t-CWT 3.00 Documentation
Copyright © 2003-2017 Vladimir Bostanov <tcwt_help use>
This HTML file was automatically generated from the
t-CWT help texts contained in the source code files.
t-CWT is a method for multivariate statistical assessment of event-related
brain potentials (ERP). The help texts describe the t-CWT software. The
underlying mathematical algorithm is described elsewhere <tcwt_help math>.
Table of Contents
Themes
help
tcwt_help invoked with no arguments displays this text;
tcwt_help main also displays this text;
tcwt_help help does the same.
tcwt_help NAME displays help text for the script or function tcwt_NAME.
t-CWT version 3.00
Copyright (C) 2003-2017 Vladimir Bostanov <http://tcwt.de/>
t-CWT comes with ABSOLUTELY NO WARRANTY. This is free software, and you
are welcome to redistribute it under certain conditions. See the file
tcwt_use.m <tcwt_help use>. For more details, see the file COPYING or
tcwt_gpl.m <tcwt_help gpl>. If not, see <http://www.gnu.org/licenses/>.
t-CWT is a method for multivariate statistical assessment of event-related
brain potentials (ERP). The help texts describe the t-CWT software. The
underlying mathematical algorithm is described elsewhere <tcwt_help math>.
DOWNLOAD, INSTALLATION AND CONFIGURATION: <tcwt_help install>
GETTING STARTED: <tcwt_help intro>
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use
TERMS OF USE
t-CWT Copyright (C) 2003-2017 Vladimir Bostanov <http://tcwt.de/>
t-CWT is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published
by the Free Software Foundation, either version 3 of the License,
or (at your option) any later version.
t-CWT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty
of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with t-CWT; see the file COPYING or the file tcwt_gpl.m
<tcwt_help gpl>. If not, see <http://www.gnu.org/licenses/>.
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changelog
t-CWT 2.01 --> 3.00 Change Log
Semi-Log-Grid
The code of the t-CWT version 2.01 was almost fully vectorized with
one notable exception: the procedure that finds the local extrema of the
t-value scalogram was vectorized in the time dimension but not in the
scale dimension where it used for-loops. The reason for this was that the
scalogram was sampled on a logarithmic grid <tcwt_help math>. Historically,
this solution was chosen for saving RAM in a time when memory resources
were scarce. In the current t-CWT version, 3.00, the introduction of a
semi-logarithmic grid allows for complete vectorization of the code and
tremendous speed up of the computations.
Mindfulness Project
The previous t-CWT version, 2.01, contained example scripts for the
assessment of example oddball ERP data <tcwt_help math>. These are not
included in the present t-CWT version, 3.00. Instead, the assessment
scripts of the Mindfulness Project (Bostanov et al.. Measuring Mindfulness:
A Psychophysiological Approach; currently in preparation) are included
in the tcwtROOT/jobs directory.
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math
t-CWT MATH
A detailed description of the mathematical algorithm implemented
by the t-CWT software and the results from the assessment of some
example oddball ERP data can be found in
Bostanov V. (2015). Multivariate Assessment of Event-Related
Potentials with the t-CWT Method. BMC Neuroscience.
DOI: 10.1186/s12868-015-0185-z
<http://doi.org/10.1186/s12868-015-0185-z>.
The first version of t-CWT was originally introduced in
Bostanov V. (2004). BCI Competition 2003 -- data sets Ib and IIb:
feature extraction from event-related brain potentials with
the continuous wavelet transform and the t-value scalogram.
IEEE Trans Biomed Eng 51:1057-61.
If you use t-CWT in your research, please cite Bostanov (2015),
or both Bostanov (2015) and Bostanov (2004).
BibTeX ENTRIES:
@article{bostanov15tcwt,
author={Bostanov, Vladimir},
title={Multivariate Assessment of Event-Related Potentials
with the {t-CWT} Method},
journal={BMC Neuroscience},
note={DOI: 10.1186/s12868-015-0185-z,
http://doi.org/10.1186/s12868-015-0185-z},
year={2015}}
@article{bostanov04tcwt,
author={Bostanov, Vladimir},
title={{BCI} {C}ompetition 2003 - Data Sets {I}b and {II}b:
{F}eature Extraction from Event-Related Brain Potentials with
the Continuous Wavelet Transform and the t-Value Scalogram},
journal={IEEE Trans Biomed Eng},
volume={51},
pages={1057-1061},
year={2004}}
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install
DOWNLOAD, INSTALLATION AND CONFIGURATION
1. Download the t-CWT source code from <http://tcwt.de/>
or from <http://bioinformatics.org/tcwt/>.
2. Unpack the t-CWT source code archive file at the desired location
in your file system.
3. Open tcwt_setup.m and change the value of tcwtROOT to the full path
of the t-CWT root directory according to the installation in step 1.
4. Set the value of tcwtWORK in tcwt_setup.m. tcwtWORK is the full path
to the location in your file system where your input and output ERP
data will be stored.
5. Start MATLAB or GNU Octave in interactive mode, change directory to
the t-CWT root directory, and type "tcwt_setup". You should get the
t-CWT Copyright message confirming that t-CWT is ready for use.
6. Add the statements in tcwt_setup.m to your MATLAB startup.m and/or
to your GNU Octave octaverc file, if you wish to have t-CWT ready
for use at startup (without having to type "tcwt_setup" every time).
NOTE: If t-CWT jobs are executed in MATLAB, some t-CWT functions
use probability distributions from the Statistics Toolbox.
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intro
INTRODUCTION TO t-CWT
1. Read this introduction. Then, you can download and install t-CWT version
2.01 <tcwt_help install>, download the example ERP data <tcwt_help math>
and assess them with t-CWT 2.01 to get an impression of how t-CWT works.
Then, you can create your own project following the steps below, or you
can take a look at tcwtROOT/jobs/mbct_ind.m and the other scripts of the
Mindfulness Project contained in the tcwtROOT/jobs directory of this
version (project name: mbct). The mindfulness ERP data are not available,
because the datasets are too big.
2. Choose a new project name (prjNAME) and make a directory
tcwtWORK/prjNAME (Here and further, tcwtROOT and tcwtWORK denote
the t-CWT root path and the t-CWT work path <tcwt_help install>.)
3. Perform EOG correction, technical artifact rejection, segmentation and
binary-to-ASCII conversion of your ERP data with some other software,
and save the obtained ASCII datasets to tcwtWORK/prjNAME/_ascii.
4. Choose a new job input parameter file name (prmNAME) and copy
the demo job input parameter file tcwtROOT/demo/tcwt_prm.m to
tcwtROOT/jobs/prjNAME_prmNAME.m <tcwt_help prm>. Then, open
prjNAME_prmNAME.m with an appropriate text editor and make the
necessary changes. For instance, set ASCIIext, isMultiplex, the
analog-to-digital time-sampling rate a2dR, etc. according to the
results from the binary-to-ASCII conversion <tcwt_help ascii2tmat>.
