Working with data in protovis: part 5 of 5

previous: reshaping complex arrays (4/5)

Working with layouts

In this final part, we’re going to look at how we can shape our data to use the protovis built-in layouts such as stacked areas, treemaps or force-directed graphs.
This is not a tutorial on how to use layouts stricto sensu, and I advise anyone interested to first look at the protovis documentation to see what can be done with this and to understand the underlying concepts.

But if there is one thing to know about layouts, it’s that they allow you to create non-trivial visualizations in even less code than regular protovis, provided that you pass them data in a form they can use, and this is precisely where we come in.

Three great categories of layouts

Currently, there are no fewer than 13 types of layouts in Protovis. Fortunately, there are examples for all of them in the gallery.
There are layouts for:

In addition, there are layouts like pv.Layout.Bullet which require data to have a certain specific shape but the example from the gallery is very explicit. (et tu, Horizon layout).

Arrays of data

In order to work with this kind of layout, the simplest thing is to put your data in a 2-dimensional array:

var data=[
   [8,3,7,2,5],
   [9,6,1,7,4],
    ...
   [7,4,3,6,8]
];

For the grid layout, this gives you an array of cells divided in columns (number of elements in each line) and rows (number of lines).
The idea of the grid layout is that your cells are automatically positioned and sized, so afaik the only thing you can do is add a mark such as a pv.Bar which would fill them completely, but which you could still style with fillStyle or strokeStyle. You can’t really access the underlying data with functions but you can use methods that rely on default values, like adding labels.

For instance, you can use it to generate a QR code:

var qr=[
"000000000000000000000000000",
"011111110001010100011111110",
"010000010101001110010000010",
"010111010000010100010111010",
"010111010111011110010111010",
"010111010010000001010111010",
"010000010110110010010000010",
"011111110101010101011111110",
"000000000011100100000000000",
"011111011110101110101010100",
"000010101001010111101000100",
"010101111001001011111010110",
"001011000100010101010100010",
"001100010111011010010101110",
"010101100110001101001010100",
"010011010011111111100110110",
"010111101010100101000010010",
"010100110010111101111101000",
"000000000101010111000111000",
"011111110100011001010111110",
"010000010000110011000110110",
"010111010110001011111111000",
"010111010101101100110101110",
"010111010100000111001001010",
"010000010111010101101110010",
"011111110101001100011111110",
"000000000000000000000000000",
].map(function(i) i.split(""));

var vis = new pv.Panel()
    .width(216)
    .height(216);
vis.add(pv.Layout.Grid)
    .rows(qr)
 	.cell.add(pv.Bar)
 	    .fillStyle(pv.colors("#fff", "#000"))
     ;
vis.render();
(BTW, this is the QR code to this page)

On line 29, I’m using a map function to turn this array of strings, which is easier and shorter to type, into a bona fide 2-dimensional array.

That’s all there is to grids, of all the layouts they are among the easiest to reproduce with regular protovis.

Now, stacks.
The easiest way to use them is to pass them 2-dimensional arrays. Now it doesn’t have to be arrays of numbers, it can be arrays of associative arrays in case you need to do something exotic. But for the following examples let’s just assume you don’t. Here is how you’d do a stacked area, stacked columns and stacked bars respectively:

var data=[
[[1000,1200,1500,1700]]
[[100,500,300,200]]
]
var vis=new pv.Panel().width(200).height(200);
vis.add(pv.Layout.Stack)
    .layers(data)
    .x(function() 50*this.index)
    .y(function(d) d/20)
    .layer.add(pv.Area)

all you need is to feed the layers, x, y properties of your stack, then say what you want to add to your layers.
Now, columns:

vis.add(pv.Layout.Stack)
    .layers(data)
    .x(function() 50*this.index)
    .y(function(d) d/20)
    .layer.add(pv.Bar).width(40)

and finally, bars:

vis.add(pv.Layout.Stack)
    .layers(data)
    .orient("left")
    .x(function() 50*this.index)
    .y(function(d) d/20)
    .layer.add(pv.Bar).height(40)

For bars, there is a little trick here. I specify that the layer orientation is horizontal (“left”) and I change the height instead of the width of the added pv.Bar.
And that all there is. You can create various streamgraphs by playing with the order and offset properties of the stack but this doesn’t change anything to the data structure, so we’re done here.

