Adjusting x-axis to reflect psuedo-time using XTickLabel

I apologize in advance for the lengthy post.

I currently am writing a function to read in IMU data 'real time' and plot the data. The IMU data is generated at 2460Hz but is stored on internal IMU memory and output at 10Hz. In other words, I read 246 samples of data every 100msec through Matlab.

As soon as I read the data from the IMU, I timestamp it using the 'now' function. I then plot the data with time (in datenum format) on the x-axis and the IMU data on the y-axis. The problem I encountered was that I could not zoom in to the level of detail I wanted (say ~10msec on x-axis). I found this strange and did some googling and noticed that others had similar issues and they suggested using a 'psuedo time' scale.

In order to create this psuedo time, I basically use the sample number instead of a datenum. In other words, the first 246 samples I collect are 'samples' 1-246, the next are 247 - 492 and so on. So now I plot this psuedo-time on the x-axis and IMU data on the y-axis and I get the zoom resolution I want so life is good.

Since I'm reading in data real-time, I want the last minute of data to be on the plot, and have the plot gradually shift right as time progresses (like a scope or any other stripchart recorder would do). I implemented that without issue by changing the xlims.

Now the fun part. I need to 'mask' the x-axis so it appears to be time. I use XTickLabel and I get labels, but the times/values they use aren't what I want them to be. I would expect the date ticks to be -1 minute of the current time at the left and +1 minute at the right but instead it looks like it's roughly +/- 2 seconds. I've made a 'mock up' code of what's happening below by just using rand to 'generate' the IMU data and plot it. Can someone help me figure out why my x-labels aren't working out? Please don't tell me to use datenum as the x-axis as I've tried that and it didn't work (due to resolution).

An aside, but so you understand why I'm doing what I am in the code. I originally was plotting the data as soon as it came in, but Matlab was getting 'behind' such that if I moved the IMU, it wouldn't show up until several seconds later. To alleviate that problem, I still read in the data at 10Hz but only plot it every 500msec. Matlab seems to like this just fine :)

% Initialize
count = 0;
Offset = 0;
BufferData = [];

% Setup Time Constants (found manually in command window)
onehundredmsec = 1.157401129603386e-06;
onesec = 1.157401129603386e-05;
onemin = 6.944444030523300e-04;

% Create figure and axes
handles.fig = figure;
handles.axis =  axes('Tag','X_Axes','Position',[0.07,0.1,0.9,0.80],'ylim',[-1,1]);
hold(handles.axis,'on')

for i = 1:120
    % Add to our counter for how many msec of data we have
    count = count + 1;
    % "Read in" 246 samples (0.1 seconds worth of data)
    StreamedData = rand(246,1);
    % Grab Time of data read in (as close as possible)
    % and Interpolate time of each sample
    Time(1:246,1) = linspace(now - onehundredmsec, now,246);
    % Add to buffer to hold 500msec of data
    BufferData = [BufferData; Time, StreamedData];

      % Once 500msec of data reached, plot it
      if count > 4
          % Used for adjusting plot so we can use psuedo-time on axis
          Offset = Offset + 1;
          %Initialize x, aka psuedo time
          x = (Offset-1)*1230+1:1230*Offset; 

          % Grab first time entry since that's where we start
          % Note: This is datenum time aka actual time
          CurrentTime = BufferData(1,1);

          % Setup Time arrays for the axes
          TimeLabels = linspace(CurrentTime-onemin,CurrentTime+onemin,1230);

          % Set axis so that it is +/- 1 minute (i.e. data always plots in
          % center)
          set(handles.axis,'XLim',[-1230*(120-Offset),1230*(120+Offset)])

          % Only update axis time labels at the start of the plot and then
          % every minute thereafter
          if Offset == 1 || rem(Offset, 120) == 0
              set(handles.axis,'XTickLabel',datestr(TimeLabels,'HH:MM:SS'))
          end %if

          plot(handles.axis,x,BufferData(:, 2))

          % Reset buffer/counters
          BufferData = [];
          count = 0;
      end %if

      % Pause to simulate the 100msec, plus it's needed to update plot 'real
      % time'
      pause(0.1)
  end %for

Thanks, Mike

[dpb]

What time is it you're trying to display? The tick labels will correlate with the tick values of the axis based on the variable (x) you used to plot against and the xlim range in effect at the time. Hence, it's not surprising you get a mismatch when try to set tick labels independently.

