Customizing X-axis label for groups of 7 (weeks)

Question

I have a set of data organized as a list where each list entry represents a day of the week. The data starts on a Sunday. It represents about 5 months of data. Each element of the list is {date,value} where date is a full calendar date. Thus, the data looks like {{date,value},{date,value},...}.

I have been successful with the DateListPlot function but I want the labeling of the X-Axis to show groups of 7 data points labeled as "Week 1", "Week 2", and so forth. I would like a single tic-mark between the weekly groups of 7.

I am very new to Mathematica graphics functions and I must admit that finding out and learning how to do this from the documentation is not easy.

Answer 1

wd = WeatherData["SanDiego", "Temperature", {"Jan. 1, 2014", "Aug. 1, 2014", "Day"}];

(*   for version 10+ evaluate:  wd = wd // Normal // QuantityMagnitude;   *)

sundays = Pick[wd[[All, 1]], DayName /@ wd[[All, 1]], Sunday];
wednesdays = Pick[wd[[All, 1]], DayName /@ wd[[All, 1]], Wednesday];

Ticks at Wednesday noon:

ticks = MapIndexed[{AbsoluteTime[#] + 60 60 12, 
     Rotate["Week " <> ToString[First@#2], Pi/2]} &, wednesdays];

DateListPlot[wd, BaseStyle -> Thick, AspectRatio -> 1/4,
 FrameTicks -> {ticks, Automatic, None, None}, 
 GridLines -> {sundays, None}, ImageSize -> 900, Joined -> True]

Update:

You can also use DayMatchQ instead of DayName[#]==...:

Pick[wd[[All, 1]], DayMatchQ[#, Wednesday] & /@ wd[[All, 1]]] == wednesdays
(* True *)

Use different colors for different weeks:

wd = WeatherData["Kirkland", "Temperature", {"Jan. 1, 2014", "Aug. 1, 2014", "Day"}];
wd2 = wd /. {x_, y_} /; DayMatchQ[x, Sunday] :> Sequence[{x, y}, {x, y}];
wd2b = Split[wd2, ! (DayMatchQ[#[[1]], Sunday] && DayMatchQ[#2[[1]], Sunday]) &];
DateListPlot[wd2b, BaseStyle -> Thick, AspectRatio -> 1/4, 
 FrameTicks -> {ticks, Automatic, None, None}, GridLines -> {sundays, None},
 ImageSize -> 900, Joined -> True, Filling -> Bottom]

Update 2: If there are gaps in the data so that some Sundays and/or Wednesdays are skipped as in the example provided by @penguin77 in the comments, then you can use

dr = DateRange[wd[[1, 1]], wd[[-1, 1]]];
wednesdays = Pick[dr, DayMatchQ[#, Wednesday] & /@ dr];
sundays = Pick[dr, DayMatchQ[#, Sunday] & /@ dr];

Stealing and modifying @penguin77's great find we get a much cleaner way to get the dates we need for ticks and grid lines:

{wednesdays, sundays} = DayRange[## & @@ wd[[{1, -1}, 1]], #]&/@ {Wednesday, Sunday}

Splitting the data into separate weeks would be more involved in this case.

Answer 2

Creating a data set dset with date values for the period of 5 months starting on a Sunday associated with random integers ( DayName @ {2015, 04, 12} (* Sunday*)).

dset = DateRange[{2015, 04, 12}, 
     DatePlus[{2015, 04, 12}, {5, "Month"}], 
     Quantity[1, "Days"]] // {#, RandomInteger[100, Length @  #]} &  //
    Transpose ;

To create tick marks, FoldList gets all Wednesdays (Sunday + 4) from the dset by using DatePlus which is then associated with tick labels in the postfix expressions.

ticks = FoldList[DatePlus[#, {1, "Week"}] &, DatePlus[dset[[1, 1]], {4, "Day"}], 
 dset[[All, 1]]] // {#, 
  Rotate["Week " <> ToString @#, \[Pi]/2] & /@ 
   Range @ Length@# } &   // Transpose;

The grid corresponds to the starting of a week. E.g. Week 1 starts on the first Sunday. Therefore the value associated with Sunday lays on the first line and 6 points lay in between.

grid = FoldList[DatePlus[#, {1, "Week"}] &, dset[[1, 1]], 
  dset[[All, 1]]];

And here the plot

DateListPlot[dset, Ticks -> {ticks, Automatic}, 
 AxesOrigin -> {DatePlus[dset[[1, 1]], {-1, "Week"}], 0}, 
 GridLines -> {grid, None}, Axes -> True, ImageSize -> 800, 
 Frame -> False]

Update 1

To demonstrate that above solution works as well if there are gaps of data points, because the ticks and grid lines do not depend on availability of data points.

Here a data set from Amundsen-Scott 90°00’S with temperature measurements in irregular intervals.

dset = WeatherData["WMO89009", 
   "Temperature", {"Jun. 1, 2014", "Dec. 1, 2014", "Day"}];

Here a more robust way to generate ticks and grid lines, in order NOT to be dependent on first date value being a Sunday. Derived from idea presented by @kguler

ticks = Select[DateRange[dset[[1, 1]], dset[[-1, 1]]] , 
    DayMatchQ[#, Wednesday] &] // {#, 
     Rotate["Week " <> ToString@#, \[Pi]/2] & /@ Range@Length@#} & // 
  Transpose;

grid = Select[DateRange[dset[[1, 1]], dset[[-1, 1]]] , 
      DayMatchQ[#, Sunday] &];

And here the plot again

DateListPlot[dset, Ticks -> {ticks, Automatic}, 
 AxesOrigin -> {DatePlus[dset[[1, 1]], {-1, "Week"}], 0}, 
 GridLines -> {grid, None}, Axes -> True, ImageSize -> 800, 
 Frame -> False]

Points have intentionally not be joined in order to see the irregularity of measurements being taken. (I know, the question assumes 7 data points within 7 days, by the way not stating one on each day. Whereas the data points from Amundsen-Scott have an irregular number of measurements within 7 days and is only meant for demonstrating how to handle this special case.

Update 2

Weather data from the South Pole:

dset = WeatherData["WMO89009", 
   "Temperature", {"Jun. 1, 2014", "Dec. 1, 2014", "Day"}];

Using DayRange is about 100 times faster to create ticks and grid than using Pick or Select in combination with DateRange.

fnDayDates[d_, dset_] := DayRange[First@First@#, First@Last@#, d]&[dset]

ticks = fnDayDates[Wednesday,dset] // 
        {#,Rotate["Week " <> ToString@#, \[Pi]/2] & /@ Range@Length@#}& //
        Transpose;

Here we go:

colorAntarctic[ z_ ] := Lighter @ RGBColor[z/2, 1 - z, 1];

DateListPlot[dset, Ticks -> {ticks, Automatic}, 
 TicksStyle -> Directive[ Bold, 12], 
 AxesOrigin -> {DatePlus[dset[[1, 1]], {-1, "Week"}], 0}, 
 GridLines -> {fnDayDates[Sunday, dset], None}, 
 ColorFunction -> colorAntarctic, Axes -> True, Filling -> Axis, 
 PlotMarkers -> Automatic,  Joined -> True, AspectRatio -> 1/3, 
 ImageSize -> 800, Frame -> False, 
 PlotLabel -> 
  Style["South Pole 90\[Degree]00\[CloseCurlyQuote]S - Jun. 1, \
2014-Dec. 1, 2014", Bold, 14]]

PS: by the way, penguins don't care, hi,hi,hi