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bmarechal
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allan.m
allan_modified.m
allan_overlap.m
allanplot.m
dsplot.m
pt100.m
res2temp16941.m
res2temp16943.m
res2temp16944.m
res2temp16945.m
res2temp16947.m
res2temp625.m
res2temp627.m
res2temp628.m
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+function [retval, s, errorb, tau] = allan(data,tau,name,verbose)
+% ALLAN  Compute the Allan deviation for a set of time-domain frequency data
+% [RETVAL, S, ERRORB, TAU] = ALLAN(DATA,TAU,NAME,VERBOSE)
+%
+% Inputs:
+% DATA should be a structure and have the following fields:
+%  DATA.freq or DATA.phase
+%               A vector of fractional frequency measurements (df/f) in
+%                DATA.freq *or* phase offset data (seconds) in DATA.phase .
+%               If frequency data is not present, it will be generated by
+%                differentiating the phase data.
+%               If both fields are present, then DATA.freq will be used.
+%               Note: for general-purpose calculations of Allan deviation,
+%                (i.e. a two-sample variance) use DATA.freq .
+%
+%  DATA.rate or DATA.time
+%               The sampling rate in Hertz (DATA.rate) or a vector of
+%               timestamps for each measurement in seconds (DATA.time).
+%               DATA.rate is used if both fields are present.
+%               If DATA.rate == 0, then the timestamps are used.
+%
+%  DATA.units (optional)
+%               The units for the data. If present, the string DATA.units
+%               is added to the plot y-axis label.
+%
+% TAU is an array of tau values for computing Allan deviation.
+%     TAU values must be divisible by 1/DATA.rate (data points cannot be
+%     grouped in fractional quantities!) and invalid values are ignored.
+%     Leave empty to use default values.
+% NAME is an optional label that is added to the plot titles.
+% VERBOSE sets the level of status messages:
+%     0 = silent & no data plots;
+%     1 = status messages & minimum plots;
+%     2 = all messages and plots (default)
+%
+% Outputs:
+% RETVAL is the array of Allan deviation values at each TAU.
+% S is an optional output of other statistical measures of the data (mean, std, etc).
+% ERRORB is an optional output containing the error estimates for a 1-sigma
+%   confidence interval. These values are shown on the figure for each point.
+% TAU is an optional output containing the array of tau values used in the
+% calculation (which may be a truncated subset of the input or default values).
+%
+% Example:
+%
+% To compute the Allan deviation for the data in the variable "lt":
+% >> lt
+% lt = 
+%     freq: [1x86400 double]
+%     rate: 0.5
+%
+% Use:
+%
+% >> ad = allan(lt,[2 10 100],'lt data',1);
+%
+% The Allan deviation will be computed and plotted at tau = 2,10,100 seconds.
+%  1-sigma confidence intervals will be indicated by vertical lines at each point.
+% You can also use the default settings, which are usually a good starting point:
+%
+% >> ad = allan(lt);
+%
+%
+% Notes:
+%  This function calculates the standard Allan deviation (ADEV), *not* the
+%   overlapping ADEV. Use "allan_overlap.m" for overlapping ADEV.
+%  The calculation is performed using fractional frequency data. If only
+%   phase data is provided, frequency data is generated by differentiating
+%   the phase data.
+%  No pre-processing of the data is performed, except to remove any
+%   initial offset (i.e., starting gap) in the time record.
+%  For rate-based data, ADEV is computed only for tau values greater than the
+%   minimum time between samples and less than the half the total time. For
+%   time-stamped data, only tau values greater than the maximum gap between
+%   samples and less than half the total time are used.
+%  The calculation for fixed sample rate data is *much* faster than for
+%   time-stamp data. You may wish to run the rate-based calculation first,
+%   then compare with time-stamp-based. Often the differences are insignificant.
+%  To show the "tau bins" (y_k samples) on the data plot, set the variable
+%   TAUBIN to 1 (search for "#TAUBIN").
+%  You can choose between loglog and semilog plotting of results by
+%   commenting in/out the appropriate line. Search for "#PLOTLOG".
+%  I recommend installing "dsplot.m", which improves the performance of
+%   plotting large data sets. Download from File Exchange, File ID: #15850.
+%   allan.m will use dsplot.m if it is present on your MATLAB path.
+%  This function has been validated using the test data from NBS Monograph
+%   140, the 1000-point test data set given by Riley [1], and the example data
+%   given in IEEE standard 1139-1999, Annex C.
+%   The author welcomes other validation results, see contact info below.
+%
+% For more information, see:
+% [1] W. J. Riley, "The Calculation of Time Domain Frequency Stability,"
+% Available on the web:
+%  http://www.ieee-uffc.org/frequency_control/teaching.asp?name=paper1ht
+%
+%
+% M.A. Hopcroft
+%      mhopeng at gmail dot com
+%
+% I welcome your comments and feedback!
+%
+% MH Mar2014
+% v2.24 fix bug related to generating freq data from phase with timestamps
+%       (thanks to S. David-Grignot for finding the bug)
+% MH Oct2010
+% v2.22 tau truncation to integer groups; tau sort
+%       plotting bugfix
+% v2.20 sychronize updates across allan, allan_overlap, allan_modified
+% v2.16 add TAU as output, fixed unusual error with dsplot v1.1
+% v2.14 update plotting behaviour, default tau values
+%
+
+versionstr = 'allan v2.24';
+
+% MH Jun2010
+% v2.12 bugfix for rate data row/col orientation
+%       add DATA.units for plotting
+%       use dsplot.m for plotting
+%
+% MH MAR2010
+% v2.1  minor interface and bugfixes
+%       update data consistency check
+%
+% MH FEB2010
+% v2.0  Consistent code behaviour for all "allan_x.m" functions:
+%       accept phase data
+%       verbose levels
+%
+%
+% MH JAN2010
+% v1.84  code cleanup
+% v1.82  typos in comments and code cleanup
+%        tau bin plotting changed for performance improvement
+% v1.8   Performance improvements:
+%        vectorize code for rate data
+%        logical indexing for irregular rate data
+% MH APR2008
+% v1.62  loglog plot option
+% v1.61  improve error handling, plotting
+%        fix bug in regular data calc for high-rate data
+%        fix bug in timestamp data calc for large starting gap
+%         (thanks to C. B. Ruiz for identifying these bugs)
+%        uses timestamps for DATA.rate=0
+%        progress indicator for large timestamp data processing
+% MH JUN2007
+% v1.54 Improve data plotting and optional bin plotting
+% MH FEB2007
+% v1.5  use difference from median for plotting
+%       added MAD calculation for outlier detection
+% MH JAN2007
+% v1.48 plotting typos fixes
+% MH DEC2006
+% v1.46 hack to plot error bars
+% v1.44 further validation (Riley 1000-pt)
+%       plot mean and std
+% MH NOV2006
+% v1.42 typo fix comments
+% v1.4  fix irregular rate algorithm
+%       irregular algorithm rejects tau less than max gap in time data
+%       validate both algorithms using test data from NBS Monograph 140
+% v1.3  fix time calc if data.time not present
+%       add error bars (not possible due to bug in MATLAB R14SP3)
+%       remove offset calculation
+% v1.24 improve feedback
+% MH SEP2006
+% v1.22 updated comments
+% v1.2  errors and warnings
+% v1.1  handle irregular interval data
+%#ok<*AGROW>
+
+% defaults
+if nargin < 4, verbose=2; end
+if nargin < 3, name=''; end
+if nargin < 2 || isempty(tau), tau=2.^(-10:10); end
+
+% plot "tau bins"? #TAUBIN
+TAUBIN = 0; % set 0 or 1 % WARNING: this has a significant impact on performance
+
+% Formatting for plots
+FontName = 'Arial';
+FontSize = 14;
+plotlinewidth=2;
+
+if verbose >= 1, fprintf(1,'allan: %s\n\n',versionstr); end
+
+%% Data consistency checks
+if ~(isfield(data,'phase') || isfield(data,'freq'))
+    error('Either ''phase'' or ''freq'' must be present in DATA. See help file for details. [con0]');
+end
+if isfield(data,'time')
+    if isfield(data,'phase') && (length(data.phase) ~= length(data.time))
+        if isfield(data,'freq') && (length(data.freq) ~= length(data.time))
+            error('The time and freq vectors are not the same length. See help for details. [con2]');
+        else
+            error('The time and phase vectors are not the same length. See help for details. [con1]');
+        end
+    end
+    if isfield(data,'phase') && (any(isnan(data.phase)) || any(isinf(data.phase)))
+        error('The phase vector contains invalid elements (NaN/Inf). [con3]');
+    end
+    if isfield(data,'freq') && (any(isnan(data.freq)) || any(isinf(data.freq)))
+        error('The freq vector contains invalid elements (NaN/Inf). [con4]');
+    end
+    if isfield(data,'time') && (any(isnan(data.time)) || any(isinf(data.time)))
+        error('The time vector contains invalid elements (NaN/Inf). [con5]');
+    end
+end
+
+% sort tau vector
+tau=sort(tau);
+
+
+%% Basic statistical tests on the data set
+if ~isfield(data,'freq')
+    if isfield(data,'rate') && data.rate ~= 0
+        data.freq=diff(data.phase).*data.rate;
+    elseif isfield(data,'time')
+        data.freq=diff(data.phase)./diff(data.time);
+    end
+    if verbose >= 1, fprintf(1,'allan: Fractional frequency data generated from phase data (M=%g).\n',length(data.freq)); end
+    data.time(1)=[]; % make time stamps correspond to freq data 
+end
+if size(data.freq,2) > size(data.freq,1), data.freq=data.freq'; end % ensure columns
+    
+s.numpoints=length(data.freq);
+s.max=max(data.freq);
+s.min=min(data.freq);
+s.mean=mean(data.freq);
+s.median=median(data.freq);
+if isfield(data,'time')
+    if size(data.time,2) > size(data.time,1), data.time=data.time'; end % ensure columns
+    s.linear=polyfit(data.time(1:length(data.freq)),data.freq,1);
+elseif isfield(data,'rate') && data.rate ~= 0;
+    s.linear=polyfit((1/data.rate:1/data.rate:length(data.freq)/data.rate)',data.freq,1);
+else
+    error('Either "time" or "rate" must be present in DATA. Type "help allan" for details. [err1]');
+end
+s.std=std(data.freq);
+
+if verbose >= 2
+    fprintf(1,'allan: input data statistics:\n');
+    disp(s);
+end
+
+
+% center at median for plotting
+medianfreq=data.freq-s.median;
+sm=[]; sme=[];
+
+% Screen for outliers using 5x Median Absolute Deviation (MAD) criteria
+s.MAD = median(abs(medianfreq)/0.6745);
+if verbose >= 2
+    fprintf(1, 'allan: 5x MAD value for outlier detection: %g\n',5*s.MAD);
+end
+if verbose >= 1 && any(abs(medianfreq) > 5*s.MAD)
+    fprintf(1, 'allan: NOTE: There appear to be outliers in the frequency data. See plot.\n');
+end
+
+
+%%%%
+% There are two cases, either using timestamps or fixed sample rate:
+
+%% Fixed Sample Rate Data
+%  If there is a regular interval between measurements, calculation is much
+%   easier/faster
+if isfield(data,'rate') && data.rate > 0 % if data rate was given
+    if verbose >= 1, fprintf(1, 'allan: regular data (%g data points @ %g Hz)\n',length(data.freq),data.rate); end
+    
+    % string for plot title
+    name=[name ' (' num2str(data.rate) ' Hz)'];
+    
+    % what is the time interval between data points?
+    tmstep = 1/data.rate;
+   
+    % Is there time data? Just for curiosity/plotting, does not impact calculation
+    if isfield(data,'time')
+        % adjust time data to remove any starting gap; first time step
+        %  should not be zero for comparison with freq data
+        dtime=data.time-data.time(1)+mean(diff(data.time));
+        if verbose >= 2
+            fprintf(1,'allan: End of timestamp data: %g sec.\n',dtime(end));
+            if (data.rate - 1/mean(diff(dtime))) > 1e-6
+                fprintf(1,'allan: NOTE: data.rate (%f Hz) does not match average timestamped sample rate (%f Hz)\n',data.rate,1/mean(diff(dtime)));
+            end
+        end
+    else
+        % create time axis data using rate (for plotting only)
+        dtime=(tmstep:tmstep:length(data.freq)*tmstep)'; % column oriented
+    end
+
+    % check the range of tau values and truncate if necessary
+    % find halfway point of time record
+    halftime = round(tmstep*length(data.freq)/2);
+    % truncate tau to appropriate values
+    tau = tau(tau >= tmstep & tau <= halftime);
+    if verbose >= 2, fprintf(1, 'allan: allowable tau range: %g to %g sec. (1/rate to total_time/2)\n',tmstep,halftime); end  
+    
+    % save the freq data for the loop
+    dfreq=data.freq;
+    % find the number of data points in each tau group
+    m = data.rate.*tau;
+    % only integer values allowed (no fractional groups of points)
+    %tau = tau(m-round(m)<1e-8); % numerical precision issues (v2.1)
+    tau = tau(m==round(m));  % The round() test is only correct for values < 2^53
+    %m = m(m-round(m)<1e-8); % change to round(m) for integer test v2.22
+    m = m(m==round(m));
+    %m=round(m);
+    
+    if verbose >= 1, fprintf(1,'allan: calculating Allan deviation...\n       '); end
+    
+    % calculate the Allan deviation for each value of tau
+    k=0; tic;
+    for i = tau
+        if verbose >= 2, fprintf(1,'%g ',i); end
+        k=k+1;
+
+        % truncate frequency set to an even multiple of this tau value
+        freq=dfreq(1:end-rem(length(dfreq),m(k)));
+        % group the data into tau-length groups or bins
+        f = reshape(freq,m(k),[]); % Vectorize!     
