 1984 Order within Chaos Towards a Deterministic Approach to Turbulence New York John Wiley and Sons Moon F C 1992 Chaotic and Fractal Dynamics New York John Wiley and Sons Gaponov Grekhov A V M I Rabinovich 1992 Nonlinearities in Action Oscillations Chaos Order Fractals Berlin Springer Lauterborn W J Holzfuss 1991 Acoustic chaos Int J Bifurcation and Chaos 1 pp 13 26 Lauterborn W T Kurz U Parlitz 1997 Experimental Nonlinear Physics Int J Bifurca tion and Chaos 7 pp 2003 2033 Lauterborn W U Parlitz 1988 Methods of chaos physics and their application t
10. Mac OS X and Solaris However since the compiled mex files are not compatible between all MATLAB versions are operating systems you may have to compile the mex files yourself see the installation section for details 7 2 1 4 What about Octave or other Matlab like programming environments Octavd is a freely available language for scientific computing that strongly resembles MATLAB Unfortunately Octave is not fully compatible to MATLAB so TSTOOL does not work with it TSTOOL makes extended use of the object oriented features of MATLAB In the current version of Octave 3 0 there s no full support of classes Even if classes will be supported in future it s not sure wheter TSTOOL will work properly There are several other Matlab like programming environments e g Mideva or Scilalf Up to now it is not possible to use TSTOOL with these packages See URL http www gnu org software octave See URL http www mathtools com 3See URL http www rocq inria fr scilab 94 7 2 2 Installation of TSTOOL 7 2 2 1 All lines in the OpenTSTOOL tstoolbox mex m are comments is this right Yes this are the comment texts for the compiled mex functions e g type help amutual at the matlab prompt 7 2 2 2 Where are the precompiled Mex Files They are in OpenTSTOOL tstoolbox mex lt MEXEXT gt where lt MEXEXT gt is the extension for mex files on your system You can determine this extension by using the command mexext in Ma
11. Nonlinear Time Series Analysis Section 1 10 2 2 Eq 1 10 6 20 3 72 surrogatel Syntax e rs surrogatel s create surrogate data for a scalar time series by randomizing phases of fourier spectrum see James Theiler et al Using Surrogate Data to Detect Nonlinearity in Time Series APPENDIX ALGORITHM I 6 20 3 73 surrogate2 Syntax e rs surrogate2 s create surrogate data for a scalar time series see James Theiler et al Using Surrogate Data to Detect Nonlinearity in Time Series APPENDIX ALGORITHM II 6 20 3 74 surrogate3 Syntax e rs surrogate3 s create surrogate data for a scalar time series by permuting samples randomly 6 20 3 75 surrogate_test Syntax e rs surrogate_test s ntests method func Input Arguments e s has to be a real scalar signal 68 e ntests is the number of surrogate data sets to create e method method to generate surrogate data sets 1 surrogatel 2 surrogate2 3 surrogate3 e func string with matlab code have to return a signal object with a scalar time series The data to process is a signal object referred by the qualifier s see example Output Arguments e rs is a signal object with a three dimensional time series The first component is the result of the func function applied to the original data set s The second component is the mean of the result of the func function applied to the ntests surrogate data sets The third component is the s
12. description name 73 ed description name type e d description yunit An object of class description contains auxiliary descriptive information for a signal e g information about data unit creator how the signal should be plotted a user specified comment text a processing history and the commandlines that were used to generate this signal 6 21 3 8 display description display 6 21 3 9 history description history 6 21 3 10 label 6 21 3 11 makescript Syntax e makescript signal scriptfilename creates a Matlab m file that contains exactly the the processing steps that have been applied to get the input signal This gives a kind of macro facility for tstool Example signal s was calculated through several processing steps from signal sO the raw or original signal Now makescript s foo m will create a Matlab m file named foo m which applied to sO will give s 6 21 3 12 merge Syntax e d merge di d2 merge two descriptions Most items are taken from first description History is taken from both descriptions This function may be useful when writing binary operators for class signal 6 21 3 13 name description name Syntax e n name d Get signal s name 74 6 21 3 14 newcomment Syntax e d newcomment d string e d newcomment d list Replace old comment with new comment 6 21 3 15 optparams Syntax e param optparams d nr get optional parameter number nr 6 21
13. exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments e index a matrix of size R by k which contains the indices of the nearest neighbors Each row of index contains k indices of the nearest neighbors to the corresponding query point e distance a matrix of size R by k which contains the distances of the nearest neighbors to the corresponding query points sorted in increasing order 6 10 gendimest Estimate generalized dimension spectrum The Renyi dimension spectrum of a points set can be estimated using information about the dis tribution of the interpoint distances Since we are interested in the scaling behaviour of the Renyi information for small distances we don t need to compute all interpoint distances the distances to k nearest neighbors for each reference point are sufficient 150 Robust estimation is used instead of mean square error fitting Syntax e dimensions moments gendimest dists gammas kmin_low kmin high kmax Input arguments e dists a matrix of size R by k which contains distances from reference points to their k nearest neighbors sorted in increasing order This matrix can be obtained by calling nn_search cf Section 6 14 or fnearneigh cf Section 6 9 on the point set whose dimension spectrum is to be investigated e gammas vector of the moment orders e kmin_low first kmin 1 lt kmin_low e kmin
14. pointset Npairs range exclude e c d e f g corrsum atria pointset Npairs range exclude bins e c d e f g corrsum atria pointset Npairs range exclude bins opt_flag Input arguments e atria output of nn prepare for pointset optional cf Section 6 13 e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e Npairs Number of pairs to find within each length scale The algorithm will adapt the number of reference points while computing the correlation sum Reference points are chosen randomly from the pointset Optionally a vector of the form Npairs Nref_min Nref_max may be given For no length scale less than Nref_min reference points will be used Additionally not more than Nref_max reference points will be used at all e range search range may be given in one of two ways If only a single value is given this value is taken as maximal search radius relative to attractor diameter 0 lt relative range lt 1 The minimal search radius is determined automatically be searching for the minimal interpoint distance in the data set Ifa vector of length two is given the values are interpreted as absolut minimal and maximal search radius e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search E g if the index of the query point is 124 and exclude is s
15. 1 to N e k number of nearest neighbors to compute Cao s method can be extended to use more than only the first nearest neighbor k 1 Output arguments e E and Ex are vectors of size D Please refer the Cao s article 38 for a precise description of their meaning 6 6 chaosys integrate dynamical system given by a set of ordinary differential equations chaosys gives the user the possibility to compute time series data for a couple of dynamical systems among which are Lorenz Chua Roessler etc This routine is not meant as a replacement for Matlab s suite of functions for solving ODEs but as a fast way to generate some data sets to evaluate the processing capabilities of TSTOOL The integration is done by an ODE solver using an Adams Pece scheme with local extrapolation 151 It is at least faster than Matlab s native ODE solver However it is not possible to extend the set of systems without recompiling chaosys Syntax e x chaosys length stepwidth initial_conditions mode parameters Input arguments e length number of samples to generate e stepwidth integration step size e initial_conditions vector of initial conditions e mode Lorenz Generalized Chua Double Scroll Generalized Chua Five Scroll Duffing Roessler Toda Oscillator Van der Pol Oscillator Pendulum Noo F WN EF For an exact definition of the ODE systems please refer to this header file e parameters v
16. 3 16 plothint 6 21 3 17 setlabel Syntax e d setlabel d label the label field of a description is used to give a signal some tag which remains constant through various processing steps e g which topic this signal belongs to 6 21 3 18 setname Syntax e d setname d name the name field of a descriptiom is used when the signal is loaded from file it will not be continued through several processing steps 6 21 3 19 setoptparams Syntax e d setoptparams d nr param set optional parameter number nr 6 21 3 20 setplothint 6 21 3 21 settype Syntax e d settype d string Set a new type for signal 75 6 21 3 22 setyname Syntax e d setyunit d string Set signal s y name e g d setyunit d V 6 21 3 23 setyunit Syntax ed setyunit d unit e d setyunit d string Set signal s y unit eg d setyunit d V 6 21 3 24 type return signal type e g Correlation function Spectrogram etc 6 21 3 25 yname return name of the measured data e g Heartbeat rate Current etc 6 21 3 26 yunit return y unit of the sampled data values e g Volt Pa etc 6 22 Class core 6 22 1 Overview Class core is a base class of class signal cf Section 6 20 An object of type core stores the pure sample values of a signal without any additional descriptive information The separation of the numerical and the descriptive part of a signal simplifies the writing o
17. 72121 452 13678 59332 26022 16718 86042 38436 24830 44434 distance 22 0101 0078 0132 0050 0087 0124 0129 0046 0101 0156 Oo0o0O0OO0O0O0O0OoO0ooOo 0175 0134 0167 0223 0097 0189 0168 0110 0103 0177 oOOoooo00o0000 now do a range search for radius 0 0224 using points 1 to 10 as query points excluding self matches count ne count pa ow ON PND MD y neighbors 1x4 1x10 1x7 1x2 1x5 1x6 1x2 1x4 1x7 1x5 ighbors double double double double double double double double double double 1x4 1x10 1x7 1x2 1x5 1x6 1x2 1x4 1x7 1x5 let s see the indices of neighbors ans 569 1 1 21 97100 range_search pointset atria 1 10 0 0224 0 double double double double double double double double double double the points that are within range to the first query point 96574 5618 let s see the corresponding distances of the points that are within range to the first query point neighbors 1 2 23 ans 0 0176 0 0186 0 0175 0 0101 24 Chapter 5 Handling the Graphical User Interface With the Graphical User Interface GUI most of TSTOOLs methods are available without coping with the command line syntax of every function To invoke the GUI simply type opentstool at the matlab command prompt If you invoke the GUI for the first time you get informed
18. Selecting one of these menus apply the corresponding script to the actual selected signal 5 3 7 Options Here some settings can be edited All these settings will be saved in the file tstool mat in the temporary data directory e PARAMETERS RECONSTRUCTION PARAMETERS The default settings for the Reconstruction dialog box can be edited here see menu ME THODS I RECONSTRUCTION TIME DELAY VECTORS 5 3 2 DEFAULT WINDOW TYPE Used by FFT etc e FILE AND DIRECTORY OPTIONS The actual search directory for LOAD and SAVE can be edited here Also the default file extension can be altered e INSTANT VIEW SMALL WINDOW If you switch on this feature the small figure at the right of the filelist will show you the selected signal immediatly after selection LARGE WINDOW Every time a new signal is generate e g applying a command to an existing signal e new figure window will be opened displaying it 31 5 3 8 Help The menu USAGE will start your web browser with the HTML Version of this manual shipped with the OpenTSTOOL distribution Run help docopt at the matlab command prompt to configure your web brower correctly After the seperation line you can view the matlab command line help for every method of the signal class The same information is in the HTML and in the PDF Version of the manual in class reference section 6 20 5 3 9 View This menu invokes a new figure window viewing the selected signal using t
19. Selectivity of Spatial Queries Using the Correlation Fractal Dimension Conference Proceedings of VLDB Zurich Switzerland Sept 1995 pp 299 310 S Berchtold C B hm D A Keim and H P Kriegl A cost model for nearest neighbor search in high dimensional data space PODS 97 Tuscon AZ pp 78 86 P Grassberger R Hegger H Kantz C Schaffrath and T Schreiber On noise reduction methods for chaotic data Chaos Vol 3 Nr 2 1993 pp 127 141 T C Halsey M H Jensen L P Kadanoff I Procaccia and B I Shraiman Fractal measures and their singularities The characterization of strange sets Phys Rev A Vol 33 Nr 2 1986 pp 1141 1151 H Kantz and T Schreiber Nonlinear Time Series Analysis Cambridge UP Cambridge 1997 J McNames A Nearest Trajectory Strategy for Time Series Prediction Proc of the Internatio nal Workshop on Advanced Black box Techniques for Nonlinear Modeling 1998 pp 112 128 U Parlitz Nonlinear Time Series Analysis in Nonlinear Modeling Advanced Black Box Tech niques Eds J A K Suykens and J Vandewalle Kluwer Academic Publishers 1998 pp 209 239 V Pestov On the geometry of similarity search dimensionality curse and contraction of mea sure Maths and comp science research report 99 02 VUW January 1999 pp 7 submitted for publication 148 T Schreiber Efficient neighbor searching in nonlinear time series analysis Int J Bifurcation and Chaos 5 pp
20. achse models an axis e g a time axis or a frequency axis A signal has a least one axis if it is a one dimensional signal A multidimensional signal has several achse objects An achse object is basically described by an object of class unit and the spacing values The spacing may be linear logarithmic or arbitrary in case of non uniform sampling 6 23 1 1 Why is class achse not called class axis The names axis and axes are already occupied in Matlab So achse which is the german translation of axis was used as name for that class 6 23 2 Attributes e name string name of axis e g Time e quantity string e unit object of type unit cf Section 6 24 e resolution string may be linear logarithmic or arbitrary e first double value starting value of this axis e delta double value stepwidth for this axis e values double vector stores spacing values in case of arbitrary resolution e opt cell array may be used to store optional information 6 23 3 Member functions 6 23 3 1 achse achse class constructor Syntax e a achse creates default achse object 85 e a achse axs copies achse object axs into a e a achse unt creates achse object using unit unt with linear spacing first 0 delta 1 e a achse vec creates achse object with arbitrary spacing using values in vec as spacing data e a achse unt vec creates achse object using unit unt
