# [Maxima] mini / maxi functions

Stavros Macrakis macrakis at alum.mit.edu
Mon Jun 28 14:54:50 CDT 2010

```Maxima functions should have clear, simple, and universal semantics.  Though
I do understand why column-wise min can be useful when matrices are used to
represent datasets, I find it poor practice to overload that functionality
on a function generically called 'mini'.  Why not col_min and row_min?

As for the expectations of users working in a statistical context, I'll
point out that in R, min(matrix(1:4,2,2)) = min(data.frame(a=1:2,b=3:4)) =
1, NOT a column-wise minimum*, which requires the use of the 'apply'
function, which has an argument specifying the dimension along which to
group.

-s

* I admit I find this strange in the case of data frames, but then there are
many things I find strange in R.

On Mon, Jun 28, 2010 at 13:51, Barton Willis <willisb at unk.edu> wrote:

> -----maxima-bounces at math.utexas.edu wrote: -----
>
> >Perhaps, a user not working in an statistical context would expect lmax
> >to return the maximum element of the matrix, not a list of column wise
> >maxima, which is what we are looking for.
> >
> >--
> >Mario
>
> I'd guess that users would sometimes assume that lmax on a matrix gives
> the largest matrix entry. I suppose lmax and lmin could have optional
> arguments that control all this, but I think it's more useful to unify
> lmax with maxi. Plus, for matrices, we have the one and infinity norms
>
> Maybe something like (now that transpose is less spendy)
>
> (defmacro opapply (op l)
>  `(simplify (cons (list ,op) ,l)))
>
> (defun \$lmax (x)
>  (cond ((or (\$listp x) (\$setp x)) (opapply '\$max (margs x)))
>     ((\$matrixp x)
>       (opapply 'mlist (mapar #'(lambda (s) (opapply '\$max s)) (transpose
> (mcx (margs x))))))
>      (t (merror "The argument to 'lmax' must be a list, set, or
> matrix."))))
>
> (defun \$lmin (x)
>  (cond ((or (\$listp x) (\$setp x)) (opapply '\$min (margs x)))
>     ((\$matrixp x)
>      (opapply 'mlist (mapar #'(lambda (s) (opapply '\$min s)) (transpose
> (mcx (margs x))))))
>     (t (merror "The argument to 'lmin' must be a list, set, or matrix."))))
>
>
> --Barton
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