+        % find average in each "tau group", y_k (each colummn of f)
+        fa=mean(f,1);
+        % first finite difference
+        fd=diff(fa);
+        % calculate two-sample variance for this tau
+        M=length(fa);
+        sm(k)=sqrt(0.5/(M-1)*(sum(fd.^2)));
+
+        % estimate error bars
+        sme(k)=sm(k)/sqrt(M+1);
+        
+        if TAUBIN == 1
+            % save the binning points for plotting
+            fs(k,1:length(freq)/m(k))=m(k):m(k):length(freq); fval{k}=mean(f,1);
+        end
+        
+    end % repeat for each value of tau
+    
+    if verbose >= 2, fprintf(1,'\n'); end
+    calctime=toc; if verbose >= 2, fprintf(1,'allan: Elapsed time for calculation: %e seconds\n',calctime); end
+    
+       
+    
+%% Irregular data (timestamp)   
+elseif isfield(data,'time')
+    % the interval between measurements is irregular
+    %  so we must group the data by time
+    if verbose >= 1, fprintf(1, 'allan: irregular rate data (no fixed sample rate)\n'); end
+    
+    % string for plot title
+    name=[name ' (timestamp)'];
+    
+    % adjust time to remove any initial offset or zero
+    dtime=data.time-data.time(1)+mean(diff(data.time));
+    %dtime=data.time;
+    % where is the maximum gap in time record?
+    gap_pos=find(diff(dtime)==max(diff(dtime)));
+    % what is average data spacing?
+    avg_gap = mean(diff(dtime));
+    
+    if verbose >= 2
+        fprintf(1, 'allan: WARNING: irregular timestamp data (no fixed sample rate).\n');
+        fprintf(1, '       Calculation time may be long and the results subject to interpretation.\n');
+        fprintf(1, '       You are advised to estimate using an average sample rate (%g Hz) instead of timestamps.\n',1/avg_gap);
+        fprintf(1, '       Continue at your own risk! (press any key to continue)\n');
+        pause;
+    end
+    
+    if verbose >= 1
+        fprintf(1, 'allan: End of timestamp data: %g sec\n',dtime(end));
+    	fprintf(1, '       Average rate: %g Hz (%g sec/measurement)\n',1/avg_gap,avg_gap);
+        if max(diff(dtime)) ~= 1/mean(diff(dtime))
+            fprintf(1, '       Max. gap: %g sec at position %d\n',max(diff(dtime)),gap_pos(1));
+        end
+        if max(diff(dtime)) > 5*avg_gap
+            fprintf(1, '       WARNING: Max. gap in time record is suspiciously large (>5x the average interval).\n');
+        end        
+    end
+ 
+
+    % find halfway point
+    halftime = fix(dtime(end)/2);
+    % truncate tau to appropriate values
+    tau = tau(tau >= max(diff(dtime)) & tau <= halftime);
+    if isempty(tau)
+        error('allan: ERROR: no appropriate tau values (> %g s, < %g s)\n',max(diff(dtime)),halftime);
+    end
+    
+    % save the freq data for the loop
+    dfreq=data.freq;
+    dtime=dtime(1:length(dfreq));
+
+    if verbose >= 1, fprintf(1,'allan: calculating Allan deviation...\n'); end
+
+    k=0; tic;
+    for i = tau
+        if verbose >= 2, fprintf(1,'%d ',i); end
+        
+        k=k+1; fa=[]; %f=[];
+        km=0;
+        
+        % truncate data set to an even multiple of this tau value
+        freq=dfreq(dtime <= dtime(end)-rem(dtime(end),i));
+        time=dtime(dtime <= dtime(end)-rem(dtime(end),i));
+        %freq=dfreq;
+        %time=dtime;
+        
+        % break up the data into groups of tau length in sec
+        while i*km < time(end)
+            km=km+1;
+                        
+            % progress bar
+            if verbose >= 2
+                if rem(km,100)==0, fprintf(1,'.'); end
+                if rem(km,1000)==0, fprintf(1,'%g/%g\n',km,round(time(end)/i)); end
+            end
+
+            f = freq(i*(km-1) < time & time <= i*km);
+            f = f(~isnan(f)); % make sure values are valid
+            
+            if ~isempty(f)
+                fa(km)=mean(f);
+            else
+                fa(km)=0;
+            end
+
+            if TAUBIN == 1 % WARNING: this has a significant impact on performance
+                % save the binning points for plotting
+                %if find(time <= i*km) > 0
+                    fs(k,km)=max(time(time <= i*km));
+                %else
+                if isempty(fs(k,km))
+                    fs(k,km)=0;
+                end
+                fval{k}=fa;
+            end % save tau bin plot points
+            
+        end
+        
+        if verbose >= 2, fprintf(1,'\n'); end
+
+        % first finite difference of the averaged results
+        fd=diff(fa);
+        % calculate Allan deviation for this tau
+        M=length(fa);
+        sm(k)=sqrt(0.5/(M-1)*(sum(fd.^2)));
+
+        % estimate error bars
+        sme(k)=sm(k)/sqrt(M+1);
+        
+
+    end
+
+    if verbose == 2, fprintf(1,'\n'); end
+    calctime=toc; if verbose >= 2, fprintf(1,'allan: Elapsed time for calculation: %e seconds\n',calctime); end
+    
+
+else
+    error('allan: WARNING: no DATA.rate or DATA.time! Type "help allan" for more information. [err2]');
+end
+
+
+%%%%%%%%
+%% Plotting
+
+if verbose >= 2 % show all data
+    
+    % plot the frequency data, centered on median
+    if size(dtime,2) > size(dtime,1), dtime=dtime'; end % this should not be necessary, but dsplot 1.1 is a little bit brittle
+    try
+        % dsplot makes a new figure
+        hd=dsplot(dtime,medianfreq);
+    catch ME
+        figure;
+        if length(dtime) ~= length(medianfreq)
+            fprintf(1,'allan: Warning: length of time axis (%d) is not equal to data array (%d)\n',length(dtime),length(medianfreq));
+        end
+        hd=plot(dtime,medianfreq);
+        if verbose >= 1, fprintf(1,'allan: Note: Install dsplot.m for improved plotting of large data sets (File Exchange File ID: #15850).\n'); end
+        if verbose >= 2, fprintf(1,'             (Message: %s)\n',ME.message); end
+    end
+    set(hd,'Marker','.','LineStyle','none','Color','b'); % equivalent to '.-'
+    hold on;
+
+    % show center (0)
+    plot(xlim,[0 0],':k');
+    % show 5x Median Absolute Deviation (MAD) values
+    hm=plot(xlim,[5*s.MAD 5*s.MAD],'-r');
+    plot(xlim,[-5*s.MAD -5*s.MAD],'-r');
+    % show linear fit line
+    hf=plot(xlim,polyval(s.linear,xlim)-s.median,'-g');
+    title(['Data: ' name],'FontSize',FontSize+2,'FontName',FontName);
+    %set(get(gca,'Title'),'Interpreter','none');
+    xlabel('Time [sec]','FontSize',FontSize,'FontName',FontName);
+    if isfield(data,'units')
+        ylabel(['data - median(data) [' data.units ']'],'FontSize',FontSize,'FontName',FontName);
+    else
+        ylabel('freq - median(freq)','FontSize',FontSize,'FontName',FontName);
+    end
+    set(gca,'FontSize',FontSize,'FontName',FontName);
+    legend([hd hm hf],{'data (centered on median)','5x MAD outliers',['Linear Fit (' num2str(s.linear(1),'%g') ')']},'FontSize',max(10,FontSize-2));
+    % tighten up
+    xlim([dtime(1) dtime(end)]);
+
+
+    % Optional tau bin (y_k samples) plot
+    if TAUBIN == 1
+        % plot the tau divisions on the data plot
+        rfs=size(fs,1);
+        colororder=get(gca,'ColorOrder');
+        axis tight; kc=2;
+        %ap=axis;
+        for j=1:rfs
+            kc=kc+1; if rem(kc,length(colororder))==1, kc=2; end
+            %for b=1:max(find(fs(j,:))); % new form of "find" in r2009a
+            for b=1:find(fs(j,:), 1, 'last' );
+                % plot the tau division boundaries
+                %plot([fs(j,b) fs(j,b)],[ap(3)*1.1 ap(4)*1.1],'-','Color',colororder(kc,:));
+                % plot tau group y values
+                if b == 1
+                    plot([dtime(1) fs(j,b)],[fval{j}(b)-s.median fval{j}(b)-s.median],'-','Color',colororder(kc,:),'LineWidth',4);
+                else
+                    plot([fs(j,b-1) fs(j,b)],[fval{j}(b)-s.median fval{j}(b)-s.median],'-','Color',colororder(kc,:),'LineWidth',4);
+                end
+            end
+        end
+        axis auto
+    end % End optional bin plot
+    
+end % end plot raw data
+
+
+if verbose >= 1 % show ADEV results
+
+    % plot Allan deviation results
+    if ~isempty(sm)
+        figure
+
+        % Choose loglog or semilogx plot here    #PLOTLOG
+        %semilogx(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
+        loglog(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
+
+        % in R14SP3, there is a bug that screws up the error bars on a semilog plot.
+        %  When this is fixed in a future release, uncomment below to use normal errorbars
+        %errorbar(tau,sm,sme,'.-b'); set(gca,'XScale','log');
+        % this is a hack to approximate the error bars
+        hold on; plot([tau; tau],[sm+sme; sm-sme],'-k','LineWidth',max(plotlinewidth-1,2));
+
+        grid on;
+        title(['Allan Deviation: ' name],'FontSize',FontSize+2,'FontName',FontName);
+        %set(get(gca,'Title'),'Interpreter','none');
+        xlabel('\tau [sec]','FontSize',FontSize,'FontName',FontName);
+        if isfield(data,'units')
+            ylabel(['\sigma_y(\tau) [' data.units ']'],'FontSize',FontSize,'FontName',FontName);
+        else
+            ylabel('\sigma_y(\tau)','FontSize',FontSize,'FontName',FontName);
+        end
+        set(gca,'FontSize',FontSize,'FontName',FontName);
+        % expand the x axis a little bit so that the errors bars look nice
+        adax = axis;
+        axis([adax(1)*0.9 adax(2)*1.1 adax(3) adax(4)]);
+        
+        % display the minimum value
+        fprintf(1,'allan: Minimum ADEV value: %g at tau = %g seconds\n',min(sm),tau(sm==min(sm)));
+        
+    elseif verbose >= 1
+        fprintf(1,'allan: WARNING: no values calculated.\n');
+        fprintf(1,'       Check that TAU > 1/DATA.rate and TAU values are divisible by 1/DATA.rate\n');
+        fprintf(1,'Type "help allan" for more information.\n\n');
+    end
+
+end % end plot ADEV data
+    
+retval = sm;
+errorb = sme;
+
+return
@@ -0,0 +1,561 @@
+function [retval, s, errorb, tau] = allan_modified(data,tau,name,verbose)
+% ALLAN_MODIFIED  Compute the modified Allan deviation for a set of
+%   time-domain frequency data
+% [RETVAL, S, ERRORB, TAU] = ALLAN_MODIFIED(DATA,TAU,NAME,VERBOSE)
+%
+% Inputs:
+% DATA should be a struct and have the following fields:
+%  DATA.freq or DATA.phase
+%               A vector of fractional frequency measurements (df/f) in
+%               DATA.freq *or* phase offset data (seconds) in DATA.phase
+%               If phase data is not present, it will be generated by
+%               integrating the fractional frequency data.
+%               If both fields are present, then DATA.phase will be used.
