An important remark pertaining to all programs:
if the user would like to obtain any additional or differently written (see below for comments) output from the programs
written on disk (for example the third, fourth,..., embedding coordinate),
she/he should feel free to contact me, so I can make appropriate changes and redeliver the program.
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DELAY COORDINATE EMBEDDING |
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44 KB
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The program
embedd.exe reads the time series from a single-column ASCII input file and draws 2D phase space projections
for 4 different embedding delays, whereby the coordinates to be drawn can be chosen arbitrarily.
Parameters that have to be provided are the number of points in the input file, 4 embedding delays, and 4 pairs of coordinates (each pair is used for one particular 2D projection of the whole phase space). Additionally, you can change the size of the drawings and whether
you would like the drawings in colour or black-white. You can also choose if the program should
remember the last set parameters or not. After completion, the program writes 4 files to
the disk (1_embedding1.dat, 1_embedding2.dat, 1_embedding3.dat, 1_embedding4.dat), each consisting of
two ASCII columns. First column lists the
n-th embedding coordinate, whereas the second column
lists the
m-th embedding coordinate, whereby (
n,
m) is the coordinate pair used for the 2D phase space projection.
The number at the beginning of each output file indicates in which consecutive run of the program the file was recorded.
In the second run files written to the disk would be 2_embedding1.dat, 2_embedding2.dat, 2_embedding3.dat, 2_embedding4.dat.
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NONLINEAR NOISE REDUCTION |
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44 KB
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The program
noisered.exe reads the time series from a single-column ASCII input file and draws 2D phase space projections obtained from the original (upper two pictures) and the “clean” time series (lower two pictures).
Parameters that have to be provided are the number of points in the input
file, embedding parameters, and the neighbourhood size for searching neighbours. Additionally, you can choose if the program should remember the last set parameters
or not. After completion, the program draws the above-described graphs.
Files that are written to disk are 1_noisered.dat and 1_series_clean.dat. The first file consists of three ASCII columns.
The first column is the consecutive number of each data point, the second column lists the “clean” time series, whereas
the third column lists how many points were found inside the neighbourhood. The second file has only one ASCII column, which contains
the “clean” time series. The second file is written separately to allow immediate use of the “clean” time series for other applications.
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MUTUAL INFORMATION METHOD |
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44 KB
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The program
mutual.exe reads the time series from a single-column ASCII input file and draws the mutual information
(M. I.) and the autocorrelation (Ac.) in dependence on the embedding delay
(tau). Parameters that have to be provided are the number of points in the input
file, number of bins in which the time series is partitioned for the calculation of the mutual
information, and the maximal embedding delay for which the mutual information and autocorrelation
are calculated. Additionally, you can choose if the program should remember the last set parameters
or not, and if besides the mutual information the autocorrelation should be calculated or not.
After completion, the program draws the above-described graphs as well as returns all minima of
the mutual information and the value of the embedding delay at which the autocorrelation decays to 1/e.
Files that are written to disk are 1_mutual.dat and 1_autocorr.dat, which both consist of two ASCII columns.
The first column in both files is the embedding delay, whereas the second column in the 1_mutual.dat file
lists the mutual information, while in the 1_autocorr.dat file the second column list
the pertaining autocorrelation.
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FALSE NEAREST NEIGHBOR METHOD |
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44 KB
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The program
fnn.exe reads the time series from a single-column ASCII input file and draws the fraction of false nearest neighbors (FNN) in dependence on the
embedding dimension (DIM). Parameters that have to be provided are the number of points
in the input file, the embedding delay, the minimal and the maximal embedding dimension
for which the fraction of false nearest neighbors is to be determined, the starting neighbor
distance, the factor for increasing the starting neighbor distance, the threshold for false
neighbors, and the percent of data that is allowed to be wasted (that is, how many points,
at most, are allowed not to have a close neighbor to still obtain a relevant statistic).
Additionally, you can choose if the program should remember the last set parameters or not.
