Models — J

flip   =: 0&|:
dotcj  =: 2 : 'u/@:v"1/ flip' 

lr     =: 1 : '1{u b. 0'  NB. left rank
dotrj  =: 2 : 'u/@(v"(1+(v lr),_))'
dotrj0 =: 2 : 'u/@(v"1 _)'

dotc6  ← {∘.(⍺⍺/at ⍵⍵)under↓∘flip}
dotr1  ← {↑ (↓⍺) ⍺⍺⌿at(⍵⍵[0])¨ ⊂⍵}