+%
+%  DATA.rate or DATA.time
+%               The sampling rate in Hertz (DATA.rate) or a vector of
+%               timestamps for each measurement in seconds (DATA.time).
+%               DATA.rate is used if both fields are present.
+%               If DATA.rate == 0, then the timestamps are used.
+%
+% TAU is an array of tau values for computing Allan deviation.
+%     TAU values must be divisible by 1/DATA.rate (data points cannot be
+%     grouped in fractional quantities!). Invalid values are ignored.
+% NAME is an optional label that is added to the plot titles.
+% VERBOSE sets the level of status messages:
+%     0 = silent & no data plots; 1 = status messages; 2 = all messages
+%
+% Outputs:
+% RETVAL is the array of modified Allan deviation values at each TAU.
+% S is an optional output of other statistical measures of the data (mean, std, etc).
+% ERRORB is an optional output containing the error estimates for a
+%   1-sigma confidence interval. These values are shown on the figure for each point.
+% TAU is an optional output containing the array of tau values used in the
+%   calculation (which may be a truncated subset of the input or default values).
+%
+% Example:
+%
+% To compute the modified Allan deviation for the data in the variable "lt":
+% >> lt
+% lt = 
+%     freq: [1x86400 double]
+%     rate: 0.5
+%
+% Use:
+%
+% >> adm = allan_modified(lt,[2 10 100],'lt data',1);
+%
+% The modified Allan deviation will be computed and plotted at tau = 2,10,100 seconds.
+%  1-sigma confidence intervals will be indicated by vertical lines at each point.
+% You can also use the default settings, which are usually a good starting point:
+%
+% >> adm = allan_modified(lt);
+%
+%
+% Notes:
+%  This function calculates the modifed Allan deviation (MDEV).
+%  The calculation is performed using phase data. If only frequency data is
+%   provided, phase data is generated by integrating the frequency data.
+%  No pre-processing of the data is performed.
+%  For rate-based data, MDEV is computed only for tau values greater than the
+%   minimum time between samples and less than the half the total time. For
+%   time-stamped data, only tau values greater than the maximum gap between
+%   samples and less than half the total time are used.
+%  The calculation for fixed sample rate data is *much* faster than for
+%   time-stamp data. You may wish to run the rate-based calculation first,
+%   then compare with time-stamp-based. Often the differences are insignificant.
+%  When phase data is generated by integrating time-stamped frequency data,
+%   the final data point is dropped, because there is no timestamp for it.
+%   This will create a [usually small] difference between the results from
+%   analyzing the same data set with timestamp data and analyzing with a
+%   fixed sample rate. See note in the code near line 350.
+%  You can choose between loglog and semilog plotting of results by
+%   commenting in/out the appropriate line. Search for "#PLOTLOG".
+%  This function has been validated using the test data from NBS Monograph
+%   140, the 1000-point test data set given by Riley [1], and the example data
+%   given in IEEE standard 1139-1999, Annex C.
+%   The author welcomes other validation results, see contact info below.
+%
+% For more information, see:
+% [1] W. J. Riley, "The Calculation of Time Domain Frequency Stability,"
+% Available on the web:
+%  http://www.ieee-uffc.org/frequency_control/teaching.asp?name=paper1ht
+%
+%
+% M.A. Hopcroft
+%      mhopeng at gmail dot com
+%
+% I welcome your comments and feedback!
+%
+% MH Mar2014
+% v1.24 fix bug related to generating freq data from phase with timestamps
+%       (thanks to S. David-Grignot for finding the bug)
+% MH Oct2010
+% v1.22 tau truncation to integer groups; tau sort
+%       plotting bugfix
+% v1.20 update to match allan.m (dsplot.m, columns)
+%       discard tau values with timestamp irregularities
+%
+
+versionstr = 'allan_modified v1.24';
+
+% MH MAR2010
+% v1.1  bugfixes for irregular sample rates
+%       update consistency check
+%
+% MH FEB2010
+% v1.0  based on allan_overlap v2.0
+%
+
+%#ok<*AGROW>
+
+
+% defaults
+if nargin < 4, verbose = 2; end
+if nargin < 3, name=''; end
+if nargin < 2 || isempty(tau), tau=2.^(-10:10); end
+if isfield(data,'rate') && isempty(data.rate), data.rate=0; end % v1.1
+
+% Formatting for plots
+FontName = 'Arial';
+FontSize = 14;
+plotlinewidth=2;
+
+if verbose >= 1, fprintf(1,'allan_modified: %s\n\n',versionstr); end
+
+%% Data consistency checks
+if ~(isfield(data,'phase') || isfield(data,'freq'))
+    error('Either ''phase'' or ''freq'' must be present in DATA. See help file for details. [con0]');
+end
+if isfield(data,'time')
+    if isfield(data,'phase') && (length(data.phase) ~= length(data.time))
+        if isfield(data,'freq') && (length(data.freq) ~= length(data.time))
+            error('The time and freq vectors are not the same length. See help for details. [con2]');
+        else
+            error('The time and phase vectors are not the same length. See help for details. [con1]');
+        end
+    end
+    if isfield(data,'phase') && (any(isnan(data.phase)) || any(isinf(data.phase)))
+        error('The phase vector contains invalid elements (NaN/Inf). [con3]');
+    end
+    if isfield(data,'freq') && (any(isnan(data.freq)) || any(isinf(data.freq)))
+        error('The freq vector contains invalid elements (NaN/Inf). [con4]');
+    end
+    if isfield(data,'time') && (any(isnan(data.time)) || any(isinf(data.time)))
+        error('The time vector contains invalid elements (NaN/Inf). [con5]');
+    end
+end
+
+% sort tau vector
+tau=sort(tau);
+
+
+%% Basic statistical tests on the data set
+if ~isfield(data,'freq')
+    if isfield(data,'rate') && data.rate ~= 0
+        data.freq=diff(data.phase).*data.rate;
+    elseif isfield(data,'time')
+        data.freq=diff(data.phase)./diff(data.time);
+    end
+    if verbose >= 1, fprintf(1,'allan_modified: Fractional frequency data generated from phase data (M=%g).\n',length(data.freq)); end
+end
+if size(data.freq,2) > size(data.freq,1), data.freq=data.freq'; end % ensure columns
+
+s.numpoints=length(data.freq);
+s.max=max(data.freq);
+s.min=min(data.freq);
+s.mean=mean(data.freq);
+s.median=median(data.freq);
+if isfield(data,'time')
+    if size(data.time,2) > size(data.time,1), data.time=data.time'; end % ensure columns
+    s.linear=polyfit(data.time(1:length(data.freq)),data.freq,1);
+elseif isfield(data,'rate') && data.rate ~= 0;
+    s.linear=polyfit((1/data.rate:1/data.rate:length(data.freq)/data.rate)',data.freq,1);
+else
+    error('Either "time" or "rate" must be present in DATA. Type "help allan_modified" for details. [err1]');
+end
+s.std=std(data.freq);
+
+if verbose >= 2
+    fprintf(1,'allan_modified: fractional frequency data statistics:\n');
+    disp(s);
+end
+
+% scale to median for plotting
+medianfreq=data.freq-s.median;
+sm=[]; sme=[];
+
+% Screen for outliers using 5x Median Absolute Deviation (MAD) criteria
+MAD = median(abs(medianfreq)/0.6745);
+if verbose >= 1 && any(abs(medianfreq) > 5*MAD)
+    fprintf(1, 'allan_modified: NOTE: There appear to be outliers in the frequency data. See plot.\n');
+end
+
+%%%%
+% There are two cases, either using timestamps or rate:
+
+%% Fixed Sample Rate Data
+%   If there is a regular interval between measurements, calculation is much
+%   easier/faster
+if isfield(data,'rate') && data.rate > 0 % if data rate was given
+    if verbose >= 1
+        fprintf(1, 'allan_modified: regular data ');
+        if isfield(data,'freq')
+            fprintf(1, '(%g freq data points @ %g Hz)\n',length(data.freq),data.rate);
+        elseif isfield(data,'phase')
+            fprintf(1, '(%g phase data points @ %g Hz)\n',length(data.phase),data.rate);
+        else
+            error('\n phase or freq data missing [err10]');
+        end
+    end
+    
+    % string for plot title
+    name=[name ' (' num2str(data.rate) ' Hz)'];
+
+    % what is the time interval between data points?
+    tmstep = 1/data.rate;
+    
+    % Is there time data? Just for curiosity/plotting, does not impact calculation
+    if isfield(data,'time')
+        % adjust time data to remove any starting gap; first time step
+        %  should not be zero for comparison with freq data
+        dtime=data.time-data.time(1)+mean(diff(data.time));
+        dtime=dtime(1:length(medianfreq)); % equalize the data vector lengths for plotting (v1.1)
+        if verbose >= 2
+            fprintf(1,'allan_modified: End of timestamp data: %g sec.\n',dtime(end));
+            if (data.rate - 1/mean(diff(dtime))) > 1e-6
+                fprintf(1,'allan_modified: NOTE: data.rate (%f Hz) does not match average timestamped sample rate (%f Hz)\n',data.rate,1/mean(diff(dtime)));
+            end
+        end
+    else
+        % create time axis data using rate (for plotting only)
+        dtime=(tmstep:tmstep:length(data.freq)*tmstep);
+    end
+    
+    
+    % is phase data present? If not, generate it
+    if ~isfield(data,'phase')
+        nfreq=data.freq-s.mean;
+        dphase=zeros(1,length(nfreq)+1);
+        dphase(2:end) = cumsum(nfreq).*tmstep;
+        if verbose >= 1, fprintf(1,'allan_modified: phase data generated from fractional frequency data (N=%g).\n',length(dphase)); end
+    else
+        dphase=data.phase;
+    end
+
+    
+    % check the range of tau values and truncate if necessary
+    % find halfway point of time record
+    halftime = round(tmstep*length(data.freq)/2);
+    % truncate tau to appropriate values
+    tau = tau(tau >= tmstep & tau <= halftime);
+    if verbose >= 2, fprintf(1, 'allan_modified: allowable tau range: %g to %g sec. (1/rate to total_time/2)\n',tmstep,halftime); end
+  
+    % find the number of data points in each tau group
+    % number of samples
+    N=length(dphase);
+    m = data.rate.*tau;
+    % only integer values allowed (no fractional groups of points)
+    %tau = tau(m-round(m)<1e-8); % numerical precision issues (v1.1)
+    tau = tau(m==round(m));  % The round() test is only correct for values < 2^53
+    %m = m(m-round(m)<1e-8); % change to round(m) for integer test v1.22
+    m = m(m==round(m));
+    %m=round(m);
+    
+    if verbose >= 1, fprintf(1,'allan_modified: calculating modified Allan deviation...\n       '); end
+    
+    
+    % calculate the modified Allan deviation for each value of tau
+    k=0; tic;
+    for i = tau
+        k=k+1;
+        pa=[];
+        if verbose >= 2, fprintf(1,'%d ',i); end
+        
+        mphase = dphase;
+            
+        % calculate overlapping "phase averages" (x_k)
+        for p=1:m(k)
+            
+            % truncate frequency set length to an even multiple of this tau value
+            mphase=mphase(1:end-rem(length(mphase),m(k)));
+            % group phase values
+            mp=reshape(mphase,m(k),[]);
+            % find average in each "tau group" (each column of mp)
+            pa(p,:)=mean(mp,1);
+            % shift data vector by -1 and repeat
+            mphase=circshift(dphase,(size(dphase)>1)*-p);
+            
+        end
+            
+        % create "modified" y_k freq values
+        mfreq=diff(pa,1,2)./i;
+        mfreq=reshape(mfreq,1,[]);
+        
+        % calculate modified frequency differences
+        mfreqd=reshape(mfreq,m(k),[]); % Vectorize!
+        mfreqd=diff(mfreqd,1,2);
+        mfreqd=reshape(mfreqd,1,[]);
+        
+       
+        % calculate two-sample variance for this tau
+        sm(k)=sqrt((1/(2*(N-3*m(k)+1)))*(sum(mfreqd(1:N-3*m(k)+1).^2)));
+
+        % estimate error bars
+        sme(k)=sm(k)/sqrt(N-3*m(k)+1);
+
+        
+    end % repeat for each value of tau
+    
+    if verbose >= 2, fprintf(1,'\n'); end
+    calctime=toc; if verbose >= 2, fprintf(1,'allan_modified: Elapsed time for calculation: %g seconds\n',calctime); end
+
+       
+    
+%% Irregular data (timestamp)   
+elseif isfield(data,'time')
+    % the interval between measurements is irregular
+    %  so we must group the data by time
+    if verbose >= 1, fprintf(1, 'allan_modified: irregular rate data (no fixed sample rate)\n'); end
+    
+    % string for plot title
+    name=[name ' (timestamp)'];
+    
+    % adjust time to remove any initial offset
+    dtime=data.time-data.time(1)+mean(diff(data.time));
+    %dtime=data.time-data.time(1);
+    % where is the maximum gap in time record?