21. and spatiotemporal synchronization Phys Rev Lett 75 pp 3 6 124 Braiman Y W L Ditto K Wiesenfeld M L Spano 1995 Disorder enhanced synchroni zation Phys Lett A 206 pp 54 60 Braiman Y J F Lindner W L Ditto 1995 Taming spatiotemporal chaos with disorder Nature 378 pp 465 467 125 Pecora L M T L Carroll 1990 Synchronization in chaotic systems Phys Rev Lett 64 pp 821 824 126 Brown R N F Rulkov E R Tracy 1994 Modelling and synchronizing chaotic systems from experimental data Phys Lett A 194 pp 71 76 127 Kocarev L U Parlitz 1995 General approach for chaotic synchronization with applications to communication Phys Rev Lett 74 25 pp 5028 5031 128 Parlitz U L Junge L Kocarev 1996 Synchronization based parameter estimation from time series Phys Rev E 54 pp 6253 6529 107 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 Parlitz U L Kocarev T Stojanovski H Preckel 1996 Encoding messages using chaotic synchronization Phys Rev E 53 5 pp 4351 4361 Rulkov N F K M Sushchik L S Tsimring H D I Abarbanel 1995 Generalized synchro nization of chaos in directionally coupled chaotic systems Phys Rev E 51 pp 980 994 Kocarev L U Parlitz 1996 Generalized synch
22. double matrix containing the coordinates of the point set organized as N points of dimension D e query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N e relative_range search radius relative to attractor diameter 0 lt relative range lt 1 e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For examples if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments e D scalar value estimation of correlation dimension 46 6 19 tentmap Generate tentmap time series Generate samples of the generalized iterated tentmap Syntax e x tentmap length h e s x0 Input arguments e length number of samples to generate e h e s x0 vector of parameters and initial conditions Output arguments e x time series Example x tentmap 500 0 1 0 97 rand 1 1 plot x plot x 1 end 1 x 2 end 47 6 20 Class signal 6 20 1 Overview Class signal is TSTOOL s main class Objects of this type model real world signals A signal does not only store the pure sample values it holds much more information like axes units of sample values or the axes units and even more descriptive inf
23. histogram might be a sign of periodicity in the data Syntax e r return time pointset query_indices k max_time exclude e r return_time atria pointset query_indices k max_time exclude Input arguments 45 e atria output of nn_prepare for pointset optional cf Section 6 13 e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N e k number of nearest neighbors to be determined e max_time integer scalar gives an upper limit for return times that should be considered e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments e r vector of length max time containing the histogram of return times 6 18 takens_estimator Syntax e D takens_estimator pointset query_indices relative_range exclude e D takens_estimator atria pointset query_indices relative_range exclude Input arguments e atria output of nn prepare for pointset optional cf Section 6 13 e pointset a N by D
24. into the GUI more precise load a signal and save it to the temporary data directory A line in the fileview will be added with its filename e SAVE Write the marked signal in the fileview to disk e IMPORT FILE FROM Generate a signal from foreign formats like ASCII Matlab Vector Soundfiles etc See signal class constructor reference 6 20 3 66 for more information e EXPORT FILE FROM Write the marked signal in the fileview to disk in a foreign format See signal write reference 6 20 3 83 for more information e GENERATE This menu item can generate signals See mex chaosys reference 6 6 e AUDIO PLAYBACK Plays a scalar signal as audio with the matlab function soundsc If there is no sampling rate set in the signal 8KHz will be used e RESCAN Normally all files with the correct extension in the temporary directory are displayed in the filelist For some reason it is possible that a signal is displayed in the filelist but doesnt exist e g an other process deleted this file or some files missing in the filelist e g if you simply copy a signal file in the temporary directory without using the LOAD menu item In such situation use the RESCAN menu item to let TSTOOL look up all files again correctly This can take some time on slow machines or large signal files Simply restarting the GUI will not make a rescan e REMOVE ENTRY If you want to remove a filelist entry use this menu item or simply type Ctrl d The selected fil
25. matlab s file format 6 21 Class description 6 21 1 Overview Class description is the second base class of class signal cf Section 6 20 An object of type description stores all descriptive information belonging to a signal 72 6 21 2 Attributes e label string e name string e type string e plothint string e comment object of type list cf Section 6 25 e history object of type list cf Section 6 25 e creator string e yname string e yunit object of type unit cf Section 6 24 e commandlines object of type list cf Section 6 25 e optparam cell array may be used to store optional information 6 21 3 Member functions 6 21 3 1 addcommandlines adds new commandline to list of commands that have been applied to that signal example 1 addcommandlines s s spec2 s 512 Hanning will add s spec2 s 512 Hanning to the list of applied commands example 2 len 512 text Hanning addcommandlines s s spec2 s 512 Hanning will add s spec2 s 512 Hanning to the list of applied commands 6 21 3 2 addcomment adds new comment to current list of comments 6 21 3 3 addhistory adds text to current history list always the current time and date is written into the first line 6 21 3 4 commandlines 6 21 3 5 comment 6 21 3 6 creator 6 21 3 7 description description class constructor Syntax e d description ed
26. mmig M F Mitschke 1993 Estimation of Lyapunov exponents from time series the stochastic case Phys Lett A 178 pp 385 394 115 Rosenstein M T J J Collins C J de Luca 1993 A practical method for calculating largest Lyapunov exponents from small data sets Physica D 65 pp 117 116 Kantz H 1994 A robust method to estimate the maximal Lyapunov exponent of a time series Phys Lett A 185 pp 77 87 117 Fujisaka H T Yamada 1993 Stability theory of synchronized motion in coupled oscillator systems Prog Theor Phys 69 pp 32 46 118 Singer W 1993 Synchronization of cortical activity and its putative role in information processing and learning Annu Rev Physiol 55 pp 349 374 119 Ashwin P J Buescu I Stewart 1994 Bubbling of attractors and synchronisation of chaotic oscillators Phys Lett A 193 pp 126 139 120 Heagy J F T L Carroll L M Pecora 1994 Synchronous chaos in coupled oscillator sys tems Phys Rev E 50 pp 1874 1885 121 Lai Y C C Grebogi 1994 Synchronization of spatiotemporal chaotic systems by feedback control Phys Rev E 50 pp 1894 1899 122 Collins J J I Stewart 1994 A group theoretic approach to rings of coupled biological oscil lators Biol Cybern 71 pp 95 103 123 Lindner J F B K Meadows W L Ditto M E Inchiosa A R Bulsara 1995 Array enhanced stochastic resonance
27. reconstruction of a scalar time series using fast nearest neighbor search Four methods of computing the prediction output are possible 63 6 20 3 56 rang Syntax e rs rang s Transform scalar time series to rang values 6 20 3 57 removeaxis Syntax e s removeaxis s dim Remove axis one of the current xaxes No bound checking for dim 6 20 3 58 return_time Syntax e rs return time s nnr maxT gt past 1 e rs return_time s nnr maxT past e rs return_time s nnr maxT past N Input arguments e nnr number of nearest neighbors e maxT maximal return time to consider e past a nearest neighbor is only valid if it is as least past timesteps away from the reference point past 1 means use all points but tt ref_point itself e N number of reference indices Compute histogram of return times 6 20 3 59 reverse Syntax e rs reverse s Reverse signal along dimension 1 6 20 3 60 rms Syntax e rs rms s Calculate root mean square value for signal along dimension 1 64 6 20 3 61 scale Syntax e scale signal factor Scale signal by factor f 6 20 3 62 scalogram Syntax e rs scalogram s gt scalemin 0 1 e rs scalogram s scalemin gt scalemax 1 ers scalogram s scalemin scalemax gt scalestep 0 1 ers scalogram s scalemin scalemax scalestep gt mlen 10 ers scalogram s scalemin scalemax scalestep mlen Scalogram of signal s using morlet wavelet S
28. that the GUI will generate a directory for temporary files This will reside at OpenTSTOOL datafiles on Windows systems and at tstool on Unix systems First of all how does the GUI looks like TSTOOL V1 1 Signal Methods Methods Il Utilities Modify Macro Options Help View Roessler Roessler acf_Roessler1 surrogate_test_Roessler1_2 amutual_Roessler1 surrogate1_Roesaler1 amutual_surrogate1_Roessler1 embed_surrogatel_Roessler1 embed_surrogate1_Roessler1_1 embed_Roessler1 boxcdim_embed_Roessler diff_boxdim_embed_Roessler1 jed _Roessler1 1 3 sler 1 te surrogate_test_Roessler 05 0 1 0 05 0 0 05 There are three parts e Filelist e Figure e Menubar 5 1 Filelist Every loaded or generated signal shows its name in an own line they arranged hierarchicaly The data of the signals is stored in seperated files in the directory generated at the first run To process a special method click on one of the signals in the filelist an choose the method from the menubar 25 5 2 Figure This figure can show you the signal you have choosen from the filelist Normaly this feature is switched off because of the time consumption especialy for large signals To switch on this feature choose the menu item OPTION INSTANT VIEW SMALL WINDOW 5 3 Menus 5 3 1 Signal All menu items in this menu have something to do with the filelist and the storage of the signals e LOAD This menu item simply loads data
29. to be within dynamic_limit dynamic limit A low value for dynamic_limit will introduce nonlinear distortions to the signal To prevent the feedback loops from adapting to a zero level in case all input values are zero a tiny threshold is given as 4th argument The scaling factors will not shrink below this threshold 58 6 20 3 38 localdensity Syntax e rs localdensity s n past Input arguments e n number of nearest neighbour to compute e past a nearest neighbour is only valid if it is as least past timesteps away from the reference point past 1 means use all points but ref_point itself Uses accelerated searching distances are calculated with euclidian norm 6 20 3 39 max Syntax e maximum yunit xpos xunit max s Give information about maximum of scalar signal s Example disp maximum of signal disp y num2str m label yunit s disp x num2str xpos label a 6 20 3 40 medianfilt Syntax e rs medianfilt s len Moving median filter of width len samples for a scalar time series len should be odd 6 20 3 41 merge Syntax e merge signal1 signal2 dB e merge signal1 signal2 Input arguments e signall signal2 Signals e dB energy ratio optional default 0 Merges signal s1 and s2 into a new signal with energy ration dB in decibel a positive value of dB increases the amount of signal in the resulting signal 59 6 20 3 42 m
30. to ergodic problems of dissipative dynamical systems Prog Theor Phys 61 pp 1605 1616 Eckmann J P D Ruelle 1985 Ergodic theory of chaos and strange attractors Rev Mod Phys 57 pp 617 656 105 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 Geist K U Parlitz W Lauterborn 1990 Comparison of Different Methods for Computing Lyapunov Exponents Prog Theor Phys 83 pp 875 893 Wolf A J B Swift L Swinney J A Vastano 1985 Determining Lyapunov exponents from a time series Physica D 16 pp 285 317 Sano M Y Sawada 1985 Measurement of the Lyapunov spectrum from a chaotic time series Phys Rev Lett 55 pp 1082 1085 Eckmann J P S O Kamphorst D Ruelle S Ciliberto 1986 Lyapunov exponents from time series Phys Rev A 34 pp 4971 4979 Stoop R P F Meier 1988 Evaluation of Lyapunov exponents and scaling functions from time series J Opt Soc Am B 5 pp 1037 1045 Holzfuss J W Lauterborn 1989 Liapunov exponents from a time series of acoustic chaos Phys Rev A 39 pp 2146 2152 Stoop R J Parisi 1991 Calculation of Lyapunov exponents avoiding spurious elements Physica D 50 pp 89 94 Zeng X R Eykholt R A Pielke 1991 Estimating the Lyapunov exponent spectrum from short time series of low precision Phys Rev Lett 66 pp 3229 3232
31. with arbitrary spacing using values in vec as spacing data e a achse unt first delta creates achse object with linear spacing using delta and first e a achse unt first delta log creates achse object with logarithmic spacing using delta and first achse used to describe the different dimensions axes of a signal object Example e a achse unit Hz 0 01 10 log creates a logarithmic frequency axis with values 0 01 Hz 0 1 Hz 1 Hz 10 Hz e a achse label samplerate has the same result as a achse unit label 0 1 samplerate see also delta first horzcat label name quantity resolution samplerate scale setname spacing unit 6 23 3 2 cut Syntax e a cut a start stop Cut a part out of achse a beginning from index start up to index stop stop is only needed in case of arbitrary spacing cut ensures the following If values spacing achse1 N and N gt n then values n N spacing cut achsel n N 1 n See also horzcat 6 23 3 3 delta 6 23 3 4 display 6 23 3 5 eq Test if achse a and achse b are equal first is not taken into account for this test 86 6 23 3 6 first 6 23 3 7 horzcat 6 23 3 8 label 6 23 3 9 name 6 23 3 10 quantity 6 23 3 11 resolution 6 23 3 12 samplerate Syntax e rate samplerate a samplerate returns samplerate of achse object 6 23 3 13 scale Syntax e r scale a f Scale achses delta by factor f 6 23 3 14 setdelta Syntax
32. 0 Output arguments e bc scaling of boxes with partititon sizes log log e in scaling of information with partititon sizes log log e co scaling of correlation with partititon sizes log loga Compute boxcounting information and correlation dimension of a time delay reconstructed timeseries s for dimensions from 1 to D where D is the dimension of the input vectors using boxcounting approach Scale data to be within 0 and 1 Give a sortiment of integer partitionsizes with almost exponential behaviour 6 20 3 20 display 6 20 3 21 embed Syntax e emb embed s dim delay shift windowtype Input arguments e dim embedding dimension e delay time delay optional e shift shift for two sequent time delay vectors optional e windowtype type of window optional Output arguments e emb n by dim array each row contains the coordinates of one point Embeds signal s with embedding dimension dim and delay delay in samples s must be a scalar time series The default values for dim and delay are equal to one The default value for windowtype is Rect which is currently the only possible value 54 6 20 3 22 fft Syntax e f fft s Output arguments e f n by 2 array the first column contains the magnitudes the second one the phases Fourier transform of scalar signal s 6 20 3 23 filterbank Syntax e filterbank s depth filterlen Filter scalar signal s into 2 P ban
33. 20 3 4 e FILTER MOVING AVERAGE see signal movav 6 20 3 44 MEDIAN FILTER see signal medianfilt 6 20 3 40 MULTIRESOLUTION ANALYSIS see signal mutlires 6 20 3 45 27 e SURROGATE DATA GENERATION PERMUTATION OF SAMPLES see signal surrogate3 6 20 3 74 THEILER ALG I see signal surrogatei 6 20 3 72 THEILER Arc Il see signal surrogate2 6 20 3 73 e SURROGATE DATA TEST TIME REVERSIBILITY see signal trev 6 20 3 80 HIGHER ORDER MOMENTS see signal tc3 6 20 3 78 FUNCTION see signal surrogate_test 6 20 3 75 e PREDICTION LOCAL CONSTANT see signal predict2 6 20 3 55 e Misc SQUARED MAGNITUDE see signal power 6 20 3 53 ABSOLUTE VALUE see signal abs 6 20 3 1 DECIBEL VALUE see signal db 6 20 3 16 HISTOGRAM see signal histo 6 20 3 30 5 3 3 Methods II In this menu all methods with multivariate input signals are grouped e DECOMPOSITIONS PCA KARHUNEN LOEVE see signal pca 6 20 3 49 ARCHETYPAL ANALYSIS see signal arch 6 20 3 7 e LYAPUNOV EXPONENTS LARGEST see signal largelyap 6 20 3 36 e FRACTAL DIMENSIONS Box CouNTING APPROACH 28 CAPACITY DIMENSION DO see signal boxdim 6 20 3 8 INFORMATION DIMENSION D1 see signal infodim 6 20 3 31 CORRELATION DIMENSION D2 see signal corrdim 6 20 3 11 CORRELATION SUM APPROACH CORRELATION S
