Using PDL for rotations

Anonymous Monk has asked for the wisdom of the Perl Monks concerning the following question:

Ok, for a certain program I am writing (protein folding), I need to be able perform rotations. I was first planning to do it manually by defining rotation matrices and change of basis matrices etc but I think pdl might save me time. However I am not sure how to use its use PDL::Transform to do so. Here is a piece of code that I was using to experiment with pdl

use PDL;        
use PDL::Transform;

@a = [[1,0,0],[0,1,0],[0,0,1]];   

$c= pdl @a; 
     
$e = t_rot(45,45,45);

$c = $e * $c 

print $c;
[download]

I was hoping this would rotate my 1,1,1 vector in all directions by 45 degrees but it gives the error. "Hash given as a pdl - but not {PDL} key!". I am not able to understand what this error is for? Also I have seen no tutorial where these rotationa matrices are explained so I would appreciate any help, thanks.

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Re: Using PDL for rotations by pc88mxer (Vicar) on Apr 29, 2008 at 16:38 UTC
`t_rot` takes a single argument, so you need to use (but see update below): `$e = t_rot([45,45,45]);` [download] The other thing is that `$e` will be a transform object which requires you to use it like this: `$d = $e->apply($c);` [download] The final thing is that matrix multiplication is the `x` operator whereas `*` is component-wise multiplication. Update: There's a bug in the code/documentation for `t_rot`. The work-around is to use `t_linear` and also specify a `dims` argument: `$e = t_linear({ rot => [45,45,45], dims => 3});` [download] The problem can be demonstrated by setting `$PDL::Transform::debug = 1;`: `$PDL::Transform::debug = 1; $e = t_linear({ rot => [45,45,45] }); # the above will emit: # PDL::Transform::Linear: assuming 2-D transform (set dims option to + change)` [download]	[reply] [d/l] [select]
Re^2: Using PDL for rotations by etj (Priest) on Jun 07, 2022 at 02:53 UTC
Note from THE FUTURE: this bug was in fact still there! And impressively, there was not a single test for any of the rotation stuff. Now there is a single test, which also caught another recently-introduced bug. The code will now use the number of elements in the rotation if neither `dims` nor `matrix` are supplied. Both bugs now have fixes, which will be in PDL 2.081.	[reply] [d/l] [select]
Re^2: Using PDL for rotations by Anonymous Monk on Apr 29, 2008 at 19:09 UTC
Okay one more question, upon doing rotations perl some times returns infitesmaly small numbers instead of zero (where it should be zero, as I check them my-self). Is there a simple way to have perl return them zero by changing precision somehow? Thanks...	[reply]
Re^3: Using PDL for rotations by plobsing (Friar) on Apr 29, 2008 at 20:23 UTC
Floating-point math can get ugly little rounding errors. You're seeing them here. No need to set any precision, simply make sure the magnitude of the values are above some $eps (epsilon) or set them to zero. Like so: `$pdl = $pdl * ( (abs $pdl) > $eps);`	[reply] [d/l]