bmarechal / octave_scripts

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add cov test scripts

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  1 +function [retval, s, errorb, tau] = allan_cov(data,tau,name,verbose)
  2 +% ALLAN Compute the Allan deviation for a set of time-domain frequency data
  3 +% [RETVAL, S, ERRORB, TAU] = ALLAN(DATA,TAU,NAME,VERBOSE)
  4 +%
  5 +% Inputs:
  6 +% DATA should be a structure and have the following fields:
  7 +% DATA.freq or DATA.phase
  8 +% A vector of fractional frequency measurements (df/f) in
  9 +% DATA.freq *or* phase offset data (seconds) in DATA.phase .
  10 +% If frequency data is not present, it will be generated by
  11 +% differentiating the phase data.
  12 +% If both fields are present, then DATA.freq will be used.
  13 +% Note: for general-purpose calculations of Allan deviation,
  14 +% (i.e. a two-sample variance) use DATA.freq .
  15 +%
  16 +% DATA.rate or DATA.time
  17 +% The sampling rate in Hertz (DATA.rate) or a vector of
  18 +% timestamps for each measurement in seconds (DATA.time).
  19 +% DATA.rate is used if both fields are present.
  20 +% If DATA.rate == 0, then the timestamps are used.
  21 +%
  22 +% DATA.units (optional)
  23 +% The units for the data. If present, the string DATA.units
  24 +% is added to the plot y-axis label.
  25 +%
  26 +% TAU is an array of tau values for computing Allan deviation.
  27 +% TAU values must be divisible by 1/DATA.rate (data points cannot be
  28 +% grouped in fractional quantities!) and invalid values are ignored.
  29 +% Leave empty to use default values.
  30 +% NAME is an optional label that is added to the plot titles.
  31 +% VERBOSE sets the level of status messages:
  32 +% 0 = silent & no data plots;
  33 +% 1 = status messages & minimum plots;
  34 +% 2 = all messages and plots (default)
  35 +%
  36 +% Outputs:
  37 +% RETVAL is the array of Allan deviation values at each TAU.
  38 +% S is an optional output of other statistical measures of the data (mean, std, etc).
  39 +% ERRORB is an optional output containing the error estimates for a 1-sigma
  40 +% confidence interval. These values are shown on the figure for each point.
  41 +% TAU is an optional output containing the array of tau values used in the
  42 +% calculation (which may be a truncated subset of the input or default values).
  43 +%
  44 +% Example:
  45 +%
  46 +% To compute the Allan deviation for the data in the variable "lt":
  47 +% >> lt
  48 +% lt =
  49 +% freq: [1x86400 double]
  50 +% rate: 0.5
  51 +%
  52 +% Use:
  53 +%
  54 +% >> ad = allan(lt,[2 10 100],'lt data',1);
  55 +%
  56 +% The Allan deviation will be computed and plotted at tau = 2,10,100 seconds.
  57 +% 1-sigma confidence intervals will be indicated by vertical lines at each point.
  58 +% You can also use the default settings, which are usually a good starting point:
  59 +%
  60 +% >> ad = allan(lt);
  61 +%
  62 +%
  63 +% Notes:
  64 +% This function calculates the standard Allan deviation (ADEV), *not* the
  65 +% overlapping ADEV. Use "allan_overlap.m" for overlapping ADEV.
  66 +% The calculation is performed using fractional frequency data. If only
  67 +% phase data is provided, frequency data is generated by differentiating
  68 +% the phase data.
  69 +% No pre-processing of the data is performed, except to remove any
  70 +% initial offset (i.e., starting gap) in the time record.
  71 +% For rate-based data, ADEV is computed only for tau values greater than the
  72 +% minimum time between samples and less than the half the total time. For
  73 +% time-stamped data, only tau values greater than the maximum gap between
  74 +% samples and less than half the total time are used.
  75 +% The calculation for fixed sample rate data is *much* faster than for
  76 +% time-stamp data. You may wish to run the rate-based calculation first,
  77 +% then compare with time-stamp-based. Often the differences are insignificant.
  78 +% To show the "tau bins" (y_k samples) on the data plot, set the variable
  79 +% TAUBIN to 1 (search for "#TAUBIN").
  80 +% You can choose between loglog and semilog plotting of results by
  81 +% commenting in/out the appropriate line. Search for "#PLOTLOG".
