A second generation DOMINO for statisticians

The use of 'domino' (⊞) is one of the many attractive features of APL. To a statistician, it is particularly useful in its dyadic form, returning least-squares estimates Y⊞D necessary to predict data in the 'Y' vector using as prediction variables, the columns of the “design matrix” D.

Second generation APL interpreters supporting nested array structures present a unique opportunity to make such dyadic uses of domino even more attractive. The householder algorithm employed by domino provides much information that is lost to the user. This paper discusses how this information can be captured by Y⊞D returning a nested array. The essential ideas are presented using APL functions. An auxiliary processor written in C for the Dyalog interpreter demonstrates an implementation of these ideas.