After completion, the program draws the above-described graph as well as returns the standard
deviation of data to allow a better estimation of the starting neighbor distance and the factor
for increasing it. The written file 1_fnn.dat consists of five ASCII columns.
The first column lists the embedding dimension, while the second column lists
the pertaining fraction of false nearest neighbors. The third and fourth column are the number of
points that have a false nearest neighbor and the number of points for which an initially close-enough
neighbor has been found, respectively. If you divide the third and the fourth column you should obtain
the fraction of false nearest neighbors. The fifth column lists the largest neighborhood size that was
used for finding neighbors. If the neighborhood size increases above [(std. of data)/(threshold)] an
additional entry to the output file is made. If the neighborhood size increases above [(std. of data)/2.0]
the program terminates (prior to that a warning message is diplayed).
In this case try to enlarge the “amount of data that is allowed to be wasted” parameter.
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DETERMINISM TEST |
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60 KB
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The program
determinism.exe reads the time series from a single-column ASCII input file and draws the embedding space as well
as the pertaining approximated directional vector field. Parameters that have to be provided
are the number of points in the input file, the embedding delay, the embedding dimension,
the number of boxes in one dimension (the whole reconstructed phase space is then partitioned
into [(number of boxes) to the power of embedding dimension] boxes), and the so-called significance,
which determines at least how many times a box must be visited by the trajectory to include it (the box)
into the statistic for the determinism factor. Additionally, you can choose if the program should remember
the last set parameters or not. Besides these parameters pertaining to the calculations, you may also adjust
certain parameters pertaining to the drawings. In particular, the main size of the drawings, the length of
the unit vector, the arrowhead length, the arrowhead angle, and the color of drawings can be adjusted.
After completion, the program draws the above-described graph as well as returns the calculated determinism
factor. Files that are written to disk are 1_determinism.dat and 1_vectfield.dat. The first file consists of
two ASCII columns; the first column lists the number of times each occupied box was visited by the trajectory,
while the second column lists the pertaining average vector size for that box. The 1_vectfield.dat file consists
of four ASCII columns; the first two columns represent the first (
x,
y) coordinate and the second two columns
the second (
x,
y) coordinate of each vector (of the vector field), respectively. As previously, some graphic
programs might require block written data to draw vector fields. If you would prefer such an output in the
1_vectfield.dat file let me know.
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STATIONARITY TEST |
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52 KB
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The program
stationarity.exe reads the time series from a single-column ASCII input file and draws a colour map,
where the colour of each map segment indicates the cross-prediction error of using segment
i
as the neighbour source for making predictions in segment
j. Parameters that have to be provided
are the number of points in the input file, the embedding delay, the embedding dimension, the
number of points in one segment (number of points in the file/number of points in one segment = number of segments),
the minimal number of neighbours that have to be found in order to make a prediction, the starting neighbour distance,
the factor for increasing the starting neighbour distance, the number of time steps (ahead) for prediction,
and the percent of data that is allowed to be wasted (that is, how many points, at most, are allowed not
to have enough close neighbours to make a prediction.
If this parameter is set >50%, then the starting neighbour size is left constant, while each
time a point is encountered for which not enough close neighbours are found to make the prediction,
the predicted values is simply set to equal the average value of the data segment in which neighbours
are searched for). Additionally, you can choose to rescale the data to unit variance, but in this
case make sure you also change the starting neighbour size accordingly (0.25 is then usually recommended).
As always, you can also choose if the program should remember the last set parameters or not. You may
also choose if the colour map should be displayed in colour or in black/white contrast. After completion,
the program also returns the standard deviation of data, and the minimal, maximal and the average
cross-prediction error. Files that are written to disk are 1_stationarity.dat and 1_stdev.dat. The first
file consists of three ASCII columns; the first two columns list the data segments used for cross-predictions,
while the third column lists the pertaining cross-prediction errors. The 1_stdev.dat file consists of three ASCII
columns; first column indexes the various data segments, while the second and the third column list the running
average and standard deviation, respectively. First two lines in the 1_stdev.dat file, however, hold information
about the mean and standard deviation of the whole time series. Some graphic programs require block written data
to draw colour maps. If you would prefer such an output in the 1_stationarity.dat file let me know!