Representing networks

Protovis provides 3 cool layouts to easily exhibit relationships between nodes: arc diagrams, matrix diagrams and force-directed layouts.
The good news is that the shape of the data required by those three layouts is identical.

They require an array that correponds to the nodes. This can be as simple as a pv.range(), or as sophisticated as an array of associative arrays if you want to style your network graph according to several potential attributes of the node.

And they also require an array for the links. This array has a more rigid form, it must be an array of associative arrays of the shape: {source: #, target: #, value: #} where the values for source and target correspond to the position of a node in the node array, and value indicates the strength of the link.

So let’s do a simple one.

var nodes=pv.range(6); // why more complex, right?
var links=[
{source:0, target:1, value:2},
{source:1, target:2, value:1},
{source:1, target:3, value:1},
{source:2, target:4, value:4},
{source:3, target:5, value:1},
{source:4, target:5, value:1},
{source:1, target:5, value:3}
]
var vis = new pv.Panel()
    .width(200)
    .height(200)
    ;
var arc = vis.add(pv.Layout.Arc)
    .nodes(nodes)
    .links(links)
	.bottom(100)
arc.link.add(pv.Line);
arc.node.add(pv.Dot)
    .size(50)
vis.render();

Here, by varying the strength of the link, the thickness of the arcs changes accordingly. The nodes are left unstyled, had we passed a more complicated dataset to the nodes array, we could have changed their properties (fillStyle, size, strokeStyle, labels etc.) with appropriate accessor functions.

With little modifications we can create a force-directed layout and a matrix diagram.

var force = vis.add(pv.Layout.Force)
    .nodes(nodes)
    .links(links);

force.link.add(pv.Line);

force.node.add(pv.Dot)
	.size(50)
	.anchor("center").add(pv.Label)
		.text(function() this.index);

vis.render();

Here I labelled the nodes so one can tell which is which. This is done by adding a pv.Label to the pv.Dot that’s attached to the node, just like with any other mark.

var Matrix = vis.add(pv.Layout.Matrix)
	.nodes(nodes)
	.directed(true)
	.links(links)
	.top(20).left(20)

Matrix.link.add(pv.Bar)
    .fillStyle(function(d) pv.Scale.linear(0, 2, 4)
      .range('#eee', 'yellow', 'green')(d.linkValue))

Matrix.label.add(pv.Label).text(function() Math.floor(this.index/2))

vis.render();

For the matrix things are slightly more complex than for the previous 2. Here I opted for a directed matrix, as opposed to a bidirectional one: this means that each link is shown once, to its source from its target, and not twice (ie from its target back to its source) which is the default.
I chose to color the bar attached to my links (which are cells of the matrix) according to the strength of my links. Again, if my nodes field was more qualified, I could have used these properties.

Finally, we’ve added labels to the custom property Matrix.label. Only, the labels are numbered from 0 to 11 so to get numbers from 0 to 5 for both rows and columns I used Math.floor(this.index/2) (integer part of half of this number).

Hierarchized data

Like for networks, the shape of the data we can feed to treemaps, icicles and other hierarchical representation doesn’t change. So once you have your data in order, you can easily switch representations.

Essentially, you will be passing a tree of the form:

var myTree={
   rootnode: {
      node: {
      ...  
         node: {
            leaf: value,
            leaf: value,
            ...
            leaf: value
         },
      ...  
}

The protovis examples use the hierarchy of flare source code as an example, which really shows what can be done with a treemap and other tree represenations.

For our purpose we are going for a simpler tree, inspired by the work of Periscopic on congressspeaks.com which Kim Rees showed at Strata.
Kim presentation featured tiny treemaps that showed the voting record for a congressperson, and whether they had voted for or against their party.