+    gap_pos=find(diff(dtime)==max(diff(dtime)));
+    % what is average data spacing?
+    avg_gap = mean(diff(dtime));
+    
+    if verbose >= 2
+        fprintf(1, 'allan_modified: WARNING: irregular timestamp data (no fixed sample rate).\n');
+        fprintf(1, '       Calculation time may be long and the results subject to interpretation.\n');
+        fprintf(1, '       You are advised to estimate using an average sample rate (%g Hz) instead of timestamps.\n',1/avg_gap);
+        fprintf(1, '       Continue at your own risk! (press any key to continue)\n');
+        pause;
+    end
+    
+    if verbose >= 1
+        fprintf(1, 'allan_modified: End of timestamp data: %g sec\n',dtime(end));
+    	fprintf(1, '       Average sample rate: %g Hz (%g sec/measurement)\n',1/avg_gap,avg_gap);
+        if max(diff(dtime)) ~= 1/mean(diff(dtime))
+            fprintf(1, '       Max. gap in time record: %g sec at position %d\n',max(diff(dtime)),gap_pos(1));
+        end
+        if max(diff(dtime)) > 5*avg_gap
+            fprintf(1, '       WARNING: Max. gap in time record is suspiciously large (>5x the average interval).\n');
+        end
+    end
+
+    % is phase data present? If not, generate it
+    if ~isfield(data,'phase')
+        nfreq=data.freq-s.mean;
+        % NOTE: uncommenting the following two lines will artificially
+        % allow the code to give equivalent results for validation data
+        % sets using fixed rate data and timestamped data by adding a
+        % "phantom" data point for frequency integration. Use of this
+        % phantom point can skew the results of calculations on real data.
+        %nfreq(end+1)=0; % phantom freq point, with average value
+        %dtime(end+1)=dtime(end)+avg_gap; % phantom average time step
+        dphase=zeros(1,length(nfreq));
+        dphase(2:end) = cumsum(nfreq(1:end-1)).*diff(dtime);
+        if verbose >= 1, fprintf(1,'allan_modified: Phase data generated from fractional frequency data (N=%g).\n',length(dphase)); end
+    else
+        dphase=data.phase;
+    end
+
+    % find halfway point
+    halftime = fix(dtime(end)/2);
+    % truncate tau to appropriate values
+    tau = tau(tau >= max(diff(dtime)) & tau <= halftime);
+    if isempty(tau)
+        error('allan_modified: ERROR: no appropriate tau values (> %g s, < %g s)\n',max(diff(dtime)),halftime);
+    end
+
+%     % save the freq data for the loop
+%     dfreq=data.freq;
+    
+    % number of samples
+    N=length(dphase);
+    m=round(tau./mean(diff(dtime)));
+    
+    if verbose >= 1, fprintf(1,'allan_modified: calculating modified Allan deviation...\n'); end
+
+    k=0; tic;
+    for i = tau
+        
+        k=k+1; pa=[];
+        
+        mphase = dphase; time = dtime;
+
+        if verbose >= 2, fprintf(1,'%d ',i); end
+        
+        % calculate overlapping "phase averages" (x_k)
+        %for j = 1:i
+        for j = 1:m(k) % (v1.1)
+            km=0;
+            %fprintf(1,'j: %d ',j);
+            
+            % (v1.1) truncating not correct for overlapping samples
+            % truncate data set to an even multiple of this tau value
+            %mphase = mphase(time <= time(end)-rem(time(end),i));
+            %time = time(time <= time(end)-rem(time(end),i));
+            
+        
+            % break up the data into overlapping groups of tau length
+            while i*km < time(end)
+                km=km+1;
+
+                % progress bar
+                if verbose >= 2
+                    if rem(km,100)==0, fprintf(1,'.'); end
+                    if rem(km,1000)==0, fprintf(1,'%g/%g\n',km,round(time(end)/i)); end
+                end
+
+                mp = mphase(i*(km-1) < (time) & (time) <= i*km);
+
+                if ~isempty(mp)
+                    pa(j,km)=mean(mp);
+                else
+                    pa(j,km)=0;
+                end
+
+            end
+                        
+            % shift data vector by -1 and repeat
+            mphase=circshift(dphase,(size(mphase)>1)*-j);
+            mphase(end-j+1:end)=[];
+            time=circshift(dtime,(size(time)>1)*-j);
+            time(end-j+1:end)=[];
+            time=time-time(1)+avg_gap; % remove time offset
+            
+        end        
+
+        % create "modified" y_k freq values
+        mfreq=diff(pa,1,2)./i;
+        mfreq=reshape(mfreq,1,[]);
+        
+        % calculate modified frequency differences
+        mfreqd=reshape(mfreq,m(k),[]); % Vectorize!
+        mfreqd=diff(mfreqd,1,2);
+        mfreqd=reshape(mfreqd,1,[]);
+
+        % calculate two-sample variance for this tau
+        %  only the first N-3*m(k)+1 samples are valid
+        if length(mfreqd) >= N-3*m(k)+1
+            sm(k)=sqrt((1/(2*(N-3*m(k)+1)))*(sum(mfreqd(1:N-3*m(k)+1).^2)));
+
+            % estimate error bars
+            sme(k)=sm(k)/sqrt(N);
+            
+            if verbose >= 2, fprintf(1,'\n'); end
+        else
+            if verbose >=2, fprintf(1,' tau=%g dropped due to timestamp irregularities\n',tau(k)); end
+            sm(k)=0; sme(k)=0;
+        end            
+        
+
+    end
+
+    if verbose >= 2, fprintf(1,'\n'); end
+    calctime=toc; if verbose >= 2, fprintf(1,'allan_modified: Elapsed time for calculation: %g seconds\n',calctime); end
+    
+    % remove any points that were dropped
+    tau(sm==0)=[];
+    sm(sm==0)=[];
+    sme(sme==0)=[];
+    
+    % modify time vector for plotting
+    dtime=dtime(1:length(medianfreq));
+
+else
+    error('allan_modified: WARNING: no DATA.rate or DATA.time! Type "help allan_modified" for more information. [err2]');
+end
+
+
+%%%%%%%%
+%% Plotting
+
+if verbose >= 2 % show all data
+    
+    % plot the frequency data, centered on median
+    if size(dtime,2) > size(dtime,1), dtime=dtime'; end % this should not be necessary, but dsplot 1.1 is a little bit brittle
+    try
+        % dsplot makes a new figure
+        hd=dsplot(dtime,medianfreq);
+    catch ME
+        figure;
+        hd=plot(dtime,medianfreq);
+        if verbose >= 1, fprintf(1,'allan_modified: Note: Install dsplot.m for improved plotting of large data sets (File Exchange File ID: #15850).\n'); end
+        if verbose >= 2, fprintf(1,'             (Message: %s)\n',ME.message); end
+    end
+    set(hd,'Marker','.','LineStyle','none','Color','b'); % equivalent to '.-'
+    hold on;
+
+    fx = xlim;
+    % plot([fx(1) fx(2)],[s.median s.median],'-k');
+    plot([fx(1) fx(2)],[0 0],':k');
+    % show 5x Median Absolute deviation (MAD) values
+    hm=plot([fx(1) fx(2)],[5*MAD 5*MAD],'-r');
+    plot([fx(1) fx(2)],[-5*MAD -5*MAD],'-r');
+    % show linear fit line
+    hf=plot(xlim,polyval(s.linear,xlim)-s.median,'-g');    
+    title(['Data: ' name],'FontSize',FontSize+2,'FontName',FontName);
+    %set(get(gca,'Title'),'Interpreter','none');
+    xlabel('Time [sec]','FontSize',FontSize,'FontName',FontName);
+    if isfield(data,'units')
+        ylabel(['data - median(data) [' data.units ']'],'FontSize',FontSize,'FontName',FontName);
+    else
+        ylabel('freq - median(freq)','FontSize',FontSize,'FontName',FontName);
+    end
+    set(gca,'FontSize',FontSize,'FontName',FontName);
+    legend([hd hm hf],{'data (centered on median)','5x MAD outliers',['Linear Fit (' num2str(s.linear(1),'%g') ')']},'FontSize',max(10,FontSize-2));
+    % tighten up
+    xlim([dtime(1) dtime(end)]);
+
+
+end % end plot raw data
+
+
+if verbose >= 1 % show analysis results
+
+    % plot Allan deviation results
+    if ~isempty(sm)
+        figure
+
+        % Choose loglog or semilogx plot here    #PLOTLOG
+        %semilogx(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
+        loglog(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
+
+        % in R14SP3, there is a bug that screws up the error bars on a semilog plot.
+        %  When this is fixed, uncomment below to use normal errorbars
+        %errorbar(tau,sm,sme,'.-b'); set(gca,'XScale','log');
+        % this is a hack to approximate the error bars
+        hold on; plot([tau; tau],[sm+sme; sm-sme],'-k','LineWidth',max(plotlinewidth-1,2));
+
+        grid on;
+        title(['Modified Allan Deviation: ' name],'FontSize',FontSize+2,'FontName',FontName);
+        %set(get(gca,'Title'),'Interpreter','none');
+        xlabel('\tau [sec]','FontSize',FontSize,'FontName',FontName);
+        ylabel('Modified \sigma_y(\tau)','FontSize',FontSize,'FontName',FontName);
+        set(gca,'FontSize',FontSize,'FontName',FontName);
+        % expand the x axis a little bit so that the errors bars look nice
+        adax = axis;
+        axis([adax(1)*0.9 adax(2)*1.1 adax(3) adax(4)]);
+        
+        % display the minimum value
+        fprintf(1,'allan: Minimum modified ADEV value: %g at tau = %g seconds\n',min(sm),tau(sm==min(sm)));        
+        
+    elseif verbose >= 1
+        fprintf(1,'allan_modified: WARNING: no values calculated.\n');
+        fprintf(1,'       Check that TAU > 1/DATA.rate and TAU values are divisible by 1/DATA.rate\n');
+        fprintf(1,'Type "help allan_modified" for more information.\n\n');
+    end
+
+end % end plot analysis
+        
+retval = sm;
+errorb = sme;
+
+return
@@ -0,0 +1,547 @@
+function [retval, s, errorb, tau] = allan_overlap(data,tau,name,verbose)
+% ALLAN_OVERLAP  Compute the overlapping Allan deviation for a set of
+%   time-domain frequency data
+% [RETVAL, S, ERRORB, TAU] = ALLAN_OVERLAP(DATA,TAU,NAME,VERBOSE)
+%
+% Inputs:
+% DATA should be a struct and have the following fields:
+%  DATA.freq or DATA.phase
+%               A vector of fractional frequency measurements (df/f) in
+%               DATA.freq *or* phase offset data (seconds) in DATA.phase
+%               If phase data is not present, it will be generated by
+%                integrating the fractional frequency data.
+%               If both fields are present, then DATA.phase will be used.
+%
+%  DATA.rate or DATA.time
+%               The sampling rate in Hertz (DATA.rate) or a vector of
+%                timestamps for each measurement in seconds (DATA.time).
+%               DATA.rate is used if both fields are present.
+%               If DATA.rate == 0, then the timestamps are used.
+%
+% TAU is an array of tau values for computing Allan deviation.
+%     TAU values must be divisible by 1/DATA.rate (data points cannot be
+%     grouped in fractional quantities!). Invalid values are ignored.
+% NAME is an optional label that is added to the plot titles.
+% VERBOSE sets the level of status messages:
+%     0 = silent & no data plots; 1 = status messages; 2 = all messages 
+%
+% Outputs:
+% RETVAL is the array of overlapping Allan deviation values at each TAU.
+% S is an optional output of other statistical measures of the data (mean, std, etc).
+% ERRORB is an optional output containing the error estimates for a 1-sigma
+%   confidence interval. Error bars are plotted as vertical lines at each point.
+% TAU is an optional output containing the array of tau values used in the
+%   calculation (which may be a truncated subset of the input or default values).
+%
+% Example:
+%
+% To compute the overlapping Allan deviation for the data in the variable "lt":
+% >> lt
+% lt = 
+%     freq: [1x86400 double]
+%     rate: 0.5
+%
+% Use:
+%
+% >> ado = allan_overlap(lt,[2 10 100],'lt data',1);
+%
+% The Allan deviation will be computed and plotted at tau = 2,10,100 seconds.
+%  1-sigma confidence intervals will be indicated by vertical lines.