5. Choose a new job input variable file name (varNAME) and copy
the demo job input variable file tcwtROOT/demo/tcwt_var.m to
tcwtROOT/jobs/prjNAME_varNAME.m <tcwt_help var>. Then, open
prjNAME_varNAME.m and make the necessary changes. Change, e.g.,
the PCA criteria, the outlier criteria, etc. <tcwt_help f2pc>.
6. Choose a new job script file name (scrNAME) and copy
the demo job script file tcwtROOT/demo/tcwt_scr.m to
tcwtROOT/jobs/prjNAME_scrNAME.m <tcwt_help scr>. Then,
open prjNAME_scrNAME.m and make changes, if necessary.
7. Copy the demo main script file tcwtROOT/demo/tcwt_scr_prm_var.m to
tcwtROOT/jobs/prjNAME_scrNAME_prmNAME_varNAME.m and then just run
prjNAME_scrNAME_prmNAME_varNAME with MATLAB or with GNU Octave, either
in interactive mode, or from the command line, or from a shell script,
e.g.: matlab -r "myprj_scr_prm_var" -logfile myprj_scr_prm_var.log
or: octave --eval "myprj_scr_prm_var" &> myprj_scr_prm_var.log
The main script extracts scrNAME, prmNAME, and varNAME from its own
name, calls the corresponding scripts and saves the results of their
execution in the directory tcwtWORK/prjNAME/prmNAME_varNAME (which is
newly created by the main script, if it does not exist).
8. In order to view the results from the t-CWT assessment of your ERP
data, open the file tcwtWORK/prjNAME/prmNAME_varNAME/_A_run_scrNAME.log
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prm
A t-CWT job input parameter file prjNAME_prmNAME is called from
the main job script prjNAME_scrNAME_prmNAME_varNAME <tcwt_help main>.
The job input parameters are job constants <tcwt_help prm2mat>.
The main script saves a copy of the job input parameter
file tcwtROOT/jobs/prjNAME_prmNAME.m in './_A_prm_prmNAME.m'
(i.e. in tcwtWORK/prjNAME/prmNAME_varNAME/_A_prm_prmNAME.m).
Create a new input parameter file prjNAME_prmNAME by copying
the demo input parameter file tcwtROOT/demo/tcwt_prm.m
to tcwtROOT/jobs/prjNAME_prmNAME.m and editing the copy.
Use tcwt_prm2info(prjNAME_prmNAME) <tcwt_help prm2info>
to estimate the approximate computational demand of the job
that should be executed with these input parameter settings.
JOB INPUT PARAMETERS
Window = [time1 time2];
Beginning and end (in seconds) of the time window
in which ERP assessment should be performed.
Window must be within the range defined by Epoch (see below).
cutoffScale = time;
Cutoff scale in seconds.
logGridR = pps; or logGridR = [ppo pps];
Log-grid sampling rate in points per scale (pps); or the two semi-log-grid
sampling rates in points per octave (ppo) and points per scale (pps).
Usings semi-log-grid consumes more memory, but is much faster than log-grid.
BaseLine = [time1 time2];
Beginning and end (in seconds) of the baseline
to which the EEG in Window will be referenced.
fadeInOut = [time1 time2];
Fadein and Fadeout time for the Tukey window function.
NcwMax = number;
Maximum number ot trials processed by CWT in one step.
If there are many trials to be processed and NcwMax is too big
t-CWT may run out of memory.
Epoch = [time1 time2];
Beginning and end (in seconds) of EEG epoch, defined by the input data.
NtimePt = number;
Number of time sampling points in the Epoch.
For an ERP ASCII file 'dataset.dat' exported from Brain Broducts EEG
format, the value of NtimePt can be obtained from 'dataset.vhdr'.
If NtimePt <= 0, its value is ignored. If both a2dR > 0 and NtimePt > 0,
their values must be in the right relationship with each other and
with the length of the EEG epoch.
a2dR = number;
Analog-to-digital time-sampling rate in Hz, defined by the input data.
For an ASCII ERP file 'dataset.dat' exported from Brain Broducts EEG
format, the value of a2dR can be obtained from 'dataset.vhdr'.
If a2dR <= 0, its value is ignored. If both a2dR > 0 and NtimePt > 0,
their values must be in the right relationship with each other and
with the length of the EEG epoch.
ASCIIext = string;
File extension (without the leading '.')
of the ASCII ERP datasets that will be imported into t-CWT.
isMultiplex = 0 or 1;
isMultiplex tells t-CWT whether the imported ASCII data are in vectorized
(isMultiplex = 0) or in multiplexed format <tcwt_help ascii2tmat>. For an
ASCII ERP file 'dataset.dat' exported from Brain Broducts EEG format,
this information can be obtained from 'dataset.vhdr'.
ChannelList = ['ChannelName1 '; 'ChannelName2 ';... 'ChannelNameN~';... ];
A character array whose rows are the names of the EEG channels. Both
the names and the order of the channels are defined by the input data.
For an ERP ASCII file 'dataset.dat' exported from Brain Broducts EEG
format, the channels can be obtained from 'dataset.vhdr'. Only channels
whose names end with a blank are processed; the rest is discarded.
Change channel names to tell t-CWT which channels should be processed,
but don't change the order defined by the imported ERP data!
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var
A t-CWT job input variable script prjNAME_varNAME is called from
the main job script prjNAME_scrNAME_prmNAME_varNAME <tcwt_help main>.
Job input variables define all input factors which are not defined by
input parameters <tcwt_help prm>, e.g., PCA criteria, outlier criteria,
etc. Unlike job input parameters, input variables are passed to a t-CWT
function directly through the function arguments when the function
is called from the job script prjNAME_scrNAME <tcwt_help scr>.
The main script saves a copy of the job input variable
file tcwtROOT/jobs/prjNAME_varNAME.m in './_A_var_varNAME.m'
(i.e. in tcwtWORK/prjNAME/prmNAME_varNAME/_A_var_varNAME.m).
Create a new input variable file prjNAME_varNAME by copying
the demo input variable file tcwtROOT/demo/tcwt_var.m
to tcwtROOT/jobs/prjNAME_varNAME.m and editing the copy.
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scr
A t-CWT job script prjNAME_scrNAME is called from the main
job script prjNAME_scrNAME_prmNAME_varNAME <tcwt_help main>.
The job script is executed in the project directory
tcwtWORK/prjNAME/prmNAME_varNAME, where tcwtWORK
denotes the t-CWT work path <tcwt_help install>
A job script is mostly a list of function calls to t-CWT functions, whose
source files are in tcwtROOT/func/ (tcwtROOT denotes the t-CWT root path).
t-CWT functions using one or more job constants access them by loading
the file './_A_const.mat' <tcwt_help prm2mat>. Job constants are computed
and stored in './_A_const.mat' by the main script before calling the
job script. They are computed from the job input parameters defined
by the input parameter script prjNAME_prmNAME <tcwt_help prm>.
The main script calls also the input variable script prjNAME_varNAME.
Unlike job input parameters, job input variables are passed to t-CWT
functions directly through the function arguments <tcwt_help var>.
The main script saves a copy of the job script file
tcwtROOT/jobs/prjNAME_scrNAME.m in './_A_scr_scrNAME.m'
(i.e. in tcwtWORK/prjNAME/prmNAME_varNAME/_A_scr_scrNAME.m).