  82 +% I recommend installing "dsplot.m", which improves the performance of
  83 +% plotting large data sets. Download from File Exchange, File ID: #15850.
  84 +% allan.m will use dsplot.m if it is present on your MATLAB path.
  85 +% This function has been validated using the test data from NBS Monograph
  86 +% 140, the 1000-point test data set given by Riley [1], and the example data
  87 +% given in IEEE standard 1139-1999, Annex C.
  88 +% The author welcomes other validation results, see contact info below.
  89 +%
  90 +% For more information, see:
  91 +% [1] W. J. Riley, "The Calculation of Time Domain Frequency Stability,"
  92 +% Available on the web:
  93 +% http://www.ieee-uffc.org/frequency_control/teaching.asp?name=paper1ht
  94 +%
  95 +%
  96 +% M.A. Hopcroft
  97 +% mhopeng at gmail dot com
  98 +%
  99 +% I welcome your comments and feedback!
  100 +%
  101 +% MH Mar2014
  102 +% v2.24 fix bug related to generating freq data from phase with timestamps
  103 +% (thanks to S. David-Grignot for finding the bug)
  104 +% MH Oct2010
  105 +% v2.22 tau truncation to integer groups; tau sort
  106 +% plotting bugfix
  107 +% v2.20 sychronize updates across allan, allan_overlap, allan_modified
  108 +% v2.16 add TAU as output, fixed unusual error with dsplot v1.1
  109 +% v2.14 update plotting behaviour, default tau values
  110 +%
  111 +
  112 +versionstr = 'allan v2.24';
  113 +
  114 +% MH Jun2010
  115 +% v2.12 bugfix for rate data row/col orientation
  116 +% add DATA.units for plotting
  117 +% use dsplot.m for plotting
  118 +%
  119 +% MH MAR2010
  120 +% v2.1 minor interface and bugfixes
  121 +% update data consistency check
  122 +%
  123 +% MH FEB2010
  124 +% v2.0 Consistent code behaviour for all "allan_x.m" functions:
  125 +% accept phase data
  126 +% verbose levels
  127 +%
  128 +%
  129 +% MH JAN2010
  130 +% v1.84 code cleanup
  131 +% v1.82 typos in comments and code cleanup
  132 +% tau bin plotting changed for performance improvement
  133 +% v1.8 Performance improvements:
  134 +% vectorize code for rate data
  135 +% logical indexing for irregular rate data
  136 +% MH APR2008
  137 +% v1.62 loglog plot option
  138 +% v1.61 improve error handling, plotting
  139 +% fix bug in regular data calc for high-rate data
  140 +% fix bug in timestamp data calc for large starting gap
  141 +% (thanks to C. B. Ruiz for identifying these bugs)
  142 +% uses timestamps for DATA.rate=0
  143 +% progress indicator for large timestamp data processing
  144 +% MH JUN2007
  145 +% v1.54 Improve data plotting and optional bin plotting
  146 +% MH FEB2007
  147 +% v1.5 use difference from median for plotting
  148 +% added MAD calculation for outlier detection
  149 +% MH JAN2007
  150 +% v1.48 plotting typos fixes
  151 +% MH DEC2006
  152 +% v1.46 hack to plot error bars
  153 +% v1.44 further validation (Riley 1000-pt)
  154 +% plot mean and std
  155 +% MH NOV2006
  156 +% v1.42 typo fix comments
  157 +% v1.4 fix irregular rate algorithm
  158 +% irregular algorithm rejects tau less than max gap in time data
  159 +% validate both algorithms using test data from NBS Monograph 140
  160 +% v1.3 fix time calc if data.time not present
  161 +% add error bars (not possible due to bug in MATLAB R14SP3)
  162 +% remove offset calculation
  163 +% v1.24 improve feedback
  164 +% MH SEP2006
  165 +% v1.22 updated comments
  166 +% v1.2 errors and warnings
  167 +% v1.1 handle irregular interval data
  168 +%#ok<*AGROW>
  169 +
  170 +% defaults
  171 +if nargin < 4, verbose=2; end
  172 +if nargin < 3, name=''; end
  173 +if nargin < 2 || isempty(tau), tau=2.^(-10:10); end
  174 +
  175 +% plot "tau bins"? #TAUBIN
  176 +TAUBIN = 0; % set 0 or 1 % WARNING: this has a significant impact on performance
  177 +
  178 +% Formatting for plots
  179 +FontName = 'Arial';