34. 3 11 filterbank Syntax e filterbank cin H G ORDER BASIS Input Arguments e H lowpass filter 79 e G highpass filter e ORDER indicates the type of tree 0 band sorting according to the filter bank 1 band sorting according to the frequency decomposition e BASIS desired subband decomposition calculates the Wavelet Packet Transform of cin It can be obtained using a selection algorithm function It may be switched from one format to another using CHFORMAT The different bands are sorted according to ORDER and BASIS If BASIS is omitted the output is a matrix with the coefficients obtained from all the wavelet packet basis in the library Each column in the matrix represents the outputs for a level in the tree The first column is the original signal If the length of X is not a power of 2 the columns are zero padded to fit the different lengths Run the script BASIS for help on the basis format See also IWPK CHFORMAT PRUNEADD PRUNENON GROWADD GROWNON 6 22 3 12 int Syntax e cout int cin delta Input Arguments e cin core object e delta time period between two data samples numerical integration along dimension 1 when data was sampled equidistantly with samplerate 1 delta 6 22 3 13 intermutual Syntax e intermutual cin1 cin2 n Input Arguments e cini cin2 core objects Calculates the mutual information of cinl and cin2 6 22 3 14 isempty Syntax e r isempty s Input Arg
35. 349 358 108 149 R Sedgewick Algorithms in C Third Edition Addison Wesley 1998 150 W van de Water and P Schram Generalized dimensions from near neighbor information Phys Rev A Vol 37 Nr 8 1988 pp 3318 3125 151 L F Shampine and M K Gordon The inital value problem 109
36. 5000 0 025 0 1 0 1 0 02 0 generate data from Lorenz system x x 5001 end discard first 5000 samples due to transient now compute correlation sum up to five percent of attractor diameter c d corrsum x randref 1 20000 1000 0 05 0 loglog d c and show the result as log log plot 38 6 8 corrsum2 Computation of the correlation sum This is an extended version of the correlation sum algorithm It tries to accelerate the computation of the correlation sum by using a different number of reference points at each length scale For large length scales only a few number of reference points will be used since for this scale quite a lot of neighbors will fall within this range and also the search time will be high The smaller the length scale the more reference points are used The algorithm tries to keep the number of pairs found within each range roughly constant at Npairs to ensure a good statistic even for the smallest length scales However the number of reference points actually used may be limited to be within Nref_min Nref_max to give at least some control to the user All reference points are chosen randomly from the data set without reoccurences of the same index Syntax e c d e f g corrsum pointset Npairs range exclude e c d e f g corrsum pointset Npairs range exclude bins e c d e f g corrsum pointset Npairs range exclude bins opt_flag e c d e f g corrsum atria
37. 7 499 Kaplan D T Schreiber 1996 Signal separation by nonlinear projections The fetal electro cardiogram Phys Rev E 53 5 pp R4326 R4329 Grassberger P R Hegger H Kantz C Schaffrath T Schreiber 1993 On noise reduction methods for chaotic data CHAOS 3 pp 127 141 Kantz H T Schreiber I Hoffmann T Buzug G Pfister C G Flepp J Simonet R Badii E Brun 1993 Nonlinear noise reduction A case study on experimental data Phys Rev E 48 pp 1529 1538 Kostelich E J T Schreiber 1993 Noise reduction in chaotic time series data A survey of common methods Phys Rev E 48 pp 1752 1763 Theiler J B Galdrikian A Longtin S Eubank J D Farmer 1992 Using surrogate data to detect nonlinearity in time series in Nonlinear Modeling and Forecasting eds M Casdagli and S Eubank SFI Studies in the Sciences of Complexity Vol XII Reading MA Addison Wesley pp 163 188 Theiler J S Eubank A Longtin B Galdrikian J D Farmer 1992 Testing for nonlinearity in time series the method of surrogate data Physica D 58 pp 77 94 Provenzale A L A Smith R Vio G Murante 1992 Distiguishing between low dimensional dynamics and randomness in measured time series Physica D 58 pp 31 49 Smith L 1992 Identification and prediction of low dimensional dynamics Physica D 58 pp 50 76 Takens F 1993 Detecting nonlineariti
38. L cf Section 7 2 1 2 On which systems does TSTOOL run cf Section 7 2 1 3 What about Octave or other Matlab like programming environments cf Section 7 2 1 4 2 Installation of TSTOOL All lines in the OpenTSTOOL tstoolbox mex m are comments is this right cf Sec ton 221 Where are the precompiled Mex Files cf Section 7 2 2 2 There are more than one file called e g amutual m why cf Section 7 2 2 3 What does the error message Attempt to execute SCRIPT as a function mean cf Section What does the error message This application has failed to start because the application configuration is incorrect mean cf Section 7 2 2 5 3 Working with TSTOOL cf Section 7 2 3 How do I create a signal from my time series data cf Section 7 2 3 1 How do I create a signal with logarithmic spacing cf Section 7 2 3 2 How do I create a signal from non uniformly sampled data cf Section 7 2 3 3 How do I change the type of plot that I get with view cf Section 7 2 3 4 What is class signal for cf Section 7 2 3 5 What is class core for cf Section 7 2 3 6 What is class description for cf Section 7 2 3 7 What is class achse for cf Section 7 2 3 8 Why is class achse called achse and not axis cf Section 7 2 3 9 What is class unit for cf Section 7 2 3 10 How is class unit used in TSTOOL cf Sectio
39. OpenTSTOOL User Manual Version 1 2 2 2009 Christian Merkwirth Ulrich Parlitz Immo Wedekind David Engster Werner Lauterborn Drittes Physikalisches Institut Universitat Gottingen Contact tstool physik3 gwdg de Contents 1 Ata glance 2 Download and Installation 2 1 Installation 2 1 1 Installation methods ee ee AA E A a 2 1 3 Deinstalling TSTOOL o e eee A AE e E Oi de ee a e e te ee ee a ce os a gee tierras ee 2 3 1 Problems with compiling mex files o o 2A Pital A a a ia A E Oe A a ei a ek A a ee cee GS GO erry 4 Nearest Neighbors Searching a OA ds ee en dd a 4 2 Approximate nearest neighbors searching 00 0002 eee eee 4 3 Range searching 24 43 dead dea a a e a aA 44 Matlab mex functionsl 2 2 ee 4 4 1 fin prepare es ese 04 4 44 ERE RE Ree RRR eee eee werk 442 nn search 46 8 oa eee aR ae ee REPRESS AAAS EE AE A 4 4 3 Tange search 26 4 28 2 a DOP a POA MES ow ee De MASE S444 bP AA ee Deeg beeen eda AA sic 6 4G 24 G44 DAA SA RADE ea ee bow eee ed ba Lito nk oa be BEES OAD ee REESE EE Oe ke GEE eS 5 3 Mens s 4 42 02 eb ee Pe ee Ee ORES eee Cae ee AA 10 10 10 10 11 12 12 13 15 15 19 19 19 20 20 20 20 21 22 5 3 2 Methods I oir eee a bee ee ea eS 27 5 3 3 Methods U aoa a 22002 ed aa Zee we A 28 Aa oA ok a ee ORS ES ee PEGE Ee aes 29 53 9 Modify seks a e ome w
40. Syntax e cout scalogram cin smin smax sstep tim 6 22 3 26 spec Syntax e cout spec cin Input Arguments e cin core object compute power spectrum for real valued signals 6 22 3 27 spec2 Syntax e cout spec2 cin fensterlen fenster vorschub Input Arguments e cin core object e fensterlen window size e fenster type of window e vorschub moving step spectrogramm of data using short time fft 83 6 22 3 28 surrogatel Syntax e cout surrogatei cin Input Arguments e cin core object create surrogate data for a scalar time series by randomizing phases of fourier spectrum see James Theiler et al Using Surrogate Data to Detect Nonlinearity in Time Series APPENDIX ALGORITHM I 6 22 3 29 surrogate2 Syntax e cout surrogate2 cin Input Arguments e cin core object create surrogate data for a scalar time series see James Theiler et al Using Surrogate Data to Detect Nonlinearity in Time Series APPENDIX ALGORITHM II 6 22 3 30 surrogate3 Syntax e cout surrogate3 cin Input Arguments e cin core object create surrogate data for a scalar time series by permuting samples randomly 6 22 3 31 uminus Syntax e r uminus c Input Arguments e c core object negate time series 84 6 22 3 32 vertcat Syntax e r vertcat c1 c2 Input Arguments e ci c2 core objects catenate two timeseries verticaly 6 23 Class achse 6 23 1 Overview Class
41. UM D2 GPA LIKE APPROACH see signal corrsum 6 20 3 12 CORRELATION DIMENSION D2 FIXED NUMBER OF PAIRS see signal corrsum2 6 20 3 13 TAKENS ESTIMATOR D2 see signal takens_estimator 6 20 3 77 NEAREST NEIGHBOR ALGORITHMS INFORMATION DIMENSION D1 NNK see signal infodim2 6 20 3 32 FRACTAL DIMENSION SPECTRUM see signal fracdims 6 20 3 27 PERIODICITY RETURN TIMES see signal return_time 6 20 3 58 RECIPROCAL LOCAL DENSITY see signal localdensity 6 20 3 38 MODELING POLYNOM SELECTION see util pauswahl e POINCARE SECTION see signal poincare 6 20 3 52 PREDICTION LOCAL CONSTANT see signal predict 6 20 3 54 5 3 4 Utilities Some useful information about the signals can be retrieved by functions in this menu e MINIMUM see signal min 6 20 3 42 e MAXIMUM see signal max 6 20 3 39 e FIRST LOCAL MINIMUM see signal firstmin 6 20 3 25 e FIRST LOCAL MAXIMUM see signal firstmax 6 20 3 24 29 e FIRST ZERO CROSSING see signal firstzero 6 20 3 26 e MEAN see mean Matlab reference e STANDARD DEVIATION see std Matlab reference e RMS root mean square e COMPARE TWO SIGNALS Only the data values are compared See core compare 6 22 3 3 5 3 5 Modify e CUT see signal cut 6 20 3 15 e SWAP DIMENSIONS see signal swap 6 20 3 76 e REVERSE see signal reverse 6 20 3 59 e INTERPOLATIONS CUBIC SPLINE see si
42. VE AU SUN AUDIO s signal data Sounds hat au AU old NLD Format s signal test nld NLD 66 6 20 3 67 spacing ev spacing s dim 1 e v spacing s dim return spacing values for xaxis nr dim 6 20 3 68 spec Syntax e rs spec s compute power spectrum for real valued scalar signals Multivariate signals are accepted but may produce unwanted results as only the spectrum of the first column is returned 6 20 3 69 spec2 Syntax e rs spec2 s Input Arguments e fensterlen size of window optional e fenster window type optional e vorschub shift in samples optional spectrogramm of signal s using short time fft Examples view spec2 sine 10000 1000 8000 512 Hanning 6 20 3 70 stts Syntax ers stts s I J 0 K 1 L 1 ers stts s I J K 1 L 1 ers stts s I J K L 1 ers stts s I J K L Input Arguments e s input data set of N snapshots of length M given as N by M matrix e I number of spatial neighbours e J number of temporal neighbours in the past e K spatial shift spatial delay e L temporal delay Spatiotemporal prediction conforming to U Parlitz NONLINEAR TIME SERIES ANALYSIS Chap ter 1 10 2 1 67 6 20 3 71 sttserror Syntax e rs sttserror si s2 Input Arguments e si original signal e s2 predicted signal compute error function for prediction of spatial temporal systems see U Parlitz
43. Zeng X R A Pielke R Eykholt 1992 Extracting Lyapunov exponents from short time series of low precision Modern Phys Lett B 6 pp 55 75 Parlitz U 1993 Lyapunov exponents from Chua s circuit J Circuits Systems and Compu ters 3 pp 507 523 Kruel Th M M Eiswirth F W Schneider 1993 Computation of Lyapunov spectra Effect of interactive noise and application to a chemical oscillator Physica D 63 pp 117 137 Briggs K 1990 An improved method for estimating Liapunov exponents of chaotic time series Phys Lett A 151 pp 27 32 Bryant P R Brown H D I Abarbanel 1990 Lyapunov exponents from observed time se ries Phys Rev Lett 65 pp 1523 1526 Brown R P Bryant H D I Abarbanel 1991 Computing the Lyapunov spectrum of a dy namical system from an observed time series Phys Rev A 43 pp 2787 2806 Abarbanel H D I R Brown M B Kennel 1991 Lyapunov exponents in chaotic systems their importance and their evaluation using observed data Int J Mod Phys B 5 pp 1347 1375 104 Holzfuss J U Parlitz 1991 Lyapunov exponents from time series Proceedings of the Confe 105 106 107 108 rence Lyapunov Exponents Oberwolfach 1990 eds L Arnold H Crauel J P Eckmann in Lecture Notes in Mathematics Springer Verlag Parlitz U 1992 Identification of true and spurios Lyapunov exponents from time series
44. dices is a vector of length R which contains the indices of the query points e r range or search radius r gt 0 e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments e count a vector of length R contains the number of points within distance r to the corresponding query point e neighbors a Matlab cell structure of size R by 2 which contains vectors of indices and vectors of distances to the neighbors for each given query point This output argument can not be stored in a standard Matlab matrix because the number of neighbors within distance r is not the same for all query points The vectors if indices and distances for one query point have exactly the length that is given in count The values in the distances vectors are not sorted 4 5 Example session create a 3 dimensional data set with 100000 points pointset rand 100000 3 do the preprocessing for this point set atria nn_prepare pointset euclidian now search for 2 exact nearest neighbors using points 1 to 10 as query points excluding self matches index distance nn_search pointset atria 1 10 2 0 index 5618 96574 38209 84549 54991 60397 38429 59732 4114 76991
45. display 6 24 3 5 double gives a row vector which s first element contains the unit s factor and the remaining elements contain the exponents of the SI basic units 6 24 3 6 eq 6 24 3 7 exponents returns dimension exponents of unit q 6 24 3 8 factor returns factor of unit q 6 24 3 9 label 6 24 3 10 mpower Syntax e mpower u p take unit u to power p p must be a scalar 6 24 3 11 mrdivide 6 24 3 12 mtimes 6 24 3 13 name returns name of unit q 6 24 3 14 quantity returns quantity name of unit q If argument which is omitted the english quantity name will be returned 89 6 24 3 15 unit unit class constructor Class unit tries to modell physical units a physical unit is mainly can be described by the exponents of the basic SI units namely mass length time current temperature luminal_intensity mole and plane_angle Each unit belongs to a quantity e g the unit s second is used when measuring the quantity TIME Each unit has a name e g Ampere Volt Joule hour and an abbreviation called label A V J h Unfortunately the correspondence between these items is not always bijectiv to find corresponding items a table of units in the file units mat is used A unit object can be created with different types of arguments e by giving the label unit Hz looks up the remaining data exponents name quantity in the table e by giving the exponents
46. ds of equal bandwith using maximally flat filters 6 20 3 24 firstmax Syntax e xpos unit firstmax s Give information about first local maximum of scalar signal s 6 20 3 25 firstmin Syntax e xpos unit firstmin s Give information about first local minimum of scalar signal s 6 20 3 26 firstzero Syntax e xpos unit firstzero s Give information about first zero of scalar signal s using linear interpolation 55 6 20 3 27 fracdims Syntax e rs fracdims s kmin kmax Nref gstart gend past steps e rs fracdims s kmin kmax Nref gstart gend past e rs fracdims s kmin kmax Nref gstart gend Input arguments e kmin minimal number of neighbors for each reference point e kmax maximal number of neighbors for each reference point e Nref number of randomly chosen reference points n 1 means use all points e gstart starting value for moments e gend end value for moments e past optional number of samples to exclude before and after each reference index default is 0 e steps optional number of moments to calculate default is 32 Compute fractal dimension spectrum D q using moments of neighbor distances for time delay re constructed timeseries s Do the main job computing nearest neighbors for reference points 6 20 3 28 getaxis Syntax e a getaxis s dim Get one of the currend xaxes 6 20 3 29 gmi Syntax e gmi s D eps NNR len N
