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== Description == | == Description == | ||
At takes two operands, each of which can be an [[array]] or [[function]], with varying effect: | At takes two operands, each of which can be an [[array]] or [[function]], with varying effect: | ||
A call to At is of the form < | A call to At is of the form <syntaxhighlight lang=apl inline>X(f@g)Y</syntaxhighlight> where <syntaxhighlight lang=apl inline>X</syntaxhighlight> is optional. | ||
* < | * <syntaxhighlight lang=apl inline>g</syntaxhighlight> specifies the indices of the right argument that should be modified. | ||
** '''Function''': Must apply monadically to < | ** '''Function''': Must apply monadically to <syntaxhighlight lang=apl inline>Y</syntaxhighlight>, and return a boolean array of the same shape as <syntaxhighlight lang=apl inline>Y</syntaxhighlight>, with ones at positions that should be amended. | ||
** '''Array''': A [[vector]] (or [[scalar]]) of [[cell]] indices (of equal lengths) to amend. If the same index appears multiple times, the last amendment overrules any previous ones, meaning that amendments are not stacked. This is in contrast to [[modified assignment]] where multiple specifications of the same parts of the array will be processed sequentially. | ** '''Array''': A [[vector]] (or [[scalar]]) of [[cell]] indices (of equal lengths) to amend. If the same index appears multiple times, the last amendment overrules any previous ones, meaning that amendments are not stacked. This is in contrast to [[modified assignment]] where multiple specifications of the same parts of the array will be processed sequentially. | ||
* < | * <syntaxhighlight lang=apl inline>f</syntaxhighlight> specifies what happens to the elements at those positions. | ||
** '''Function''': Is applied once on an array whose [[major cell]]s are the selected cells. If < | ** '''Function''': Is applied once on an array whose [[major cell]]s are the selected cells. If <syntaxhighlight lang=apl inline>X</syntaxhighlight> is present, then it is bound to <syntaxhighlight lang=apl inline>f</syntaxhighlight> so <syntaxhighlight lang=apl inline>X f@g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>X∘f@g Y</syntaxhighlight>. | ||
** '''Array''': Replaces the selected elements and must either have the same shape as the array whose major cells are the selected cells, or be a scalar, which then replaces all selected cells. | ** '''Array''': Replaces the selected elements and must either have the same shape as the array whose major cells are the selected cells, or be a scalar, which then replaces all selected cells. | ||
Each possible [[derived function]] can be applied [[monadic]]ally or [[dyadic]]ally, except if the left operand (< | Each possible [[derived function]] can be applied [[monadic]]ally or [[dyadic]]ally, except if the left operand (<syntaxhighlight lang=apl inline>f</syntaxhighlight>) is an array, in which case, only the monadic derived function is defined. | ||
== Examples == | == Examples == | ||
< | <syntaxhighlight lang=apl> ⍝ Simple replacement | ||
(1 2 3@4 5 6)7 5 4 10 3 6 9 2 1 8 | (1 2 3@4 5 6)7 5 4 10 3 6 9 2 1 8 | ||
7 5 4 1 2 3 9 2 1 8 | 7 5 4 1 2 3 9 2 1 8 | ||
| Line 30: | Line 30: | ||
30 10 4 10 5 | 30 10 4 10 5 | ||
⌽@(2∘|) 1 2 3 4 5 ⍝ Reversal of sub-array 1 3 5 | ⌽@(2∘|) 1 2 3 4 5 ⍝ Reversal of sub-array 1 3 5 | ||
5 2 3 4 1</ | 5 2 3 4 1</syntaxhighlight> | ||
== External Links == | == External Links == | ||
=== Lessons === | === Lessons === | ||
Latest revision as of 22:17, 10 September 2022
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At (@) is a primitive dyadic operator that is similar to J and K's Amend in functionality. In Dyalog APL, At handles a subset of the cases of the Under operator that pertain to modifying elements at specific positions in an array.
Description
At takes two operands, each of which can be an array or function, with varying effect:
A call to At is of the form X(f@g)Y where X is optional.
gspecifies the indices of the right argument that should be modified.- Function: Must apply monadically to
Y, and return a boolean array of the same shape asY, with ones at positions that should be amended. - Array: A vector (or scalar) of cell indices (of equal lengths) to amend. If the same index appears multiple times, the last amendment overrules any previous ones, meaning that amendments are not stacked. This is in contrast to modified assignment where multiple specifications of the same parts of the array will be processed sequentially.
- Function: Must apply monadically to
fspecifies what happens to the elements at those positions.- Function: Is applied once on an array whose major cells are the selected cells. If
Xis present, then it is bound tofsoX f@g Yis equivalent toX∘f@g Y. - Array: Replaces the selected elements and must either have the same shape as the array whose major cells are the selected cells, or be a scalar, which then replaces all selected cells.
- Function: Is applied once on an array whose major cells are the selected cells. If
Each possible derived function can be applied monadically or dyadically, except if the left operand (f) is an array, in which case, only the monadic derived function is defined.
Examples
⍝ Simple replacement
(1 2 3@4 5 6)7 5 4 10 3 6 9 2 1 8
7 5 4 1 2 3 9 2 1 8
(0@2 4) 1 2 3 4 5
1 0 3 0 5
⍝ f is a function
10 (×@2 4) 1 2 3 4 5
1 20 3 40 5
(÷@2 4) 1 2 3 4 5
1 0.5 3 0.25 5
⍝ g is a function
'*'@(2∘|) 1 2 3 4 5 ⍝ Boolean selection 1 0 1 0 1
* 2 * 4 *
⍝ f and g are functions
10 (×@(≤∘3)) 3 1 4 1 5
30 10 4 10 5
⌽@(2∘|) 1 2 3 4 5 ⍝ Reversal of sub-array 1 3 5
5 2 3 4 1
External Links
Lessons
Documentation
Publications
Prefix friendly @ by Aaron Hsu and Roger Hui