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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]]. 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>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</syntaxhighlight> (assuming [[ | 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>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</syntaxhighlight> (assuming [[index origin]] 1). 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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The <syntaxhighlight lang=apl>⊃⍤0⊢(↓⍺)∘.(⍺⍺/⍵⍵¨)↓(¯1⌽⍳⍴⍴⍵)⍉⍵</syntaxhighlight> line of IP above can be rewritten as <syntaxhighlight lang=apl>⍺(⍺⍺⌿⍵⍵¨⍤¯1)⍤1 99⊢⍵</syntaxhighlight> which uses the more efficient major-cell-at-a-time algorithm (rather than row-by-column). The ISO/IEC 13751:2001(E) inner product, conversely, can only be calculated row-by-column, 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. | The <syntaxhighlight lang=apl>⊃⍤0⊢(↓⍺)∘.(⍺⍺/⍵⍵¨)↓(¯1⌽⍳⍴⍴⍵)⍉⍵</syntaxhighlight> line of IP above can be rewritten as <syntaxhighlight lang=apl>⍺(⍺⍺⌿⍵⍵¨⍤¯1)⍤1 99⊢⍵</syntaxhighlight> which uses the more efficient major-cell-at-a-time algorithm (rather than row-by-column). The ISO/IEC 13751:2001(E) inner product, conversely, can only be calculated row-by-column, 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. | ||
Some implementations extend the inner product by implementing Iverson's monadic variant<ref>https://www.jsoftware.com/papers/satn42.htm</ref>, which takes a single argument and performs the operation of computing the alternant, as modelled by [https://dfns.dyalog.com/n_alt.htm dfns.alt]. | Some implementations extend the inner product by implementing Iverson's monadic variant<ref>[[Ken Iverson|K.E. Iverson]]. [https://www.jsoftware.com/papers/satn42.htm Determinant-Like Functions Produced by the Dot Operator.] SHARP APL Technical Note 42. 1982-04-01.</ref>, which takes a single argument and performs the operation of computing the alternant, as modelled by [https://dfns.dyalog.com/n_alt.htm dfns.alt]. | ||
== External links == | == External links == | ||