Organizing similar datasets using DownValues instead of Contexts

Question

In his answer to this question, Leonid helped me find a way to programmatically generate contexts for holding sets of symbols with the same names. Perhaps a simpler way is to use DownValues so:

dataRaw["Paris"] = Import["Paris.csv"];
data["Paris"] = Differences[dataRaw["Paris"]];
dataMax["Paris"] = Max[dataRaw["Paris"]];

dataRaw["Madrid"] = Import["Madrid.csv"];
data["Madrid"] = Differences[dataRaw["Madrid"]];
dataMax["Madrid"] = Max[dataRaw["Madrid"]];

lets me make a plot using

ListLinePlot[data /@ {"Paris", "Madrid"}]

and can be implemented with a simple function

importCity[cityName_String] := (
    dataRaw[cityName] = Import[cityName ~~ ".csv"];
    data[cityName] = Differences[dataRaw[cityName]];
    dataMax[cityName] = Max[dataRaw[cityName]];
)

Other than cluttering everything with a lot of [cityName], are there hidden perils to using DownValues in this way? Is there some disadvantage to storing every dataRaw as DownValues of the same symbol instead of individually in multiple contexts?

Answer 1

Since no other answer has been posted yet I'll give my opinion.

Using DownValues, which I believe is a hash table of sorts, is the normal and accepted way to store this kind of information in Mathematica, to the best of my knowledge. I cannot think of any real disadvantages compared to direct symbol assignment.

Either form (direct assignment or DownValues) may take up considerably more memory than storing the information in large array, packed or sparse if possible. The nature of the data and how it is accessed best determine which method to use.

The other option you should be aware of is to use replacement rules. When optimized using Dispatch this will be similar to DownValues in many ways, but it allows different usages and has strengths that can make it superior in some applications.

data = Dispatch @ {"Madrid" -> 7, "Paris" -> 2, "Porto" -> 4, "Perth" -> 1};

{"Madrid", "Paris"} /. data

{7, 2}

---

By the way you can write importCity like this:

importCity[cityName_String] :=
  With[{raw = Import[cityName ~~ ".csv"]},
    dataRaw[cityName] = raw;
    data[cityName]    = Differences @ raw;
    dataMax[cityName] = Max @ raw;
  ]

Answer 2

I use this way of storing data extensively for what I do. I collected in my answer here https://mathematica.stackexchange.com/a/999/66 several ideas I developed over time around this type of structure. The Keys function based on what dreeves once submitted on StackOverflow ( https://stackoverflow.com/a/154704/884752 ) is what makes this structure practical as you can see all the indices of a symbol used to index its values.

I was lucky to have found this data structure as I began learning Mathematica because it allowed me to do things I couldn't have done without it.

SetAttributes[RemoveHead, {HoldAll}];
RemoveHead[h_[args___]] := {args};
NKeys[_[symbol_Symbol]]:=NKeys[symbol]; (*for the head[object] case*)
NKeys[symbol_] := RemoveHead @@@ DownValues[symbol(*,Sort->False*)][[All,1]];
Keys[symbol_] := Replace[NKeys[symbol], {x_} :> x, {1}];

a["b"]=2;
a["c",1]=3;
Keys[a]

Answer 3

In contrast to symbols, part replacement with downvalues requires use of a temporary variable, (unless there is a better way). E.g.