Create a new job script prjNAME_scrNAME by simply copying
the demo job script file tcwtROOT/demo/tcwt_scr.m to
tcwtROOT/jobs/prjNAME_scrNAME.m and editing the copy.
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prm2mat
tcwt_prm2mat(prmFILE) reads job input parameters <tcwt_help prm> from
the file prmFILE.m, computes other job constants and saves all of them
into the file './_A_const.mat'. The term 'job constants' means that,
once defined, these variables do not change any more during job execution.
This definition includes all job input parameters and all variables
computed from them by tcwt_prm2mat which is called from the main script
<tcwt_help main> before calling the job script <tcwt_help scr>.
During job execution, t-CWT functions using one or more job
constants access them by loading the file './_A_const.mat'.
JOB CONSTANTS
fullTime A vector consisting of the time-sampling points defined
by the job input parameters a2dR and Epoch <tcwt_help prm>.
NtimePt The length of fullTime.
Time The part of fullTime contained in the time interval
defined by the job input parameter Window <tcwt_help prm>.
fTerp The matrix of the transformation of the EEG from the time
domain into the frequency domain; defined by Time and the job
input parameters cutoffScale and fadeInOut <tcwt_help prm>.
tTerp The matrix of the transformation of the EEG from
the frequency domain back into the time domain
cwTerp The matrix of the continuous wavelet transform (CWT) from
the frequency domain onto a log-grid in the time-scale plane.
logGrid A two-row matrix of coordinates in the time-scale plane
of the vertices of the CWT log-grid; defined by Time and
job input parameters cutoffScale and logGridR <tcwt_help prm>.
ALL JOB INPUT PARAMETERS ARE SAVED AS JOB CONSTANTS AS WELL.
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prm2info
tcwt_prm2info(prmFILE) displays the following values
computed from the input parameter file prmFILE <tcwt_help prm>:
T Length of the time window ( = Window(2) - Window(1) )
S Cut-off scale ( = cutoffScale )
R Log-grid sampling rate ( = logGridR )
NcwMax Maximum number of trials processed by CWT in one step
Nc Number of channels to be processed by t-CWT
Nf Number of frequency components
Nv Number of log-grid vertexes
Npca = 2*(Nc*Nf)^2 Number of PCT and covariance matrix elements
Ncwt = Nc*Nf*Nv Exact number of non-zero CWT matrix elements
NcwtA = 12*Nc*((R*T)/S)^2 Approximate number of non-zero CWT ME
Tpca Estimated processing time for one PCA iteration
assuming 1 microsecond per PCA matrix element
Tcwt Estimated processing time for one CWT scalogram
assuming 1 microsecond per CWT matrix element
Mpca Estimated minimum amount of memory needed for PCA
Mcwt Estimated maximum amount of memory needed for CWT
TIP: Try different parameter settings using the test parameter file
tcwtROOT/jobs/test_prm.m' and typing "tcwt_prm2info test_prm".
NOTE: When a semi-log-grid is used <tcwt_help prm>, tcwt_prm2info
does not provide correct estimates of the resources.
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dir2dsnl
DSNL = tcwt_dir2dsnl(dsPATH,filenamePattern) creates a DataSet Name List
(DSNL) from the output of a directory listing shell command executed
in the directory specified by dsPATH with filenamePattern as a parameter.
INPUT VARIABLES
dsPATH Full or relative path of the datasets' directory
filenamePattern File name pattern with wildcards ('*' and/or '?')
OUTPUT VARIABLES
DSNL The DataSet Name List, a character array. Each row of DSNL
is a DataSet Name (DSN). The DSNs are truncated names
(basenames), i.e., dsPATH and all extensions are removed.
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dsnl2xdsnl
XDSNL = tcwt_dsnl2xdsnl(prefix,DSNL,suffix) creates an eXtended
DataSet Name List (XDSNL) from an existing DataSet Name List
(DSNL) <tcwt_help dir2dsnl> by adding a prefix to the beginning
and a suffix to the end of each row (DSN) of DSNL.
FUNCTION ARGUMENTS
DSNL An existing DataSet Name List
prefix The prexic added to each DSN
suffix The suffix added to each DSN
OUTPUT VARIABLES
XDSNL The new eXtended DataSet Name List
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ascii2tmat
tcwt_ascii2tmat(DSNL,cndN) converts ASCII ERP to binary ERP.
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
cndN A positive integer number denoting the experimental condition
to which all trials in all ASCII files specified in DSNL belong.
INPUT FILES INPUT VARIABLES
../_ascii/DSN.ASCIIext ASCII matrix, vectorized or multiplexed
(see below)
ASCIIext is a job input parameter <tcwt_help prm>.
OUTPUT FILES OUTPUT VARIABLES (for details, see below)
../_tmat/DSN.t.mat Verp,RIerp,CIerp
INPUT ASCII DATA STRUCTURE
Vectorized:
v(1,1,1) v(1,1,2) v(1,1,3) ... v(2,1,1) v(2,1,2) v(2,1,3) ... ...
v(1,2,1) v(1,2,2) v(1,2,3) ... v(2,2,1) v(2,2,2) v(2,2,3) ... ...
v(1,3,1) v(1,3,2) v(1,3,3) ... v(2,3,1) v(2,3,2) v(2,3,3) ... ...
...
...
...
Multiplexed:
v(1,1,1) v(1,2,1) v(1,3,1) ...
v(1,1,2) v(1,2,2) v(1,3,2) ...
...
...
...
v(2,1,1) v(2,2,1) v(2,3,1) ...
v(2,1,2) v(2,2,2) v(2,3,2) ...
...
...
...
...
...
...
Notations used above:
v(N,K,M) Voltage value corresponding to the Nth trial,
Kth channel, and Mth time point.
The ASCII-to-binary conversion is performed according
to the job input parameter isMultiplex <tcwt_help prm>.
OUTPUT VARIABLES: CIerp =
[ time(1) time(2) time(3) ... ]
RIerp = Verp =
[ 0 cndN 1 ; [ v(1,1,1) v(1,1,2) v(1,1,3) ... ;
0 cndN 2 ; v(1,2,1) v(1,2,2) v(1,2,3) ... ;
... ; ... ;
... ; ... ;
... ; ... ;
0 cndN 1 ; v(2,1,1) v(2,1,2) v(2,1,3) ... ;
0 cndN 2 ; v(2,2,1) v(2,2,2) v(2,2,3) ... ;
... ; ... ;
... ; ... ;
... ; ... ;
... ; ... ;
... ; ... ;
... ] ... ]
Notations used above:
Verp ERP matrix in the time domain
CIerp Verp column index
RIerp Verp row index
v(N,K,M) Voltage value corresponding to the Nth trial,
Kth channel, and Mth time point.
time(M) Time (in seconds) corresponding to the Mth time point.
cndN Condition (experimental condition denoted
by a number), to which all trials in this file belong.
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t2f
tcwt_t2f(DSNL) converts time domain ERP to frequency domain ERP.