I suspect probably the easiest solution is to use two overlapping x axes that are linked -- use one in 'x' against which to plot and a second in the desired datenum range to display the time-of-day labels.

[Mike]

Whenever I plot data, I'm plotting 1230 samples at a time(500msec worth). I also shift the x-axis using Xlims so that it's +/- 1 minute (hence the 1230*(120+/-Offset)).

For the first plot (Offset = 1), my axis x-axis should be [-146370,148830] aka +/- 1 minute in psuedo-time. I then try to change that axis to really be the TimeLabels value which is also +/- 1 minute but in datenum format.

I appreciate the suggestion of overlapping axes but this should work without the need (thats one of the major reasons for being able to change the xticklabel right?)

[dpb]

Excepting afaik the only way the time formatting routines work is with the Matlab datenum range and afaict you're trying to format an "ordinary" linear variable as if it were -- but it isn't.

You could compute the h,m,s from some arbitrary point and create those labels w/ sprintf() and use those but I don't see any way to make datestr work on anything except a "real" datenum.

ADDENDUM:

You say you want an x-axis limits of [-146370,148830] in "pseudo time". For my elucidation and potential playing around, what would you ideally have the axes tick labels be? And how does that relate to the above value range?

[Mike]

Ideally, I'd like 5 tick marks. From left to right they'd read (in datestr HH:MM:SS):

CurrentTime - 1 min, CurrentTime - 30 sec, Current Time, CurrentTime + 30 sec, CurrentTime + 1 min

Answer 1

[dpb]

OK, try this...looks like I think yours would given the aforementioned fact that the actual data range is so compacted into the limits that there's nothing but a blob going to show up...but it does handle the ticks and labels as I think you want...

Note that the full five tick marks/labels show up at the very beginning where they matchup precisely but after that since you're continually munging on the limits the number in range varies as they shift off to the left until refreshed. This may be okay for your purpose.

hax=axes('Position',[0.07,0.1,0.9,0.80],'ylim',[-1,1],'box','on');
set(hax,'xtick',[],'xticklabel',[])
set(gcf,'position',[579 344 560 420])  % get it out of the way...
hold(hax,'on')

 % Initialization constants
onehundredmsec = 1/864000;
Fs=2460;                       % sample rate in case changes
Fs2=Fs/2;
xLen=Fs2-1; x1=0; x2=x1;       % data buffer lengths, start
xLLen=Fs2*2*120;               % xlim width
xLDel=Fs2;                     % xlim delta
xl1=-Fs2*120;                  % axis limit initialization
xl2=xl1+xLLen;
tix=xl1:xLLen/4:xl2;           % 5 tick positions based on above

 idx=0;
cntr=0;
B=[];
for i = 1:120
  idx = idx + 1;
  D = rand(246,1);
  T = linspace(now - onehundredmsec, now,246)';
  B = [B; [T D]];
  if idx>4
    cntr=cntr+1;
    x1=x2+1; x2=x1+xLen;  % increment x-axis value ranges (no mult needed)
    xl1=xl1+xLDel; xl2=xl1+xLLen;   % xlimit ranges
    tix=tix+xLDel;                  % update ticks, too...
    xlim(hax,[xl1,xl2])

    x=[x1:x2]';              % new x range
    plot(x,B(:,2))
    if cntr==1 || rem(cntr,120)==0
      CTime = B(1,1);
      [y,mo,d,h,m,s]=datevec(CTime);
      ds=datestr(datenum(y,mo,d,h,m-1,fix(s)+[0:30:120]'),'hh:MM:ss');
      set(hax,'xtick',tix,'xticklab',ds)
    end
    B=[];
    idx=0;
  end
  pause(0.1)
end

Also, note for overhead reduction you really don't need the T vector at all for the plotting, only the current time with the 100 msec subtracted is the only actual value used, at least for the plotting. If you need it for archiving purposes, that's the obvious reason to keep it anyway, of course.

ADDENDUM:

The real overhead in the above is the use of plot() repeatedly--this is creating a new line object every call and all the associated overhead of a full call and the associated handles, etc. I suspect it will eventually fail on memory and/or handles or somesuch.