  180 +FontSize = 14;
  181 +plotlinewidth=2;
  182 +
  183 +if verbose >= 1, fprintf(1,'allan: %s\n\n',versionstr); end
  184 +
  185 +%% Data consistency checks
  186 +if ~(isfield(data,'phase') || isfield(data,'freq'))
  187 + error('Either ''phase'' or ''freq'' must be present in DATA. See help file for details. [con0]');
  188 +end
  189 +if isfield(data,'time')
  190 + if isfield(data,'phase') && (length(data.phase) ~= length(data.time))
  191 + if isfield(data,'freq') && (length(data.freq) ~= length(data.time))
  192 + error('The time and freq vectors are not the same length. See help for details. [con2]');
  193 + else
  194 + error('The time and phase vectors are not the same length. See help for details. [con1]');
  195 + end
  196 + end
  197 + if isfield(data,'phase') && (any(isnan(data.phase)) || any(isinf(data.phase)))
  198 + error('The phase vector contains invalid elements (NaN/Inf). [con3]');
  199 + end
  200 + if isfield(data,'freq') && (any(isnan(data.freq)) || any(isinf(data.freq)))
  201 + error('The freq vector contains invalid elements (NaN/Inf). [con4]');
  202 + end
  203 + if isfield(data,'time') && (any(isnan(data.time)) || any(isinf(data.time)))
  204 + error('The time vector contains invalid elements (NaN/Inf). [con5]');
  205 + end
  206 +end
  207 +
  208 +% sort tau vector
  209 +tau=sort(tau);
  210 +
  211 +
  212 +%% Basic statistical tests on the data set
  213 +if ~isfield(data,'freq')
  214 + if isfield(data,'rate') && data.rate ~= 0
  215 + data.freq=diff(data.phase).*data.rate;
  216 + elseif isfield(data,'time')
  217 + data.freq=diff(data.phase)./diff(data.time);
  218 + end
  219 + if verbose >= 1, fprintf(1,'allan: Fractional frequency data generated from phase data (M=%g).\n',length(data.freq)); end
  220 + data.time(1)=[]; % make time stamps correspond to freq data
  221 +end
  222 +if size(data.freq,2) > size(data.freq,1), data.freq=data.freq'; end % ensure columns
  223 +
  224 +s.numpoints=length(data.freq);
  225 +s.max=max(data.freq);
  226 +s.min=min(data.freq);
  227 +s.mean=mean(data.freq);
  228 +s.median=median(data.freq);
  229 +if isfield(data,'time')
  230 + if size(data.time,2) > size(data.time,1), data.time=data.time'; end % ensure columns
  231 + s.linear=polyfit(data.time(1:length(data.freq)),data.freq,1);
  232 +elseif isfield(data,'rate') && data.rate ~= 0;
  233 + s.linear=polyfit((1/data.rate:1/data.rate:length(data.freq)/data.rate)',data.freq,1);
  234 +else
  235 + error('Either "time" or "rate" must be present in DATA. Type "help allan" for details. [err1]');
  236 +end
  237 +s.std=std(data.freq);
  238 +
  239 +if verbose >= 2
  240 + fprintf(1,'allan: input data statistics:\n');
  241 + disp(s);
  242 +end
  243 +
  244 +
  245 +% center at median for plotting
  246 +medianfreq=data.freq-s.median;
  247 +sm=[]; sme=[];
  248 +
  249 +% Screen for outliers using 5x Median Absolute Deviation (MAD) criteria
  250 +s.MAD = median(abs(medianfreq)/0.6745);
  251 +if verbose >= 2
  252 + fprintf(1, 'allan: 5x MAD value for outlier detection: %g\n',5*s.MAD);
  253 +end
  254 +if verbose >= 1 && any(abs(medianfreq) > 5*s.MAD)
  255 + fprintf(1, 'allan: NOTE: There appear to be outliers in the frequency data. See plot.\n');
  256 +end
  257 +
  258 +
  259 +%%%%
  260 +% There are two cases, either using timestamps or fixed sample rate:
  261 +
  262 +%% Fixed Sample Rate Data
  263 +% If there is a regular interval between measurements, calculation is much
  264 +% easier/faster
  265 +if isfield(data,'rate') && data.rate > 0 % if data rate was given
  266 + if verbose >= 1, fprintf(1, 'allan: regular data (%g data points @ %g Hz)\n',length(data.freq),data.rate); end
  267 +
  268 + % string for plot title
  269 + name=[name ' (' num2str(data.rate) ' Hz)'];
  270 +
  271 + % what is the time interval between data points?