47. e query points can be given explicitly or taken from the data set of points see below Before one can use nn_search one has to call nn_prepare to compute the preprocessing information However as long as the input point set isn t modified the preprocessing information is valid and can be re used for multiple calls to nn_search or range_search Syntax 20 index distance nn_search pointset atria query_points k index distance nn_search pointset atria query_points k epsilon index distance nn_search pointset atria query_indices k exclude index distance nn_search pointset atria query_indices k exclude epsilon Input arguments pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D atria output of nn_prepare for pointset query_points a R by D double matrix containing the coordinates of the query points orga nized as R points of dimension D query _indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N k number of nearest neighbors to compute epsilon optional relative error for approximate nearest neighbors queries defaults to 0 exact search exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of
48. e Rl a a ee Se a a Oa 30 3 0 MACIO i 2 by a bb bw we A ER Se ei Bak 31 5 3 L OPtiOns sain 4 ee baa bee o a a o a a Wh 31 AAA EA 32 ALIAS AAN o O rio a 32 33 6 1 akimaspline Cubic spline interpolation using Akima splines 33 Doma ital Ghee ed ee 34 6 3 baker Generate Baker time series ee 34 a eae WE eee ee ee Ree 35 6 5 cao Determine minimum embedding dimension by Cao s method 35 6 6 chaosys integrate dynamical system given by a set of ordinary differential equations 36 6 7 corrsum Computation of the correlation SUM nn nn 38 6 8 corrsum2 Computation of the correlation sum 2 2 2 2 nn 39 6 9 fnearneigh Fast nearest neighbor search 2 2 2 o oo ooo 40 po uaia casona tl 41 6 11 henon Generate henon time series nn ee 42 oer Teeere teers e 42 6 13 nn_prepare Do nearest neighbor preprocessing o 43 6 14 nn Search i a 8 a A eee ade a ead 43 CR AME ANE Bop we oe A AA eee le oe ee ee ote eo 44 De ee a a a A 45 aae u ad OG Be ee ew ela eae ane re EY aa a A 45 BOGS AA Bee ect ee ohare A a A 46 6 19 tentmap Generate tentmap time series o ee e 47 6 20 Class signall cis 24 aaa das a ee A 49 Ladder ind a s a ad 49 6 20 22 AGETIDULES e o SA a aa 49 6 20 3 Member functions 2 2 nn nn 49 ee ee BR 72 cia AAA 72 6 21 2 Attributes s s s s sa Sue a A Poe bad 73 6 21 3 Member fu
49. ector of systems parameters The order of the parameters is exactly the same as in the constructors of the DGL subclasses in the above file Output arguments 36 e x contains the output of the integration organized as matrix of size samples by dim where dim is the number of ODEs that define the system Example x chaosys 20000 0 025 0 1 0 1 0 02 0 plot x 1 Definitions of the ODEs The parameters of the odes are a vector of a b Lorenz d aly ya dya b dt Y Y2 Y1Y3 d Ya ae Y ya CY3 Generalized Chua d ar a y bya dys SAA E ye dt Y Ya Y3 dys __ di Y2 Duffing de _ dt SA Ya dya di Y1 Yi by2 a cos y3 dys _ dt Rossler Yi e amp dt Y2 Y3 d dys ACES dt yaly1 Toda oscillator d 1 asin bt bya exp y dya _ dt Ez y van der Pol oscillator d asin bt c by3 1 d y dya _ dt y 37 pendulum d ee asin bt cbya d sin y dt dyz _ dt y 6 7 corrsum Computation of the correlation sum The topics correlation sum and correlation dimension estimation can also be found here Syntax e c d corrsum pointset query_indices range exclude e c d corrsum pointset query_indices range exclude bins e c d corrsum atria pointset query_indices range exclude e c d corrsum atria pointset query_indices range exclude bins Input argument
50. ee also spec2 6 20 3 63 setaxis Syntax e s setaxis s dim achse Change one of the current xaxes 6 20 3 64 setunit Syntax e s setunir s dim u Change unit of one of the current xaxes 6 20 3 65 shift Syntax e n ll shift s distance dim 1 e s shift s distance dim shift signal on axis No dim by distance measured in the unit of the axis to the right 65 6 20 3 66 signal Syntax e s signal array creates a new signal object from a data array array the data inside the object can be retrieved with x data s e s signal array achsel achse2 creates a new signal object from a data array array using achsel etc as xachse entries e s signal array uniti unit2 creates a new signal object from a data array array using unitl etc to create xachse objects e s signal array sampleratel samplerate2 creates a new signal object from a data array array using as xunit s second and scalar sampleratel as samplerate s A signal object contains signal data that is a collection of real or complex valued samples A signal can be one or multi dimensional The number of dimensions is the number of axes that are needed to describe the the data An example for an one dimensional signal is a one channel measurement timeseries or the power spectrum of a one channel measurement An example for a two dimensional signal is a twelve channel measurement with
51. elist entry will disappear and the corresponding temporary file will be deleted e SHOW A signal stores many information about the data This information can be displayed by this menu item e EDIT DESIRED TYPE OF PLOT Here you can choose the type of plot TSTOOL should use for your signal See signal view reference 6 20 3 82 for additional information 26 DESCRIPTIVE PARAMETERS AXES LABELS COMMENT TEXT 5 3 2 Methods I In this menu all methods with scalar input are grouped Most of this methods invokes the underlying TSTOOL function directly and do not need addition explanations To enter the parameters a dialog box will be opened For some parameters there is a checkbox at the right side named in units Normally this parameter is entered in the units of samples When you switch on the checkbox you can also enter this parameters in units of the first axis e RECONSTRUCTION TIME DELAY VECTORS see signal embed 6 20 3 21 MINIMUM EMBEDDING DIMENSION CAO S see signal cao 6 20 3 9 e SPECTRAL FFT see signal fft PERIODOGRAM see signal spec SPECTROGRAM see signal spec2 SCALOGRAM see signal scalogram 6 20 3 62 e DERIVATIVE INTEGRATION INTEGRATE see signal int 6 20 3 33 DIFFERENTIATE see signal diff 6 20 3 18 e CORRELATION AND MORE AUTO CORRELATION see Signal acf 6 20 3 2 AUTO MUTUAL INFORMATION see signal amutual 6
52. ength of prediction number of output values e nnr number of nearest neighbors to use default is one e step stepsize in samples default is one e mode 0 Output vectors are the mean of the images of the nearest neighbors 1 Output vectors are the distance weighted mean of the images of the nearest neighbors 2 Output vectors are calculated based on the local flow using the mean of the images of the neighbors 3 Output vectors are calculated based on the local flow using the weighted mean of the images of the neighbors Local constant iterative prediction for scalar data using fast nearest neighbor search Four methods of computing the prediction output are possible 6 20 3 55 predict2 Syntax e rs predict2 s len nnr step mode Input arguments e len length of prediction number of output values e nnr number of nearest neighbors to use default is one e step stepsize in samples default is one e mode 0 Output vectors are the mean of the images of the nearest neighbors 1 Output vectors are the distance weighted mean of the images of the nearest neighbors 2 Output vectors are calculated based on the local flow using the mean of the images of the neighbors 3 Output vectors are calculated based on the local flow using the weighted mean of the images of the neighbors Local constant iterative prediction for phase space data e g data stemming from a time delay
53. ere exist a special plothint surrbar for the view function to show this kind of result in the common way This function calculates a special value for the original data set and the n generated surrogate data sets The T 3 value is defined as followed Ln Ln 7rLn 27 TnTn r 2 Tos n T In terms of surrogate data test this is a test statistics for higher order moments The original tc3 function is located under utils tc3 m and use simple matlab vectors 6 20 3 79 trend Syntax e rs trend s len trend correction calculate moving average of width len samples for a scalar time series len should be odd and remove the result from the input signal 6 20 3 80 trev Syntax e rs trev s tau n method Input Arguments e tau see explaination below e n number of surrogate data sets to generate 70 e method method to generate the surrogate data sets 1 surrogatel 2 surrogate2 3 surrogate3 Output Arguments e rs is a row vector returned as signal object The first item is the Trey value for the original data set s The following n values are the T rgy values for the generated surrogates There exist a special plothint surrbar for the view function to show this kind of result in the common way This function calculates a special value for the original data set and the n generated surrogate data sets The Trey value is defined as followed Trev n T In
54. es in stationary time series Int J of Bifurcation and Chaos 3 pp 241 256 Wayland R D Bromley D Pickett A Passamante 1993 Recognizing determinism in a time series Phys Rev Lett 70 pp 580 582 Palus M V Albrecht I Dvorak 1993 Information theoretic test for nonlinearity in time series Phys Lett A 175 pp 203 209 Kaplan D 1994 Exceptional events as evidence for determinism Physica D 73 pp 38 48 Salvino L W R Cawley 1994 Smoothness implies determinism a method to detect it in time series Phys Rev Lett 73 pp 1091 1094 Savit R M Green 1991 Time series and dependent variables Physica D 50 pp 95 116 Rapp P E A M Albano I D Zimmerman M A Jim nez Molta o 1994 Phase randomized surrogates can produce spurious identifications of non random structure Phys Lett A 192 pp 27 33 Theiler J 1995 On the evidence for low dimensional chaos in an epileptic electroencephalo gram Phys Lett A 196 pp 335 341 Schreiber T A Schmitz 1996 Improved surrogate data for nonlinearity tests Phys Rev Lett 77 4 pp 635 638 Schreiber T 1998 Constrained randomization of time series data Phys Rev Lett 80 10 pp 2105 2108 Judd K A Mees 1995 On selecting models for nonlinear time series Physica D 82 pp 426 444 104 67 68 69 70 71 72 73 74 75 76 77 78
55. et to 3 points with indices 121 to 127 are omitted from search exclude 0 means exclude self matches e bins number of distance values at which the correlation sum is evaluated defaults to 32 e opt_flag optional flag to control the algorithm 0 Use euclidian distance be verbose don t allow to count a pair of points twice 1 Use maximum distance be verbose don t allow to count a pair of points twice 39 se euclidian distance be verbose allow to count a pair of points twice se maximum distance be verbose allow to count a pair of points twice se euclidian distance be silent don t allow to count a pair of points twice se maximum distance be silent don t allow to count a pair of points twice se euclidian distance be silent allow to count a pair of points twice se maximum distance be silent allow to count a pair of points twice If the preprocessing output atria is given the type of metric used to create this overrides the settings by opt flag Output arguments e c vector of correlation sums length c bins e d vector of the corresponding distances at which the correlation sums stored in c where computed d is exponentially spaced length c bins e e vector of the number of pairs found within this range length e bins e f vector of the number of total pairs that were tested length f bins g vector containing the indices of the reference points actually used by the algor
56. ew methods for specific data analysis problems e Create an expandable platform for signal processing Implementation The package is written partly in Matlab and partly in C Advantages of Matlab are e Reduced code development time e Extensive collection of intrinsic mathmatical functions e Excellent graphic capabilities e High portability from Unix to Windows NT and other platforms C is used for computationally demanding algorithms Graphical user interface A graphical user interface GUI gives access to the underlying signal processing commands Para meters for the commands are set via dialog windows Chapter 2 Download and Installation 2 1 Installation Unpack the compressed TSTOOL distribution into a directory e g C Program Files on Windows usr local on Unix This can be done with an unpacking tool like Winzip if you are working with Windows or gzip dc filename tgz tar xvf if you are working with Unix After unpacking you will get a new directory named OpenTSTOOL which should now contain e tstoollnit m script that calls settspath m if necessary e settspath m script that does path settings e tstoolbox the directory that contains all TSTOOL functions compiled mex files etc e mex dev Source code of the C parts of TSTOOL e Doc HTML PDF Documentation e info xml tstoolicon gif Files for the Matlab start menu e gpl txt Gnu General Public License Important note for Windows users I
57. f data set s2 0 1 e past number of samples to exclude before and after each reference index e bins number of bins optional Compute scaling of cross correlation sum for time delay reconstructed timeseries s against signal s2 with same dimension as s using fast nearest neighbor search Reference points are taken out of signal s while neigbors are searched in s2 The default number of bins is 32 6 20 3 15 cut Syntax e rs cut s dim start stop Input arguments e dim dimension along which the signal is cutted e start position where to start the cut e stop position where to stop optional Cut a part of the signal If stop is ommited only the data at start is cutted 6 20 3 16 db Syntax e db s dbmin Compute decibel values of signal relative to a reference value that is determined by the signal s yunit values below dbmin are set to dbmin If dbmin is ommited it is set to 120 6 20 3 17 delaytime Syntax e tau delaytime s maxdelay past Input arguments e maxdelay maximal delay time e past Compute optimal delaytime for a scalar timeseries with method of Parlitz and Wichard 53 6 20 3 18 diff Syntax e diff s nth Compute the nth numerical derivative along dimension 1 s has be to sampled equidistantly 6 20 3 19 dimensions Syntax e bc in co dimensions s bins Input arguments e s data points row vectors e bins maximal number of partition per axis default is 10
58. f m files that work on signals 6 22 2 Attributes e data double matrix one two or multidimensional TSTOOL stores a one dimensional time series always as a row vector Rows correspond to the first xaxis columns to the second e dlens double vector storing size of data 76 6 22 3 Member functions 6 22 3 1 acf Syntax e acf cin m Input Arguments e cin core object e m fft length acf calculates the autocorrelation function of cin via fft of length m 6 22 3 2 amutual2 Syntax e amutual cin len Input Arguments e cin core object e len maximal lag amutual2 calculates the mutual information of a time series against itself with increasing lag uses equidistant partitioning to compute histograms 6 22 3 3 compare Syntax e compare c1 c2 tolerance Input Arguments e c1 c2 core object of two signals e tolerance tolerance of the signals s RMS value default tolerance 1e 6 compare compare two signals whether they have equal values slight differences due to rounding errors are ignored depending on the value of tolerance when signals are found to be not equal a zero is returned 6 22 3 4 core core class constructor Syntax e c core arg Input Arguments e arg double array A core object contains the pure data part of a signal object Methods ndim dlens data 77 6 22 3 5 data Syntax e d data c varargin e c core object Input Arguments e varargin selector string for data e