So let’s play with the voting record of an hypothetic congressperson:

var hasVoted={
	didnt: 100,
	voted: {
	    yes: {
	        yesWithParty: 241,
	        yesAgainstParty: 23
	    },
	    no: {
	        noWithParty: 73,
	        noAgainstParty: 5
	    }
	}
};

Once you have your tree, you will need to pass it to your layout using pv.dom, like this:

pv.dom(hasVoted).root("hasVoted").nodes()

Based on that let’s do two hierarchical representations.
Let’s start with a tree:

var vis = new pv.Panel()
    .width(500)
    .height(200)
    ;
var tree = vis.add(pv.Layout.Tree)
    .nodes(pv.dom(hasVoted).root("hasVoted").nodes())
    .depth(40)
    .breadth(100)
    .top(30)
    .right(100)
    ;
tree.link.add(pv.Line);
tree.node.add(pv.Dot)
    .size(function(n) n.nodeValue)
	.anchor("center").add(pv.Label).textAlign("center").text(function(n) n.nodeName)
vis.render();

And here is the result:

There are many styling possibilities obviously left unexplored in this simple example (you can control properties of the tree.link, tree.node, tree.labels which we didn’t use here, etc.), but this won’t change much as far as data are concerned.

Now let’s try a treemap with the same dataset.

var vis = new pv.Panel()
    .width(400)
    .height(200)
    ;

var tree = vis.add(pv.Layout.Treemap)
	.width(200).height(200)
    .nodes(pv.dom(hasVoted).root("hasVoted").nodes())
    ;

tree.leaf.add(pv.Panel)
	.fillStyle(function(d) d.nodeName=="didnt"?"darkgrey":d.nodeName.slice(0,3)=="yes"?
	d.nodeName.slice(-9)=="WithParty"?"powderblue":"steelblue":
	d.nodeName.slice(-9)=="WithParty"?"lightsalmon":"salmon")

vis.add(pv.Panel)
	.data([
		   {label:"yes with party", 	color: "powderblue"},
		   {label:"yes against party", 	color: "steelblue"},
		   {label:"no with party", 		color: "lightsalmon"},
		   {label:"no against party", 	color: "salmon"},
		   {label:"didn't vote", 		color: "darkgrey"}
		   ])
	.left(220)
	.top(function() 50+20*this.index)
	.height(15)
	.width(20)
	.fillStyle(function(d) d.color)
	.anchor("right").add(pv.Label).textAlign("left").text(function(d) d.label)

vis.render();

and what took the longest part of the code was making the legend.

Here is the outcome:

 

Working with data in protovis – part 4 of 5

Previous: array functions in javascript and protovis

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.

Nesting

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()
    .width(600)
    .height(200)
;
vis.add(pv.Bar)
	.data(barley)
	.left(function() this.index*5)
	.width(4)
	.bottom(0)
	.height(function(d) d.yield*2)
	.fillStyle(function(d) d.year==1931?"steelBlue":"Orange")
;
vis.render();

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()
    .width(710)
    .height(150)
;
var cell=vis.add(pv.Panel)
	.data(barley2)
	.left(function() this.index*70)
	.width(70)
	.top(0)
	.height(150);
cell.anchor("top").add(pv.Label).textAlign("center").font("9px sans-serif").text(function(d) d.key)
cell.add(pv.Bar)
		.data(function(d) d.values)
		.left(function() 5+this.index%6*10)
		.width(8)
		.bottom(0)
		.height(function(d) d.yield*2)
		.fillStyle(function(d) d.year==1931?"steelBlue":"Orange")
		.add(pv.Label).text(function(d) d.site).textAngle(-Math.PI/2)
			.textAlign("left").left(function() 15+this.index%6*10).textStyle("#222")
	;
vis.render();

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:

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

And/or

  • 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():

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

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,

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

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:

vis.add(pv.Panel)
    .data(barley)

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)

.add(pv.Panel)
    .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)

.add(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)

etc.

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"],
    years=[1931,1932];

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:

vis.add(pv.Panel)
     .data(yields)

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:

.add(pv.Panel)
    .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

.add(pv.Bar)
    .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.

Aggregating

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"}
   ]
  },
etc.

