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Leading axis agreement: Difference between revisions
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Leading axis agreement (view source)
Revision as of 22:17, 10 September 2022
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A scalar dyadic function works when the two arrays have the same shape: | A scalar dyadic function works when the two arrays have the same shape: | ||
< | <syntaxhighlight lang=j> | ||
]x =: 2 3 $ 10 | ]x =: 2 3 $ 10 | ||
10 10 10 | 10 10 10 | ||
| Line 17: | Line 17: | ||
10 11 12 | 10 11 12 | ||
13 14 15 | 13 14 15 | ||
</ | </syntaxhighlight> | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
as well as when one is a [[scalar]]: | as well as when one is a [[scalar]]: | ||
< | <syntaxhighlight lang=j> | ||
]x =: 10 | ]x =: 10 | ||
10 | 10 | ||
| Line 31: | Line 31: | ||
10 11 12 | 10 11 12 | ||
13 14 15 | 13 14 15 | ||
</ | </syntaxhighlight> | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
The two cases above are already supported in other APLs in the form of [[scalar extension]]. J goes one step further, allowing the lower-rank array argument to have nonzero rank, as long as the leading dimensions match: | The two cases above are already supported in other APLs in the form of [[scalar extension]]. J goes one step further, allowing the lower-rank array argument to have nonzero rank, as long as the leading dimensions match: | ||
< | <syntaxhighlight lang=j> | ||
]x =: 10 20 | ]x =: 10 20 | ||
10 20 | 10 20 | ||
| Line 45: | Line 45: | ||
10 11 12 | 10 11 12 | ||
23 24 25 | 23 24 25 | ||
</ | </syntaxhighlight> | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
In this case, < | In this case, <syntaxhighlight lang=j inline>x</syntaxhighlight> has shape <syntaxhighlight lang=j inline>2</syntaxhighlight> and <syntaxhighlight lang=j inline>y</syntaxhighlight> has shape <syntaxhighlight lang=j inline>2 3</syntaxhighlight>. Since the leading axes agree and the rank difference is 1, each atom (or 0-[[cell]]) of <syntaxhighlight lang=j inline>x</syntaxhighlight> is matched with each row (or 1-cell) of <syntaxhighlight lang=j inline>y</syntaxhighlight>, and the two rows in the result are the results of <syntaxhighlight lang=j inline>10 + 0 1 2</syntaxhighlight> and <syntaxhighlight lang=j inline>20 + 3 4 5</syntaxhighlight>, respectively. | ||
== Model == | == Model == | ||
In dialects that do not feature leading axis agreement, it can nevertheless be utilised by the introduction of an explicit operator: | In dialects that do not feature leading axis agreement, it can nevertheless be utilised by the introduction of an explicit operator: | ||
< | <syntaxhighlight lang=apl> | ||
_LA←{⍺ ⍺⍺⍤(-⍺⌊⍥(≢⍴)⍵)⊢⍵} | _LA←{⍺ ⍺⍺⍤(-⍺⌊⍥(≢⍴)⍵)⊢⍵} | ||
⊢x ← 10 20 | ⊢x ← 10 20 | ||
| Line 63: | Line 63: | ||
10 11 12 | 10 11 12 | ||
23 24 25 | 23 24 25 | ||
</ | </syntaxhighlight> | ||
{{Works in|Dyalog APL}} | {{Works in|Dyalog APL}} | ||
== Aligning axes using the Rank operator == | == Aligning axes using the Rank operator == | ||
When using the [[Rank (operator)|Rank operator]] for dyadic functions as in < | When using the [[Rank (operator)|Rank operator]] for dyadic functions as in <syntaxhighlight lang=apl inline>X (f⍤m n) Y</syntaxhighlight>, the [[Frame|frames]] of <syntaxhighlight lang=apl inline>X</syntaxhighlight> and <syntaxhighlight lang=apl inline>Y</syntaxhighlight> are checked for conformability. Combined with leading axis agreement, the Rank operator can be used to align the [[axis|axes]] to be matched. | ||
< | <syntaxhighlight lang=j> | ||
NB. $x : 2|3 | NB. $x : 2|3 | ||
NB. $y : |3 2 | NB. $y : |3 2 | ||
| Line 90: | Line 90: | ||
53 54 | 53 54 | ||
65 66 | 65 66 | ||
</ | </syntaxhighlight> | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
[[Category:Leading axis theory]][[Category:Function characteristics]][[Category:Conformability]]{{APL features}} | [[Category:Leading axis theory]][[Category:Function characteristics]][[Category:Conformability]]{{APL features}} | ||