59. f you want to use the pre compiled mex files which ship with OpenTSTOOL you will probably have to install the Visual C 2008 run time libraries which can be downloaded from the Microsoft web site As of the writing of this document the URLs for these packages are http www microsoft com downloads details aspx FamilyID 9b2da534 3e03 4391 8a4d 074b9f 2bc1bf for 32bit and http www microsoft com downloads details aspx familyid bd2a6171 e2d6 4230 b809 9a8d7548c1b6 for 64bit If these URLs are no longer valid just search for Microsoft Visual C 2008 Redistribu table Package and x86 or x64 for 32bit and 64bit respectively If you do not have these run time libraries installed you will get the following error message when trying to run a mex file This application has failed to start because the application configuration is incorrect 2 1 1 Installation methods The simplest way to invoke Open TSTOOL is to start Matlab and change to the OpenTSTOOL directory using the GUI or the cd command Once you have entered that directory you should see the Open TSTOOL toolbox in your Matlab Start menu under the item Toolboxes and you can start the graphical user interface from there Note that TSTOOL is not really installed yet so that after restarting Matlab you will have to enter the OpenTSTOOL directory again before you will be able to use the toolbox If you want to install Open TSTOOL permanently the director
60. for Matlab 97 7 2 4 1 How can I write a script to automatize common tasks One way to obtain a script is to execute the desired analysis steps with one example signal The output of this tasks will again be a signal that has stored the syntax of the executed steps in its description Using the command commandlines result will give you this syntax With copy and paste it s possible to create a script file from that output 7 2 5 Miscellaneous questions 7 2 5 1 What s the difference between history and commandlines Both attributes of class description are used to record the processing history of a signal But while history contains a list human readable entries commandlines stores the exact syntax of the commands that were applied to the signal 7 2 5 2 Is it TSTOOL TSTool OpenTSTOOL OpenTSTool Initially it was called TSTOOL but since Matlab now has its own tstool command we changed the Matlab command to opentstool but keep mostly TSTOOL in the manual and homepage for brevity s sake Regarding the spelling we re not entirely sure either 7 2 6 Frequently encountered errors 7 2 6 1 Using a column vector to create a one dimensional signal TSTOOL stores one dimensional signals always as row vectors Giving a column vector will cause unexpected behaviour with most routines that process signals gt gt s signal sin 0 0 5 100 s signal object Dlens 1 201 X Axis 1 X Axis 2 Name Type
61. gnal upsample 6 20 3 81 AKIMA SPLINE see signal upsample 6 20 3 81 FFT BASED see signal upsample 6 20 3 81 e Normalize CENTER AROUND ZERO see signal center 6 20 3 10 SCALE BY FACTOR see signal scale 6 20 3 61 FIT TO INTERVAL see signal norm1 6 20 3 47 CENTER AND DIVIDE BY STD see signal norm2 6 20 3 48 REMOVE TREND see signal trend 6 20 3 79 TRANSFORM TO RANG VALUES see signal rang 6 20 3 56 e SPLIT MULTICHANNEL SIGNAL Splits up a n channel signal in n signals by using signal cut 6 20 3 15 30 e ADD TWO SIGNALS see signal plus 6 20 3 51 e DIFFERENCE OF TWO SIGNALS see signal minus 6 20 3 43 e MERGE TWO SIGNALS see signal merge 6 20 3 41 5 3 6 Macro TSTOOL records the processed commands for every signal So TSTOOL knows how this signal is modified and can generate a matlab script with processes the same commands to arbitrary signal The generated scripts will be saved in the directory scripts inside the directory for temporary files e CREATE MACRO FROM SIGNAL Generate script named macro m e SHOW EDIT MACRO e RENAME MACRO Renamed macros will be displayed at the end of this menu after restart of TSTOOL e APPLY MACRO TO SIGNAL Invoke macro m with the selected signal e APPLY MACRO TO ALL Invoke macro m with every loaded signal After the seperation line a list of all m Files in the directory scripts is shown
62. he application configuration is incorrect mean This happens on Windows systems without the Visual C 2008 run time libraries Since the mex files for Windows are compiled with VC 2008 these run time libraries are needed for the proper execution of the compiled Windows mex files that ship with TSTOOL Please see the installation section for details on how to install the run time libraries 95 7 2 3 Working with TSTOOL 7 2 3 1 How do I create a signal from my time series data Suppose the time series data is given as the row vector y gt gt s signal y gt gt view s If y is a column vector the following syntax must be used gt gt s signal y gt gt view s Suppose the data was recorded with a samplerate of 8 kHz gt gt s signal y 8000 gt gt view s 7 2 3 2 How do I create a signal with logarithmic spacing Suppose you have data vector y whose values were recorded at 3 Hz 6 Hz 12 Hz 24 Hz a achse unit Hz 3 2 log s signal y a view s 7 2 3 3 How do I create a signal from non uniformly sampled data Suppose you have a data vector y of length 4 whose values were recorded at 3 Hz 5 Hz 8 Hz 14 5 Hz a achse unit Hz 3 5 8 14 5 s signal y a view s 7 2 3 4 How do I change the type of plot that I get with view The way view plots a signal depends on the attributes of the signal It is possible to give view a hint which type of plo
63. he images of the nearest neighbors are used to estimate to image of the initial state vector The next iteration uses the previously computed image as new initial state vector 145 Syntax x predict pointset length k stepsize mode Input arguments pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D length number of iterations length of prediction k number of nearest neighbors stepsize prediction stepsize usually one mode optional method to estimate image of initial state vector 0 direct prediction no weight is applied to neighbors 1 direct prediction biquadratic weight is applied to neighbors 2 integrated prediction no weight is applied to neighbors 3 integrated prediction biquadratic weight is applied to neighbors Output arguments x data set as double matrix size length by D 44 6 16 range_search Syntax e count neighbors range_search pointset atria query_points r e count neighbors range search pointset atria query_indices r exclude Input arguments e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e atria output of cf Section 6 13 nn_prepare for pointset e query_points aR by D double matrix containing the coordinates of the query points organized as R points of dimension D e query_indices query p
64. he signal view command 6 20 3 82 You can also simply type Ctrl v 32 Chapter 6 Mex Function Reference Parts of TSTOOL s functionality are coded in mex files All TSTOOL mex files are located in the directory tstoolbox mex It is possible to use these mex files independently of the full TSTOOL installation 6 1 akimaspline Cubic spline interpolation using Akima splines Compared to Matlab s built in cubic spline Akima spline interpolation better copes with discontinui ties in a time series Syntax e yy akimaspline x y xx Input arguments e x y vectors describing knot data see Matlab s original spline function e xx vector of positions at which the spline is evaluated Output arguments e yy evaluated function values Example x 1 100 floor x rand 1 100 pi xx 1 0 1 100 yy akimaspline x y xx plot x y xx yy r 33 6 2 amutual compute auto mutual information function Fast but crude auto mutual information of a scalar timeseries for the timelags from zero to maxtau The input time series should be much longer than maximal timelag maxtau The algorithm uses equidistant histogram boxes so results are bad in a mathematical sense However a fast algorithm based on ternary search trees to store only nonempty boxes is used Syntax e a amutual ts maxtau partitions Input arguments e ts vector holding time series data e maxtau maximal time lag e partiti
65. high last kmin kmin_low lt kmin high lt kmax e kmax highest neigbor order up to which kmax lt k Output arguments e dimensions matrix of size length gammas by kmin_upper kmin_lower 1 holding the dimen sion estimates e moments optional matrix of size k by length gammas storing the computed moments of the neigbor distances Example x chaosys 25000 0 025 0 1 0 1 0 02 0 generate data from Lorenz system x x 5001 end discard first 5000 samples due to transient nn dist fnearneigh x randref 1 20000 1000 128 0 gammas 5 0 5 5 gedims gendimest dist gammas 8 8 128 plot 1 gammas gedims gedims xlabel q ylabel D_q title Renyi dimension 41 6 11 henon Generate henon time series Generate time series by iterating the henon map Syntax e x henon length a b xo yo Input arguments e length number of samples to generate e ab xo yo vector of parameters and initial conditions Output arguments e x vector of size D Example x henon 500 1 4 0 3 0 2 0 12 plot x 1 x 2 6 12 largelyap Compute separation of nearby trajectories largelyap is an algorithm very similar to the Wolf algorithm it computes the average exponential growth of the distance of neighboring orbits via the prediction error The increase of the prediction error vs the prediction time allows an estimation of the largest lyapunov exponent
66. ies from the toolbox must be in the Matlab path There are several methods to include these directories depending on you having full control over the Matlab installation or using a network wide installation as a normal user with reduced privileges e If you have full control over the installation Enter the Open TSTOOL directory and choose the item Installation under Toolboxes gt Open TS Tool in the Matlab Start menu It will install the OpenTSTool directories in the Matlab search path and call the path tool Now simply click save to store the current path for future sessions e If you are working with a networked installation Enter the path tool as just described in the previous paragraph but after you click on save you will get an error which states that the path could not be saved Now choose Yes to save the file pathdef m in your userpath which you can see by calling the command userpath in the Matlab shell on UNIX this is usually the directory lt HOMEDIR gt matlab or lt HOMEDIR gt Documents matlab Create it if it does not yet exist You might have to set the environment variable MATLAB_USE_USERPATH to 1 to make this work e If dont have a graphical display and are working with the shell Enter the Open TSTOOL directory call tstoolInit and then savepath e Another possibility is to create a file startup m in your userpath usually lt HOMEDIR gt matlab or lt HOMEDIR gt Documents matlab containing the following lines addpa
67. imental data Physica D 20 pp 217 236 Landa P S M G Rosenblum 1991 Time series analysis for system identification and diag nostics Physica D 48 pp 232 254 Palus M I Dvorak 1992 Singular value decomposition in attractor reconstruction pitfalls and precautions Physica D 55 pp 221 234 Sauer T 1994 Reconstruction of dynamical systems from interspike intervals Phys Rev Lett 72 pp 3811 3814 Castro R T Sauer 1997 Correlation dimension of attractors through interspike intervals Phys Rev E 55 1 pp 287 290 102 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Racicot D M A Longtin 1997 Interspike interval attractors from chaotically driven neuron models Physica D 104 pp 184 204 Stark J D S Broomhead M E Davies J Huke 1996 Takens embedding theorems for forced and stochastic systems in Proceedings of the 2nd World Congress of Nonlinear Analysts Athens greece July 1996 Kennedy M P 1994 Chaos in the Colpitts oscilator IEEE Trans Circuits Syst 41 11 pp 771 774 Cenys A K Pyragas 1988 Estimation of the number of degrees of freedom from chaotic time series Phys Lett A 129 pp 227 230 Buzug Th T Reimers G Pfister 1990 Optimal reconstruction of strange Attractors from purely geometrical arguments Euro
68. in Syntax e minimum yunit xpos xunit min s Give information about minimum of scalar signal s Example disp minimum of signal disp y num2str m label yunit s disp x num2str xpos label a 6 20 3 43 minus Syntax e rs minus s offset e rs minus s1 s2 Input arguments e s si s2 signal object e offset scalar value Calculate difference of signals s1 and s2 or substract a scalar value from s 6 20 3 44 movav Syntax e rs movav s len windowtype e rs movav s len Moving average of width len samples along first dimension 6 20 3 45 multires Syntax multires s gt scale 3 Oo 5 n Il e rs multires s scale Multires perform multiresolution analysis Y MULTIRES X H RH G RG SC obtains the SC succes sive details and the low frequency approximation of signal in X from a multiresolution scheme The analysis lowpass filter H synthesis lowpass filter RH analysis highpass filter G and synthesis highpass filter RG are used to implement the scheme Results are given in a scale 1 channels The first scale channels are the details corresponding to the scales 2 to 2 1 the last row contains the approximation at scale 2 The original signal can be restored by summing all the channels of the resulting signal 60 6 20 3 46 nearneigh Syntax e rs nearneigh s n gt past 1 ers nearneigh s n past Input arguments
69. ithm Example x chaosys 25000 0 025 0 1 0 1 0 02 0 x 5001 end discard first 5000 samples due to transient now compute correlation sum up to five percent of attractor diameter c d corrsum2 x 1000 100 2000 0 05 200 loglog d c and show the result as log log plot ES I 6 9 fnearneigh Fast nearest neighbor search fnearneigh is based on the advanced triangle inequality algorithm ATRIA However it does not support approximate queries The functionality of fnearneigh is almost the same as that of nn_search cf Section 6 14 so fnearneigh might become obsolete in future versions of TSTOOL Syntax e index distance fnearneigh pointset query_points k e index distance fnearneigh pointset query_indices k exclude Input arguments e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e query_points aR by D double matrix containing the coordinates of the query points organized as R points of dimension D e query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N e k number of nearest neighbors to be determined 40 e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and
