The first vector-oriented programming language I ever learned or used was APL, and APL makes *no* distinction between row vectors and column vectors. It has rank-0 (scalar), rank-1 (vector), rank-2 (matrix), rank-3 ... and so on arrays. A rank-1 array is a rank-1 array is a rank-1 array and there is an algebra of arrays to go with it. I learned PL/I around the same time, which also has array expressions (but at least back then it did not have matrix product). Again, a 1D array is a 1D array is a 1D array. Since 1990, Fortran has been an array-processing language, and there has never been any distinction between row vectors and column vectors in Fortran and isn't any such distinction now. One thing that these three languages have in common is the view that a rank-N array and a rank-(N+1) array are not the same kind of thing.
I can understand MATLAB distinguishing between row and column vectors, although nothing in my undergraduate numerical analysis education prepared me to expect or even like it. But from an APL perspective it is confusing and limiting. And for that matter S and R are confusing in their own way. But to call R's approach "unique" within the family of array-oriented programming languages is an exaggeration. The BASIS system from Lawrence Livermore does not make any distinction between row and column vectors; a 1D array is a 1D array is a 1D array. Most notably in modern times, Julia belongs to the a-1D-array-is-a-1D-array-is-a-1D-array and a-1D-array-is-not-a-2D-array camp. As one person writing ina Julia thread put it, <quote> Back when I wrote everything in Matlab, those years were characterized by a series of mild annoyances of always having to worry about whether a was a row vector or a column vector, and sprinkling a(:) and a(:)' like pixie dust to fix problems. It’s a huge relief to have real one-dimensional objects. </quote> On Wed, 28 Feb 2024 at 22:43, Berwin A Turlach <berwin.turl...@gmail.com> wrote: > > On Tue, 27 Feb 2024 13:51:25 -0800 > Jeff Newmiller via R-help <r-help@r-project.org> wrote: > > > The fundamental data type in Matlab is a matrix... they don't have > > vectors, they have Nx1 matrices and 1xM matrices. > > Also known as column vectors and row vectors. :) > > > Vectors don't have any concept of "row" vs. "column". > > They do in (numerical) linear algebra. And MATLAB was written by > numerical analysts for numerical analysts. :-) So they distinguish > between row and column vectors. > > GAUSS also distinguishes between row and column vectors. > > R (and S) does not distinguish between row and column vectors, and is > in this aspect quite unique among the groups of vector-oriented > programming languages (AFAICT). But treating every vector as a column > vector, together with the recycling rule, allows for the easy coding of > the matrix/vector calculations that one (mostly) comes across in > statistical computing. For the rare occasion when this is not true the > sweep() command is provided, typically remembered once one was bitten > by the lack of distinction between row and column vectors. :) > > Cheers, > > Berwin > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