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
INPUT FILES INPUT VARIABLES
../_tmat/DSN.t.mat Verp,RIerp,CIerp <tcwt_help ascii2tmat>
OUTPUT FILES OUTPUT VARIABLES (for details, see below)
./DSN.f.mat Verp,CIerp
./DSN.ri0.mat RIerp,DSNLpool (DSNLpool=DSN) <tcwt_help f2pool>
The following steps precede the frequency domain transformation:
Channel selection: Channels that are not used according to the entries
in ChannelList <tcwt_help prm> are deleted.
Baseline reference: BaseLine is a job input parameter <tcwt_help prm>.
Window selection: Data points outside of the time interval defined
by the job input parameter Window are deleted.
The transform from the time domain to the frequency domain is performed
by multiplication with the t-CWT CONSTANT fTerp <tcwt_help prm2mat>.
It comprises time domain multiplication with a Tukey window function
defined by the job input parameter fadeInOut, Discrete Fourier Transform
(DFT), and low-pass filtering with a cutoff frequency = 1/cutoffScale
<tcwt_help prm>. For math details: <tcwt_help math>.
OUTPUT VARIABLES: CIerp =
[ chnum(1) chnum(1)... chnum(2) chnum(2)... ... ]
RIerp = Verp =
[ out(1) cndN ; [ v(1,1,1) v(1,1,2)... v(1,2,1) v(1,2,2)... ... ;
out(2) cndN ; v(2,1,1) v(2,1,2)... v(2,2,1) v(2,2,2)... ... ;
out(3) cndN ; v(3,1,1) v(3,1,2)... v(3,2,1) v(3,2,2)... ... ;
... ; ... ;
... ; ... ;
... ] ... ]
Notations used above:
Verp ERP matrix in the frequency domain
CIerp Verp column index
RIerp Verp row index
v(N,K,M) Value corresponding to the Nth trial,
Kth channel, and Mth frequency.
chnum(K) Channel number of the Kth channel.
out(N) Outlier mark (0 or 1) of the Nth trial (1 = marked as outlier).
cndN Condition (experimental condition denoted
by a number), to which all trials of this dataset belong.
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ri2cnd
tcwt_ri2cnd(DSNL,cndN) sets the number denoting the experimental condition.
The function iterates over DSNL reading and processing data from the
INPUT FILES and saving merged data to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
cndN A positive integer number denoting the experimental condition
to which all trials in all ASCII files specified in DSNL belong.
INPUT FILES INPUT VARIABLES <tcwt_help t2f>
./DSN.ri0.mat RIerp,DSNLpool (DSNLpool=DSN) <tcwt_help f2pool>
./DSN.ri1.mat RIerp,DSNLpool
OUTPUT FILES OUTPUT VARIABLES
./DSN.ri0.mat RIerp,DSNLpool
./DSN.ri1.mat RIerp,DSNLpool
RIerp =
[ out(1) cndN ;
out(2) cndN ;
out(3) cndN ;
... ;
... ]
Notations used above:
RIerp Verp row index
out(N) Outlier mark (0 or 1) of the Nth trial (1 = marked as outlier).
cndN Condition (experimental condition denoted
by a number), to which all trials of this dataset belong.
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f2merge
tcwt_f2merge(DSNL,suffixLIST,mergeSFX) merges two or more ERP datasets.
The function iterates over DSNL and suffixLIST reading data from the
INPUT FILES and saving merged data to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
suffixLIST = [sfx1; sfx2; ... ] Suffix List of datasets to be merged.
mergeSFX The suffix of the resulting merger dataset.
INPUT FILES INPUT VARIABLES <tcwt_help t2f>
./DSNsfx1.f.mat Verp = Verp1, CIerp
./DSNsfx2.f.mat Verp = Verp2, CIerp
... ...
./DSNsfx1.ri0.mat RIerp = RIerp1, DSNLpool
./DSNsfx2.ri0.mat RIerp = RIerp2, DSNLpool
... ...
OUTPUT FILES OUTPUT VARIABLES
./DSNmergeSFX.f.mat Verp = [Verp1; Verp2; ... ]
CIerp
./DSNmergeSFX.ri0.mat RIerp = [RIerp1; RIerp2; ... ]
DSNLpool = [DSN mergeSFX] <tcwt_help f2pool>
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f2split
tcwt_f2split(DSNL,trialrangeLIST,suffixLIST) splits ERP datasets
into smaller subsets.
The function iterates over DSNL reading data from the INPUT FILES,
splitting it according to trialrangeLIST, and saving the split data
to the corresponding OUTPUT FILES according to suffixLIST.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
trialrangeLIST = [first1 last1 step1; first2 last2 step2; ... ]
A list of trial intervals and steps defining the
subsets into which each dataset DSN will be split
(taking trials firstN:stepN:lastN for N = 1,2,...).
If the steps are not specified they are taken to be 1.
suffixLIST = [sfx1; sfx2; ... ] A list of suffixes
corresponding to the trial intervals defined
by trialrangeLIST to be added to each DSN to
name the corresponding subsets of ERP trails
INPUT FILES INPUT VARIABLES <tcwt_help t2f>
./DSN.f.mat Verp,CIerp
./DSN.ri0.mat RIerp,DSNLpool
OUTPUT FILES OUTPUT VARIABLES
./DSNsfx1.f.mat Verp,CIerp
./DSNsfx2.f.mat Verp,CIerp
... ...
./DSNsfx1.ri0.mat RIerp,DSNLpool
./DSNsfx2.ri0.mat RIerp,DSNLpool
... ...
Table of Contents
f2diff
tcwt_f2diff(DSNL1,DSNL2,DSNLdiff) computes a difference ERP dataset.
The function iterates over DSNL reading data from the INPUT FILES
and saving difference datasets to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL1 ,DSNL2, DSNLdiff DataSet Name Lists (DSN Lists) <tcwt_help dir2dsnl>
INPUT FILES INPUT VARIABLES <tcwt_help t2f>
./DSN1.f.mat Verp = Verp1, CIerp
./DSN2.f.mat Verp = Verp2, CIerp
OUTPUT FILES OUTPUT VARIABLES
./DSNdiff.f.mat Verp = Verp2 - Verp1
CIerp
./DSNdiff.ri0.mat RIerp(:,1) = RIerp1(:,1) | RIerp2(:,1)
DSNLpool = DSNdiff <tcwt_help f2pool>
Table of Contents
f2f
tcwt_f2f(DSNL) Includes LogPower Spectrum into the *.f.mat listed in DSNL.
See the source code in tcwtROOT/func/tcwt_f2area.m
and in tcwtROOT/jobs/mbct_ind.m for more details.
Table of Contents
f2avg
tcwt_f2avg(DSNL) creates average ERPs *.avg.f.mat from the *.f.mat files.
See the source code in tcwtROOT/func/tcwt_f2area.m
and in tcwtROOT/jobs/mbct_ind.m for more details.
Table of Contents
f2area
tcwt_f2area(DSNL,areaWindow,areaSuffix) computes area under the ERP curve.
areaWindow is in seconds: areaWindow = [time1, time2].
