MaplePrimes - answers and comments on Question, Computation with Array

use ~ to force elementwise computations

Doug Meade — Thu, 04 Feb 2010 20:58:04 Z

Maple 13 introduced enhanced functionality for elementwise computations. This is what you are looking for, I believe.

Let's start with your original definitions:

crossArea:= 3.2 * 19.1;
force := array ([0., 1380.0, 2780.0, 5630.0]);
                                    61.12
                 [ 0., 1380.0, 2780.0, 5630.0 ]

You then computed:

engineeringStress := force/crossArea;
{0., 1380.0, 2780.0, 5630.0}/crossArea;
                             0.01636125654 force
                 0.01636125654 {0., 1380.0, 2780.0, 5630.0}

But, the division does not automatically get mapped elementwise to the entries in the array. To force this, use:

engineeringStress := force/~crossArea;
{0., 1380.0, 2780.0, 5630.0}/~crossArea;
                 [0., 22.57853403, 45.48429319, 92.11387435]
                 {0., 22.57853403, 45.48429319, 92.11387435}

Does this solve your problem?

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Try Array

Scott03 — Thu, 04 Feb 2010 20:59:09 Z

Try changing your array to the newer Array structure.

crossArea := 3.2*19.1;
force := Array([0., 1380.0, 2780.0, 5630.0]);
engineeringStress := force/crossArea;
engineeringStress[1].({0., 1380.0, 2780.0, 5630.0}/crossArea);

Scott
Application Developer
Maplesoft

Truly appreciate your help

mdc — Fri, 05 Feb 2010 22:16:03 Z

Hi Doug, Scott, and Acer: Thank you for all your answers; I've learned a lot from reading all the answers. ~ -- to work with elmentwise work fine Array -- work fine. Side notes: I had turned to MATLAB to get the answers quickly. I find MATLAB is a little more "intuitive" when dealing with array, list, vector; by "intuitive" I mean that users will not need to 'think' about "element operations". But I like the plotting features of Maple; I now come back to work on this problem using Maple. Thank you for your help. --mdc

yes, but

Doug Meade — Thu, 04 Feb 2010 21:04:42 Z

While changing array to Array is, generally, preferred and does help with the references to engineeringStress, it does not affect the responses when the input is a set (or list). For this you really do need to use the ~ form of division.

In my previous post I should have included a link to the online help - see ?elementwise .

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

but..

acer — Fri, 05 Feb 2010 07:59:15 Z

But one does not "need to use" ~ to get the elementwise effect, on either a set or an old-style locarcase array. One can also use map, which was available prior to Maple 13 (and would have been a usual way, for dealing with the set).

For a lowercase array (when it was not deprecated) the evalm command would have been a popular way to distribute scalar multiplication (along with effecting other arithmetic at the same time). And that still works, as does using ~ or map. But of course, as mentioned, with an newstyle Array or Matrix it happens automatically.

acer