Hi Ed, Luis and Boyd,
thanks for the replies, I haven't had the time to look into the proposed
solution yet. The problem behind this is to separate the shear component
(curl) from the compressional (div) component of sound waves travelling
through a liquid/solid medium, i.e. tissue.
Ingo
On 20.11.24 6:22 PM, Boyd Duffee wrote:
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 |mv|ing, 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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