Once you think the effect is at wanted, then can work on a much more efficient manner to present the actual data. Basically, you'll want to mung on the [x|y]data property directly after the initial data are drawn. There's an article in the 2D graphics section on animation that outlines the general ideas to use. But, before for that see if the above doesn't at least give the initial desired appearance.

Answer 2

[dpb]

OK, that can be done...

>> x=[-146370,148830];         % the ranges you mentioned
>> tix=x(1):diff(x)/4:x(2);    % compute 5 tick positions based on above
>> dn=now;                     % present clock time
>> [y,mo,d,h,m,s]=datevec(dn); % get the pieces & make the 30-sec labels
>> ds=datestr(datenum(y,mo,d,h,[m-1:0.5:m+1]',fix(s)),'hh:MM:ss');
>> set(gca,'xtick',tix)               
>> set(gca,'xticklab',ds)

ADDENDUM:

I'd recommend the following to build the datestr over the above as it uses the integer seconds field and is thus less susceptible to roundoff in general. Altho there won't be a problem w/ the short and even case above, using floating point deltas in building series of datenums can be troublesome--

ds=datestr(datenum(y,mo,d,h,m-1,fix(s)+[0:30:120]'),'hh:MM:ss');

Illustrates a very neat feature of datenum to propagate lower-level values to the higher accounting for rollover in the various fields properly while doing so as well...

[Mike]

Can you tell me exactly where you put this into the code? I put it right before the plot command and commented out the other set commands. I also had to change your variable from x to dx (since my psuedo time uses x). This did not work for me...it only produced one tick mark that moved along the x-axis. I never got 5 tick marks as I would expect...what am I doing wrong?

[dpb]

Dunno what you're doing wrong w/o the code...but--

The x above should be the result of the pseudo-time as you call it for the axis range you just plotted--I just used a couple of fixed values you mentioned for demonstration purposes.

Call it xl instead and get it as

xl=xlim;

and with that variable change the rest should follow at any point after plot and setting the x-axis limits as wanted.

You should be able to take any one set of data out of all the loop stuff and debug it independently to get rid of other interactions. Then once have that going, incorporate it into the updating stuff. I suspect you're trying to do too much at one time in debugging and have stuff stepping on other stuff.

ADDENDUM: I just noticed (or it finally registered) that you say you put this before the plot command--that can't possibly work since you're trying to set tick marks on what should be an already-existing axes.

ADDENDUM 2: Thought I'd see if I could figure out how to write a sample case to illustrate and ran into a conundrum ...

set(handles.axis,'XLim',[-1230*(120-Offset),1230*(120+Offset)])

What is this??? This is going to leave the x-axis limits at really funky values as compared to plotting it would seem...

Each plot sequence is x=1:1230, 1231:2460, etc., ... but xlim will be

[-146370,148830], [-145140,150060], etc., ...

Thus the x axis is some tiny fraction within the overall x-limits displayed.

Not sure what you really are trying to do here for certain but the above certainly isn't it methinks. That's why you're only getting a single visible tick mark I suspect--there's insufficient resolution of the plot area in the region to show anything else. The plot range is crammed into <1% the axis length.

I didn't pay attention to this futzing around w/ xlim earlier--I presumed it had something to do with the faking of time display and so would go away. But, whatever it is intended to do, it's screwed up. Perhaps you meant to subtract/add a constant 230 to the x-axis limits each time instead???

[Mike]

dpb, while I appreciate your help, I think you are trying to be too 'quick' in solving the problem and therefore not understanding the real problem.

I agree that simplifying code for the purpose of debugging is useful, and this code is simplified compared to the original. I'll take your advice and try to simplify it further.

The reason for the changing xlim is clearly commented in the code and again clarified above in a previous comment. I want the x-axis to reflect +/- 1 minute from the data being plotted. 1230 is equivalent to 500msec hence the multiplier of 120 to get 1 minute.

[dpb]

The point is that the tick mark values must reflect the x-lim values and if you put the code preceding that computes the tick times for them before the limits are set they won't be consistent.

Set a limit, use those limits as the [x1,x2] values as I did before and then the labels will show up over the range of the axes.

I did make an algebraic error, sorry, the delta is constant across...I'll try to find a few minutes more and build the demo code...