Working with data in protovis – part 4 of 5

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Reshaping complex arrays

This really is what protovis data processing is all about.
In today’s tutorial, I am going to refer extensively to protovis’s Becker’s Barley example. One reason for that is that it’s also used in the API documentation of the methods we are going to cover, and also because I am posting a line-by-line explanation of this example that you can refer to.

So far we’ve seen that :

  • Associative arrays are great as data elements, as their various values can be used for various attributes.
    For instance, if the current data element is an associative array of this shape:

    { yield: 27.00000, variety: "Manchuria", year: 1931, site: "University Farm" }

    one could imagine a bar chart where the length of the bar would come from the yield, their fillStyle color from the variety, the label from the site, etc.

  • arrays of associative arrays are very practical to manipulate thanks to accessor functions.
    An array of the shape:

    var barley = [
      { yield: 27.00000, variety: "Manchuria", year: 1931, site: "University Farm" },
      { yield: 48.86667, variety: "Manchuria", year: 1931, site: "Waseca" },
      { yield: 27.43334, variety: "Manchuria", year: 1931, site: "Morris" },
      { yield: 39.93333, variety: "Manchuria", year: 1931, site: "Crookston" },
      { yield: 32.96667, variety: "Manchuria", year: 1931, site: "Grand Rapids" },
      { yield: 28.96667, variety: "Manchuria", year: 1931, site: "Duluth" },
      { yield: 43.06666, variety: "Glabron", year: 1931, site: "University Farm" },
      { yield: 55.20000, variety: "Glabron", year: 1931, site: "Waseca" },
      { yield: 28.76667, variety: "Glabron", year: 1931, site: "Morris" },
      { yield: 38.13333, variety: "Glabron", year: 1931, site: "Crookston" },
      { yield: 29.13333, variety: "Glabron", year: 1931, site: "Grand Rapids" },
      { yield: 29.66667, variety: "Glabron", year: 1931, site: "Duluth" },
      { yield: 35.13333, variety: "Svansota", year: 1931, site: "University Farm" },
      { yield: 29.33333, variety: "Wisconsin No. 38", year: 1932, site: "Duluth" }

    could be easily sorted according to any of the keys – yield, variety, year, site, etc.

  • it is easy to access the data of an element’s parent, and in some cases it can greatly simplify the code.


For this last reason, you may want to turn one flat array of associative arrays into an array of arrays of associative arrays. This process is called nesting.

Simple nesting

If you turn a single array like the one on the left-hand side to an array of arrays like on the right-hand side, you could easily do 3 smaller charts, one next to the other, by creating them inside of panels. You could have some information at this panel level (for instance the variety) and the rest at a lower level.

Fortunately, there are protovis methods that can turn your flat list into a more complex array of arrays. And since protovis methods are meant to be chained, you can even go on and create arrays of arrays of arrays of arrays if needs be.
Even better – combined with the other data processing functions, you don’t only change the structure of your array, but you can also filter and control the order of the elements to show everything that you want and only what you want.

And how complicated can this be?
To do the above, all you have to type is

barley=pv.nest(barley).key(function(d) d.variety).entries();

What this does is that it nests your barley array, according to the variety key. entries() at the end is required to obtain the array of arrays needed.

Here is an example of what can be done with both kinds of data structures in just a few lines of code (which won’t include the data proper. The long, flat array is stored in the variable barley, as above).
Without nesting:

var vis = new pv.Panel()
	.left(function() this.index*5)
	.height(function(d) d.yield*2)
	.fillStyle(function(d) d.year==1931?"steelBlue":"Orange")

As the pv.Bar goes through the array, there is not much it can do to structure it. We can just size the bars according to the value of yield, and color them according to another key (here the year).