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MAXIMAL LYAPUNOV EXPONENT (Wolf) |
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44 KB
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The program
lyapmax.exe reads the time series from a single-column ASCII input file and draws the
embedding space as well as the convergence of the maximal Lyapunov exponent in dependence on
time. Parameters that have to be provided are the number of points in the input file,
the sampling time of data (for correct scalation of the exponent), the embedding delay, the
embedding dimension, the evolution time that determines how long each initial length element
is iterated, the minimal and the maximal initial size of the length element, the maximally
allowed angle separation between each successive length element, and the maximal multipliers
for the maximally allowed size of the initial length element and angle separation
(this multipliers set into action if the procedure cannot find a close enough
neighbor with a small enough angle separation for a particular phase space point).
As always, you can also choose if the program should remember the last set parameters or not.
After completion, the program draws the above-described graph as well as returns the calculated maximal
Lyapunov exponent. Note that for the latter task, no least-squares scheme is implemented,
but solely the last calculated value of the exponent is returned.
If the convergence of the maximal Lyapunov exponent in the presented drawing is not good,
this will then most likely not be a correctly estimated value!
Therefore, in such cases, you should try to obtain the best fit by visually inspecting the data.
The written 1_lyapmax.dat
file consists of two ASCII columns; the first column lists the number of time steps,
while the second column lists the pertaining average maximal Lyapunov exponent at the pertaining time.
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MAXIMAL LYAPUNOV EXPONENT (Kantz) |
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48 KB
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The program
lyapmaxk.exe reads the time series from a single-column ASCII input file file and draws the
S(
n) vs.
n graph (see the book by Kantz and Schreiber for details). Parameters that have to be provided are the number of points in the input file, the embedding delay, the minimal and the maximal
embedding dimension, the number of iterations that determines how long each close-by trajectory
is iterated through the attractor, the minimal and the maximal size of the neighbourhoods in which neighbours are searched for, the minimal number of neighbours (starting points for nearby trajectories) to evaluate the average divergence of nearby trajectories, and the number of reference points that determines for at most how many points the minimal number of neighbours has to be found, before returning the averaged value of averaged divergences of nearby trajectories.
After completion, the program draws the above-described graph. In order to estimate the maximal Lyapunov exponent you have to calculate the slope of the linear part (if it exists!!!) of the presented graph manually.
The written 1_lyapmaxk.dat
file consists of four ASCII columns; the first column lists the number of iterations,
the second column lists the pertaining S(
n), the third column lists the actual number of reference points used, while the fourth column lists the neighbourhood
size for a particular run. Each run for different embedding dimensions is separated by a blank row in the output file (the embedding dimensions go from the minimal to the maximal value).
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RECURRENCE PLOT |
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40 KB
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The program
recurrplot.exe reads the time series from a single-column ASCII input file and draws the
recurrence plot of the system, whereby those pairs (
i,
j) whose distance from one another is smaller than some fixed threshold (neighbourhood size) are plotted blue whilst white otherwise. Parameters that have to be provided are the number of points in the input file, the embedding delay, the
embedding dimension, and the neighbourhood size.
After completion, the program draws the recurrence plot in a maximized window, whereby different scales can be observed in detail by clicking on the “Zoom In” or “Zoom Out” links on the toolbar.
The written
n_points.dat (
n counts consecutive runs)
file consists of two ASCII columns listing (
i,
j) pairs whose distance from one another is smaller than the provided “neighbourhood size”
parameter. Additionally, the program writes the file
n_parameters.dat, which lists the parameters used for the
n-th consecutive run.
or