  272 + tmstep = 1/data.rate;
  273 +
  274 + % Is there time data? Just for curiosity/plotting, does not impact calculation
  275 + if isfield(data,'time')
  276 + % adjust time data to remove any starting gap; first time step
  277 + % should not be zero for comparison with freq data
  278 + dtime=data.time-data.time(1)+mean(diff(data.time));
  279 + if verbose >= 2
  280 + fprintf(1,'allan: End of timestamp data: %g sec.\n',dtime(end));
  281 + if (data.rate - 1/mean(diff(dtime))) > 1e-6
  282 + fprintf(1,'allan: NOTE: data.rate (%f Hz) does not match average timestamped sample rate (%f Hz)\n',data.rate,1/mean(diff(dtime)));
  283 + end
  284 + end
  285 + else
  286 + % create time axis data using rate (for plotting only)
  287 + dtime=(tmstep:tmstep:length(data.freq)*tmstep)'; % column oriented
  288 + end
  289 +
  290 + % check the range of tau values and truncate if necessary
  291 + % find halfway point of time record
  292 + halftime = round(tmstep*length(data.freq)/2);
  293 + % truncate tau to appropriate values
  294 + tau = tau(tau >= tmstep & tau <= halftime);
  295 + if verbose >= 2, fprintf(1, 'allan: allowable tau range: %g to %g sec. (1/rate to total_time/2)\n',tmstep,halftime); end
  296 +
  297 + % save the freq data for the loop
  298 + dfreq=data.freq;
  299 + dfreq2=data.freq2;
  300 + % find the number of data points in each tau group
  301 + m = data.rate.*tau;
  302 + % only integer values allowed (no fractional groups of points)
  303 + %tau = tau(m-round(m)<1e-8); % numerical precision issues (v2.1)
  304 + tau = tau(m==round(m)); % The round() test is only correct for values < 2^53
  305 + %m = m(m-round(m)<1e-8); % change to round(m) for integer test v2.22
  306 + m = m(m==round(m));
  307 + %m=round(m);
  308 +
  309 + if verbose >= 1, fprintf(1,'allan: calculating Allan deviation...\n '); end
  310 +
  311 + % calculate the Allan deviation for each value of tau
  312 + k=0; tic;
  313 + for i = tau
  314 + if verbose >= 2, fprintf(1,'%g ',i); end
  315 + k=k+1;
  316 +
  317 + % truncate frequency set to an even multiple of this tau value
  318 + freq=dfreq(1:end-rem(length(dfreq),m(k)));
  319 + freq2=dfreq2(1:end-rem(length(dfreq2),m(k)));
  320 + % group the data into tau-length groups or bins
  321 + f = reshape(freq,m(k),[]); % Vectorize!
  322 + f2 = reshape(freq2,m(k),[]); % Vectorize!
  323 + % find average in each "tau group", y_k (each colummn of f)
  324 + fa=mean(f,1);
  325 + fa2=mean(f2,1);
  326 + % first finite difference
  327 + fd=diff(fa);
  328 + fd2=diff(fa2);
  329 + % calculate two-sample variance for this tau
  330 + M=length(fa);
  331 + sm(k)=sqrt(0.5/(M-1)*(sum(fd.*fd2)));
  332 +
  333 + % estimate error bars
  334 + sme(k)=sm(k)/sqrt(M+1);
  335 +
  336 + if TAUBIN == 1
  337 + % save the binning points for plotting
  338 + fs(k,1:length(freq)/m(k))=m(k):m(k):length(freq); fval{k}=mean(f,1);
  339 + end
  340 +
  341 + end % repeat for each value of tau
  342 +
  343 + if verbose >= 2, fprintf(1,'\n'); end
  344 + calctime=toc; if verbose >= 2, fprintf(1,'allan: Elapsed time for calculation: %e seconds\n',calctime); end
  345 +
  346 +
  347 +
  348 +%% Irregular data (timestamp)
  349 +elseif isfield(data,'time')
  350 + % the interval between measurements is irregular
  351 + % so we must group the data by time
  352 + if verbose >= 1, fprintf(1, 'allan: irregular rate data (no fixed sample rate)\n'); end
  353 +
  354 + % string for plot title
  355 + name=[name ' (timestamp)'];
  356 +
  357 + % adjust time to remove any initial offset or zero
  358 + dtime=data.time-data.time(1)+mean(diff(data.time));
  359 + %dtime=data.time;
  360 + % where is the maximum gap in time record?