Now using nesting:

barley2=pv.nest(barley).key(function(d) d.variety).entries();
barley2=pv.nest(barley).key(function(d) d.variety).entries();
var vis = new pv.Panel()
var cell=vis.add(pv.Panel)
	.left(function() this.index*70)
cell.anchor("top").add(pv.Label).textAlign("center").font("9px sans-serif").text(function(d) d.key)
		.data(function(d) d.values)
		.left(function() 5+this.index%6*10)
		.height(function(d) d.yield*2)
		.fillStyle(function(d) d.year==1931?"steelBlue":"Orange")
			.textAlign("left").left(function() 15+this.index%6*10).textStyle("#222")

Here we used the same simple nesting command as above (the original example uses a more complicated one which allows for more refinement in the display). This structure allows us to create first panels, which we can style by displaying the name of the sites for instance, then, within these panels, the corresponding bars.

Doing this with the data in its original form would have been possible, but would have required writing a much longer program. So the whole idea of nesting is to take some time to plan the data structure once, so that the code is as short and useful as possible.

Going further with nesting

However, it is possible to go beyond that:

  • by nesting further, which can be done by adding other .key() methods:

      .key(function(d) d.variety)
      .key(function(d) d.year)


  • by sorting keys or values using the sortKeys() and sortValues() methods, respectively.

    For instance, we can change the order in which the variety blocks are displayed with sortKeys():

      .key(function(d) d.variety)
      .key(function(d) d.variety)

By using sortKeys without argument, the natural order is used (alphabetical, since our key is a string). But we could provide a comparison function if we wanted a more sophisticated arrangement.

Nesting and hierarchy

If you run the double nesting command we discussed above,

  .key(function(d) d.variety)
  .key(function(d) d.year)

you’ll get as a result something of the form:

var barley=[
  {key:"Manchuria", values: [
    {key:"1931", values: [
      {site:"University farm", variety: "Manchuria", year: 1931, yield: 27},
      {site:"Waseca", variety: "Manchuria", year: 1931, yield: 48.86667},
      {site:"Morris", variety: "Manchuria", year: 1931, yield: 27.43334},
      {site:"Crookston", variety: "Manchuria", year: 1931, yield: 39.93333},
      {site:"Grand Rapids", variety: "Manchuria", year: 1931, yield: 32.96667},
      {site:"Duluth", variety: "Manchuria", year: 1931, yield: 28.96667}
    {key:"1932", values: [  
      {site:"University farm", variety: "Manchuria", year: 1932, yield: 26.9},
      {site:"Waseca", variety: "Manchuria", year: 1932, yield: 33.46667},
      {site:"Morris", variety: "Manchuria", year: 1932, yield: 34.36666},
      {site:"Crookston", variety: "Manchuria", year: 1932, yield: 32.96667},
      {site:"Grand Rapids", variety: "Manchuria", year: 1932, yield: 22.13333},
      {site:"Duluth", variety: "Manchuria", year: 1932, yield: 22.56667}
  {key: "Glabron", ...

and so on and so forth for all the varieties of barley. Now how can we use this structure in a protovis script? why not use multi-dimensional arrays instead, and if so, how would the code change?

Well. You’d start using this structure by creating a first panel and and passing it the nested structure as data.
Assuming your root panel is called vis, you’d start likewise:


now, since barley has been nested first by variety, it is now an array of 10 elements. You are going to create 10 individual panels. At some point you should worry about dimensioning and positioning them. But here we are only focusing on passing data to subsequent elements.

Next, you are going to create another set of panels (or any mark, really, this doesn’t change anything for the data)

    .data(function(d) d.values)

This is how you drill down to the next level of data, by using an accessor function with the key “values”.
Congratulations! you have created 2 panels in each of our 10 individual panels, one per year.

Finally, you are going to create a final mark (let’s say, a pv.Bar)

    .data(function(d) d.values)

Again, you use an accessor function of the same form. This will create a bar chart with 6 bars.
The data element corresponding to each bar is of the form:

{site:"University farm", variety: "Manchuria", year: 1932, yield: 26.9}

So, when you style the chart, you can access these properties with accessor functions, and write for instance:

    .height(function(d) d.yield)
    .add(pv.Label).text(function(d) d.variety)


To sum it up: you can create a hierarchical structure in protovis that corresponds to the shape of your nested array by adding elements and passing data using an accessor function with the key “values”.
At the lowest level of your structure you can access all the properties of the original array using accessor functions.