+% You can also use the default settings, which are usually a good starting point:
+%
+% >> ado = allan_overlap(lt);
+%
+%
+% Notes:
+%  This function calculates the overlapping Allan deviation (ADEV), *not* the
+%   standard ADEV. Use "allan.m" for standard ADEV.
+%  The calculation is performed using phase data. If only frequency data is
+%   provided, phase data is generated by integrating the frequency data.
+%   However, the timestamp-based calculation is performed using frequency
+%   data. Phase data is differentiated to generate frequency data if necessary.
+%  No pre-processing of the data is performed, except to remove any
+%   initial offset in the time record. 
+%  For rate-based data, ADEV is computed only for tau values greater than the
+%   minimum time between samples and less than the half the total time. For
+%   time-stamped data, only tau values greater than the maximum gap between
+%   samples and less than half the total time are used.
+%  The calculation for fixed sample rate data is *much* faster than for
+%   time-stamp data. You may wish to run the rate-based calculation first,
+%   then compare with time-stamp-based. Often the differences are insignificant.
+%  The error bars at each point are calculated using the 1-sigma intervals
+%   based on the size of the data set. This is usually an overestimate for
+%   overlapping ADEV; a more accurate (and usually smaller uncertainty)
+%   value can be determined from chi-squared statistics, but that is not
+%   implemented in this version.
+%  You can choose between loglog and semilog plotting of results by
+%   commenting in/out the appropriate line. Search for "#PLOTLOG".
+%  This function has been validated using the test data from NBS Monograph
+%   140, the 1000-point test data set given by Riley [1], and the example data
+%   given in IEEE standard 1139-1999, Annex C.
+%   The author welcomes other validation results, see contact info below.
+%
+% For more information, see:
+% [1] W. J. Riley, "Addendum to a test suite for the calculation of time domain
+%  frequency stability," presented at IEEE Frequency Control Symposium,
+%  1996.
+% Available on the web:
+%  http://www.ieee-uffc.org/frequency_control/teaching.asp?name=paper1ht
+%
+%
+% M.A. Hopcroft
+%      mhopeng at gmail dot com
+%
+% I welcome your comments and feedback!
+%
+% MH Mar2014
+% v2.24 fix bug related to generating freq data from phase with timestamps
+%       (thanks to S. David-Grignot for finding the bug)
+% MH Oct2010
+% v2.22 tau truncation to integer groups; tau sort
+%       plotting bugfix
+% v2.20 update to match allan.m (dsplot.m, columns)
+%       discard tau values with timestamp irregularities
+
+versionstr = 'allan_overlap v2.24';
+
+%
+% MH MAR2010
+% v2.1  bugfixes for irregular sample rates
+%        (thanks to Ryad Ben-El-Kezadri for feedback and testing)
+%       handle empty rate field
+%       fix integer comparisons for fractional sample rates
+%       update consistency check
+%
+% MH FEB2010
+% v2.0  use phase data for calculation- much faster
+%       Consistent code behaviour for all "allan_x.m" functions:
+%       accept phase data
+%       verbose levels
+%
+% MH JAN2010
+% v1.0  based on allan v1.84
+%
+
+%#ok<*AGROW>
+
+
+% defaults
+if nargin < 4, verbose = 2; end
+if nargin < 3, name=''; end
+if nargin < 2 || isempty(tau), tau=2.^(-10:10); end
+if isfield(data,'rate') && isempty(data.rate), data.rate=0; end % v2.1 
+
+% Formatting for plots
+FontName = 'Arial';
+FontSize = 14;
+plotlinewidth=2;
+
+if verbose >= 1, fprintf(1,'allan_overlap: %s\n\n',versionstr); end
+
+%% Data consistency checks v2.1
+if ~(isfield(data,'phase') || isfield(data,'freq'))
+    error('Either ''phase'' or ''freq'' must be present in DATA. See help file for details. [con0]');
+end
+if isfield(data,'time')
+    if isfield(data,'phase') && (length(data.phase) ~= length(data.time))
+        if isfield(data,'freq') && (length(data.freq) ~= length(data.time))
+            error('The time and freq vectors are not the same length. See help for details. [con2]');
+        else
+            error('The time and phase vectors are not the same length. See help for details. [con1]');
+        end
+    end
+    if isfield(data,'phase') && (any(isnan(data.phase)) || any(isinf(data.phase)))
+        error('The phase vector contains invalid elements (NaN/Inf). [con3]');
+    end
+    if isfield(data,'freq') && (any(isnan(data.freq)) || any(isinf(data.freq)))
+        error('The freq vector contains invalid elements (NaN/Inf). [con4]');
+    end
+    if isfield(data,'time') && (any(isnan(data.time)) || any(isinf(data.time)))
+        error('The time vector contains invalid elements (NaN/Inf). [con5]');
+    end
+end
+
+% sort tau vector
+tau=sort(tau);
+
+%% Basic statistical tests on the data set
+if ~isfield(data,'freq')
+    if isfield(data,'rate') && data.rate ~= 0
+        data.freq=diff(data.phase).*data.rate;
+    elseif isfield(data,'time')
+        data.freq=diff(data.phase)./diff(data.time);
+    end
+    if verbose >= 1, fprintf(1,'allan_overlap: Fractional frequency data generated from phase data (M=%g).\n',length(data.freq)); end
+end
+if size(data.freq,2) > size(data.freq,1), data.freq=data.freq'; end % ensure columns
+    
+s.numpoints=length(data.freq);
+s.max=max(data.freq);
+s.min=min(data.freq);
+s.mean=mean(data.freq);
+s.median=median(data.freq);
+if isfield(data,'time')
+    if size(data.time,2) > size(data.time,1), data.time=data.time'; end % ensure columns
+    s.linear=polyfit(data.time(1:length(data.freq)),data.freq,1);
+elseif isfield(data,'rate') && data.rate ~= 0;
+    s.linear=polyfit((1/data.rate:1/data.rate:length(data.freq)/data.rate)',data.freq,1);
+else
+    error('Either "time" or "rate" must be present in DATA. Type "help allan_overlap" for details. [err1]');
+end
+s.std=std(data.freq);
+
+if verbose >= 2
+    fprintf(1,'allan_overlap: fractional frequency data statistics:\n');
+    disp(s);
+end
+
+
+% scale to median for plotting
+medianfreq=data.freq-s.median;
+sm=[]; sme=[];
+
+% Screen for outliers using 5x Median Absolute Deviation (MAD) criteria
+MAD = median(abs(medianfreq)/0.6745);
+if verbose >= 1 && any(abs(medianfreq) > 5*MAD)
+    fprintf(1, 'allan_overlap: NOTE: There appear to be outliers in the frequency data. See plot.\n');
+end
+
+%%%%
+% There are four cases, freq or phase data, using timestamps or rate:
+
+%% Fixed Sample Rate Data
+%   If there is a regular interval between measurements, calculation is much
+%   easier/faster
+if isfield(data,'rate') && data.rate > 0 % if data rate was given
+    if verbose >= 1
+        fprintf(1, 'allan_overlap: regular data ');
+        if isfield(data,'freq')
+            fprintf(1, '(%g freq data points @ %g Hz)\n',length(data.freq),data.rate);
+        elseif isfield(data,'phase')
+            fprintf(1, '(%g phase data points @ %g Hz)\n',length(data.phase),data.rate);
+        else
+            error('\n phase or freq data missing [err10]');
+        end
+    end
+  
+    % string for plot title
+    name=[name ' (' num2str(data.rate) ' Hz)'];
+
+    % what is the time interval between data points?
+    tmstep = 1/data.rate;      
+    
+    % Is there time data? Just for curiosity/plotting, does not impact calculation
+    if isfield(data,'time')
+        % adjust time data to remove any starting gap; first time step
+        %  should not be zero for comparison with freq data
+        dtime=data.time-data.time(1)+mean(diff(data.time)); 
+        dtime=dtime(1:length(medianfreq)); % equalize the data vector lengths for plotting (v2.1)
+        if verbose >= 2
+            fprintf(1,'allan_overlap: End of timestamp data: %g sec.\n',dtime(end));
+            if (data.rate - 1/mean(diff(dtime))) > 1e-6
+                fprintf(1,'allan_overlap: NOTE: data.rate (%f Hz) does not match average timestamped sample rate (%f Hz)\n',data.rate,1/mean(diff(dtime)));
+            end
+        end
+    else
+        % create time axis data using rate (for plotting only)
+        dtime=(tmstep:tmstep:length(data.freq)*tmstep);
+    end
+
+  
+    % is phase data present? If not, generate it
+    if ~isfield(data,'phase')
+        nfreq=data.freq-s.mean;
+        dphase=zeros(1,length(nfreq)+1);
+        dphase(2:end) = cumsum(nfreq)./data.rate;
+        if verbose >= 1, fprintf(1,'allan_overlap: phase data generated from fractional frequency data (N=%g).\n',length(dphase)); end
+    else
+        dphase=data.phase;
+    end
+    
+    % check the range of tau values and truncate if necessary
+    % find halfway point of time record
+    halftime = round(tmstep*length(data.freq)/2);
+    % truncate tau to appropriate values
+    tau = tau(tau >= tmstep & tau <= halftime);
+    if verbose >= 2, fprintf(1, 'allan_overlap: allowable tau range: %g to %g sec. (1/rate to total_time/2)\n',tmstep,halftime); end
+    
+    % number of samples
+    N=length(dphase);
+    % number of samples per tau period
+    m = data.rate.*tau;
+    % only integer values allowed for m (no fractional groups of points)
+    %tau = tau(m-round(m)<1e-8); % numerical precision issues (v2.1)
+    tau = tau(m==round(m));  % The round() test is only correct for values < 2^53
+    %m = m(m-round(m)<1e-8); % change to round(m) for integer test v2.22
+    m = m(m==round(m));
+    %m=round(m);
+    %fprintf(1,'m: %.50f\n',m)
+        
+    if verbose >= 1, fprintf(1,'allan_overlap: calculating overlapping Allan deviation...\n       '); end
+    
+    % calculate the Allan deviation for each value of tau
+    k=0; tic;
+    for i = tau
+        k=k+1;
+        if verbose >= 2, fprintf(1,'%d ',i); end
+
+
+        % pad phase data set length to an even multiple of this tau value
+        mphase=zeros(ceil(length(dphase)./m(k))*m(k),1);
+        mphase(1:N)=dphase;
+        % group phase values
+        mp=reshape(mphase,m(k),[]);
+        % compute second differences of phase values (x_k+m - x_k)
+        md1=diff(mp,1,2);
+        md2=diff(md1,1,2);
+        md1=reshape(md2,1,[]);
+        
+        % compute overlapping ADEV from phase values
+        %  only the first N-2*m(k) samples are valid
+        sm(k)=sqrt((1/(2*(N-2*m(k))*i^2))*sum(md1(1:N-2*m(k)).^2));
+        
+        % estimate error bars
+        sme(k)=sm(k)/sqrt(N-2*m(k));
+        
+
+    end % repeat for each value of tau
+    
+    if verbose >= 2, fprintf(1,'\n'); end
+    calctime=toc; if verbose >= 2, fprintf(1,'allan_overlap: Elapsed time for calculation: %g seconds\n',calctime); end
+
+        
+    
+%% Irregular data, no fixed interval    
+elseif isfield(data,'time')
+    % the interval between measurements is irregular
+    %  so we must group the data by time
+    if verbose >= 1, fprintf(1, 'allan_overlap: irregular rate data (no fixed sample rate)\n'); end
+
+    
+    % string for plot title
+    name=[name ' (timestamp)'];
+    
+
+    % adjust time to remove any starting offset
+    dtime=data.time-data.time(1)+mean(diff(data.time));
+    
+    % save the freq data for the loop
+    dfreq=data.freq;
+    dtime=dtime(1:length(dfreq));
+    
+    dfdtime=diff(dtime); % only need to do this once (v2.1)
+    % where is the maximum gap in time record?
+    gap_pos=find(dfdtime==max(dfdtime));
+    % what is average data spacing?
