Hi Ingo,
I'm quite interested in what your use case is. It sounds like a great
Advent Calendar entry (simple question, complete answer) if I could base it
on an actual need. People don't get excited about "an exercise" as much as
they do about someone trying to solve a problem, whether it's circulation
in a fluid or some EM field calculation. As any that I could think of would
be rather artificial, can you tell us yours?
Knowing the use case would also help with giving it a name in case someone
decides that their Christmas project is writing a module that computes div,
grad, curl and whether to name it PDL::Fields or PDL::VectorCalc.
(I'm now wondering if a curl over a 2D or 5D vector field makes any sense)
cheers,
Boyd
On Wed, 20 Nov 2024 at 10:18, Ed . <ej...@hotmail.com> wrote:
> This (untested) should work, as it is a fairly direct translation of the
> formula:
>
> $pP = $vec->slice('(0)')->diffover; # no mv as x dim already bottom
> $px = $coords->slice('(0)')->diffover;
> $pQ = $vec->slice('(1)')->mv(1,0)->diffover->mv(0,1);
> $py = $coords->slice('(1)')->mv(1,0)->diffover->mv(0,1);
> $pR = $vec->slice('(2)')->mv(2,0)->diffover->mv(0,2);
> $pz = $coords->slice('(2)')->mv(2,0)->diffover->mv(0,2);
>
> $curl = $vec->zeroes;
> $curl->slice('(0)') .= $pR/$py - $pQ/$pz;
> $curl->slice('(1)') .= $pP/$pz - $pR/$px;
> $curl->slice('(2)') .= $pQ/$px - $pP/$py;
>
> The $curl could be a cat of those 3 expressions, with ->mv(-1,0); there's
> probably a clever way to make one copy of each ndarray and then do inplace
> operations with less mving, and the whole thing could become a PP
> operation, but let's see if this is conceptually correct first!
>
> Best regards,
> Ed
>
> ------------------------------
> *From:* Ed . <ej...@hotmail.com>
> *Sent:* 20 November 2024 9:54 AM
> *To:* perldl <pdl-gene...@lists.sourceforge.net>; pdl-devel <
> pdl-devel@lists.sourceforge.net>; Ingo Schmid <ingo...@gmx.at>
> *Subject:* Re: [Pdl-devel] curl of vector
>
> Hi Ingo,
>
> I'm not aware of any, but I had a quick google to find the formula (I know
> vaguely what divergence and curl are having watched a 3blue1brown video
> about it some time ago). I couldn't find any implementations in Python or
> Fortran.
>
> This (
> https://openstax.org/books/calculus-volume-3/pages/6-5-divergence-and-curl
> formula
> 6.17) indicates the formula for curl is:
>
> If F=⟨P,Q,R⟩ is a vector field in R3, and Px, Py, Pz, Qy, Qx, Qz, Rz,
> Rx, and Ry all exist, then the curl of F is defined by
>
> curl F = (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k
> = (∂R/∂y − ∂Q/∂z)i + (∂P/∂z − ∂R/∂x)j + (∂Q/∂x − ∂P/∂y)k
>
> This suggests to me that for a 3D problem, you need a coordinates ndarray
> dim (3,x,y,z) and a vector field ndarray with the same dims. You can do the
> partial differentiation numerically by some mv-ing and then diffover (
> https://metacpan.org/pod/PDL::Ufunc#diffover), then the notional i,j,k
> above obviously indicate the final components of curl vector at each point.
> More to follow after I've figured out how to do the partial stuff!
>
> Best regards,
> Ed
>
> ------------------------------
> *From:* Ingo Schmid via pdl-devel <pdl-devel@lists.sourceforge.net>
> *Sent:* 19 November 2024 6:06 PM
> *To:* perldl <pdl-gene...@lists.sourceforge.net>; pdl-devel <
> pdl-devel@lists.sourceforge.net>
> *Subject:* [Pdl-devel] curl of vector
>
>
> Hi,
>
> is there any implementations of calculating the curl of a vector field
> around?
>
> Best wishes
>
> Ingo
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> pdl-devel@lists.sourceforge.net
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