[Maxima] code for the transpose of list of lists

[Stavros Macrakis]

Yes, saving cons's is a good thing.  But a destructive transpose
doesn't fit into Maxima's usual conventions.

On 2010-06-29, Pedro Garrido gomez <perogarridogomez at yahoo.es> wrote:
>
>  The big difference in transpose-pg is that it cons very little, only one
> row of the matrix.
>  The algorithm is about changing pointers in the original matrix to get the
> tranpose.
>
>  A benchmark using sbcl outside of maxima. The file has been  compiled.
>
>
> CL-USER> (progn (setq l2 (copy-tree (setq l1 (a-matrix 1000 1000)))) nil)
> NIL
> CL-USER> (time (progn (transpose-wb l1) 'done))
> Evaluation took:
>   0.184 seconds of real time
>   0.190000 seconds of total run time (0.130000 user, 0.060000 system)
>   [ Run times consist of 0.140 seconds GC time, and 0.050 seconds non-GC
> time. ]
>   103.26% CPU
>   431,324,341 processor cycles
>   32,046,400 bytes consed
>
> DONE
> CL-USER> (time (progn (transpose-pg l2) 'done))
> Evaluation took:
>   0.028 seconds of real time
>   0.030000 seconds of total run time (0.020000 user, 0.010000 system)
>   107.14% CPU
>   67,007,521 processor cycles
>   16,384 bytes consed
>
>
> --------------------------
>
>
> (defvar l1 nil)
> (defvar l2 nil)
>
> (defun transpose-pg(m)
>   (let (m1)
>     (setq m1 (loop for x on (car m) collect x))
>     (transposeaux m)
>     m1))
>
> (defun transposeaux(ll)
>   (let (next)
>     (loop for l1 in ll
>        for l2 in (cdr ll) do
>        (loop for ai = l1 then next
>           for bi on l2 do
>         (setf next (cdr ai))
>         (rplacd ai bi))
>      finally
>        (loop for bi = l2 then next
>         while (cdr bi) do
>         (setf next (cdr bi)
>               (cdr bi) nil)))
>     ll))
>
>
>
> (defun a-matrix(i j)
>   "construct a rectangular matrix"
>   (loop repeat i collect
>        (loop repeat j collect (random 20))))
>
>
> (defun transpose-wb (ll)
>   (let ((acc nil))
>     (loop while (car ll) do
>       (push (mapcar #'car ll) acc)
>       (setq ll (mapcar #'cdr ll)))
>     (nreverse acc)))
>
>
>
>
>