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

pv.nest(scores)
  .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)
  .rollup(meanScore);
var avgExam=pv.nest(scores)
  .key(function(d) d.exam)
  .rollup(meanScore);

Flattening

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().

barley=pv.flatten(barley).key("variety").key("site").key("year").key("yield").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

barley=pv.nest(barley).key("variety").entries()

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

barley=pv.flatten(barley).key("variety").key("site").key("year").key("yield").array()

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

 

Protovis: analysis of the Becker’s barley example sketch

We are taking a look at the Protovis Becker’s Barley example.

<html>
  <head>
    <title>Barley Yields</title>
    <link type="text/css" rel="stylesheet" href="ex.css?3.2"/>
    <script type="text/javascript" src="../protovis-r3.2.js"></script>
    <script type="text/javascript" src="barley.js"></script>
    <style type="text/css">

#fig {
  width: 350px;
  height: 833px;
}

    </style>
  </head>
  <body><div id="center"><div id="fig">
    <script type="text/javascript+protovis">

/* Compute yield medians by site and by variety. */
function median(data) pv.median(data, function(d) d.yield);
var site = pv.nest(barley).key(function(d) d.site).rollup(median);
var variety = pv.nest(barley).key(function(d) d.variety).rollup(median);

/* Nest yields data by site then year. */
barley = pv.nest(barley)
    .key(function(d) d.site)
    .sortKeys(function(a, b) site[b] - site[a])
    .key(function(d) d.year)
    .sortValues(function(a, b) variety[b.variety] - variety[a.variety])
    .entries();

/* Sizing and scales. */
var w = 242,
    h = 132,
    x = pv.Scale.linear(10, 70).range(0, w),
    c = pv.Colors.category10();

/* The root panel. */
var vis = new pv.Panel()
    .width(w)
    .height(h * pv.keys(site).length)
    .top(15)
    .left(90)
    .right(20)
    .bottom(25);

/* A panel per site-year. */
var cell = vis.add(pv.Panel)
    .data(barley)
    .height(h)
    .top(function() this.index * h)
    .strokeStyle("#999");

/* Title bar. */
cell.add(pv.Bar)
    .height(14)
    .fillStyle("bisque")
  .anchor("center").add(pv.Label)
    .text(function(site) site.key);

/* A dot showing the yield. */
var dot = cell.add(pv.Panel)
    .data(function(site) site.values)
    .top(23)
  .add(pv.Dot)
    .data(function(year) year.values)
    .left(function(d) x(d.yield))
    .top(function() this.index * 11)
    .size(12)
    .lineWidth(2)
    .strokeStyle(function(d) c(d.year));

/* A label showing the variety. */
dot.anchor("left").add(pv.Label)
    .visible(function() !this.parent.index)
    .left(-1)
    .text(function(d) d.variety);

/* X-ticks. */
vis.add(pv.Rule)
    .data(x.ticks(7))
    .left(x)
    .bottom(-5)
    .height(5)
    .strokeStyle("#999")
  .anchor("bottom").add(pv.Label);

/* A legend showing the year. */
vis.add(pv.Dot)
    .extend(dot)
    .data([{year:1931}, {year:1932}])
    .left(function(d) 170 + this.index * 40)
    .top(-8)
  .anchor("right").add(pv.Label)
    .text(function(d) d.year);

vis.render();

    </script>
  </div></div></body>
</html>

Data:

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" },
etc.

The code begins by defining a function that will be used throughout the program.

function median(data) pv.median(data, function(d) d.yield);

this function expects an array of associative arrays which have the key “yield”. What it does is that it returns the median of all the values of the key yield.
If run against barley, it will return the median yield of all observations. If run against a subset of barley, it will return the median of the yield of that subset.
The point of this function is to simplify the writing of otherwise obfuscated statements.

Now let’s see it put to good use.

var site = pv.nest(barley).key(function(d) d.site).rollup(median);

The output of this statement is easier to understand than itself. It returns an associative array, with each site as a key, and their corresponding value is the median yield for all observations for that site.