70. lements in matlab notation Return signal s data values With no extra arguments data returns the data array of a signal object Another possible call is data signal 1 20 6 22 3 6 db Syntax e cout db cin ref scf dbmin Input Arguments e cin core object e ref reference value e scf scaling factor e dbmin minimal db value compute decibel values to reference value ref and scaling factor 10 or 20 scf 6 22 3 7 diff Syntax e cout diff cin nth delta Input Arguments e cin core object e nth number of derivations e delta time difference between to signal values nth numerical derivative along dimension 1 when data was sampled equidistantly with samplerate 1 delta 78 6 22 3 8 display Syntax e display c Input Arguments e c core object 6 22 3 9 dlens Syntax e d dlens c nr Input Arguments e c core object returns sizes of dimensions same as function size under matlab 6 22 3 10 embed Syntax e cout embed cin dim delay shift windowtype Input Arguments e cin core object e dim embed dimension e delay delay time in samples for time delay vectors shift shift in samples for two sequent time delay vectors e windowtype type of window Create time delay vectors with dimension dim delay is measured in samples The input must be a scalar time series The result is a n by dim array each row contains the coordinates of one point 6 22
71. ll descriptive information belonging to a signal 7 2 3 8 What is class achse for Class achse models an axis e g a time axis or a frequency axis A signal has a least one axis if it is a one dimensional signal A multidimensional signal has several achse objects one for each dimension An achse object is basically described by an object of class unit and the spacing values The spacing may be linear logarithmic or arbitrary in case of non uniform sampling 7 2 3 9 Why is class achse called achse and not axis The names axis and axes are already occupied in Matlab So achse which is the german translation of axis was used as name for that class 7 2 3 10 What is class unit for Objects of class unit try to model physical units No one wonders that his computer can multiply real or complex numbers But in physics or engineering you also have to mulitply or divide physical units just think of Ohm s law R U I 7 2 3 11 How is class unit used in TSTOOL Class unit is used as a part of every achse object and as part of a description object Handling and processing of units is optional for functions that work on signals because many nonlinear signal analysis functions do not allow consistent handling of units 7 2 4 Extending TSTOOL Of course it s possible to extend TSTOOL with some custom functionality or to use parts of TSTOOL in your own m files just as with other toolboxes
72. ll and will therefore not work e GNU Linux The free compiler suite gcc usually comes pre installed with most distributions You will need at least version 3 4 or newer check with gcc v Run mex setup in MATLAB and choose the gccopts sh options file for compilation e Solaris You can also use gcc but the C compiler from Sun Forte Studio should also work Version 7 or newer For using the latter make sure the command cc runs the correct compiler in the shell call mex setup in MATLAB and choose the system s ANSI compiler e Mac OS X The gcc suite is available through Apple s XCode Developer Tools which can be downloaded from http developer apple com TOOLS xcode registration required As for GNU Linux run mex setup and choose gccopts sh e Windows Unfortunately compiling mex files under Windows ist more difficult to do since each MATLAB version is pretty picky about which version of which compiler it supports If you happen to have Microsoft Visual C Professional this should usually be detected by mex setup and it should compile the C files just fine If you want to use the Express edition which you can download free of charge from Microsoft usually only the newest MATLAB version currently 7 7 will support it directly For older MATLAB versions you will also have to install the Microsoft Windows SDK for Windows Server 2008 and NET Framework and copy some files in the right places Fortunately there s an tuto
73. n 7 2 3 11 un 4 Extending TSTOOL cf Section 7 2 4 93 e How can I write a script to automatize common tasks cf Section 7 2 4 1 5 Miscellaneous questions cf Section 7 2 5 e What s the difference between history and commandlines cf Section 7 2 5 1 e Is it TSTOOL TSTool OpenTSTOOL OpenTSTool cf Section 7 2 5 2 6 Frequently encountered errors cf Section 7 2 6 e Using a column vector to create a one dimensional signal cf Section 7 2 6 1 e What does the error message Attempt to execute SCRIPT as a function mean cf Section 7 2 Answers 7 2 1 Introduction and general information 7 2 1 1 What is TSTOOL TSTOOL is a software package for nonlinear time series analysis though it has a lot of features a general signal analysis package would also have 7 2 1 2 What software is required to run TSTOOL TSTOOL is written in MATLAB a powerful language for scientific computing and in C The refore you need MATLAB version 6 5 or higher to run tstool Unfortunately MATLAB is not free software 7 2 1 3 On which systems does TSTOOL run TSTOOL should run on all platforms which run MATLAB and for which you can compile the included mex files which are functions written in Cor C that extend MATLAB s set of build in functions We try to ship pre compiled mex files with TSTOOL for the most popular operating systems namely Windows XP 32 and 64 bit Linux 32 and 64 bit
74. nctions 22 222 2 on nn 73 bg ey Be en A ee dr IR See O 76 6 22 1 OvervieW 2 22 0 22 wee a bee rr ad 76 6 22 2 Attributes ea 4 om adit Get ce gy pw eae ea a ee ae a we A 76 6 22 3 Member functions e 77 Sct Gee Se Ges Oe ye tt Gey aly Bent ee neta Gtk Ok pa ad ee 85 Bd AA Oe Oe Go Sa RS SS RAR Ree ip ees 85 6 23 2 Attributes 2 6 ee es 22 2 na EE ee A we BP A 85 6 23 3 Member functions 2 2 2 un m nn nn 85 6 24 Class untl 2 4 4944 66 2 0 0 0 REAR ne we ae Se 88 LO Ge ae aay de li DE II Eee se a De Ai Bee de ad e 88 624 2 Attrib tesia sr a bed 88 6 24 3 Member functions 2 mn nn nn 88 6 20 Class TISEI 2 ica de 4 ma aa EES ie A AA A ee u om a A 90 Ss oS Rk ee ee ees a ge Settee a 90 6 25 2 Attributes 4444244 94 RPE ar Ee eee deere ee Ye Pee ead 90 6 25 3 Member functions 2 2 2 mn m nn 90 93 GL Questions 444248 5 OS NA 93 T2 Answersl i bod A Kun wen A BEERS ee eee eS 94 7 2 1 Introduction and general information 2 2 nn nn 94 7 2 2 Installation of TSTOOL 22 2 2 Co oo onen 95 7 2 3 Working with TSTOOL 2 222 2 0 ou 96 7 2 4 Extending STOOL e s sa 2 04 0000 a a nun aha nn 97 ee A ne o ee Ge ee a do A 98 De ee Sean aA 98 Chapter 1 At a glance What is TSTOOL TSTOOL is a software package for signal processing with emphasis on nonlinear time series analysis Objectives e Implement existing algorithms for nonlinear time series analysis e Develop n
75. nput signal s length The default for maxdim is 8 and for nref it is 10 of the input signal s length 6 20 3 4 amutual Syntax e amutual s maxtau bins Input arguments e maxtau maximal delay should be much smaller than the lenght of s optional e bins number of bins used for histogram calculation optional Auto mutual information function for real scalar signals can be used to determine a proper delay time for time delay reconstruction The default value for maxtau is 25 of the input signal s length The default number of bins is 128 6 20 3 5 amutual2 Syntax e amutual2 s len Input arguments e len maximal lag Auto mutual information average function for real scalar signals using 128 equidistant partitions 6 20 3 6 analyze Syntax e analyze s maxdim Input arguments e maxdim analyze will not use a dimension higher than this limit Try to do a automatic analysis procedure of a time series The time series is embedded using the first zero of the auto mutual information function for the delay time 50 6 20 3 7 arch Syntax e rs archetypes arch s na mode normalized Input arguments e na number of generated archetypes e mode mode can be one of the following normalized mean raw optional Archetypal analysis of column orientated data set e each row of data is one observation e g the sample values of all channels in a multichannel measurement a
76. nstallation for doing this e Second option Set the environment variable LD_PRELOAD to enforce usage of your installed system libraries For example you may call Matlab the following way from the command line LD_PRELOAD usr lib libstdct so 6 lib libgcc_s so 1 matlab This option is a bit more cumbersome but has the advantage that you can do this as normal user Note that this command is only an example check your library directories for the correct paths and file names 2 4 Pitfalls See also the FAQ Frequently Asked Questions 1 As of TSTOOL version 1 2 the main function for creating the TSTOOL GUI is called opentstool instead of tstool to avoid collision with the time series toolbox from The Ma thworks 2 When using Winzip enable Use path information to make sure that subdirectories are created 3 TSTOOL will not work with Matlab version prior to 6 5 4 It s not a good idea to place the TSTOOL distribution into the Matlab directory We obtai ned reports about strange bugs occuring when the TSTOOL distribution is extracted into the directory where the Matlab system is installed 12 2 5 Copyright notice TSTOOL falls unter the GNU General Public License See gp1 txt in the OpenTSTOOL directory or http www physik3 gwdg de tstool gpl txt 13 Chapter 3 First Steps 3 1 Example analysis of a time series from a chaotic Colpitts oscillator In this section we briefly demonstrate basic steps for anaysing a chao
77. o acoustics J Acoust Soc Am 84 pp 1975 1993 Packard N H J P Crutchfield J D Farmer R S Shaw 1980 Geometry from a time series Phys Rev Lett 45 pp 712 716 Takens F 1981 Detecting strange attractors in turbulence in Dynamical Systems and Tur bulence eds Rand D A amp Young L S Berlin Springer pp 366 381 Kantz H amp T Schreiber 1997 Nonlinear Time Series Analysis Cambridge University Press Cambridge Abarbanel H D I 1996 Analysis of Observed Chaotic Data Springer New York Abarbanel H D I Brown R Sidorowich J J amp Tsimring L S 1993 The analysis of obser ved chaotic data in physical systems Rev Mod Phys 65 4 pp 1331 1392 Grassberger P Schreiber T amp Schaffrath C 1991 Nonlinear time sequence analysis Int J Bif Chaos 1 3 pp 521 547 Sauer T Y Yorke M Casdagli 1991 Embedology J Stat Phys 65 pp 579 616 Sauer T J A Yorke 1993 How many delay coordinates do you need Int J Bifurcation and Chaos 3 pp 737 744 Casdagli M S Eubank J D Farmer J Gibson 1991 State space reconstruction in the presence of noise Physica D 51 pp 52 98 Gibson J F J D Farmer M Casdagli S Eubank 1992 An analytic approach to practical state space reconstruction Physica D 57 pp 1 30 Broomhead D S G P King 1986 Extracting qualitative dynamics from exper
78. of dimension D D is limited to 128 e partitions number of partitions per axis limited to 16384 For convenience if a vector is given boxcount will iterate over all values of this vector Output arguments e a vector of size D with log2 sum Number of nonempty boxes e b vector of size D with sum p log2 p where p is the relative frequency of points falling into a box e c vector of size D with log2 sum p p where p is the relative frequency of points falling into a box Example p rand 50000 4 p p min min p p p max max p a b c boxcount p 16 6 5 cao Determine minimum embedding dimension by Cao s method This mex file applies Cao s method 38 to the input data set If the data set contains points of dimension D it computes E and E for a data set of dimension 1 taken from the first column of the input data set then for a data set of dimension 2 taken from the first two columns up to a dimension of D Optionally this algorithm extends Cao s method in a straightforward manner to use more than one nearest neighbors Syntax e E E cao pointset query_indices k Input arguments 35 e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from
79. oints are taken out of the pointset query indices is a vector of length R which contains the indices of the query points e r range or search radius r gt 0 e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments e count a vector of length R contains the number of points within distance r to the corresponding query point e neighbors a Matlab cell structure of size R by 2 which contains vectors of indices and vectors of distances to the neighbors for each given query point This output argument can not be stored in a standard Matlab matrix because the number of neighbors within distance r is not the same for all query points The vectors if indices and distances for one query point have exactly the length that is given in count The values in the distances vectors are not sorted 6 17 return time return_time may be used to find hidden periodicity in multivariate data e g embedded time series data It computes a histogram of return times For any given reference point return_time calculates the time span until the time series returns to that location in phase space by means of nearest neighbors A histogram of these time spans is computed Strong peaks in this
80. one time axis and a channel axis Another example for a two dimensional signal is a short time spectrogramm of a time series where we have a time axis and a frequency axis Each axis can have a physical unit e g s or Hz a starting point and a step value E g if a time series is sampled with 1000 Hz beginning at 1 min 12 sec the unit is s the starting point is 72 and the step value delta is 0 001 But not only the axes have physical units also the sample value themselve can have a unit maybe V or Pa depending on what the sampled data represent yunit All units are stored as objects of class unit all axes are stored as objects of class achse this somewhat peculiar name was chosen because of conflicts with reserved matlab keywords axis and axes which otherwise would have been the first choice Example for creating a 2 dimensional signal with y unit set to Volt the first dimension s unit is second time the second dimension s unit is n Channels Examples e tmp rand 100 10 s signal tmp unit s unit n s setyunit s unit V s addcomment s Example signal with two dimensions e Loading from disk s signal filename loads a previously stored signal object e Importing from other file formats ASCII s signal data spalteil dat ASCII WAVE s signal data Sounds hat wav WA
81. ons number of partitions for the one dimensional histogram Output arguments e a vector of length maxtau 1 holding auto mutual information 6 3 baker Generate Baker time series Generate time series from the iterated Baker map 150 Syntax e x baker length eta 11 12 x0 y0 Input arguments e length number of samples to generate e eta 11 12 x0 y0 vector of parameters and initial conditions Output arguments e x time series Example x baker 2000 0 6 0 25 0 4 rand 1 1 rand 1 1 plot x 1 end 1 2 x 2 end 2 34 6 4 boxcount Classical boxcounting algorithm boxcount is a fast algorithm that partitions a data set of points into equally spaced and sized boxes The algorithm is based on Robert Sedgewick s Ternary Search Trees 149 which offer a fast and efficient way to create and search a multidimensional histogram Empty boxes require no storage space therefore the maximum number of boxes and memory used can not exceed the number of points in the data set regardless of the data set s dimension and the number of partitions per axis During processing data values are scaled to be within the range 0 1 All columns of the input matrix are scaled by the same factor so no skewing is introduced into the point set Syntax e a b c boxcount point_set partitions Input arguments e pointset a N by D double matrix containing the coordinates of the point set organized as N points