See the source code in tcwtROOT/func/tcwt_f2area.m
and in tcwtROOT/jobs/mbct_ind.m for more details.
Table of Contents
f2pool
tcwt_f2pool(DSNL,poolNAME) pools two or more individual ERP datasets
together into one large group dataset.
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL reading data from the INPUT FILES
and saving the pooled data to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
poolNAME The Name of the pooled dataset
INPUT FILES INPUT VARIABLES <tcwt_help t2f>
./DSN1.f.mat Verp1,CIerp1
./DSN2.f.mat Verp2,CIerp2
... ...
./DSN1.ri0.mat RIerp1,DSNLpool
./DSN2.ri0.mat RIerp2
... ...
OUTPUT FILES OUTPUT VARIABLES
./poolNAME.f.mat Verp = [Verp1; Verp2; ... ]
CIerp = CIerp1
./poolNAME.ri0.mat RIerp = [RIerp1; RIerp2; ... ]
DSNLpool = DSNL
Table of Contents
f2pc
tcwt_f2pc(DSNL,Npc,Nstd,MinGood) Principal Component Transform (PCT),
Principal Component Analysis (PCA), and Multivariate Outlier Detection.
The function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
Npc VALUE defines PCA CRITERION <tcwt_help math>
Npc > 1 the first Npc eigenvalues will be retained
Npc = 1 all eigenvalues will be retained
0 < Npc < 1 percentage of variance to be explained
Npc = 0 average eigenvalue criterion
Nstd > 2 Number of standard deviations for the single-trial outlier
detection criterion: D > Mean(D) + Nstd * StdDev(D), where
D = single-trial Mahalanobis Distance from mean <tcwt_help math>
MinGood Defines the dataset outlier detection criterion <tcwt_help math>:
number_of_good_trials < MinGood * number_of_trials_in_dataset
INPUT FILES INPUT VARIABLES <tcwt_help t2f>
./DSN.f.mat Verp,CIerp
./DSN.ri0.mat RIerp, DSNLpool <tcwt_help f2pool>
OUTPUT FILES OUTPUT VARIABLES
./DSN.pc.mat pcTerp,pcEV
./DSN.ri1.mat RIerp, DSNLpool
./DSN.ri1.txt Text output
OUTPUT VARIABLES
pcTerp Reduced PCT matrix. <tcwt_help math>. The principal components
pcVerp of the ERP sample Verp are: pcVerp = Verp * pcTerp
pcEV Reduced PCT eigenvalues <tcwt_help math>
RIerp ERP Row Index; 1st row contains outlier marks <tcwt_help t2f>
Table of Contents
f2cwss
tcwt_f2cwss(DSNL) computes the Sums of Squares (SS) of the Continuous
Wavelet Transform (CWT) for subsequent Student's t-tests <tcwt_help math>.
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
INPUT FILES INPUT VARIABLES
./DSN.f.mat Verp,CIerp <tcwt_help t2f>
./DSN.pc.mat pcTerp <tcwt_help f2pc>
./DSN.ri1.mat RIerp <tcwt_help t2f>
OUTPUT FILES OUTPUT VARIABLES
./DSN.cwss.mat cwVerpSS
Table of Contents
ri2ri1out
tcwt_ri2ri1out(poolNAME) creates 1out-indexes from the row index
of a pooled dataset excluding one individual dataset at a time.
FUNCTION ARGUMENTS
poolNAME The Name of the pooled dataset
INPUT FILE INPUT VARIABLES
./poolNAME.ri1.mat RIerp,DSNLpool <tcwt_help f2pool>
OUTPUT FILES OUTPUT VARIABLES
./DSNp.out.poolNAME.ri1.mat RIerp,DSNLpool
DSNp is taken from DSNLpool.
The function iterates over DSNLpool. At each iteration, DSNp is read
from the next row of DSNLpool and all trials belonging to the dataset
DSNp are marked as artifacts. RIerp, thus modified, is stored in the
corresponding OUTPUT FILE.
Table of Contents
pc2cnd2ri
tcwt_pc2cnd2ri(is1out,DSNL,Cnd,Nstd,MinGood) Multivariate Outlier Detection
from fixed principal components, separately for each experimental condition.
The function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
If is1out = 1, a second DSNLpool of 1out index names <tcwt_help ri2ri1out>
is created at each step, and the function iterates throuh DSNLpool.
FUNCTION ARGUMENTS
is1out = 0 or 1; defines whether 1out indexes are used (see below)
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
Cnd List of experimental conditions <tcwt_help t2f>
Nstd <tcwt_help f2pc>
MinGood <tcwt_help f2pc>
INPUT FILES INPUT VARIABLES
./DSN.f.mat Verp,CIerp <tcwt_help t2f>
./DSN.pc.mat pcTerp,pcEV <tcwt_help f2pc>
./DSN.ri1.mat RIerp, DSNLpool <tcwt_help f2pool>
If is1out == 1
./DSNp.out.DSN.ri1.mat RIerp
DSNp is taken from DSNLpool.
OUTPUT FILES OUTPUT VARIABLES
./DSN.ri2.mat RIerp, DSNLpool
./DSN.ri2.txt Text output
If is1out == 1
./DSNp.out.DSN.ri2.mat RIerp, DSNLpool
./DSNp.1out.ri2.mat Text output
Table of Contents
f2x
tcwt_f2x(is1out,DSNL,Cnd) t-CWT & Extremum Detection <tcwt_help math>.
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
If is1out = 1, a second DSNLpool of 1out index names <tcwt_help ri2ri1out>
is created at each step, and the function iterates throuh DSNLpool.
FUNCTION ARGUMENTS
is1out = 0 or 1; defines whether 1out indexes are used (see below)
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
Cnd List of exactly 2 experimental conditions <tcwt_help t2f>
INPUT FILES INPUT VARIABLES
./DSN.f.mat Verp,CIerp <tcwt_help t2f>
./DSN.pc.mat pcTerp,pcEV <tcwt_help f2pc>
./DSN.cwss.mat cwVerpSS <tcwt_help f2cwss>
./DSN.ri1.mat RIerp, DSNLpool <tcwt_help f2pool>
./DSN.ri2.mat RIerp, DSNLpool
If is1out == 1
./DSNp.out.DSN.ri2.mat RIerp
DSNp is taken from DSNLpool.