  361 + gap_pos=find(diff(dtime)==max(diff(dtime)));
  362 + % what is average data spacing?
  363 + avg_gap = mean(diff(dtime));
  364 +
  365 + if verbose >= 2
  366 + fprintf(1, 'allan: WARNING: irregular timestamp data (no fixed sample rate).\n');
  367 + fprintf(1, ' Calculation time may be long and the results subject to interpretation.\n');
  368 + fprintf(1, ' You are advised to estimate using an average sample rate (%g Hz) instead of timestamps.\n',1/avg_gap);
  369 + fprintf(1, ' Continue at your own risk! (press any key to continue)\n');
  370 + pause;
  371 + end
  372 +
  373 + if verbose >= 1
  374 + fprintf(1, 'allan: End of timestamp data: %g sec\n',dtime(end));
  375 + fprintf(1, ' Average rate: %g Hz (%g sec/measurement)\n',1/avg_gap,avg_gap);
  376 + if max(diff(dtime)) ~= 1/mean(diff(dtime))
  377 + fprintf(1, ' Max. gap: %g sec at position %d\n',max(diff(dtime)),gap_pos(1));
  378 + end
  379 + if max(diff(dtime)) > 5*avg_gap
  380 + fprintf(1, ' WARNING: Max. gap in time record is suspiciously large (>5x the average interval).\n');
  381 + end
  382 + end
  383 +
  384 +
  385 + % find halfway point
  386 + halftime = fix(dtime(end)/2);
  387 + % truncate tau to appropriate values
  388 + tau = tau(tau >= max(diff(dtime)) & tau <= halftime);
  389 + if isempty(tau)
  390 + error('allan: ERROR: no appropriate tau values (> %g s, < %g s)\n',max(diff(dtime)),halftime);
  391 + end
  392 +
  393 + % save the freq data for the loop
  394 + dfreq=data.freq;
  395 + dtime=dtime(1:length(dfreq));
  396 +
  397 + if verbose >= 1, fprintf(1,'allan: calculating Allan deviation...\n'); end
  398 +
  399 + k=0; tic;
  400 + for i = tau
  401 + if verbose >= 2, fprintf(1,'%d ',i); end
  402 +
  403 + k=k+1; fa=[]; %f=[];
  404 + km=0;
  405 +
  406 + % truncate data set to an even multiple of this tau value
  407 + freq=dfreq(dtime <= dtime(end)-rem(dtime(end),i));
  408 + time=dtime(dtime <= dtime(end)-rem(dtime(end),i));
  409 + %freq=dfreq;
  410 + %time=dtime;
  411 +
  412 + % break up the data into groups of tau length in sec
  413 + while i*km < time(end)
  414 + km=km+1;
  415 +
  416 + % progress bar
  417 + if verbose >= 2
  418 + if rem(km,100)==0, fprintf(1,'.'); end
  419 + if rem(km,1000)==0, fprintf(1,'%g/%g\n',km,round(time(end)/i)); end
  420 + end
  421 +
  422 + f = freq(i*(km-1) < time & time <= i*km);
  423 + f = f(~isnan(f)); % make sure values are valid
  424 +
  425 + if ~isempty(f)
  426 + fa(km)=mean(f);
  427 + else
  428 + fa(km)=0;
  429 + end
  430 +
  431 + if TAUBIN == 1 % WARNING: this has a significant impact on performance
  432 + % save the binning points for plotting
  433 + %if find(time <= i*km) > 0
  434 + fs(k,km)=max(time(time <= i*km));
  435 + %else
  436 + if isempty(fs(k,km))
  437 + fs(k,km)=0;
  438 + end
  439 + fval{k}=fa;
  440 + end % save tau bin plot points
  441 +
  442 + end
  443 +
  444 + if verbose >= 2, fprintf(1,'\n'); end
  445 +
  446 + % first finite difference of the averaged results
  447 + fd=diff(fa);
  448 + % calculate Allan deviation for this tau
  449 + M=length(fa);
  450 + sm(k)=sqrt(0.5/(M-1)*(sum(fd.^2)));
  451 +
  452 + % estimate error bars
  453 + sme(k)=sm(k)/sqrt(M+1);
  454 +
  455 +
  456 + end
  457 +
  458 + if verbose == 2, fprintf(1,'\n'); end
  459 + calctime=toc; if verbose >= 2, fprintf(1,'allan: Elapsed time for calculation: %e seconds\n',calctime); end
  460 +
  461 +
  462 +else