{
  Crookston: 39.03333,
  Duluth: 28.533335,
  Grand Rapids: 23.983335,
  Morris: 34.699995,
  University Farm: 31.383335,
  Waseca: 47.949995}

pv.nest(barley) means that we are going to create an associative array based on barley with a hierarchy. (tree)
.key(function(d) d.site) means that they first key in the hierarchy of that tree will be the site. So, we are going to run an operation on all the entries of “barley” with the same site.
That operation is called by .rollup(median ) at the end of the line: this crunches all the entries and replace them by the result of the function “median” applied to all those records.

var variety = pv.nest(barley).key(function(d) d.variety).rollup(median);

This does the same as above, but by variety instead of by site.

{
  Glabron: 32.4,
  Manchuria: 30.96667,
  No. 457: 33.966665,
  No. 462: 30.45,
  No. 475: 31.066665,
  Peatland: 32.383335,
  Svansota: 28.550005,
  Trebi: 39.199995,
  Velvet: 32.149995000000004,
  Wisconsin No. 38: 36.95
}
/* Nest yields data by site then year. */
  barley = pv.nest(barley)
    .key(function(d) d.site)
    .sortKeys(function(a, b) site[b] - site[a])
    .key(function(d) d.year)
    .sortValues(function(a, b) variety[b.variety] - variety[a.variety])
    .entries();

This will transform the variable barley, which is now a flat list of records, into a tree form.
pv.nest(barley) indicates we are turning barley into a tree.
.key(function(d) d.site) says that the first order of the hierarchy will be “site”.
So our tree should look like:

[{key:”Crookston”, values: {….},
  {key:”Duluth”, values:{…},
…

Well, the order of the keys may not be alphabetical, thanks to the next statement.
sortKeys sorts the keys using a comparator function: this function(a,b) thing goes through all the pairs of keys and will order them according to that function, so if for a key the value of site is higher than for another one, it will be put first.
As a result, the first key should be Waseca, then Crookston, etc.
The next order of hierarchy will be after year. No sortkeys here, so the values of keys will just be presented in natural order.
So our tree will look like:

[
{ key: “Waseca”, values: [
	{key: 1931, values: [ … ]},
	{key: 1932, values: [ … ]}
  ]
}, 
{key: “Crookston”, values: [
	{key: 1931, values: [ … ]},
	{key: 1932, values: [ … ]}
  ]
}, etc.

The next statement will rank the values.
What is in that values field (where the ellipses are) will now be ranked using another comparator function, on variety this time.
The sortKeys statement worked on keys: “Crookston”, “Duluth”, etc. so one could write directly site[a] and get a value.
But this sortValues statement works on entries (fields like: { yield: 48.86667, variety: “Manchuria”, year: 1931, site: “Waseca” } ), so one can’t write variety[a] but instead, variety[a.variety].

Finally, the last statement, entries(), says that the values thing should be filled by the actual records, as opposed to using rollup in order to crush an aggregate value from the records.

So the final tree will look like this:

[{key: “Waseca”, values: [
 {key: 1931, values: 	[{site: "Waseca", variety: "Trebi", year: 1931, yield: 63.8333},
 {site: "Waseca",variety: "Wisconsin No. 38", year: 1931, yield: 58.8},
 {site: "Waseca", variety: "No. 457", year: 1931, yield: 58.1},
…
]},
{key: 1932, values: 	[…]}
]}, 
{key: “Crookston”, values: […]}, 
…
{key: “Grand Rapids”, values: […]}]

The next block of statements is more straightforward.

/* Sizing and scales. */
var w = 242,
    h = 132,
    x = pv.Scale.linear(10, 70).range(0, w),
    c = pv.Colors.category10();

w and h are constants for the width and heights of the cells,
x is a scale to transform the yields in horizontal coordinates, so 10 will be represented at the left-most sied of the cell and 70 at the right-most side,
c is the standard color palette.

Now, we create the panels.

/* The root panel. */
var vis = new pv.Panel()
    .width(w)
    .height(h * pv.keys(site).length)
    .top(15)
    .left(90)
    .right(20)
    .bottom(25);

/* A panel per site-year. */
var cell = vis.add(pv.Panel)
    .data(barley)
    .height(h)
    .top(function() this.index * h)
    .strokeStyle("#999");

First we create the root panel. The height of the panel is determined by the number of sites.
Since site is an associative array, we first derive an array of the same length with pv.keys(site), which contains the names of the keys of that associative array (in plain English, the names of the sites). What we need is just the number of them, that’s what the length property is for.
(btw, we could have simply written barley.length)
We multiply that number by the height of each cell to get the height of the root panel.