OUTPUT FILES OUTPUT VARIABLES
./DSN.tcw.mat tcwVerp,tcwCIerp
./DSN.x.mat xTerp,xCIerp
If is1out == 1
./DSNp.out.DSN.tcw.mat tcwVerp,tcwCIerp
./DSNp.out.DSN.x.mat xTerp,xCIerp
OUTPUT VARIABLES
tcwCIerp =
[ chnum(1) chnum(1)... chnum(1) chnum(1)... chnum(2) chnum(2)... ... ;
scale(1) scale(1)... scale(2) scale(2)... scale(1) scale(1)... ... ;
time(1,1)time(1,2)...time(2,1)time(2,2)...time(1,1)time(1,2)... ... ]
tcwVerp =
[ t(1,1,1) t(1,1,2)... t(1,2,1) t(1,2,2)... t(2,1,1) t(2,1,2)... ... ]
xCIerp =
[ xchnum(1) ... xchnum(2) ... ... ;
xscale(1) ... xscale(2) ... ... ;
xtime(1) ... xtime(2) ... ... ;
xpolarity(1) ... xpolarity(2) ... ... ;
xtcwindex(1) ... xtcwindex(2) ... ... ;
xtcwvalue(1) ... xtcwvalue(2) ... ... ]
Notations used above:
tcwVerp t-CWT scalogram
tcwCIerp t-CWT column index
xTerp Transformation matrix from the principal components of the
frequency domain ERP Verp to the t-CWT features (extrema):
xVerp = pcVerp * xTerp = Verp * pcTerp * xTerp
xCIerp t-CWT extrema (i.e. xVerp column index)
t(K,N,M) t-CWT-value corresponding to the Kth channel, and the Mth
time point of the Nth scale line of logGrid <tcwt_help prm2mat>
chnum(K) Channel number of the Kth channel
scale(N) Scale in seconds of the Nth scale line of logGrid
time(N,M) Time in seconds of the Mth time point of the Nth scale line
xchnum(I) Channel number of the Ith extremum
xscale(I) Scale in seconds of the Ith extremum
xtime(I) Time in seconds of the Ith extremum
xpolarity(I) Polarity of the Ith extremum (-1 = min, 1 = max)
xtcwindex(I) Absolute tcwVerp index of the Ith extremum
xtcwvalue(I) = tcwVerp( xtcwindex(I) )
Table of Contents
x2ld
tcwt_x2ld(is1out,DSNL,Cnd,Npc,sdAlpha) Principal Component Analysis
(PCA), from the t-CWT features, Step-Down Selection of components, and
computation of the Linear Discriminant Function (LDF) <tcwt_help math>
The function iterates over DSNL reading and processing data from
the INPUT FILES and saving results to the corresponding OUTPUT FILES.
If is1out = 1, a second DSNLpool of 1out index names <tcwt_help ri2ri1out>
is created at each step, and the function iterates throuh DSNLpool.
FUNCTION ARGUMENTS
is1out = 0 or 1; defines whether 1out indexes are used (see below)
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
Cnd List of exactly 2 experimental conditions <tcwt_help t2f>
Npc PCA criterion for the step-down test <tcwt_help f2pc>
sdAlpha Overall alpha level for the step-down test <tcwt_help math>
INPUT FILES INPUT VARIABLES
./DSN.f.mat Verp,CIerp <tcwt_help t2f>
./DSN.pc.mat pcTerp,pcEV <tcwt_help f2pc>
./DSN.x.mat xCIerp,xTerp <tcwt_help f2x>
./DSN.ri1.mat RIerp, DSNLpool <tcwt_help f2pool>
./DSN.ri2.mat RIerp, DSNLpool
If is1out == 1
./DSNp.out.DSN.x.mat xCIerp,xTerp
./DSNp.out.DSN.ri2.mat RIerp
DSNp is taken from DSNLpool.
OUTPUT FILES OUTPUT VARIABLES
./DSN.ld.mat Nxtr,sdTerp,ldTerp,ldMean,CIerp
If is1out == 1
./DSNp.out.DSN.ld.mat Nxtr,sdTerp,ldTerp,ldMean,CIerp
OUTPUT VARIABLES
Nxtr The number of t-CWT extrema (features)
sdTerp Transformation matrix from the frequency domain ERP Verp
to the principal components obtained from the t-CWT features
and reduced by step-down selection sdVerp = Verp * sdTerp
ldTerp Frequency domain LDF obtained from sdVerp. The scalar product
with the frequency domain ERP Verp is simply: Verp * ldTerp
ldMean = (1/2) * ( mean(Verp1) + mean(Verp2) ) * ldTerp
Verp1 and Verp2 are the ERP samples corresponding to the
experimental conditions Cnd(1) and Cnd(2), respectively.
CIerp ERP column index in the frequency domain <tcwt_help t2f>
Table of Contents
f2stats
tcwt_f2stats(is1out,DSNL1,DSNL2,statsNAME,Cnd,aPriori,LD0) performs
LDA classification of single trials from test datasets by LDFs
obtained from training datasets <tcwt_help x2ld>.
The function iterates over DSNL2 reading and processing data from
the INPUT FILES and then saves the results into the OUTPUT FILES.
FUNCTION ARGUMENTS
is1out = 0 or 1; defines whether 1out indexes are used (see below)
DSNL1 Training DataSet Name List (DSN1 List) <tcwt_help dir2dsnl>
DSNL2 Test DataSet Name List (DSN2 List)
statsNAME Name of the OUTPUT FILES (without the extensions)
Cnd List of exactly 2 experimental conditions <tcwt_help t2f>
aPriori = 0 or 1; defines whether the a priori error rate is computed
from the numbers of trials in Cnd(1) and Cnd(2).
If aPriori == 0, the a priori error rate and the a priori
hit rate are taken to be equal (p1=p2=0.5) and log(p2/p1)=0.
LD0 If present and LD0=='ld0', then *.ld0.mat will be used
instead of *.ld0.mat.
INPUT FILES INPUT VARIABLES
./DSN2.f.mat Verp,CIerp <tcwt_help t2f>
./DSN2.ri0.mat RIerp, DSNLpool <tcwt_help f2pool>
If is1out == 0
./DSN1.ld.mat Nxtr,sdTerp,ldTerp,ldMean,CIerp <tcwt_help x2ld>
If is1out == 1, and DSNL1 has only one row, DSN1
./DSN2.out.DSN1.ld.mat Nxtr,sdTerp,ldTerp,ldMean,CIerp <tcwt_help x2ld>
OUTPUT FILES OUTPUT VARIABLES
./statsNAME.stats0.mat dsnl = DSNL2,
(if aPriori == 0) NtCWTextr,NsdPC,Photelling
./statsNAME.statsA.mat Ntrials,Nerrors,ErrP100,Pbinomi
(if aPriori == 1) NtrialsSum,NerrorsSum,ErrP100Sum,PbinomiSum
./statsNAME.stats0.txt Text output
./statsNAME.statsA.txt
If DSNL1 == DSNL2
./statsNAME.biased.stats0.mat
./statsNAME.biased.stats0.txt
./statsNAME.biased.statsA.mat
./statsNAME.biased.statsA.txt
If is1out == 1, and DSNL1 has only one row
./statsNAME.1dataset.out.stats0.mat
./statsNAME.1dataset.out.stats0.txt
./statsNAME.1dataset.out.statsA.mat
./statsNAME.1dataset.out.statsA.txt
OUTPUT VARIABLES
NtCWTextr Number of t-CWT features for each training dataset
(DSN1.ld.mat or DSN2.out.DSN1.ld.mat, see INPUT FILES)
NsdPC Number of step-down-selected components
in each training dataset
Photelling P-Value of Hotelling's test performed on each test
dataset DSN2 using the step-down-selected components
from the corresponding training dataset
Ntrials Nubmer of trials, for each condition and total,
in each DSN2. Ntrials(:,1) corresponds to Cnd(1)
Ntrials(:,2) corresponds to Cnd(2), and Ntrials(:,3)
is the total nubmer of trials
Nerrors Number of errors of LDA classification, for Cnd(1), Cnd(2),
and total, for each DSN2. Cnd(1) --> Nerrors(:,1), etc.
