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Leading axis agreement: Difference between revisions
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Leading axis agreement (view source)
Revision as of 19:49, 19 February 2021
, 19:49, 19 February 2021List languages that use it in the intro
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'''Leading axis agreement''', sometimes called '''prefix agreement''', is a [[conformability]] rule designed for [[leading axis theory]]. It states that a [[dyadic]] [[scalar function]] can be applied between two | '''Leading axis agreement''', sometimes called '''prefix agreement''', is a [[conformability]] rule designed for [[leading axis theory]] and used by [[J]] and [[BQN]]. It states that a [[dyadic]] [[scalar function]] can be applied between two [[array]]s only if one of their [[shape]]s is a [[prefix]] of the other. The shape of the result is that of the [[argument]] with higher [[rank]]. | ||
== Examples == | == Examples == | ||
| Line 20: | Line 20: | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
as well as when one is a scalar: | as well as when one is a [[scalar]]: | ||
<source lang=j> | <source lang=j> | ||
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In this case, <source lang=j inline>x</source> has shape <source lang=j inline>2</source> and <source lang=j inline>y</source> has shape <source lang=j inline>2 3</source>. Since the leading axes agree and the rank difference is 1, each atom (or 0-[[cell]]) of <source lang=j inline>x</source> is matched with each row (or 1-cell) of <source lang=j inline>y</source>, and the two rows in the result are the results of <source lang=j inline>10 + 0 1 2</source> and <source lang=j inline>20 + 3 4 5</source>, respectively. | In this case, <source lang=j inline>x</source> has shape <source lang=j inline>2</source> and <source lang=j inline>y</source> has shape <source lang=j inline>2 3</source>. Since the leading axes agree and the rank difference is 1, each atom (or 0-[[cell]]) of <source lang=j inline>x</source> is matched with each row (or 1-cell) of <source lang=j inline>y</source>, and the two rows in the result are the results of <source lang=j inline>10 + 0 1 2</source> and <source lang=j inline>20 + 3 4 5</source>, respectively. | ||
== Model == | |||
In dialects that do not feature leading axis agreement, it can nevertheless be utilised by the introduction of an explicit operator: | |||
<source lang=apl> | |||
_LA←{⍺ ⍺⍺⍤(-⍺⌊⍥(≢⍴)⍵)⊢⍵} | |||
⊢x ← 10 20 | |||
10 20 | |||
⊢y ← 2 3 ⍴ ⍳ 6 | |||
0 1 2 | |||
3 4 5 | |||
x +_LA y | |||
10 11 12 | |||
23 24 25 | |||
</source> | |||
{{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 <source lang=apl inline>X (f⍤m n) Y</source>, the [[Frame|frames]] of <source lang=apl inline>X</source> and <source lang=apl inline>Y</source> are checked for conformability. Combined with leading axis agreement, the Rank operator can be used to align the axes to be matched. | When using the [[Rank (operator)|Rank operator]] for dyadic functions as in <source lang=apl inline>X (f⍤m n) Y</source>, the [[Frame|frames]] of <source lang=apl inline>X</source> and <source lang=apl inline>Y</source> are checked for conformability. Combined with leading axis agreement, the Rank operator can be used to align the [[axis|axes]] to be matched. | ||
<source lang=j> | <source lang=j> | ||
| Line 75: | Line 91: | ||
65 66 | 65 66 | ||
</source> | </source> | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
[[Category:Leading axis theory]][[Category:Function characteristics]][[Category:Conformability]]{{APL features}} | |||