  463 + error('allan: WARNING: no DATA.rate or DATA.time! Type "help allan" for more information. [err2]');
  464 +end
  465 +
  466 +
  467 +%%%%%%%%
  468 +%% Plotting
  469 +
  470 +if verbose >= 2 % show all data
  471 +
  472 + % plot the frequency data, centered on median
  473 + if size(dtime,2) > size(dtime,1), dtime=dtime'; end % this should not be necessary, but dsplot 1.1 is a little bit brittle
  474 + try
  475 + % dsplot makes a new figure
  476 + hd=dsplot(dtime,medianfreq);
  477 + catch ME
  478 + figure;
  479 + if length(dtime) ~= length(medianfreq)
  480 + fprintf(1,'allan: Warning: length of time axis (%d) is not equal to data array (%d)\n',length(dtime),length(medianfreq));
  481 + end
  482 + hd=plot(dtime,medianfreq);
  483 + if verbose >= 1, fprintf(1,'allan: Note: Install dsplot.m for improved plotting of large data sets (File Exchange File ID: #15850).\n'); end
  484 + if verbose >= 2, fprintf(1,' (Message: %s)\n',ME.message); end
  485 + end
  486 + set(hd,'Marker','.','LineStyle','none','Color','b'); % equivalent to '.-'
  487 + hold on;
  488 +
  489 + % show center (0)
  490 + plot(xlim,[0 0],':k');
  491 + % show 5x Median Absolute Deviation (MAD) values
  492 + hm=plot(xlim,[5*s.MAD 5*s.MAD],'-r');
  493 + plot(xlim,[-5*s.MAD -5*s.MAD],'-r');
  494 + % show linear fit line
  495 + hf=plot(xlim,polyval(s.linear,xlim)-s.median,'-g');
  496 + title(['Data: ' name],'FontSize',FontSize+2,'FontName',FontName);
  497 + %set(get(gca,'Title'),'Interpreter','none');
  498 + xlabel('Time [sec]','FontSize',FontSize,'FontName',FontName);
  499 + if isfield(data,'units')
  500 + ylabel(['data - median(data) [' data.units ']'],'FontSize',FontSize,'FontName',FontName);
  501 + else
  502 + ylabel('freq - median(freq)','FontSize',FontSize,'FontName',FontName);
  503 + end
  504 + set(gca,'FontSize',FontSize,'FontName',FontName);
  505 + legend([hd hm hf],{'data (centered on median)','5x MAD outliers',['Linear Fit (' num2str(s.linear(1),'%g') ')']},'FontSize',max(10,FontSize-2));
  506 + % tighten up
  507 + xlim([dtime(1) dtime(end)]);
  508 +
  509 +
  510 + % Optional tau bin (y_k samples) plot
  511 + if TAUBIN == 1
  512 + % plot the tau divisions on the data plot
  513 + rfs=size(fs,1);
  514 + colororder=get(gca,'ColorOrder');
  515 + axis tight; kc=2;
  516 + %ap=axis;
  517 + for j=1:rfs
  518 + kc=kc+1; if rem(kc,length(colororder))==1, kc=2; end
  519 + %for b=1:max(find(fs(j,:))); % new form of "find" in r2009a
  520 + for b=1:find(fs(j,:), 1, 'last' );
  521 + % plot the tau division boundaries
  522 + %plot([fs(j,b) fs(j,b)],[ap(3)*1.1 ap(4)*1.1],'-','Color',colororder(kc,:));
  523 + % plot tau group y values
  524 + if b == 1
  525 + plot([dtime(1) fs(j,b)],[fval{j}(b)-s.median fval{j}(b)-s.median],'-','Color',colororder(kc,:),'LineWidth',4);
  526 + else
  527 + plot([fs(j,b-1) fs(j,b)],[fval{j}(b)-s.median fval{j}(b)-s.median],'-','Color',colororder(kc,:),'LineWidth',4);
  528 + end
  529 + end
  530 + end
  531 + axis auto
  532 + end % End optional bin plot
  533 +
  534 +end % end plot raw data
  535 +
  536 +
  537 +if verbose >= 1 % show ADEV results
  538 +
  539 + % plot Allan deviation results
  540 + if ~isempty(sm)
  541 + figure
  542 +
  543 + % Choose loglog or semilogx plot here #PLOTLOG
  544 + %semilogx(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
  545 + loglog(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
  546 +
  547 + % in R14SP3, there is a bug that screws up the error bars on a semilog plot.