ErrP100 = 100 * Nerrors / Ntrials (error percentages)
Pbinomi P-Values of the binomial distribution testing the hypotheses
that the LDA classifications were better than chance,
i.e., that ErrP100 < 50%
NtrialsSum = sum(Ntrials)
NerrorsSum = sum(Nerrors)
ErrP100Sum = 100 * NerrorsSum / NtrialsSum (average error percentages)
PbinomiSum P-Values for testing whether ErrP100Sum < 50%
Table of Contents
f2holdout
tcwt_f2holdout(DSNL,statsNAME,Cnd,Nstd,MinGood,Npc,sdAlpha) computes
the error rates of LDA classificaion of single trials using the
hold-out method <tcwt_help math>.
The function iterates over DSNL reading and processing data from
the INPUT FILES and then saves the results into the OUTPUT FILES.
For each DSN, the hold-out method is applied by iterating through all
trials of the dataset, excluding the current trial, doing t-CWT with
the other trials <tcwt_help pc2ri2cnd> <tcwt_help f2x> <tcwt_help x2ld>
and applying the obtained LDF to the current trial <tcwt_help math>.
Classification errors and binomial p-values are computed and saved
in the OUTPUT FILES <tcwt_help stats>.
FUNCTION ARGUMENTS
DSNL Test DataSet Name List (DSN List) <tcwt_help dir2dsnl>
statsNAME Name of the OUTPUT FILES (without the extensions)
Cnd List of exactly 2 experimental conditions <tcwt_help t2f>
Nstd Criterion for single-trial outlier detection <tcwt_help f2pc>
MinGood Criterion for dataset outlier detection <tcwt_help f2pc>
Npc PCA criterion for the step-down test <tcwt_help f2pc>
sdAlpha Overall alpha level for the step-down test <tcwt_help math>
INPUT FILES INPUT VARIABLES
./DSN.f.mat Verp,CIerp <tcwt_help t2f>
./DSN.pc.mat pcTerp,pcEV <tcwt_help f2pc>
./DSN.cwss.mat cwVerpSS <tcwt_help f2cwss>
./DSN.ri0.mat RIerp, DSNLpool <tcwt_help f2pool>
./DSN.ri1.mat RIerp, DSNLpool
OUTPUT FILES OUTPUT VARIABLES <tcwt_help f2stats>
./statsNAME.1trial.out.stats0.mat dsnl = DSNL,
./statsNAME.1trial.out.statsA.mat Ntrials,Nerrors,ErrP100,Pbinomi
NtrialsSum,NerrorsSum,ErrP100Sum,
PbinomiSum
./statsNAME.1trial.out.stats0A.txt Text output
Suffix '0' denotes that the priori probabilities are taken to be equal;
'A' means they are computed; from the number of trials in each condition.
Table of Contents
f2plot
tcwt_f2plot(DSNL,cxyFILE,Cnd,CndWidth,CndRGB,tTestWidth,tTestRGB) plots
two average ERPs and Student's t-test of the difference ERP.
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL reading data from the INPUT FILES,
computing ERP averages corresponding to two different experimental
conditions and Student's t-test of the difference ERP, plotting the
results, and saving the plots to the corresponding OUTPUT PDF FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
cxyFILE The basename (without the path and the '.m' extension)
of the file, containing the X-Y-coordinates of
the channels in the subplot array <tcwt_help cxy>.
Cnd = [cnd1; cnd2] Experimental conditions <tcwt_help t2f>
CndWidth = [width1; width2] Line widths of the average ERP curves
corresponding to cnd1 and cnd2 respectively
CndRGB = [R1 G1 B1; R2 G2 B2] Line colors (defined as RGB vectors) of
the average ERPs corresponding to cnd1 and cnd2 respectively
tTestWidth Line width of the t-test curve
tTestRGB Line color (defined as an RGB vector) of the t-test curve
INPUT FILES INPUT VARIABLES
./DSN.f.mat Verp,CIerp <tcwt_help t2f>
./DSN.pc.mat pcTerp <tcwt_help f2pc>
./DSN.ri2.mat RIerp <tcwt_help t2f>
OUTPUT FILES OUTPUT VARIABLES
./DSN.plot.avg.jpg average ERP plot as JPG
./DSN.plot.ttest.jpg Student's t-test plot as JPG
Note that ERP averaging is done after PCA filtering and double outlier
rejection (first, regardless of experimental conditions, and second,
performed on each condition separately). The t-test is also done with
the corresponding ERP subsamples, which means that it is biased and
should be used only for visualization purposes.
Table of Contents
ld2plot
tcwt_ld2plot(DSNL,cxyFILE,normC,LineWidth,ColorRGB) plots the normalized
Linear Discriminant Function (LDF).
The job constants are loaded from './_A_const.mat' <tcwt_help prm2mat>.
Then, the function iterates over DSNL plotting the Linear Discriminant
Functions (LDFs) <tcwt_help x2ld> stored in the INPUT FILES and saving
the plots to the corresponding OUTPUT PDF FILES.
FUNCTION ARGUMENTS
DSNL DataSet Name List (DSN List) <tcwt_help dir2dsnl>
cxyFILE The basename (without the path and the '.m' extension)
of the file, containing the X-Y-coordinates of
the channels in the subplot array <tcwt_help cxy>.
normC A coefficient with which the LDF is multiplied
for better visualization (can be negative).
LineWidth The line width
ColorRGB = [R, G, B] The line color defined as an RGB vector
INPUT FILES INPUT VARIABLES
./DSN.ld.mat Nxtr,sdTerp,ldTerp,ldMean,CIerp <tcwt_help x2ld>
OUTPUT FILES OUTPUT VARIABLES
./DSN.plot.ld.jpg ldTerp plot as JPG
Table of Contents
gpl
GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
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public, and in some countries other activities as well.
To "convey" a work means any kind of propagation that enables other
parties to make or receive copies. Mere interaction with a user through
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An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License. If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.
1. Source Code.
The "source code" for a work means the preferred form of the work
for making modifications to it. "Object code" means any non-source
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A "Standard Interface" means an interface that either is an official
standard defined by a recognized standards body, or, in the case of
interfaces specified for a particular programming language, one that
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The "System Libraries" of an executable work include anything, other
than the work as a whole, that (a) is included in the normal form of
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Component, and (b) serves only to enable use of the work with that
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implementation is available to the public in source code form. A
"Major Component", in this context, means a major essential component
(kernel, window system, and so on) of the specific operating system
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The "Corresponding Source" for a work in object code form means all
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which are not part of the work. For example, Corresponding Source
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such as by intimate data communication or control flow between those
subprograms and other parts of the work.
The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.
The Corresponding Source for a work in source code form is that
same work.
