Outer Product: Difference between revisions

[[J]]'s Table differs from APL's Outer Product by enabling Cartesian pairing between [[cell]]s of [[rank]]s other than 0, and between cells of different rank for the left vs. right arguments, without needing to first [[enclose]] the relevant cells. It is defined as <syntaxhighlight lang=j inline>u"(lu, _)</syntaxhighlight>, where <syntaxhighlight lang=j inline>lu</syntaxhighlight> is the left rank of operand <syntaxhighlight lang=j inline>u</syntaxhighlight> (<syntaxhighlight lang=j inline>_</syntaxhighlight> denotes infinity in J). The results of the individual applications of u are collectively [[frame]]d by the catenation of the frames of the left and right arguments relative to their lu- and ru-cells respectively, where lu and ru are the dyadic ranks of the operand u. Unlike APL's Outer Product, J's Table does not use an implicit [[Each]], so the results of the individual applications of its operand are not boxed (unless the given operand itself does so).

In APL this behavior can be accomplished by enclosing the relevant cells of each argument before applying the outer product operation (or by successive applications of [[rank_(operator)|Rank]], e.g. <syntaxhighlight lang=apl inline>f⍤2 99⍤99 1</syntaxhighlight>). Conversely, the behavior of APL's Outer Product can be accomplished in terms of J's Table by adding the Each modifier, as in <syntaxhighlight lang=j inline>u&.>/</syntaxhighlight> or <syntaxhighlight lang=j inline>u&>/</syntaxhighlight>, depending on whether the given operand is a [[scalar function]].