Inner Product: Difference between revisions
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== History == | == History == | ||
Inner product appeared in early [[Iverson Notation]] as <math>^f_g</math> and applied even to non-[[scalar function]]s, like [[Compress]], Iverson bringing: | Inner product appeared in early [[Iverson Notation]] as <math>^f_g</math> and applied even to non-[[scalar function]]s, like [[Compress]], Iverson bringing:<ref>[[Ken Iverson]]. [[A Programming Language]. §1.11 ''The language''.</ref> | ||
:<math> | :<math> | ||
\begin{align} | \begin{align} | ||
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∇ | ∇ | ||
</source> | </source> | ||
== 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>. | ||