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Subarray: Difference between revisions
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A cell ''is'' a part with lesser rank.
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(A cell ''is'' a part with lesser rank.) |
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:''The term sub-array may also be used to refer | :''The term sub-array may also be used to refer part of an array with lesser [[rank]] (i.e. a [[cell]]) or [[depth]].'' | ||
A '''subarray''' (or '''sub-array''') of an array is another array which can be formed by selecting a contiguous section along each [[axis]]. The subarrays of an array are all those that result from [[indexing]] that array by a full set of [[index]] arrays each of which is either a [[scalar]] or a [[vector]] of sequential indices. The term subarray is used loosely in APL and rarely defined directly. Depending on context, scalar indices may be allowed only for [[Axis ordering|leading]] axes or not at all. If scalar indices are not allowed than a subarray shares every [[axis]] with the array that contains it and has equal [[rank]] to it; we might call such subarrays ''equal-rank'' subarrays. Otherwise a subarray has rank less than or equal to its containing array. | A '''subarray''' (or '''sub-array''') of an array is another array which can be formed by selecting a contiguous section along each [[axis]]. The subarrays of an array are all those that result from [[Bracket indexing|indexing]] that array by a full set of [[index]] arrays each of which is either a [[scalar]] or a [[vector]] of sequential indices. The term subarray is used loosely in APL and rarely defined directly. Depending on context, scalar indices may be allowed only for [[Axis ordering|leading]] axes or not at all. If scalar indices are not allowed than a subarray shares every [[axis]] with the array that contains it and has equal [[rank]] to it; we might call such subarrays ''equal-rank'' subarrays. Otherwise a subarray has rank less than or equal to its containing array. | ||
A vector subarray of a [[vector]] is a subvector. In languages outside of the APL family which have only 1-dimensional arrays, "subarray" may have this meaning: for example, the [[wikipedia:maximum subarray problem|maximum subarray problem]] is usually taken to apply to 1-dimensional arrays only. The term "slice" may also be used to refer to a subvector outside of APL. | A vector subarray of a [[vector]] is a subvector. In languages outside of the APL family which have only 1-dimensional arrays, "subarray" may have this meaning: for example, the [[wikipedia:maximum subarray problem|maximum subarray problem]] is usually taken to apply to 1-dimensional arrays only. The term "slice" may also be used to refer to a subvector outside of APL. | ||
The [[Find]] (< | The [[Find]] (<syntaxhighlight lang=apl inline>⍷</syntaxhighlight>) function searches for occurrences of the left argument as a subarray of the right argument. For Find, a subarray may have leading axes dropped but not others. We might also say that Find searches for the left argument after extending its [[shape]] with leading 1s, or that it searches for the left argument as a subarray of any equal-[[rank]] [[cell]] of the right argument. | ||
< | <syntaxhighlight lang=apl> | ||
⎕←A ← 5 4⍴⎕A | |||
ABCD | ABCD | ||
EFGH | EFGH | ||
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0 0 0 0 | 0 0 0 0 | ||
0 0 0 0 | 0 0 0 0 | ||
</ | </syntaxhighlight> | ||
Special types of equal-rank subarrays include: | Special types of equal-rank subarrays include: | ||