4,493
edits
Inner Product: Difference between revisions
Jump to navigation
Jump to search
→External links
| Line 117: | Line 117: | ||
== Differences between dialects == | == Differences between dialects == | ||
Implementations differ on the exact behaviour of inner product when the right operand is not a [[scalar function]]. It follows from page 121 of the ISO/IEC 13751:2001(E) [[standard]] specifies that <source lang=apl inline>X f.g Y</source> is equivalent to <source lang=apl inline>⊃⍤0 f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</source>. This is indeed what [[APL2]], [[APLX]], and [[ngn/apl]] follow, while [[Dyalog APL]] and [[GNU APL]] use <source lang=apl inline>⊃⍤0 f/¨ (⊂[⍴⍴x]x)∘.(g¨) ⊂[1]y</source>. | Implementations differ on the exact behaviour of inner product when the right operand is not a [[scalar function]]. It follows from page 121 of the ISO/IEC 13751:2001(E) [[standard]] specifies that <source lang=apl inline>X f.g Y</source> is equivalent to <source lang=apl inline>⊃⍤0 f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</source>. This is indeed what [[APL2]], [[APLX]], and [[ngn/apl]] follow, while [[Dyalog APL]] and [[GNU APL]] use <source lang=apl inline>⊃⍤0 f/¨ (⊂[⍴⍴x]x)∘.(g¨) ⊂[1]y</source>. | ||
== Model == | |||
[[Roger Hui]] writes:<ref>[[Roger Hui]]. ''inner product''. Internal Dyalog email. 24 July 2020.</ref> | |||
<blockquote> | |||
The following dop models inner product in Dyalog APL, with caveats. If you find a case where <source lang=apl inline>f.g</source> differs from <source lang=apl inline>f IP g</source>, not covered by the caveats, I'd be interested. | |||
<source lang=apl> | |||
IP←{ | |||
assert((⊃⌽⍴⍺)≡≢⍵)∨(1=×/⍴⍺)∨1=×/⍴⍵: | |||
⊃⍤0 ⊢ (↓⍺) ∘.(⍺⍺/⍵⍵¨) ↓(¯1⌽⍳⍴⍴⍵)⍉⍵ | |||
} | |||
assert←{⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕SIGNAL 8 ⋄ shy←0} | |||
</source> | |||
(Explanation: What's with the <source lang=apl inline>⊃⍤0</source> in <source lang=apl inline>IP</source>? It's because <source lang=apl inline>∘.f</source> has an implicit each, applying <source lang=apl inline>⊂</source> to each item of its result. But the <source lang=apl inline>⍺⍺/</source> in <source lang=apl inline>(⍺⍺/⍵⍵¨)</source> also has an implicit each. So the <source lang=apl inline>⊃⍤0</source> gets rid of one of those encloses.) | |||
Caveats: | |||
* You can not use the hybrid <source lang=apl inline>/</source> directly as an operand as it runs afoul of the parser in weird and wonderful ways. Instead, you have to use <source lang=apl inline>{⍺/⍵}</source>. The same goes for <source lang=apl inline>\</source> and <source lang=apl inline>{⍺\⍵}</source> I guess. | |||
* It differs from ISO/IEC 13751:2001(E) in using <source lang=apl inline>⍵⍵¨</source> instead of just <source lang=apl inline>⍵⍵</source> in the central key expression (i.e. <source lang=apl inline>(⍺⍺/⍵⍵¨)</source> instead of <source lang=apl inline>(⍺⍺/⍵⍵)</source>). So does the primitive <source lang=apl inline>f.g</source>. | |||
* It differs from ISO/IEC 13751:2001(E) in doing full-blown single extension instead of just scalar and 1-element vector extension (as in APL2). So does the primitive <source lang=apl inline>f.g</source>. e.g.<source lang=apl> | |||
(3 4⍴5)+.×1 1 1 1⍴6 ⍝ works in Dyalog, not in ISO or APL2</source> | |||
* It differs from NARS2000 or APL\360 in not permitting unit axis extension. So does the primitive <source lang=apl inline>f.g</source>. e.g.<source lang=apl> | |||
(3 4⍴5)+.×1 5⍴6 ⍝ works in NARS2000 or APL\360, not in Dyalog APL</source> | |||
</blockquote> | |||
== External links == | == External links == | ||
| Line 125: | Line 151: | ||
* [https://microapl.com/apl_help/ch_020_020_880.htm APLX] | * [https://microapl.com/apl_help/ch_020_020_880.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d300.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/dot#dyadic NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d300.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/dot#dyadic NuVoc] | ||
== References == | |||
<references/> | |||
{{APL built-ins}}[[Category:Primitive operators]] | {{APL built-ins}}[[Category:Primitive operators]] | ||