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Problems
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The monadic case, <source lang=apl inline>f⌸Y</source> is equivalent to <source lang=apl inline>Y f⌸ ⍳≢Y</source>. | The monadic case, <source lang=apl inline>f⌸Y</source> is equivalent to <source lang=apl inline>Y f⌸ ⍳≢Y</source>. | ||
== Problems == | |||
=== Vocabulary === | |||
A common problem with Key is the inability to control the order of the result (as Key will use the order of appearance) and the "vocabulary" (as Key will never include information for a major cell that doesn't occur). For example, here we want to count occurrences of the letters A, C, G, T: | |||
<source lang=apl> | |||
{⍺,≢⍵}⌸'TCCGCGGTGGCG' | |||
T 2 | |||
C 4 | |||
G 6 | |||
</source> | |||
Since A is entirely missing in the argument, it isn't mentioned in the result either. Likewise, the result is mis-ordered due to G and T appearing before the first C. A common solution is to inject the vocabulary before the actual data, and then decrement from the counts: | |||
<source lang=apl> {⍺,¯1+≢⍵}⌸'ACGT','TCCGCGGTGGCG' | |||
A 0 | |||
C 4 | |||
G 6 | |||
T 2 | |||
</source> | |||
Now that the meaning of each count is known, the operand's left argument can be ignored, and the decrementing can be factored out from the operand: | |||
<source lang=apl> | |||
¯1+{≢⍵}⌸'ACGT','TCCGCGGTGGCG' | |||
0 4 6 2 | |||
</source> | |||
=== Computing the unique === | |||
Key computes the set of [[unique]] major cells. Often, this collection is needed separately from the occurrence information, but can be hard to extract. For example, to get the most frequently occurring letter: | |||
<source lang=apl> | |||
⊃⍒{≢⍵}⌸'TCCGCGGTGGCG' | |||
3 | |||
</source> | |||
Notice that 3 is the index in the unique set of letters, and so it is tempting to write: | |||
<source lang=apl> | |||
{(⊃⍒{≢⍵}⌸⍵)⌷∪⍵}'TCCGCGGTGGCG' | |||
G | |||
</source> | |||
However, while this code works, it is inefficient in that the unique is computed twice. This can be avoided by letting Key return the unique and using that: | |||
<source> | |||
(keys counts)←,⌿{⍺,≢⍵}⌸'TCCGCGGTGGCG' | |||
keys⌷⍨⊃⍒counts | |||
G | |||
</source> | |||
Unfortunately, this can introduce a different inefficiency, in that the result of Key's operand can end up being a [[heterogeneous array]] (containing multiple [[datatype]]s), and these are stored as pointer arrays, consuming memory for one pointer per element, and forcing "pointer chasing" when addressing the data. A possible work-around is to collect the unique keys separately from the result of counts: | |||
<source> | |||
data←'TCCGCGGTGGCG' | |||
keys←0⌿data | |||
counts←{keys⍪←⍺ ⋄ ≢⍵}⌸data | |||
keys⌷⍨⊃⍒counts | |||
G | |||
</source> | |||
If there are a large number of unique values, the repeated updating of the accumulating <source lang=apl inline>keys</source> variable can be an issue in itself. | |||
== External links == | == External links == | ||