82. ormation like labels command lines and a processing history The majority of functions in the tstoolbox take a signal as input argument and return a processed signal as output This allows for combining or chaining of several processing steps in order to get the desired output 6 20 2 Attributes e xaxes cellarray of at least one object of type achse e core object of type core cf Section 6 22 e description object of type description cf Section 6 21 6 20 3 Member functions 6 20 3 1 abs Syntax e abs s Take absolut value of all data values of signal s If sample values are complex abs s returns the complex modulus magnitude of each sample 6 20 3 2 acf Syntax e acf s len Input arguments e len length of the fft optional Autocorrelation function for real scalar signals using fft of length len If len is ommited a default value is calculated The maximum of the calculated length is 128 6 20 3 3 acp Syntax e acp s tau past maxdelay maxdim nref Input arguments 49 e tau proper delay time for s e past number of samples to exclude before and after reference index to avoid correlation effects e maxdelay maximal delay should be much smaller than the lenght of s optional e maxdim maximal dimension to use optional e nref number of reference points optional Auto crossprediction function for real scalar signals for increasing dimension The default value for maxdelay is 25 of the i
83. orrelation dimension of a time delay reconstructed timeseries s for dimensions from 1 to D where D is the dimension of the input vectors using boxcounting approach The default number of bins is 100 6 20 3 12 corrsum Syntax e rs corrsum s n range past bins Input arguments e n number of randomly chosen reference points n 1 means use all points e range maximal relative search radius relative to attractor size 0 1 e past number of samples to exclude before and after each reference index e bins number of bins optional Compute scaling of correlation sum for time delay reconstructed timeseries s Grassberger Proccacia Algorithm using fast nearest neighbor search Default number of bins is 20 6 20 3 13 corrsum2 Syntax e rs corrsum2 s npairs range past bins Input arguments e npairs number of pairs per bins e range maximal relative search radius relative to attractor size 0 1 e past number of samples to exclude before and after each reference index e bins number of bins optional defaults to 32 Compute scaling of correlation sum for time delay reconstructed timeseries s Grassberger Proccacia Algorithm using fast nearest neighbor search 52 6 20 3 14 crosscorrdim Syntax e rs crosscorrdim s s2 n range past bins Input arguments e n number of randomly chosen reference points n 1 means use all points e range maximal relative search radius relative to size o
84. our a maximal dimension of eight three nearest neighbors and 1000 reference points c cao s 8 4 3 1000 view c Minimum embedding dimension using Cao s method E1 d 2 3 4 5 6 7 8 Dimension d There s a kink in the graph produced by Cao s method at three So now do a time delay reconstruction of the Colpitts signal with embedding dimension 3 and delay 4 16 e embed s 3 4 view e 200 100 What s the correlation dimension of the reconstructed data set First let s take a look at the scaling of the correlation sum versus the radius as log log plot view corrsum e 1 0 05 40 32 Correlation sum P 8 e Fa 10 ae 712 ie 3 2 G 14 ral ra 16 Pi 18 a ae 2 1 0 1 2 3 Next we use the Takens estimator for the correlation dimension It needs basically the same input arguments as the function corrdim2 gt gt takens_estimator e 1 0 05 40 ans 1 9483 And what about it s largest Lyapunov exponent To estimate the largest Lyapunov exponent we take a look at the scaling of the prediction error view largelyap e 1000 300 40 2 17 Prediction error 50 100 150 18 200 250 300 Chapter 4 Nearest Neighbors Searching An integral part of a majority of methods for nonlinear time series analysis is searching for nearest neighbors The perfomance of these methods depends strongly of the perfomance of the empl
85. oyed nearest neighbor algorithm Thus choosing an efficient nearest neighbor algorithm should be done very carefully 4 1 Definition Definition A set P of data points in D dimensional space is given Then we define the nearest neighbor to some reference point q also called query point to be the point of data set P that has the smallest distance to q we don t issue the problem of ambiguity at this point The more general task of finding more than one nearest neighbor is called k nearest neighbors problem In general the reference point q is an arbitrarily located point but it is also possible that q is itself a member of data set P as illustrated in the figure where five neighbors to q excluding self match are found N 4 2 Approximate nearest neighbors searching Approximate nearest neighbors algorithms report neighbors to the query point q with distances pos sibly greater than the true nearest neighbors distances The maximal allowed relative error epsilon is given as a parameter to the algorithm For epsilon 0 the approximate search returns the true exact nearest neighbor s Computing exact nearest neighbors for data set with fractal dimension much higher than 6 seems to be a very time consuming task Few algorithms seem to perform significantly better than a brute force computation of all distances However it has been shown that by computing nearest neighbors approximately it is possible to achieve significantly faste
86. phys Lett 13 pp 605 610 Alecsi Z 1991 Estimating the embedding dimension Physica D 52 pp 362 368 Buzug Th G Pfister 1992 Optimal delay time and embedding dimension for delay time coordinates by analysis of the global static and local dynamical behavior of strange attractors Phys Rev A 45 pp 7073 7084 Gao J Z Zheng 1993 Local exponential divergence plot and optimal embedding of a chaotic time series Phys Lett A 181 pp 153 158 Gao J Z Zheng 1994 Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series Phys Rev E 49 pp 3807 3814 Huerta R C Santa Cruz J R Dorronsore V Lopez 1995 Local state space reconstruction using averaged scalar products of dynamical system flow vectors Europhys Lett 29 pp 13 18 Liebert W K Pawelzik H G Schuster 1991 Optimal embeddings of chaotic attractors from topological considerations Europhys Lett 14 pp 521 526 Kennel M B R Brown H D I Abarbanel 1992 Determining embedding dimension for phase space reconstruction using a geometrical construction Phys Rev A 45 pp 3403 3411 Fredkin D R J A Rice 1995 Method of false nearest neigbors a cautionary note Phys Rev E 51 4 pp 2950 2954 Cao L 1997 Practical method for determining the minimum embedding dimension of a scalar time series Physcai D 110 pp 43 50 Kembe
87. pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e atria output of cf Section 6 13 nn_prepare for pointset 43 query_points aR by D double matrix containing the coordinates of the query points organized as R points of dimension D query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N k number of nearest neighbors to be determined epsilon optional relative error for approximate nearest neighbors queries defaults to 0 exact search exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments index a matrix of size R by k which contains the indices of the nearest neighbors Each row of index contains k indices of the nearest neighbors to the corresponding query point distance a matrix of size R by k which contains the distances of the nearest neighbors to the corresponding query points sorted in increasing order 6 15 predict State space based prediction using nearest neighbors The algorithms computes one or more nearest neighbors to an initial state vector T
88. r G A C Fowler 1993 A correlation function for choosing time delays in phase portrait reconstructions Phys Lett A 179 pp 72 80 Rosenstein M T J J Collins C J De Luca 1994 Reconstruction expansion as a geometry based framework for choosing proper delay times Physica D 73 pp 82 98 Frazer A M H L Swinney 1986 Independent coordinates in strange attractors from mutual information Phys Rev A 33 pp 1134 1140 Frazer A M 1989 Reconstructing attractors from scalar time series a comparison of singular system and redundancy criteria Physica D 34 pp 391 404 Frazer A M 1989 Information and entropy in strange attractors IEEE Trans Info Theory 35 pp 245 262 Liebert W H G Schuster 1989 Proper choice of the time delay for the analysis of chaotic time series Phys Lett A 142 pp 107 111 Martinerie J M A M Albano A I Mees P E Rapp 1992 Mutual information strange attractors and the optimal estimation of dimension Phys Rev A 45 pp 7058 7064 103 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Broomhead D S J P Huke M R Muldoon 1992 Linear filters and nonlinear systems J Roy Stat Soc B54 pp 373 382 Davies M E amp K M Campbell 1996 Linear recursive filters and nonlinear dynamics Non linearity 9 pp 48
89. r execution times with relatively small actual errors in the reported distances 19 4 3 Range searching In the task of range searching we ask for all points of data set P that have distance r or less from the query point q Sometimes range searching is called a fixed size approach while k nearest neighbors searching is called a fired mass approach 4 4 Matlab mex functions 4 4 1 nn_prepare nn_prepare does the preprocessing for a given data set pointset The returned data structure atria contains preprocessing information that is necessary to use nn_search or range_search Preprocessing and searching is divided into different mex files to give the user the possibility to re use the preprocessing data contained in atria when doing multiple searches on the same point set However as soon as the underlying point set is changed or modified one has to recompute atria for the changed point set Syntax e atria nn_prepare pointset e atria nn_prepare pointset metric e atria nn_prepare pointset metric clustersize Input arguments e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e metric optional either euclidian or maximum default is euclidian e clustersize optional threshold for clustering algorithm defaults to 64 4 4 2 nn search nn_ search does exact or approximate k nearest neighbor queries to one or more query points Thes
90. ref Input arguments eD e eps e NNR e len e Nref Generalized mutual information function for a scalar time series 56 6 20 3 30 histo Syntax e histo s partitions Histogram function using equidistantly spaced partitions 6 20 3 31 infodim Syntax e rs infodim s bins Input arguments e s data points row vectors e bins maximal number of partition per axis default is 100 Compute the information dimension of a time delay reconstructed timeseries s for dimensions from 1 to D where D is the dimension of the input vectors Using boxcounting approach Scale data to be within 0 and 1 Give a sortiment of integer partitionsizes with almost exponential behaviour 6 20 3 32 infodim2 Syntax e rs infodim2 s n kmax past Input arguments e n number of randomly chosen reference points n 1 means use all points e kmax maximal number of neighbors for each reference point e past number of samples to exclude before and after each reference index Compute scaling of moments of the nearest neighbor distances for time delay reconstructed timeseries s This can be used to calculate information dimension D1 Numerically compute first derivative of log y k after k 6 20 3 33 int Syntax e int s Numerical integration along dimension 1 signal s has to be sampled equidistantly 57 6 20 3 34 intspikeint Syntax e rs intspikeint s Compute the interspike intervalls for a spiked
91. rial for this which you ll find at http www mathworks com matlabcentral fileexchange 22689 Alternatively like on Unix systems you can install the free gcc compiler on Windows which is available under the name MinGW minimalist gcc for Windows Unfortunately Matlab does not officially support this compiler under Windows so you cannot use it by simply calling mex setup Instead you can try to use the free tool GnuMex to create a proper compilation batch file for you Please visit the following web sites for details and downloads GnuMex http gnumex sourceforge net MinGW http www mingw org Note that GnuMex will currently not work on 64bit Windows systems out of the box After you have set up the mex tool enter the subdirectory mex dev and call makemex This function will compile all the necessary files and copy them into the tstoolbox mex lt MEXEXT gt subdirectory 11 2 3 1 Problems with compiling mex files Dependent on the version you are using Matlab will support only a certain range of gcc compilers If you are using an unsupported gcc version you will see a warning message like this during compilation Warning You are using gcc version X X X The earliest gcc version supported with mex is Y Y Y The latest version tested for use with mex is Z Z Z To download a different version of gcc visit http gcc gnu org While compiling with a newer gcc version often works despite the warning you should still t
92. ronization predictability and equivalence of uni directionally coupled dynamical systems Phys Rev Lett 76 11 pp 1816 1819 Abarbanel H D I N F Rulkov M M Sushchik 1996 Generalized synchronization of chaos The auxiliary system approach Phys Rev E 53 5 pp 4528 4535 Parlitz U L Junge L Kocarev 1997 Subharmonic entrainment of unstable period orbits and generalized synchronization Phys Rev Lett 79 17 pp 3158 Parlitz U L Kocarev 1998 Synchronization of chaotic systems in Control of Chaos Handbook Ed H G Schuster WILEY VCH Sirovich L 1989 Chaotic dynamics of coherent structures Physica D 37 pp 126 145 Rico Martinez R K Krischer I G Kevrekidis M C Kube J L Hudson 1992 Discrete vs continuous time nonlinear signal processing of Cu electrodissolution data Chem Eng Comm 118 pp 25 48 Parlitz U amp G Mayer Kress 1995 Predicting low dimensional spatiotemporal dynamics using discrete wavelet transforms Phys Rev E 51 4 pp R2709 R2711 H D I Abarbanel Analysis of Observed Chaotic Data Springer Verlag New York Berlin Heidelberg 1996 S Arya D M Mount N S Netanyahu R Silverman and A Wu An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions Proc of the Fifth Annual ACM SIAM Symp on Discrete Algorithms 1994 pp 573 582 A Belussi and C Faloutsos Estimating the
93. ry to use a gcc version which your version of Matlab supports On many Unix systems especially most Linux distributions more than one version of gcc is installed and often you can use one certain version by using an explicit command like gcc X Y You can put the appropriate command into the mexopts sh file instead of just gcc and g which Matlab created for you during mex setup On Unix systems it can be found in the directory matlab VERSION under your home directory Another problem can occur due to Matlab coming with its own versions of the standard C C and gcc libraries at least under Unix systems This can lead to problems if your mex files were linked against another C library installed on your system You will typically get an error like the following when calling such a mex file lt MATLABROOT gt sys os glnx86 libgec_s so 1 version GCC_4 2 0 not found required by usr lib libstdc so 6 There exist basically two options for solving this problem Note that as far as we know both are not officially supported by The Mathworks but usually work nonetheless e First option move the files libstdc libgec and libg2c from lt MATLABROOT gt sys os lt SYSTEM gt to another location for example a subdirectory named old You will thereby enforce the libraries installed on your system If you encounter problem afterwards simply move the libraries back and restart Matlab Of course you need control over the Matlab i
