Key (⌸) is a primitive monadic operator which takes a dyadic function operand where specified keys group the indices or major cells of an argument. It was introduced in Dyalog APL version 14.0 and is commonly compared to SQL's GROUP BY statement.
Description
Monadically, Key will group identical major cells together and applies the function operand once for each unique major cell. The function is applied with the unique major cell as left argument, while the right argument is the indices of major cells that match it:
{⍺⍵}⌸'Mississippi'
┌─┬────────┐
│M│1 │
├─┼────────┤
│i│2 5 8 11│
├─┼────────┤
│s│3 4 6 7 │
├─┼────────┤
│p│9 10 │
└─┴────────┘
In the dyadic case, Key applies the function to collections of major cells from the right argument corresponding to unique elements of the left argument:
'Mississippi'{⍺⍵}⌸'ABCDEFGHIJK'
┌─┬────┐
│M│A │
├─┼────┤
│i│BEHK│
├─┼────┤
│s│CDFG│
├─┼────┤
│p│IJ │
└─┴────┘
The monadic case, f⌸Y is equivalent to Y f⌸ ⍳≢Y.
External links
Lessons
Documentation
| APL built-ins [edit]
|
| Primitives (Timeline) |
Functions
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| Scalar
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| Monadic
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Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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| Dyadic
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Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
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| Non-Scalar
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| Structural
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Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
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| Selection
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First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
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| Selector
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Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
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| Computational
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Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
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| Operators |
Monadic
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Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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| Dyadic
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Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
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| Quad names
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Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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