Cell: Difference between revisions
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Interactive k-cell explorer — hover over various elements! | |||
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In the APL [[array model]] and in particular [[leading axis theory]], a '''cell''' of an array is a [[subarray]] which is formed by selecting a single [[Index#Index along an axis|index]] along some number of leading [[Axis|axes]] and the whole of each trailing axis. Cells are classified by their [[rank]], which may be between 0 ([[scalar]]s) and the array's rank (in which case the cell must be the entire array). Cells with rank <source lang=apl inline>k</source> are called '''k-cells''' of an array. A [[major cell]] is a cell whose rank is one less than the entire array, or a 0-cell of a [[scalar]]. | In the APL [[array model]] and in particular [[leading axis theory]], a '''cell''' of an array is a [[subarray]] which is formed by selecting a single [[Index#Index along an axis|index]] along some number of leading [[Axis|axes]] and the whole of each trailing axis. Cells are classified by their [[rank]], which may be between 0 ([[scalar]]s) and the array's rank (in which case the cell must be the entire array). Cells with rank <source lang=apl inline>k</source> are called '''k-cells''' of an array. A [[major cell]] is a cell whose rank is one less than the entire array, or a 0-cell of a [[scalar]]. | ||
== Leading and trailing axes == | == Leading and trailing axes == | ||
The k-cells of an array with [[rank]] <source lang=apl inline>r</source> share the last <source lang=apl inline>k</source> [[Axis|axes]] with that array, and collapse the first <source lang=apl inline>r-k</source> axes by choosing a single [[Index#Index along an axis|index]] along each of them. Using [[bracket indexing]] this can be written | The k-cells of an array with [[rank]] <source lang=apl inline>r</source> share the last <source lang=apl inline>k</source> [[Axis|axes]] with that array, and collapse the first <source lang=apl inline>r-k</source> axes by choosing a single [[Index#Index along an axis|index]] along each of them. Using [[bracket indexing]] this can be written | ||
<source lang=apl> | <source lang=apl> | ||
Revision as of 14:44, 11 November 2019
Interactive k-cell explorer — hover over various elements!
In the APL array model and in particular leading axis theory, a cell of an array is a subarray which is formed by selecting a single index along some number of leading axes and the whole of each trailing axis. Cells are classified by their rank, which may be between 0 (scalars) and the array's rank (in which case the cell must be the entire array). Cells with rank k are called k-cells of an array. A major cell is a cell whose rank is one less than the entire array, or a 0-cell of a scalar.
Leading and trailing axes
The k-cells of an array with rank r share the last k axes with that array, and collapse the first r-k axes by choosing a single index along each of them. Using bracket indexing this can be written
A[3;2; ; ; ] ⍝ 3-cell of a rank-5 array
while Squad indexing allows a cell to be selected without knowing the argument's rank.
3 2⌷A ⍝ (r-2)-cell of a rank-r array