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I have a list of dates that happen throughout 2013. I wish to construct a graph showing a cumulative total of elements that happen before that date.

I have a working algorithm, but it seems too slow and inefficient.

Let's generate some random dates:

dates = {2013, #[[1]], #[[2]]} & /@ Transpose@{RandomInteger[{1, 12}, {100}], 
    RandomInteger[{1, 30}, {100}]};

Define a function that calculates the totals:

datecounts[dates_, effectivedate_, spanindays_] := Module[{range, compares},
  range = DateRange[effectivedate, DatePlus[effectivedate, spanindays]];
  compares = Partition[(AbsoluteTime[#[[1]]] > AbsoluteTime[#[[2]]]) & /@ 
     Tuples[{range, dates}], Length[dates]];
  Transpose@{range, Count[#, True] & /@ compares}]

And graph the results:

DateListPlot[datecounts[dates, {2013, 1, 1}, 365], PlotStyle -> {Thickness[0.003]},
   Joined -> True, GridLines -> Automatic, FrameLabel -> {Null, "Total Count"}]

Any help in improving efficiency or better use of functions is greatly appreciated.

enter image description here

share|improve this question
Do you really need to plot every day's value? You could try InterpolationOrder -> 0 to get your nice flat lines. – Verbeia Feb 1 '13 at 4:55
@Verbeia Great point. I'll delete that update. – kale Feb 1 '13 at 4:56
up vote 5 down vote accepted
newdata =  Transpose[{dates[[Ordering[AbsoluteTime /@ dates]]], Range@Length@dates}];
DateListPlot[newdata, Joined -> True]

enter image description here

 DateListPlot[newdata,Joined -> True, InterpolationOrder -> 0]

enter image description here

Update: Let HistogramList do the counting:

 dts = AbsoluteTime /@ dates;
 (* number of says between the earliest and latest dates - 
   to be used as the number of bins in the second argument of HistogramList*)
 daysbetween = DateDifference[Sequence @@ Through[{Min, Max}[dts]]];
     HistogramList[dts, daysbetween, "CumulativeCount"],
     {1, 1}]],
 Joined -> True, ImageSize -> 500]

enter image description here

Update 2: ... there is also EmpiricalDistribution

  {min, max} = Through[{Min, Max}[dts]]; 
  Plot[CDF[EmpiricalDistribution[dts], x], {x, min, max}]
share|improve this answer
You get my +1 for HistogramList. – rcollyer Feb 1 '13 at 13:47

Since you are just looking for counts, I would do the following:

   AbsoluteTime /@ Sort[#, AbsoluteTime[#1] < AbsoluteTime[#2]& ]& @ dates,
   Range @ Length @ dates
 PlotStyle -> {Thickness[0.003]}, Joined -> True, 
 GridLines -> Automatic, FrameLabel -> {Null, "Total Count"}, 
 InterpolationOrder -> 0

Mathematica graphics

share|improve this answer
Much faster, but only plots 100 points in this case instead of a point for each day in 2013... Not a bad thing, just haven't thought of it that way. – kale Feb 1 '13 at 4:34

You could use that:


I like this ways to accumulate the informations, it's very fast!

The result is something like your have already done.


accumulated plot

If you need the zeros (I regularly need to calculate come averages!), there is a answer that can helps you of a function that I called fillDateGaps.

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