Now, what if instead we used a multi-dimensional, normal array without keys and values? don’t they have structure and hierarchy, too?
This is not only possible, but also advised when your dataset is getting really big, as you would plague your users with annoying loading times. This changes the structure of the code though.

An equivalent multi-dimensional array would be something like:

var yields =
[ // this is the level of the variety
  [ // this is the level of the year
    [ 27, 48.86667, 27.43334, 39.93333, 32.96667, 28.96667], 
    [ 26.9, 33.46667, 34.36666, 32.96667, 22.13333, 22.56667]
    [ 43.06666, 55.2, 28.76667, 38.13333, 29.13333, 29.66667],
    [ 36.8, 37.73333, 35.13333, 26.16667, 14.43333, 25.86667]
    [ 35.13333, 47.33333, 25.76667, 40.46667, 29.66667, 25.7],
    [ 27.43334, 38.5, 35.03333, 20.63333, 16.63333, 22.23333]
    [ 39.9, 50.23333, 26.13333, 41.33333, 23.03333, 26.3],
    [ 26.8, 37.4, 38.83333, 32.06666, 32.23333, 22.46667]
    [ 36.56666, 63.8333, 43.76667, 46.93333, 29.76667, 33.93333],
    [ 29.06667, 49.2333, 46.63333, 41.83333, 20.63333, 30.6]
    [ 43.26667, 58.1, 28.7, 45.66667, 32.16667, 33.6],
    [ 26.43334, 42.2, 43.53334, 34.33333, 19.46667, 22.7]
    [ 36.6, 65.7667, 30.36667, 48.56666, 24.93334, 28.1],
    [ 25.56667, 44.7, 47, 30.53333, 19.9, 22.5]
    [ 32.76667, 48.56666, 29.86667, 41.6, 34.7, 32],
    [ 28.06667, 36.03333, 43.2, 25.23333, 26.76667, 31.36667]
    [ 24.66667, 46.76667, 22.6, 44.1, 19.7, 33.06666],
    [ 30, 41.26667, 44.23333, 32.13333, 15.23333, 27.36667]
    [ 39.3, 58.8, 29.46667, 49.86667, 34.46667, 31.6],
    [ 38, 58.16667, 47.16667, 35.9, 20.66667, 29.33333]

and that’s the whole lot. It is indeed shorter. now this array is only the yields, you may want to create an array of the possible values of varieties, sites and years for good measure.

var varieties=["Manchuria", "Glabron", "Svansota", "Velvet", "Trebi",
     "No. 457", "No. 462", "Peatland", "No. 475", "Wisconsin No. 38"], 
    sites=["University Farm", "Waseca", "Morris", "Crookston", "Grand Rapids", "Duluth"],

And by the way, it is very possible to create these arrays out of the original array using the map() method or equivalent.

how can we create an equivalent structure?
we start like the above:


Likewise, our 3-dimensional array is really an array of 10 arrays of 2 arrays of 6 elements. So we are also creating 10 panels. Let’s continue and create panels for the years:

    .data(function(d) d)

To drill down one level in an array, you have to use this form. you say that you are giving the children of your object what’s inside the data property of their parent.

So naturally, you follow by

    .data(function(d) d)

now how you style your bars will be slightly different than before. What you passed your first panel was an array of yields. So that’s what you get now from your data. If you want something else, you’ll have to get it with this.index for instance.

    .height(function(d) d) // that's the yield
    .add(pv.Label).text(function() varieties[this.index])

All in all it’s trickier to work with arrays. The code is less explicit, and if you change one array even by accident, you’ll have to check that others are still synchronized. But it could make your vis much faster.


Sometimes, what you want out of an array is not a more complex array, but a simpler list of numbers. For instance, what if you could obtain the sum of all the values in the array for such or such property? This is also possible in protovis, and in fact, it looks a lot like what we’ve done. The difference is that instead of using the method entries(), we will use the method rollup().

