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 . <[email protected]>
Sent: 20 November 2024 9:54 AM
To: perldl <[email protected]>; pdl-devel
<[email protected]>; Ingo Schmid <[email protected]>
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 <[email protected]>
Sent: 19 November 2024 6:06 PM
To: perldl <[email protected]>; pdl-devel
<[email protected]>
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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