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Inner Product: Difference between revisions
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== Differences between dialects == | == Differences between dialects == | ||
Implementations differ on the exact behaviour of inner product when the right operand is not a [[scalar function]]. | Implementations differ on the exact behaviour of inner product when the right operand is not a [[scalar function]]. Page 121 of the ISO/IEC 13751:2001(E) [[standard]] specifies that <syntaxhighlight lang=apl inline>X f.g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</syntaxhighlight>. This is indeed what [[APL2]], [[APLX]], [[APL+Win]], and [[ngn/apl]] follow, while [[Dyalog APL]], [[NARS2000]] and [[GNU APL]] differ as described by [[Roger Hui]]:<ref>[[Roger Hui]]. ''inner product''. Internal Dyalog email. 24 July 2020.</ref> | ||
<blockquote> | <blockquote> | ||
The following dop models inner product in Dyalog APL, with caveats. If you find a case where <syntaxhighlight lang=apl inline>f.g</syntaxhighlight> differs from <syntaxhighlight lang=apl inline>f IP g</syntaxhighlight>, not covered by the caveats, I'd be interested. | The following dop models inner product in Dyalog APL, with caveats. If you find a case where <syntaxhighlight lang=apl inline>f.g</syntaxhighlight> differs from <syntaxhighlight lang=apl inline>f IP g</syntaxhighlight>, not covered by the caveats, I'd be interested. | ||
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(3 4⍴5)+.×1 5⍴6 ⍝ works in NARS2000 or APL\360, not in Dyalog APL</syntaxhighlight> | (3 4⍴5)+.×1 5⍴6 ⍝ works in NARS2000 or APL\360, not in Dyalog APL</syntaxhighlight> | ||
</blockquote> | </blockquote> | ||
The <syntaxhighlight lang=apl inline>⊃⍤0⊢(↓⍺)∘.(⍺⍺/⍵⍵¨)↓(¯1⌽⍳⍴⍴⍵)⍉⍵</syntaxhighlight> line of the above dop can be written more directly as <syntaxhighlight lang=apl inline>⍺(⍺⍺⌿⍵⍵¨⍤¯1)⍤1 99⊢⍵</syntaxhighlight>, which uses the more efficient [https://www.jsoftware.com/papers/innerproduct/ip1.htm major-cell-at-a-time algorithm] (rather than row-by-column). The ISO/IEC 13751:2001(E) inner product, conversely, cannot be modeled using a major-cell-at-a-time algorithm, as computing the results one major cell (of the right argument) at a time relies on each application of the right operand being done between two scalars and producing a scalar result. | |||
== External links == | == External links == | ||