Let’s suppose we have a flat array that looks like this: these are scores of students on 3 exams.

var scores=[
{student:"Adam", exam:1, score: 77},
{student:"Adam", exam:2, score: 34},
{student:"Adam", exam:3, score: 85},
{student:"Barbara", exam:1, score: 92},
{student:"Barbara", exam:2, score: 68},
{student:"Barbara", exam:3, score: 97},
{student:"Connor", exam:1, score: 84},
{student:"Connor", exam:2, score: 54},
{student:"Connor", exam:3, score: 37},
{student:"Daniela", exam:1, score: 61},
{student:"Daniela", exam:2, score: 58},
{student:"Daniela", exam:3, score: 64}

Now, we would like to get, in one simple object, the average for each student.
We know we could reshape the array if we wanted by using pv.Nest and entries():

pv.nest(scores).key(function(d) d.student).entries()

This would be something of the shape:

[{key:"Adam", values:[
    {exam:1, score: 77, student: "Adam"},
    {exam:2, score: 34, student: "Adam"},
    {exam:3, score: 85, student: "Adam"}
  {key:"Barbara", values:[
    {exam:1, score: 92, student: "Barbara"},
    {exam:2, score: 68, student: "Barbara"},
    {exam:3, score: 97, student: "Barbara"}

Useful, for instance, if we’d want to chart the progress of each student separately.

Now if instead of using entries() at the end, we use rollup(), we could get this:

Adam: 65.33333333333333
Barbara: 85.66666666666667
Connor: 58.333333333333336
Daniela: 61}

The exact statement is

  .key(function(d) d.student)
  .rollup(function(data) pv.mean(data, function(d) d.score))

To understand how this works, it helps to visualize what the pv.nest would have returned if we had asked for entries.
What rollup does is that it would go through each of the values that correspond to the keys, and return one aggregate value, depending on the function.

For the first student, “Adam”, the corresponding values array is like this:

    {exam:1, score: 77, student: "Adam"},
    {exam:2, score: 34, student: "Adam"},
    {exam:3, score: 85, student: "Adam"}

so rollup will just look at each element of this array and apply the function.
This is what (data) in “function(data)” corresponds to.
Next, we tell protovis what to do with these elements. Here, we are interested in the average, so we take pv.mean (not pv.average, remember?)
However, we can’t directly compute the average of an array of associative arrays – we must tell protovis exactly what to average. This is why we use an accessor function, function(d) d.score.

Of course, pv.mean used in this example can be replaced by just about any function.

In the name of clarity, especially if there is only one property that can be aggregated, you can declare a function outside of the rollup() method. This is useful if you are going to aggregate your array by different dimensions:

function meanScore(data) pv.mean(data, function(d) d.score);
var avgStudent=pv.nest(scores)
  .key(function(d) d.student)
var avgExam=pv.nest(scores)
  .key(function(d) d.exam)


Protovis also provides methods that turn a “nested” array back into a flat array. And methods that turn a normal array into a tree.
The main advantage of having a flat array is that you can nest it in a different way. This is useful, for instance, if you got your data in a nested form that doesn’t work for you. Likewise, a tree is easier to reshape in protovis than an array.

To create a flat array out of a nested one, you have to use pv.flatten and specify all the keys of the array and conclude by array().


It’s important to note that you need to specify all the keys, not just the keys that correspond to actual nesting. So again, if you start from a flat array, and you do


to reverse this, you’ll have to enter the full formula, using key four times:


Finally, pv.tree – well, I haven’t seen this method used outside the documentation. It’s not used in any live example, not covered by any question in the forum, and I haven’t found any trace of it in the internet. So I’d rather leave you with the explanation in the documentation which is fairly clear than come up with my own. If you find yourself in a situation like in the documentation, where you have a flat array of associative arrays, which have a property that could be interpreted as a hierarchy, then you could use this method to turn your array in something more useful to protovis.

Putting it all together

Instead of coming up with a specific new example for this section I refer you to my explanation of the Becker’s Barley example.
On the same subject, see a comparison of how to re-create Becker’s Barley with protovis and Tableau

next: working with layouts




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