+    avg_gap = mean(dfdtime);
+    s.avg_rate = 1/avg_gap; % save avg rate for user (v2.1)
+    
+    if verbose >= 2
+        fprintf(1, 'allan_overlap: WARNING: irregular timestamp data (no fixed sample rate).\n');
+        fprintf(1, '       Calculation time may be long and the results subject to interpretation.\n');
+        fprintf(1, '       You are advised to estimate using an average sample rate (%g Hz) instead of timestamps.\n',1/avg_gap);
+        fprintf(1, '       Continue at your own risk! (press any key to continue)\n');
+        pause;
+    end
+    
+    if verbose >= 1
+        fprintf(1, 'allan_overlap: End of timestamp data: %g sec\n',dtime(end));
+    	fprintf(1, '       Average rate: %g Hz (%g sec/measurement)\n',1/avg_gap,avg_gap);
+        if max(diff(dtime)) ~= 1/mean(diff(dtime))
+            fprintf(1, '       Max. gap in time record: %g sec at position %d\n',max(dfdtime),gap_pos(1));
+        end
+        if max(diff(dtime)) > 5*avg_gap
+            fprintf(1, '       WARNING: Max. gap in time record is suspiciously large (>5x the average interval).\n');
+        end
+    end
+    
+
+    % find halfway point
+    halftime = fix(dtime(end)/2);
+    % truncate tau to appropriate values
+    tau = tau(tau >= max(dfdtime) & tau <= halftime);
+    if isempty(tau)
+        error('allan_overlap: ERROR: no appropriate tau values (> %g s, < %g s)\n',max(dfdtime),halftime);
+    end
+    
+
+    % number of samples
+    M=length(dfreq);
+    % number of samples per tau period
+    m=round(tau./avg_gap);
+
+    if verbose >= 1, fprintf(1,'allan_overlap: calculating overlapping Allan deviation...\n'); end
+
+    k=0; tic;
+    for i = tau
+        k=k+1;
+        fa=[];
+
+        if verbose >= 2, fprintf(1,'%d ',i); end
+        
+        freq = dfreq; time = dtime;
+       
+        
+        % compute overlapping samples (y_k) for this tau
+        %for j = 1:i
+        for j = 1:m(k) % (v2.1)
+            km=0;
+            %fprintf(1,'j: %d ',j);
+
+            % (v2.1) truncating not correct for overlapping samples
+            % truncate data set to an even multiple of this tau value
+            %freq = freq(time <= time(end)-rem(time(end),i));
+            %time = time(time <= time(end)-rem(time(end),i));
+                        
+            % break up the data into overlapping groups of tau length
+            while i*km <= time(end)
+                km=km+1;
+                %i*km
+
+                % progress bar
+                if verbose >= 2
+                    if rem(km,100)==0, fprintf(1,'.'); end
+                    if rem(km,1000)==0, fprintf(1,'%g/%g\n',km,round(time(end)/i)); end
+                end
+
+                f = freq(i*(km-1) < (time) & (time) <= i*km);
+
+                if ~isempty(f)
+                    fa(j,km)=mean(f);
+                else
+                    fa(j,km)=0;
+                end
+
+            end
+            %fa
+            
+            % shift data vector by -1 and repeat
+            freq=circshift(dfreq,(size(freq)>1)*-j);
+            freq(end-j+1:end)=[];
+            time=circshift(dtime,(size(time)>1)*-j);
+            time(end-j+1:end)=[];
+            time=time-time(1)+avg_gap; % remove time offset
+            
+        end
+        
+        % compute second differences of fractional frequency values (y_k+m - y_k)
+        fd1=diff(fa,1,2);
+        fd1=reshape(fd1,1,[]);
+        % compute overlapping ADEV from fractional frequency values
+        %  only the first M-2*m(k)+1 samples are valid
+        if length(fd1) >= M-2*m(k)+1
+            sm(k)=sqrt((1/(2*(M-2*m(k)+1)))*sum(fd1(1:M-2*m(k)+1).^2));
+
+            % estimate error bars
+            sme(k)=sm(k)/sqrt(M+1);
+            
+            if verbose >= 2, fprintf(1,'\n'); end
+            
+        else
+            if verbose >=2, fprintf(1,' tau=%g dropped due to timestamp irregularities\n',tau(k)); end
+            sm(k)=0; sme(k)=0;
+        end
+        
+
+    end
+
+    if verbose >= 2, fprintf(1,'\n'); end
+    calctime=toc; if verbose >= 1, fprintf(1,'allan_overlap: Elapsed time for calculation: %g seconds\n',calctime); end
+
+    % remove any points that were dropped
+    tau(sm==0)=[];
+    sm(sm==0)=[];
+    sme(sme==0)=[];
+
+
+
+else
+    error('allan_overlap: WARNING: no DATA.rate or DATA.time! Type "help allan" for more information. [err2]');
+end
+
+
+%%%%%%%%
+%% Plotting
+
+if verbose >= 2 % show all data
+    
+    % plot the frequency data, centered on median
+    if size(dtime,2) > size(dtime,1), dtime=dtime'; end % this should not be necessary, but dsplot 1.1 is a little bit brittle
+    try
+        % dsplot makes a new figure
+        hd=dsplot(dtime,medianfreq);
+    catch ME
+        figure;
+        hd=plot(dtime,medianfreq);
+        if verbose >= 1, fprintf(1,'allan_overlap: Note: Install dsplot.m for improved plotting of large data sets (File Exchange File ID: #15850).\n'); end
+        if verbose >= 2, fprintf(1,'             (Message: %s)\n',ME.message); end
+    end
+    set(hd,'Marker','.','LineStyle','none','Color','b'); % equivalent to '.-'
+    hold on;
+
+    fx = xlim;
+    % plot([fx(1) fx(2)],[s.median s.median],'-k');
+    plot([fx(1) fx(2)],[0 0],':k');
+    % show 5x Median Absolute deviation (MAD) values
+    hm=plot([fx(1) fx(2)],[5*MAD 5*MAD],'-r');
+    plot([fx(1) fx(2)],[-5*MAD -5*MAD],'-r');
+    % show linear fit line
+    hf=plot(xlim,polyval(s.linear,xlim)-s.median,'-g');    
+    title(['Data: ' name],'FontSize',FontSize+2,'FontName','Arial');
+    %set(get(gca,'Title'),'Interpreter','none');
+    xlabel('Time [sec]','FontSize',FontSize,'FontName',FontName);
+    if isfield(data,'units')
+        ylabel(['data - median(data) [' data.units ']'],'FontSize',FontSize,'FontName',FontName);
+    else
+        ylabel('freq - median(freq)','FontSize',FontSize,'FontName',FontName);
+    end
+    set(gca,'FontSize',FontSize,'FontName',FontName);
+    legend([hd hm hf],{'data (centered on median)','5x MAD outliers',['Linear Fit (' num2str(s.linear(1),'%g') ')']},'FontSize',max(10,FontSize-2));
+    % tighten up
+    xlim([dtime(1) dtime(end)]);
+
+    
+end % end plot raw data
+
+
+if verbose >= 1 % show analysis results
+
+    % plot Allan deviation results
+    if ~isempty(sm)
+        figure
+
+        % Choose loglog or semilogx plot here    #PLOTLOG
+        %semilogx(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
+        loglog(tau,sm,'.-b','LineWidth',plotlinewidth,'MarkerSize',24);
+
+        % in R14SP3, there is a bug that screws up the error bars on a semilog plot.
+        %  When this is fixed, uncomment below to use normal errorbars
+        %errorbar(tau,sm,sme,'.-b'); set(gca,'XScale','log');
+        % this is a hack to approximate the error bars
+        hold on; plot([tau; tau],[sm+sme; sm-sme],'-k','LineWidth',max(plotlinewidth-1,2));
+
+        grid on;
+        title(['Overlapping Allan Deviation: ' name],'FontSize',FontSize+2,'FontName',FontName);
+        %set(get(gca,'Title'),'Interpreter','none');
+        xlabel('\tau [sec]','FontSize',FontSize,'FontName','Arial');
+        ylabel(' Overlapping \sigma_y(\tau)','FontSize',FontSize,'FontName',FontName);
+        set(gca,'FontSize',FontSize,'FontName',FontName);
+        % expand the x axis a little bit so that the errors bars look nice
+        adax = axis;
+        axis([adax(1)*0.9 adax(2)*1.1 adax(3) adax(4)]);
+        
+        % display the minimum value
+        fprintf(1,'allan: Minimum overlapping ADEV value: %g at tau = %g seconds\n',min(sm),tau(sm==min(sm)));        
+        
+    elseif verbose >= 1
+        fprintf(1,'allan_overlap: WARNING: no values calculated.\n');
+        fprintf(1,'       Check that TAU > 1/DATA.rate and TAU values are divisible by 1/DATA.rate\n');
+        fprintf(1,'Type "help allan_overlap" for more information.\n\n');
+    end
+    
+end % end plot analysis
+        
+retval = sm;
+errorb = sme;
+
+return
@@ -0,0 +1,12 @@
+#!/usr/bin/octave-cli --persist
+
+filename = argv(){1};
+col = eval(argv(){2});
+mult = eval(argv(){3});
+
+data.freq = load(filename)(:,col).*mult;
+data.rate = 1;
+
+ad = allan(data, 2.^(0:12), strsplit(filename, '/'){end}, 1);
+input("Press to continue...");
+exit
@@ -0,0 +1,319 @@
+function hL = dsplot(x, y, numPoints)
+
+%DSPLOT Create down sampled plot.
+%   This function creates a down sampled plot to improve the speed of
+%   exploration (zoom, pan).
+%
+%   DSPLOT(X, Y) plots Y versus X by downsampling if there are large number
+%   of elements. X and Y needs to obey the following:
+%     1. X must be a monotonically increasing vector.
+%     2. If Y is a vector, it must be the same size as X.
+%     3. If Y is a matrix, one of the dimensions must line up with X.
+%
+%   DSPLOT(Y) plots the columns of Y versus their index.
+%
+%   hLine = DSPLOT(X, Y) returns the handles of the line. Note that the
+%   lines may be downsampled, so they may not represent the full data set.
+%
+%   DSPLOT(X, Y, NUMPOINTS) or DSPLOT(Y, [], NUMPOINTS) specifies the
+%   number of points (roughly) to display on the screen. The default is
+%   50000 points (~390 kB doubles). NUMPOINTS can be a number greater than
+%   500.
+%
+%   It is very likely that more points will be displayed than specified by
+%   NUMPOINTS, because it will try to plot any outlier points in the range.
+%   If the signal is stochastic or has a lot of sharp changes, there will
+%   be more points on plotted on the screen.
+%
+%   The figure title (name) will indicate whether the plot shown is
+%   downsampled or is the true representation.
+%
+%   The figure can be saved as a .fig file, which will include the actual
+%   data. The figure can be reloaded and the actual data can be exported to
+%   the base workspace via a menu.
+%
+%   Run the following examples and zoom/pan to see the performance.
+%
+%  Example 1: (with small details)
+%   x  = linspace(0, 2*pi, 1000000);
+%   y1 = sin(x)+.02*cos(200*x)+0.001*sin(2000*x)+0.0001*cos(20000*x);
+%   dsplot(x,y1);title('Down Sampled');
+%   % compare with
+%   figure;plot(x,y1);title('Normal Plot');
+%
+%  Example 2: (with outlier points)
+%   x  = linspace(0, 2*pi, 1000000);
+%   y1 = sin(x) + .01*cos(200*x) + 0.001*sin(2000*x);
+%   y2 = sin(x) + 0.3*cos(3*x)   + 0.001*randn(size(x));
+%   y1([300000, 700000, 700001, 900000]) = [0, 1, -2, 0.5];
+%   y2(300000:500000) = y2(300000:500000) + 1;
+%   y2(500001:600000) = y2(500001:600000) - 1;
+%   y2(800000) = 0;
+%   dsplot(x, [y1;y2]);title('Down Sampled');
+%   % compare with
+%   figure;plot(x, [y1;y2]);title('Normal Plot');
+%
+%  See also PLOT.
+
+%  Version:
+%   v1.0 - first version (Aug 1, 2007)
+%   v1.1 - added CreateFcn for the figure so that when the figure is saved
+%          and re-loaded, the zooming and panning works. Also added a menu
+%          item for saving out the original data back to the base
+%          workspace. (Aug 10, 2007)
+%
+%  Jiro Doke
+%  August 1, 2007
+
+debugMode = false;
+
+%--------------------------------------------------------------------------
+% Error checking
+error(nargchk(1, 3, nargin, 'struct'));
+if nargin < 3
+  % Number of points to show on the screen. It's quite possible that more
+  % points will be displayed if there are outlier points
+  numPoints = 50000;  % ~390 kB for doubles
+end
+if nargin == 1 || isempty(y)
+  noXVar = true;
+  y = x;
+  x = [];
+else
+  noXVar = false;
+end
+myErrorCheck;
+%--------------------------------------------------------------------------
+
+if size(x, 2) > 1  % it's a row vector -> transpose
+  x = x';
+  y = y';
+  varTranspose = true;
+else
+  varTranspose = false;
+end
+
+% Number of lines
+numSignals = size(y, 2);
+
+% If the number of lines is greater than the number of data points per
+% line, it's possible that the user may have mistaken the matrix
+% orientation.
+if numSignals > size(y, 1)
+  s = input(sprintf('Are you sure you want to plot %d lines? (y/n) ', ...