We then create panels inside that rootpanel.
Note the simplicity with which data is pushed into those panels:

    .data(barley)

Now barley is an array of 6 objects. So we are creating 6 panels, and their data element will be of the form:

{key: “Waseca”, values: [{key: “1931”, values:  [entries]}, {key:”1932”, values: [entries]}]}

Since these cells will be positioned from the root panel, their top value is determined using a simple function of this.index, so the 1st one will be right on top, the next one will be at h pixels from the top, the next one at 2*h pixels, etc.

/* Title bar. */
cell.add(pv.Bar)
    .height(14)
    .fillStyle("bisque")
  .anchor("center").add(pv.Label)
    .text(function(site) site.key);

This just adds a title to the cells. Here, we use a bar, but it could have been a panel.
We only specify the height: the top and left value are supposed to be 0 and the width is that of the parent. We choose the svg color “bisque” as the background color and we add a label in the middle.
Here’s how we obtain the text. Yes it is the site name, but this has nothing to do with the choice of “site” as the variable name in the accessor function.
That function just takes data from the data property, which is directly inherited from the parent. This is a complex associative array, but at its first level, the key property corresponds to the site name. So, function(site) site.key returns the site name.

/* A dot showing the yield. */
var dot = cell.add(pv.Panel)
    .data(function(site) site.values)
    .top(23)
  .add(pv.Dot)
    .data(function(year) year.values)
    .left(function(d) x(d.yield))
    .top(function() this.index * 11)
    .size(12)
    .lineWidth(2)
    .strokeStyle(function(d) c(d.year));

Here’s the data representation.
We first add a group of panels called dot to the panel cell.
This is a group, and not a single panel, because of what they get through the data method: the content of the values key of their parent.
Again, the data property of their parent, cell, is of the form:

{key: site name, values: [{key: “1931”, values: […]}, {key:”1932”, values: […]}]}

So if we isolate the content of the values key, we have an array of 2 values:

[{key: “1931”, values:[…]} , 
{key: “1932”, values:[…]} ]

Therefore, this statement creates 2, not 1, panels.
But those panels are superposed: the only positioning instruction is that they are 23 pixels from the top, so they are both taking the full width of the cell panel, and go to the bottom of that panel as well.
The system will first draw the first one, then the second one on top of that.

Then, we add a dot object to those dot panels, which is a series of circles.
How many dots will there be in those series? This, again, depends on the contents of the data method.
What we get this time is:

    .data(function(year) year.values)

What this means is that we are looking at the data element of the parent, and we are taking what’s behind values.

The data element of the parent was of the form:

{key: year name, values: 
  [
   {site: site name, variety: variety name, year: year name, yield: yield value},
   {site: site name, variety: variety name, year: year name, yield: yield value}, 
   {site: site name, variety: variety name, year: year name, yield: yield value},
…
   {site: site name, variety: variety name, year: year name, yield: yield value}
  ]
}

So what we’re getting is the array of 10 entries that were behind values.

.left(function(d) x(d.yield))

This means that each mark will be positioned from the left, according to the value of its yield property, once transformed by our scale.

.top(function() this.index * 11)

And they are simply positioned vertically depending on this.index, so one on top of the other. Remember, this is relative to the dot panel, not to cell.

.size(12)
.lineWidth(2)

We are determining a size and a line width, but no fill style, so we are drawing rings, not discs. Even if they are superposed, the back one should still be visible.

.strokeStyle(function(d) c(d.year));

Finally, we are determining the color of the ring. For that, we extract the year of the current entry using d.year. It is converted to a color using the palette c.
There are other ways to get the year, but this is the simplest to write.