  548 + % When this is fixed in a future release, uncomment below to use normal errorbars
  549 + %errorbar(tau,sm,sme,'.-b'); set(gca,'XScale','log');
  550 + % this is a hack to approximate the error bars
  551 + hold on; plot([tau; tau],[sm+sme; sm-sme],'-k','LineWidth',max(plotlinewidth-1,2));
  552 +
  553 + grid on;
  554 + title(['Allan Deviation: ' name],'FontSize',FontSize+2,'FontName',FontName);
  555 + %set(get(gca,'Title'),'Interpreter','none');
  556 + xlabel('\tau [sec]','FontSize',FontSize,'FontName',FontName);
  557 + if isfield(data,'units')
  558 + ylabel(['\sigma_y(\tau) [' data.units ']'],'FontSize',FontSize,'FontName',FontName);
  559 + else
  560 + ylabel('\sigma_y(\tau)','FontSize',FontSize,'FontName',FontName);
  561 + end
  562 + set(gca,'FontSize',FontSize,'FontName',FontName);
  563 + % expand the x axis a little bit so that the errors bars look nice
  564 + adax = axis;
  565 + axis([adax(1)*0.9 adax(2)*1.1 adax(3) adax(4)]);
  566 +
  567 + % display the minimum value
  568 + fprintf(1,'allan: Minimum ADEV value: %g at tau = %g seconds\n',min(sm),tau(sm==min(sm)));
  569 +
  570 + elseif verbose >= 1
  571 + fprintf(1,'allan: WARNING: no values calculated.\n');
  572 + fprintf(1,' Check that TAU > 1/DATA.rate and TAU values are divisible by 1/DATA.rate\n');
  573 + fprintf(1,'Type "help allan" for more information.\n\n');
  574 + end
  575 +
  576 +end % end plot ADEV data
  577 +
  578 +retval = sm;
  579 +errorb = sme;
  580 +
  581 +return
  1 +#!/usr/bin/octave-cli --persist
  2 +
  3 +filename = argv(){1};
  4 +col1 = eval(argv(){2});
  5 +col2 = eval(argv(){3});
  6 +mult1 = eval(argv(){4});
  7 +mult2 = eval(argv(){5});
  8 +
  9 +if length(col1) == length(mult1)
  10 + figure
  11 + hold all
  12 + grid on
  13 + cc = 'bkcgmry';
  14 + for i = [1:length(col1)]
  15 + data.freq = load(filename)(:,col1(i)).*mult1(i);
  16 + data.freq2 = load(filename)(:,col2(i)).*mult2(i);
  17 + if eval(argv(){end-1}) == 1
  18 + printf('\ndata1 drift removed\n\n')
  19 + data.freq = detrend(data.freq);
  20 + end
  21 + if eval(argv(){end}) == 1
  22 + printf('\ndata2 drift removed\n\n')
  23 + data.freq2 = detrend(data.freq2);
  24 + end
  25 + data.rate = 1;
  26 + [ad, S, err, tau] = allan_cov(data, 2.^[0:nextpow2(length(data.freq))-3]./data.rate, strcat(strsplit(filename, '/'){end}, num2str(i)), 0);
  27 + loglogerr(tau, ad, err, strcat(cc(mod(i, length(cc))), '-s'))
  28 + leg{i} = strcat(filename, ' cov col', num2str(col1(i)), ' col', num2str(col2(i)));
  29 + axis(10.^ceil(log10([tau(1), tau(end)])))
  30 + hold on
  31 + end
  32 + legend(leg)
  33 + input("Press to continue...");
  34 +end
  35 +exit