+    numSignals), 's');
+  if ~strcmpi(s, 'y')
+    disp('Canceled. You may want to transpose the matrix.');
+    if nargout == 1
+      hL = [];
+    end
+    return;
+  end
+end
+
+% Attempt to find outliers. Use a running average technique
+filterWidth = ceil(min([50, length(x)/10])); % max window size of 50
+a  = y - filter(ones(filterWidth,1)/filterWidth, 1, y);
+[iOutliers, jOutliers] = find(abs(a - repmat(mean(a), size(a, 1), 1)) > ...
+  repmat(4 * std(a), size(a, 1), 1));
+clear a;
+
+% Always create new figure because it messes around with zoom, pan,
+% datacursors.
+hFig    = figure;
+figName = '';
+
+% Create template plot using NaNs
+hLine   = plot(NaN(2, numSignals), NaN(2, numSignals));
+set(hLine, 'tag', 'dsplot_lines');
+
+% Define CreateFcn for the figure
+set(hFig, 'CreateFcn', @mycreatefcn);
+mycreatefcn();
+
+% Create menu for exporting data
+hMenu = uimenu(hFig, 'Label', 'Data');
+uimenu(hMenu, ...
+  'Label'   , 'Export data to workspace.', ...
+  'Callback', @myExportFcn);
+
+% Update lines
+updateLines([min(x), max(x)]);
+
+% Deal with output argument
+if nargout == 1
+  hL = hLine;
+end
+
+%--------------------------------------------------------------------------
+  function myExportFcn(varargin)
+    % This callback allows for extracting the actual data from the figure.
+    % This means that if you save this figure and load it back later, you
+    % can get back the data.
+    
+    % Determine the variable name
+    allVarNames = evalin('base', 'who');
+    newVarName = genvarname('dsplotData', allVarNames);
+    
+    % X
+    if ~noXVar
+      if varTranspose
+        dat.x = x';
+      else
+        dat.x = x;
+      end
+    end
+    
+    % Y
+    if varTranspose
+      dat.y = y';
+    else
+      dat.y = y;
+    end
+    
+    assignin('base', newVarName, dat);
+    
+    msgbox(sprintf('Data saved to the base workspace as ''%s''.', ...
+      newVarName), 'Saved', 'modal');
+    
+  end
+
+%--------------------------------------------------------------------------
+  function mycreatefcn(varargin)
+    % This callback defines the custom zoom/pan functions. It is defined as
+    % the CreateFcn of the figure, so it allows for saving and reloading of
+    % the figure.
+
+    if nargin > 0
+      hFig = varargin{1};
+    end
+    hLine = findobj(hFig, 'type', 'axes');
+    hLine(strmatch('legend', get(hLine, 'tag'))) = [];
+    hLine = get(hLine, 'Children');
+    
+    % Create Zoom, Pan, Datacursor objects
+    hZoom = zoom(hFig);
+    hPan  = pan(hFig);
+    hDc   = datacursormode(hFig);
+    set(hZoom, 'ActionPostCallback', @mypostcallback);
+    set(hPan , 'ActionPostCallback', @mypostcallback);
+    set(hDc  , 'UpdateFcn'         , @myDCupdatefcn);
+
+  end
+
+%--------------------------------------------------------------------------
+  function mypostcallback(obj, evd) %#ok
+    % This callback that gets called when the mouse is released after
+    % zooming or panning.
+
+    % single or double-click
+    switch get(hFig, 'SelectionType')
+      case {'normal', 'alt'}
+        updateLines(xlim(evd.Axes));
+
+      case 'open'
+        updateLines([min(x), max(x)]);
+
+    end
+
+  end
+
+%--------------------------------------------------------------------------
+  function updateLines(rng)
+    % This helper function is for determining the points to plot on the
+    % screen based on which portion is visible in the current limits.
+
+    % find indeces inside the range
+    id = find(x >= rng(1) & x <= rng(2));
+
+    % if there are more points than we want
+    if length(id) > numPoints / numSignals
+
+      % see how many outlier points are in this range
+      blah = iOutliers > id(1) & iOutliers < id(end);
+
+      % determine indeces of points to plot. 
+      idid = round(linspace(id(1), id(end), round(numPoints/numSignals)))';
+
+      x2 = cell(numSignals, 1);
+      y2 = x2;
+      for iSignals = 1:numSignals
+        % add outlier points
+        ididid = unique([idid; iOutliers(blah & jOutliers == iSignals)]);
+        x2{iSignals} = x(ididid);
+        y2{iSignals} = y(ididid, iSignals);
+      end
+
+      if debugMode
+        figName = ['downsampled - ', sprintf('%d, ', cellfun('length', y2))];
+      else
+        figName = 'downsampled';
+      end
+
+    else % no need to down sample
+      figName = 'true';
+
+      x2 = repmat({x(id)}, numSignals, 1);
+      y2 = mat2cell(y(id, :), length(id), ones(1, numSignals))';
+
+    end
+
+    % Update plot
+    set(hLine, {'xdata', 'ydata'} , [x2, y2]);
+    set(hFig, 'Name', figName);
+
+  end
+
+%--------------------------------------------------------------------------
+  function txt = myDCupdatefcn(empt, event_obj) %#ok
+    % This function displays appropriate data cursor message based on the
+    % display type
+
+    pos = get(event_obj,'Position');
+    switch figName
+      case 'true'
+        txt = {['X: ',num2str(pos(1))],...
+          ['Y: ',num2str(pos(2))]};
+      otherwise
+        txt = {['X: ',num2str(pos(1))],...
+          ['Y: ',num2str(pos(2))], ...
+          'Warning: Downsampled', ...
+          'May not be accurate'};
+    end
+  end
+
+%--------------------------------------------------------------------------
+  function myErrorCheck
+    % Do some error checking on the input arguments.
+
+    if ~isa(numPoints, 'double') || numel(numPoints) > 1 || numPoints < 500
+      error('Third argument must be a scalar greater than 500');
+    end
+    if ~isnumeric(x) || ~isnumeric(y)
+      error('Arguments must be numeric');
+    end
+    if length(size(x)) > 2 || length(size(y)) > 2
+      error('Only 2-D data accepted');
+    end
+    
+    % If only one input, create index vector X
+    if isempty(x)
+      if ismember(1, size(y))
+        x = reshape(1:numel(y), size(y));
+      else
+        x = (1:size(y, 1))';
+      end
+    end
+    
+    if ~ismember(1, size(x))
+      error('First argument has to be a vector');
+    end
+    if ~isequal(size(x, 1), size(y, 1)) && ~isequal(size(x, 2), size(y, 2))
+      error('One of the dimensions of the two arguments must match');
+    end
+    if any(diff(x) <= 0)
+      error('The first argument has to be a monotonically increasing vector');
+    end
+  end
+
+end
 \ No newline at end of file
@@ -0,0 +1,5 @@
+function T = pt100(R)
+
+pt100 = @(R) (R/100.-1)/0.003850+273.15;
+
+T = pt100(R);
@@ -0,0 +1,5 @@
+function T = res2temp16941(R)
+
+res2temp16941 = @(R) 10.^(2.9486 * (log10(1000./R)).^2 + 4.5862 * log10(1000./R) + 2.266);
+
+T = res2temp16941(R);
@@ -0,0 +1,5 @@
+function T = res2temp16943(R)
+
+res2temp16943 = @(R) 10.^(3.4738 * (log10(1000./R)).^2 + 5.1198 * log10(1000./R) + 2.3681);
+
+T = res2temp16943(R);
@@ -0,0 +1,5 @@
+function T = res2temp16944(R)
+
+res2temp16944 = @(R) 10.^(3.3674 * (log10(1000./R)).^2 + 5.2874 * log10(1000./R) + 2.5165);
+
+T = res2temp16944(R);
@@ -0,0 +1,5 @@
+function T = res2temp16945(R)
+
+res2temp16945 = @(R) 10.^(3.2497 * (log10(1000./R)).^2 + 5.1777 * log10(1000./R) + 2.499);
+
+T = res2temp16945(R);
@@ -0,0 +1,5 @@
+function T = res2temp16947(R)
+
+res2temp16947 = @(R) 10.^(3.4597 * (log10(1000./R)).^2 + 5.2422 * log10(1000./R) + 2.4169);
+
+T = res2temp16947(R);
@@ -0,0 +1,5 @@
+function T = res2temp625(R)
+
+res2temp625 = @(R) 0.333548856582638109 + 11.7361551595386118 * (1000./R) + -31.32988932320903987 * (1000./R).^2 + 262.878643524833024 * (1000./R).^3 + -704.163538021035492 * (1000./R).^4 + 1056.6040485650301 * (1000./R).^5 + -307.057196729816496 * (1000./R).^6;
+
+T = res2temp625(R);
@@ -0,0 +1,5 @@
+function T = res2temp627(R)
+
+res2temp627 = @(R) 0.399341181655472610 + 10.8420092277810909 * (1000./R) + -26.4597939187660813 * (1000./R).^2 + 245.9828566655493379 * (1000./R).^3 + -668.069876596331596 * (1000./R).^4 + 1001.69882618263364 * (1000./R) .^5 + -267.272089680656791 * (1000./R).^6;
+
+T = res2temp627(R);
@@ -0,0 +1,5 @@
+function T = res2temp628(R)
+
+res2temp628 = @(R) 0.463200932294057566 + 13.5049710820894688 * (1000./R) + -30.5191222755238414 * (1000./R).^2 + 231.098593852017075* (1000./R).^3 + -550.122691885568202 * (1000./R).^4 + 806.038547554984689 * (1000./R).^5 + -198.510489917360246 * (1000./R).^6;
+
+T = res2temp628(R);
...	...	@@ -0,0 +1,12 @@
	1	+#!/usr/bin/octave-cli --persist
	2	+
	3	+filename = argv(){1};
	4	+col = eval(argv(){2});
	5	+mult = eval(argv(){3});
	6	+
	7	+data.freq = load(filename)(:,col).*mult;
	8	+data.rate = 1;
	9	+
	10	+ad = allan(data, 2.^(0:12), strsplit(filename, '/'){end}, 1);
	11	+input("Press to continue...");
	12	+exit
...	...	@@ -0,0 +1,319 @@
	1	+function hL = dsplot(x, y, numPoints)
	2	+
	3	+%DSPLOT Create down sampled plot.
	4	+% This function creates a down sampled plot to improve the speed of
	5	+% exploration (zoom, pan).
	6	+%
	7	+% DSPLOT(X, Y) plots Y versus X by downsampling if there are large number
	8	+% of elements. X and Y needs to obey the following:
	9	+% 1. X must be a monotonically increasing vector.
	10	+% 2. If Y is a vector, it must be the same size as X.
	11	+% 3. If Y is a matrix, one of the dimensions must line up with X.
	12	+%
	13	+% DSPLOT(Y) plots the columns of Y versus their index.
	14	+%
	15	+% hLine = DSPLOT(X, Y) returns the handles of the line. Note that the
	16	+% lines may be downsampled, so they may not represent the full data set.
	17	+%
	18	+% DSPLOT(X, Y, NUMPOINTS) or DSPLOT(Y, [], NUMPOINTS) specifies the
	19	+% number of points (roughly) to display on the screen. The default is
	20	+% 50000 points (~390 kB doubles). NUMPOINTS can be a number greater than
	21	+% 500.
	22	+%
	23	+% It is very likely that more points will be displayed than specified by
	24	+% NUMPOINTS, because it will try to plot any outlier points in the range.
	25	+% If the signal is stochastic or has a lot of sharp changes, there will
	26	+% be more points on plotted on the screen.
	27	+%
	28	+% The figure title (name) will indicate whether the plot shown is
	29	+% downsampled or is the true representation.
	30	+%
	31	+% The figure can be saved as a .fig file, which will include the actual
	32	+% data. The figure can be reloaded and the actual data can be exported to
	33	+% the base workspace via a menu.
	34	+%
	35	+% Run the following examples and zoom/pan to see the performance.
	36	+%
	37	+% Example 1: (with small details)
	38	+% x = linspace(0, 2*pi, 1000000);
	39	+% y1 = sin(x)+.02cos(200x)+0.001sin(2000x)+0.0001cos(20000x);
	40	+% dsplot(x,y1);title('Down Sampled');
	41	+% % compare with
	42	+% figure;plot(x,y1);title('Normal Plot');
	43	+%
	44	+% Example 2: (with outlier points)
	45	+% x = linspace(0, 2*pi, 1000000);
	46	+% y1 = sin(x) + .01cos(200x) + 0.001sin(2000x);
	47	+% y2 = sin(x) + 0.3cos(3x) + 0.001*randn(size(x));
	48	+% y1([300000, 700000, 700001, 900000]) = [0, 1, -2, 0.5];
	49	+% y2(300000:500000) = y2(300000:500000) + 1;
	50	+% y2(500001:600000) = y2(500001:600000) - 1;
	51	+% y2(800000) = 0;
	52	+% dsplot(x, [y1;y2]);title('Down Sampled');
	53	+% % compare with
	54	+% figure;plot(x, [y1;y2]);title('Normal Plot');
	55	+%
	56	+% See also PLOT.