Now if we consider the statement in its entirety again:

/* A dot showing the yield. */
var dot = cell.add(pv.Panel)
    .data(function(site) site.values)
    .top(23)
  .add(pv.Dot)
    .data(function(year) year.values)
    .left(function(d) x(d.yield))
    .top(function() this.index * 11)
    .size(12)
    .lineWidth(2)
    .strokeStyle(function(d) c(d.year));

What is really assigned to dot is not the first item created (panels) but the dot chart proper. This is important to note that for the rest:

/* A label showing the variety. */
dot.anchor("left").add(pv.Label)
    .visible(function() !this.parent.index)
    .left(-1)
    .text(function(d) d.variety);

What we’re trying to do here is to write legends for the dot charts. We don’t want to do this for each year: the labels would be on top of each other, and less legible than if they were just one group of labels. This is why we use this visible statement. this.parent refers to a the parent panel of dot, so this.parent.index is worth 0 for the first panel, and 1 for the second. So here, !this.parent.index will be false for all values other than 0, so there will be only 1 set of labels, even if we add a year for instance.

Then, although we said we were adding the labels just to the left of the dot (this is what dot.anchor(“left”) does), what we really want is to have them on the left of the cell.
That’s why we use

.left(-1)
.text(function(d) d.variety)

runs on the data provided by the parent, in this case the dot chart. So it’s just the variety of the current entry.

/* X-ticks. */
vis.add(pv.Rule)
    .data(x.ticks(7))
    .left(x)
    .bottom(-5)
    .height(5)
    .strokeStyle("#999")
  .anchor("bottom").add(pv.Label);

This just adds a series of 7 ticks to the bottom of the chart. They are rules, but their height has been limited to 5 pixels. They start from below the chart – bottom(-5) – and we add the ticks to that below with anchor(“bottom”). Since all the values are 2-digit numbers, we can leave the default versions for the pv.Label objects, and not go into tickFormat or anything fancy.

/* A legend showing the year. */
vis.add(pv.Dot)
    .extend(dot)
    .data([{year:1931}, {year:1932}])
    .left(function(d) 170 + this.index * 40)
    .top(-8)
  .anchor("right").add(pv.Label)
    .text(function(d) d.year);

Finally, the legend of the chart, in form of a dot chart.
The first .extend(dot) statement just says that we are copying the properties of the other dot chart. So, if we decide to change the size of the rings or their thickness, it will be reflected in the legend.
Here, we just pass the data manually. Note that this is added to the root panel (vis), so top(-8) means that it appears over the main chart.

In this example, the authors have started from an unformated, flat list of 120 entries.
Then, they thought of the shape their final visualization will take and the hierarchy of objects needed to accommodate that:
• two superposed dot series, showing the various varieties for a given year/site combination (dot),
• each inside a panel, one for each year,
• which would be part of a parent panel, for each site (cell)
• which would be stacked vertically inside the root panel (vis).

So in order to do that seamlessly, they had to prepare a data variable with that hierarchy:
First by site, then by year, then by variety.

This is what the complex pv.nest command does at the beginning.
Once this is taken care of, the various objects can be added one to the other naturally.

 

Working with data in protovis – interlude: protovis nesting vs tableau

Protovis, like Tableau, are based on the grammar of graphics framework. In a nutshell, in both environments, a chart designer can map visual attributes (such as x or y dimension, color, shape, etc.) to dimensions of data.

The flat file which Becker’s Barley is based on can be used in Tableau public nearly as is.
Here’s a size-by-size comparison of the results:

How it’s done in Protovis

In protovis, the flat file is nested several times, so that its various elements can be called in a hierarchy from series of dots per variety, to panel per sites to a grander panel. Legend and ticks are added by hand for a perfect finish. Still, some careful planning is required to prepare the data file and to adjust the various elements (choice of colors, sizes, etc.)

How it’s done in Tableau


The data file, unsurprisingly, has 4 dimensions: site, variety, year and yield. In tableau terms, yield is a measure (a numerical dimension) while the other 3 are categorical dimensions. With a few clicks, it is possible to get a result which is similar to the original vis in Protovis. We assign yield to column (horizontal attribute), site and variety to row in that order. We also untick aggregate measures in Analysis, so we get little circles and not big bars. Here, I’ve manually sorted the sites and the varieties.

Conclusion

It is much, much easier to achieve a similar result with Tableau, however using protovis provides a finer control.