Cell: Difference between revisions
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Miraheze>Adám Brudzewsky No edit summary |
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<div class="LeadingAndTrailingCells"></div> | |||
Interactive k-cell explorer — hover over various elements! | |||
<div> | |||
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> |