94. s e atria output of nn_prepare for pointset optional cf Section 6 13 e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e query_indices query points are taken out of the pointset query_indices is a vector of length R which contains the indices of the query points indices may vary from 1 to N e range search range may be given in one of two ways If only a single value is given this value is taken as maximal search radius relative to the attractor diameter 0 lt relative range lt 1 The minimal search radius is determined automatically be searching for the minimal interpoint distance in the data set Ifa vector of length two is given the values are interpreted as absolut minimal and maximal search radius e exclude in case the query points are taken out of the pointset exclude specifies a range of indices which are omitted from search For example if the index of the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches e bins number of distance values at which the correlation sum is evaluated defaults to 32 Output arguments e c vector of correlation sums length c bins e d vector of the corresponding distances at which the correlation sums stored in c were computed d is exponentially spaced length c bins Example x chaosys 2
95. scalar timeseries using transformation on ranked va lues 6 20 3 35 intspikint Syntax e rs intspikeint s Compute the interspike intervalls for a spiked scalar timeseries using transformation on ranked va lues 6 20 3 36 largelyap Syntax e rs largelyap s n stepsahead past nnr Input arguments e n number of randomly chosen reference points 1 means use all points e stepsahead maximal length of prediction in samples e past exclude e nnr number of nearest neighbours optional Output arguments e rs Compute the largest lyapunov exponent of a time delay reconstructed timeseries s using formula 1 5 of Nonlinear Time Series Analysis Ulrich Parlitz 1998 146 6 20 3 37 level_adaption Syntax e level adaption s timeconstants dynamic_limit threshold Each channel of signal s is independently divided by a scaling factor that adapts to the current level of the samples in this channel The adaption process is simulated using a cascade of feedback loops Piischel 1998 which consists of low pass filters with time constants given as second argument to this function The number of time constants given determines the number of feedback loops that are used Higher values for time constants will result in slower adaption speed Short time changes in the signal will be transmitted almost linearily In each feedback loop a nonlinear compressing characteristic see Stefan M nkner 1993 limits the signal values
96. t one point in time e in mode normalized each column of data is centered by removing its mean and then normalized by dividing through its standard deviation before the covariance matrix is calculated e in mode mean only the mean of every column of data is removed e in mode raw no preprocessing is applied to data Default value for mode is normalized 6 20 3 8 boxdim Syntax e rs boxdim s bins Input arguments e s data points row vectors e bins maximal number of partition per axis optional Compute the boxcounting capacity dimension of a time delay reconstructed timeseries s for dimen sions from 1 to D where D is the dimension of the input vectors using boxcounting approach The default number of bins is 100 6 20 3 9 cao Syntax e E1 E2 cao s maxdim tau NNR Nref Input arguments e s scalar input signal e maxdim maximal dimension e tau delay time e NNR number of nearest neighbor to use e Nref number of reference points 1 means use all points Estimate minimum embedding dimension using Cao s method The second output argument E2 can be used to distinguish between deterministic and random data 51 6 20 3 10 center Syntax e center s Center signal by removing it s mean 6 20 3 11 corrdim Syntax e rs corrdim s bins Input arguments e s data points row vectors e bins maximal number of partition per axis optional Compute the c
97. t to prefer This hint can be set with the command setplothint The possible plot types can be obtained by issuing help signal view at the Matlab prompt However if the signal does not support the desired type of plotting e g a one dimensional time series can not be visualized as orbit view will use the default plot type for the data s signal rand 1000 3 s setplothint s 3dpoints view s 96 7 2 3 5 What is class signal for Class signal is TSTOOL s main class Objects of this type model real world signals A signal does not only store the pure sample values it holds much more information like axes units of sample values or the axes units and even more descriptive information like labels command lines and a processing history The majority of functions in the tstoolbox take a signal as input argument and return a processed signal as output This allows for combining or chaining of several processing steps in order to get the desired output 7 2 3 6 What is class core for Class core is a base class of class signal An object of type core stores the pure sample values of a signal without any additional descriptive information The separation of the numerical and the descriptive part of a signal simplifies the writing of m files that work on signals 7 2 3 7 What is class description for Class description is the second base class of class signal An object of type description stores a
98. tandard deviation There is a special plothint surrerrorbar for the view function to show this result in the common way surrogate test runs an automatic surrogate data test task It generates ntests surrogate data sets an performs the func function to each set func is a string with matlab code who returns a signal s with a scalar time series Example st surrogate_test s 10 1 1 largelyap embed s 3 1 1 128 20 10 6 20 3 76 swap Syntax Oo 5 n i swap s exchange dimension 1 and dimension 2 e rs swap s dim1 dim2 Exchange signal s dimensions and axes 6 20 3 77 takens_estimator Syntax e D2 takens estimator2 s n range past Input Arguments e n number of randomly chosen reference points n 1 means use all points e range maximal relative search radius relative to attractor size 0 1 e past number of samples to exclude before and after each reference index Takens estimator for correlation dimension 69 6 20 3 78 tc3 Syntax e rs tc3 s tau n method Input Arguments e tau see explaination below e n number of surrogate data sets to generate e method method to generate the surrogate data sets 1 surrogatel 2 surrogate2 3 surrogate3 Output Arguments e rs is a row vector returned as signal object The first item is the T 3 value for the original data set s The following n values are the T 3 values for the generated surrogates Th
99. terms of surrogate data test this is a test statistics for time reversibility The original trev function is located under utils trev m and use simple matlab vectors 6 20 3 81 upsample Syntax e rs upsample s factor method Input Arguments e method may be one of the following a EL spline akima nearest linear cubic e s has be to sampled equidistantly for fft interpolation Change sample rate of signal s by one dimensional interpolation 6 20 3 82 view Syntax e view signal fontsize 12 e view signal fontsize e view signal fontsize figurehandle 71 Signal viewer that decides from the signal s attributes which kind of plot to produce using the signal s plothint entry to get a hint which kind of plot to produce Possible plothints are e graph e bar e surrbar e surrerrorbar e points e xyplot e xypoints e scatter e 3dcurve e 3dpoints e spectrogram e image e multigraph e multipoints e subplotgraph 6 20 3 83 write Syntax e write s filename writes in TSTOOL s own file format e write s filename ASCII e write s filename WAV RIFF WAVE FORMAT e write s filename AU SUN AUDIO FORMAT e write s filename NLD old NLD FORMAT e write s filename SIPP si file format writes a signal object to file filename uses
100. th lt full path to the OpenTSTOOL Dir gt settspath lt full path to the OpenTSTOOL Dir gt Again on UNIX systems you might have to set the environment variable MATLAB_USE_USERPATH to 1 to make this work 2 1 2 Global installation Last but not least if all users of a network wide matlab installation should have access to TSTOOL just insert the paths which are set by the script settspath in the global path from Matlab 2 1 3 Deinstalling TSTOOL If you want to deinstall TSTOOL simply remove the OpenTSTOOL directory start pathtool in Matlab and remove every directory containing OpenTSTOOL Then save the path for future sessions 2 2 First Steps 1 Start Matlab 2 Install paths as described in 3 Enter tsdemo on the Matlab console This should start a short demo script 10 4 Enter tsdemo2 on the Matlab console This should run a second script that shows an analysis of a chaotic signal 5 Note that you can also start the demos through the Matlab Start menu 6 Enter opentstool to start the graphical user interface for the TSTOOL package 7 You can also access the manual any time through the OpenTSTOOL entry in the Matlab start menu 2 3 Compiling mex files If you do not find appropriate pre compiled mex files for your platform on our home page you can compile them yourself You will need an installed C compiler for doing this the C compiler that ships with MATLAB LCC does not compile C code at a
101. the query point is 124 and exclude is set to 3 points with indices 121 to 127 are omitted from search Using exclude 0 means exclude self matches Output arguments index a matrix of size R by k which contains the indices of the nearest neighbors Each row of index contains k indices of the nearest neighbors to the corresponding query point distance a matrix of size R by k which contains the distances of the nearest neighbors to the corresponding query points sorted in increasing order 4 4 3 range search The routine range_search does a range search to one or more query points These query points can be given explicitly or taken from the data set of points see below Before one can use range _search one has to call nn prepare to compute the preprocessing informa tion However as long as the input point set isn t modified the preprocessing information is valid and can be re used for multiple calls to nn_search or range_search Syntax count neighbors range_search pointset atria query_points r count neighbors range_search pointset atria query_indices r exclude Input arguments pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D 21 e query_points a R by D double matrix containing the coordinates of the query points orga nized as R points of dimension D e query_indices query points are taken out of the pointset query_in
102. tic time series The methods used will be explained ind maore detail in the following sections gt gt s signal colpitts dat ascii s signal object Dlens 6001 X Axis 1 Name colpitts Type Attributes of data values Comment History 17 Aug 1999 15 08 24 Imported from ASCII file colpitts dat By entering the above command line the overloaded constructor for class signal was called Giving a filename as argument tells the constructor to load the datafile and convert it into a signal object The datafile colpitts dat contains a time series generated by an electronical Colpitts circuit that oscillates chaotically To plot signal s just issue the following command view s 15 200 150 100 50 50 WA 2000 3000 4000 5000 6000 Lets find a good choice for a delay time by using the first minimum of the auto mutual information function a amutual s 32 view a Bit gt o the first minimum of the auto mutual information can be found at four Now we need to know the minimal embedding dimension for the colpitts signal We use Cao s method with a delay time of f
103. tlab 7 2 2 3 There are more than one file called e g amutual m why For some functions there are up to three versions of the file e OpenTSTOOL tstoolbox signal amutual m Function that invokes the underlying mex func tion It uses signal objects as output and input e OpenTSTOOL tstoolbox mex amutual m Help text for the compiled mex function e g type help amutual on the matlab prompt e OpenTSTOOL tstoolbox mex mexsol amutual mexsol OpenTSTOOL tstoolbox mex mexsg64 amutual mexsg64 OpenTSTOOL tstoolbox mex mexglx amutual mexglx OpenTSTOOL tstoolbox mex mexw32 amutual mexw32 Precompiled mex files for Linux x86 Windows Mac OS X and Solaris are shipped with TS TOOL Only one of these files may be present on your system depending on the version of TSTOOL you have downloaded 7 2 2 4 What does the error message Attempt to execute SCRIPT as a function mean Matlab cannot find the correct mex files for this systems and so it tries to execute the scripts OpenTS TOOL mex m which are only the help texts for the mex files There are many possibilities for this error e You downloaded the wrong version of TSTOOL e The path setting made by settspath m are not correct Type path at the matlab prompt and look for the path setting for the mex directory see 7 2 2 3 e The mex files are not present in the directory noted in 7 2 2 3 7 2 2 5 What does the error message This application has failed to start because t
104. ually called atria can then be used for repeated neighbor searches on the same point set Most mex files that rely on nearest neighbor or range search offer the possibility to use this variable atria as optional input argument However if the underlying point set is altered in any way the proprocessing has to be repeated for the new point set If the preprocessing output does not belong to the given point set wrong results or program termination may occur Syntax e atria nn_prepare pointset e atria nn prepare pointset metric e atria nn_prepare pointset metric clustersize Input arguments e pointset a N by D double matrix containing the coordinates of the point set organized as N points of dimension D e metric optional either euclidian or maximum default is euclidian e clustersize optional threshold for clustering algorithm defaults to 64 Example pointset rand 40000 3 atria nn_prepare pointset c d corrsum atria pointset 1 17 40000 0 05 0 plot log d log c D takens_estimator atria pointset 1 17 40000 0 05 0 6 14 nn search Syntax e index distance nn_search pointset atria query_points k e index distance nn_search pointset atria query_points k epsilon e index distance nn_search pointset atria query_indices k exclude e index distance nn_search pointset atria query_indices k exclude epsilon Input arguments e
105. uments e s core object test if core contains no valid data 80 6 22 3 15 medianfilt Syntax e medianfilt cin len Input Arguments e cin core object moving median filter 6 22 3 16 minus Syntax e minus c1 c2 Input Arguments e c1 c2 core objects subtract c2 from each columns of cl 6 22 3 17 movav Syntax e movav cin len Input Arguments e cin core object e len average length moving average 6 22 3 18 multires Syntax e multires cin h rh g rg sc Input Arguments e cin core object 81 6 22 3 19 ndim Syntax e ndim c Input Arguments e c core object return number of dimensions a scalar value has 0 dimensions 6 22 3 20 normi Syntax e cout normi cin low upp Input Arguments e cin core object e low column number e upp column number normalize each single column of a the core object to be within low upp 6 22 3 21 norm2 Syntax e cout norm2 cin Input Arguments e cin core object normalize signal by removing it s mean and dividing by the standard deviation 6 22 3 22 plus Syntax e plus c1 c2 Input Arguments e c1 c2 core objects add c2 to each columns of cl 82 6 22 3 23 rang Syntax e cout rang cin Input Arguments e cin core object 6 22 3 24 rms Syntax e cout rms cin Input Arguments e cin core object compute root mean square value of each column of cl 6 22 3 25 scalogram

OpenTSTOOL User Manual - Third Institute of Physics

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