	57	+
	58	+% Version:
	59	+% v1.0 - first version (Aug 1, 2007)
	60	+% v1.1 - added CreateFcn for the figure so that when the figure is saved
	61	+% and re-loaded, the zooming and panning works. Also added a menu
	62	+% item for saving out the original data back to the base
	63	+% workspace. (Aug 10, 2007)
	64	+%
	65	+% Jiro Doke
	66	+% August 1, 2007
	67	+
	68	+debugMode = false;
	69	+
	70	+%--------------------------------------------------------------------------
	71	+% Error checking
	72	+error(nargchk(1, 3, nargin, 'struct'));
	73	+if nargin < 3
	74	+ % Number of points to show on the screen. It's quite possible that more
	75	+ % points will be displayed if there are outlier points
	76	+ numPoints = 50000; % ~390 kB for doubles
	77	+end
	78	+if nargin == 1 \|\| isempty(y)
	79	+ noXVar = true;
	80	+ y = x;
	81	+ x = [];
	82	+else
	83	+ noXVar = false;
	84	+end
	85	+myErrorCheck;
	86	+%--------------------------------------------------------------------------
	87	+
	88	+if size(x, 2) > 1 % it's a row vector -> transpose
	89	+ x = x';
	90	+ y = y';
	91	+ varTranspose = true;
	92	+else
	93	+ varTranspose = false;
	94	+end
	95	+
	96	+% Number of lines
	97	+numSignals = size(y, 2);
	98	+
	99	+% If the number of lines is greater than the number of data points per
	100	+% line, it's possible that the user may have mistaken the matrix
	101	+% orientation.
	102	+if numSignals > size(y, 1)
	103	+ s = input(sprintf('Are you sure you want to plot %d lines? (y/n) ', ...
	104	+ numSignals), 's');
	105	+ if ~strcmpi(s, 'y')
	106	+ disp('Canceled. You may want to transpose the matrix.');
	107	+ if nargout == 1
	108	+ hL = [];
	109	+ end
	110	+ return;
	111	+ end
	112	+end
	113	+
	114	+% Attempt to find outliers. Use a running average technique
	115	+filterWidth = ceil(min([50, length(x)/10])); % max window size of 50
	116	+a = y - filter(ones(filterWidth,1)/filterWidth, 1, y);
	117	+[iOutliers, jOutliers] = find(abs(a - repmat(mean(a), size(a, 1), 1)) > ...
	118	+ repmat(4 * std(a), size(a, 1), 1));
	119	+clear a;
	120	+
	121	+% Always create new figure because it messes around with zoom, pan,
	122	+% datacursors.
	123	+hFig = figure;
	124	+figName = '';
	125	+
	126	+% Create template plot using NaNs
	127	+hLine = plot(NaN(2, numSignals), NaN(2, numSignals));
	128	+set(hLine, 'tag', 'dsplot_lines');
	129	+
	130	+% Define CreateFcn for the figure
	131	+set(hFig, 'CreateFcn', @mycreatefcn);
	132	+mycreatefcn();
	133	+
	134	+% Create menu for exporting data
	135	+hMenu = uimenu(hFig, 'Label', 'Data');
	136	+uimenu(hMenu, ...
	137	+ 'Label' , 'Export data to workspace.', ...
	138	+ 'Callback', @myExportFcn);
	139	+
	140	+% Update lines
	141	+updateLines([min(x), max(x)]);
	142	+
	143	+% Deal with output argument
	144	+if nargout == 1
	145	+ hL = hLine;
	146	+end
	147	+
	148	+%--------------------------------------------------------------------------
	149	+ function myExportFcn(varargin)
	150	+ % This callback allows for extracting the actual data from the figure.
	151	+ % This means that if you save this figure and load it back later, you
	152	+ % can get back the data.
	153	+
	154	+ % Determine the variable name
	155	+ allVarNames = evalin('base', 'who');
	156	+ newVarName = genvarname('dsplotData', allVarNames);
	157	+
	158	+ % X
	159	+ if ~noXVar
	160	+ if varTranspose
	161	+ dat.x = x';
	162	+ else
	163	+ dat.x = x;
	164	+ end
	165	+ end
	166	+
	167	+ % Y
	168	+ if varTranspose
	169	+ dat.y = y';
	170	+ else
	171	+ dat.y = y;
	172	+ end
	173	+
	174	+ assignin('base', newVarName, dat);
	175	+
	176	+ msgbox(sprintf('Data saved to the base workspace as ''%s''.', ...
	177	+ newVarName), 'Saved', 'modal');
	178	+
	179	+ end
	180	+
	181	+%--------------------------------------------------------------------------
	182	+ function mycreatefcn(varargin)
	183	+ % This callback defines the custom zoom/pan functions. It is defined as
	184	+ % the CreateFcn of the figure, so it allows for saving and reloading of
	185	+ % the figure.
	186	+
	187	+ if nargin > 0
	188	+ hFig = varargin{1};
	189	+ end
	190	+ hLine = findobj(hFig, 'type', 'axes');
	191	+ hLine(strmatch('legend', get(hLine, 'tag'))) = [];
	192	+ hLine = get(hLine, 'Children');
	193	+
	194	+ % Create Zoom, Pan, Datacursor objects
	195	+ hZoom = zoom(hFig);
	196	+ hPan = pan(hFig);
	197	+ hDc = datacursormode(hFig);
	198	+ set(hZoom, 'ActionPostCallback', @mypostcallback);
	199	+ set(hPan , 'ActionPostCallback', @mypostcallback);
	200	+ set(hDc , 'UpdateFcn' , @myDCupdatefcn);
	201	+
	202	+ end
	203	+
	204	+%--------------------------------------------------------------------------
	205	+ function mypostcallback(obj, evd) %#ok
	206	+ % This callback that gets called when the mouse is released after
	207	+ % zooming or panning.
	208	+
	209	+ % single or double-click
	210	+ switch get(hFig, 'SelectionType')
	211	+ case {'normal', 'alt'}
	212	+ updateLines(xlim(evd.Axes));
	213	+
	214	+ case 'open'
	215	+ updateLines([min(x), max(x)]);
	216	+
	217	+ end
	218	+
	219	+ end
	220	+
	221	+%--------------------------------------------------------------------------
	222	+ function updateLines(rng)
	223	+ % This helper function is for determining the points to plot on the
	224	+ % screen based on which portion is visible in the current limits.
	225	+
	226	+ % find indeces inside the range
	227	+ id = find(x >= rng(1) & x <= rng(2));
	228	+
	229	+ % if there are more points than we want
	230	+ if length(id) > numPoints / numSignals
	231	+
	232	+ % see how many outlier points are in this range
	233	+ blah = iOutliers > id(1) & iOutliers < id(end);
	234	+
	235	+ % determine indeces of points to plot.
	236	+ idid = round(linspace(id(1), id(end), round(numPoints/numSignals)))';
	237	+
	238	+ x2 = cell(numSignals, 1);
	239	+ y2 = x2;
	240	+ for iSignals = 1:numSignals
	241	+ % add outlier points
	242	+ ididid = unique([idid; iOutliers(blah & jOutliers == iSignals)]);
	243	+ x2{iSignals} = x(ididid);
	244	+ y2{iSignals} = y(ididid, iSignals);
	245	+ end
	246	+
	247	+ if debugMode
	248	+ figName = ['downsampled - ', sprintf('%d, ', cellfun('length', y2))];
	249	+ else
	250	+ figName = 'downsampled';
	251	+ end
	252	+
	253	+ else % no need to down sample
	254	+ figName = 'true';
	255	+
	256	+ x2 = repmat({x(id)}, numSignals, 1);
	257	+ y2 = mat2cell(y(id, :), length(id), ones(1, numSignals))';
	258	+
	259	+ end
	260	+
	261	+ % Update plot
	262	+ set(hLine, {'xdata', 'ydata'} , [x2, y2]);
	263	+ set(hFig, 'Name', figName);
	264	+
	265	+ end
	266	+
	267	+%--------------------------------------------------------------------------
	268	+ function txt = myDCupdatefcn(empt, event_obj) %#ok
	269	+ % This function displays appropriate data cursor message based on the
	270	+ % display type
	271	+
	272	+ pos = get(event_obj,'Position');
	273	+ switch figName
	274	+ case 'true'
	275	+ txt = {['X: ',num2str(pos(1))],...
	276	+ ['Y: ',num2str(pos(2))]};
	277	+ otherwise
	278	+ txt = {['X: ',num2str(pos(1))],...
	279	+ ['Y: ',num2str(pos(2))], ...
	280	+ 'Warning: Downsampled', ...
	281	+ 'May not be accurate'};
	282	+ end
	283	+ end
	284	+
	285	+%--------------------------------------------------------------------------
	286	+ function myErrorCheck
	287	+ % Do some error checking on the input arguments.
	288	+
	289	+ if ~isa(numPoints, 'double') \|\| numel(numPoints) > 1 \|\| numPoints < 500
	290	+ error('Third argument must be a scalar greater than 500');
	291	+ end
	292	+ if ~isnumeric(x) \|\| ~isnumeric(y)
	293	+ error('Arguments must be numeric');
	294	+ end
	295	+ if length(size(x)) > 2 \|\| length(size(y)) > 2
	296	+ error('Only 2-D data accepted');
	297	+ end
	298	+
	299	+ % If only one input, create index vector X
	300	+ if isempty(x)
	301	+ if ismember(1, size(y))
	302	+ x = reshape(1:numel(y), size(y));
	303	+ else
	304	+ x = (1:size(y, 1))';
	305	+ end
	306	+ end
	307	+
	308	+ if ~ismember(1, size(x))
	309	+ error('First argument has to be a vector');
	310	+ end
	311	+ if ~isequal(size(x, 1), size(y, 1)) && ~isequal(size(x, 2), size(y, 2))
	312	+ error('One of the dimensions of the two arguments must match');
	313	+ end
	314	+ if any(diff(x) <= 0)
	315	+ error('The first argument has to be a monotonically increasing vector');
	316	+ end
	317	+ end
	318	+
	319	+end
0	320	\ No newline at end of file
...	...	@@ -0,0 +1,5 @@
	1	+function T = pt100(R)
	2	+
	3	+pt100 = @(R) (R/100.-1)/0.003850+273.15;
	4	+
	5	+T = pt100(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp16941(R)
	2	+
	3	+res2temp16941 = @(R) 10.^(2.9486 * (log10(1000./R)).^2 + 4.5862 * log10(1000./R) + 2.266);
	4	+
	5	+T = res2temp16941(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp16943(R)
	2	+
	3	+res2temp16943 = @(R) 10.^(3.4738 * (log10(1000./R)).^2 + 5.1198 * log10(1000./R) + 2.3681);
	4	+
	5	+T = res2temp16943(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp16944(R)
	2	+
	3	+res2temp16944 = @(R) 10.^(3.3674 * (log10(1000./R)).^2 + 5.2874 * log10(1000./R) + 2.5165);
	4	+
	5	+T = res2temp16944(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp16945(R)
	2	+
	3	+res2temp16945 = @(R) 10.^(3.2497 * (log10(1000./R)).^2 + 5.1777 * log10(1000./R) + 2.499);
	4	+
	5	+T = res2temp16945(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp16947(R)
	2	+
	3	+res2temp16947 = @(R) 10.^(3.4597 * (log10(1000./R)).^2 + 5.2422 * log10(1000./R) + 2.4169);
	4	+
	5	+T = res2temp16947(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp625(R)
	2	+
	3	+res2temp625 = @(R) 0.333548856582638109 + 11.7361551595386118 * (1000./R) + -31.32988932320903987 * (1000./R).^2 + 262.878643524833024 * (1000./R).^3 + -704.163538021035492 * (1000./R).^4 + 1056.6040485650301 * (1000./R).^5 + -307.057196729816496 * (1000./R).^6;
	4	+
	5	+T = res2temp625(R);
...	...	@@ -0,0 +1,5 @@
	1	+function T = res2temp627(R)
	2	+
	3	+res2temp627 = @(R) 0.399341181655472610 + 10.8420092277810909 * (1000./R) + -26.4597939187660813 * (1000./R).^2 + 245.9828566655493379 * (1000./R).^3 + -668.069876596331596 * (1000./R).^4 + 1001.69882618263364 * (1000./R) .^5 + -267.272089680656791 * (1000./R).^6;
	4	+
	5	+T = res2temp627(R);