2. Basic Permissions.
All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met. This License explicitly affirms your unlimited
permission to run the unmodified Program. The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work. This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.
You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force. You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright. Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
your copyrighted material outside their relationship with you.
Conveying under any other circumstances is permitted solely under
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3. Protecting Users' Legal Rights From Anti-Circumvention Law.
No covered work shall be deemed part of an effective technological
measure under any applicable law fulfilling obligations under article
11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.
When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.
4. Conveying Verbatim Copies.
You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.
You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.
5. Conveying Modified Source Versions.
You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:
a) The work must carry prominent notices stating that you modified
it, and giving a relevant date.
b) The work must carry prominent notices stating that it is
released under this License and any conditions added under section
7. This requirement modifies the requirement in section 4 to
"keep intact all notices".
c) You must license the entire work, as a whole, under this
License to anyone who comes into possession of a copy. This
License will therefore apply, along with any applicable section 7
additional terms, to the whole of the work, and all its parts,
regardless of how they are packaged. This License gives no
permission to license the work in any other way, but it does not
invalidate such permission if you have separately received it.
d) If the work has interactive user interfaces, each must display
Appropriate Legal Notices; however, if the Program has interactive
interfaces that do not display Appropriate Legal Notices, your
work need not make them do so.
A compilation of a covered work with other separate and independent
works, which are not by their nature extensions of the covered work,
and which are not combined with it such as to form a larger program,
in or on a volume of a storage or distribution medium, is called an
"aggregate" if the compilation and its resulting copyright are not
used to limit the access or legal rights of the compilation's users
beyond what the individual works permit. Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.
6. Conveying Non-Source Forms.
You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
machine-readable Corresponding Source under the terms of this License,
in one of these ways:
a) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by the
Corresponding Source fixed on a durable physical medium
customarily used for software interchange.
b) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by a
written offer, valid for at least three years and valid for as
long as you offer spare parts or customer support for that product
model, to give anyone who possesses the object code either (1) a
copy of the Corresponding Source for all the software in the
product that is covered by this License, on a durable physical
medium customarily used for software interchange, for a price no
more than your reasonable cost of physically performing this
conveying of source, or (2) access to copy the
Corresponding Source from a network server at no charge.
c) Convey individual copies of the object code with a copy of the
written offer to provide the Corresponding Source. This
alternative is allowed only occasionally and noncommercially, and
only if you received the object code with such an offer, in accord
with subsection 6b.
d) Convey the object code by offering access from a designated
place (gratis or for a charge), and offer equivalent access to the
Corresponding Source in the same way through the same place at no
further charge. You need not require recipients to copy the
Corresponding Source along with the object code. If the place to
copy the object code is a network server, the Corresponding Source
may be on a different server (operated by you or a third party)
that supports equivalent copying facilities, provided you maintain
clear directions next to the object code saying where to find the
Corresponding Source. Regardless of what server hosts the
Corresponding Source, you remain obligated to ensure that it is
available for as long as needed to satisfy these requirements.
e) Convey the object code using peer-to-peer transmission, provided
you inform other peers where the object code and Corresponding
Source of the work are being offered to the general public at no
charge under subsection 6d.
A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.
A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling. In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage. For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product. A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.
"Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source. The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.
If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information. But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).
The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed. Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.
Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.
7. Additional Terms.
"Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law. If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.
When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it. (Additional permissions may be written to require their own
removal in certain cases when you modify the work.) You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.
Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:
a) Disclaiming warranty or limiting liability differently from the
terms of sections 15 and 16 of this License; or
b) Requiring preservation of specified reasonable legal notices or
author attributions in that material or in the Appropriate Legal
Notices displayed by works containing it; or
c) Prohibiting misrepresentation of the origin of that material, or
requiring that modified versions of such material be marked in
reasonable ways as different from the original version; or
d) Limiting the use for publicity purposes of names of licensors or
authors of the material; or
e) Declining to grant rights under trademark law for use of some
trade names, trademarks, or service marks; or
f) Requiring indemnification of licensors and authors of that
material by anyone who conveys the material (or modified versions of
it) with contractual assumptions of liability to the recipient, for
any liability that these contractual assumptions directly impose on
those licensors and authors.
All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10. If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term. If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.
If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.
Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.
8. Termination.
You may not propagate or modify a covered work except as expressly
provided under this License. Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).
However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.
Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License. If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.
9. Acceptance Not Required for Having Copies.
You are not required to accept this License in order to receive or
run a copy of the Program. Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance. However,
nothing other than this License grants you permission to propagate or
modify any covered work. These actions infringe copyright if you do
not accept this License. Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.
10. Automatic Licensing of Downstream Recipients.
Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License. You are not responsible
for enforcing compliance by third parties with this License.
An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations. If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.
You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License. For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.
11. Patents.
A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based. The
work thus licensed is called the contributor's "contributor version".
A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version. For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.
Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.
In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement). To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.
If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
patent license for this particular work, or (3) arrange, in a manner
consistent with the requirements of this License, to extend the patent
license to downstream recipients. "Knowingly relying" means you have
actual knowledge that, but for the patent license, your conveying the
covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
country that you have reason to believe are valid.
If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
covered work, and grant a patent license to some of the parties
receiving the covered work authorizing them to use, propagate, modify
or convey a specific copy of the covered work, then the patent license
you grant is automatically extended to all recipients of the covered
work and works based on it.
A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
specifically granted under this License. You may not convey a covered
work if you are a party to an arrangement with a third party that is
in the business of distributing software, under which you make payment
to the third party based on the extent of your activity of conveying
the work, and under which the third party grants, to any of the
parties who would receive the covered work from you, a discriminatory
patent license (a) in connection with copies of the covered work
conveyed by you (or copies made from those copies), or (b) primarily
for and in connection with specific products or compilations that
contain the covered work, unless you entered into that arrangement,
or that patent license was granted, prior to 28 March 2007.
Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.
12. No Surrender of Others' Freedom.
If conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License. If you cannot convey a
covered work so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you may
not convey it at all. For example, if you agree to terms that obligate you
to collect a royalty for further conveying from those to whom you convey
the Program, the only way you could satisfy both those terms and this
License would be to refrain entirely from conveying the Program.
13. Use with the GNU Affero General Public License.
Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU Affero General Public License into a single
combined work, and to convey the resulting work. The terms of this
License will continue to apply to the part which is the covered work,
but the special requirements of the GNU Affero General Public License,
section 13, concerning interaction through a network will apply to the
combination as such.
14. Revised Versions of this License.
The Free Software Foundation may publish revised and/or new versions of
the GNU General Public License from time to time. Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.
Each version is given a distinguishing version number. If the
Program specifies that a certain numbered version of the GNU General
Public License "or any later version" applies to it, you have the
option of following the terms and conditions either of that numbered
version or of any later version published by the Free Software
Foundation. If the Program does not specify a version number of the
GNU General Public License, you may choose any version ever published
by the Free Software Foundation.
If the Program specifies that a proxy can decide which future
versions of the GNU General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.
Later license versions may give you additional or different
permissions. However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.
15. Disclaimer of Warranty.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
16. Limitation of Liability.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.
17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.
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