On 18 November 2014 21:22, Ondřej Čertík <ondrej.cer...@gmail.com> wrote:
> On Tue, Nov 18, 2014 at 6:51 PM, Bill Page <bill.p...@newsynthesis.org>
wrote:
>> On 18 November 2014 17:40, Ondřej Čertík <ondrej.cer...@gmail.com> wrote:
>>>
>>> In my notation, the Wirtinger derivative is d f(z) / d z and d f(z) /
>>> d conjugate(z). The Df(z) / Dz is the complex derivative taking in
>>> direction theta (where it could be theta=0). Given the chain rule, as
>>> I derived above using chain rules for the Wirtinger derivative:
>>>
>>> D f(g) / D z = df/dg Dg/Dz + df/d conjugate(g) D conjugate(g) / Dz
>>>
>>>
>>> abs(f).diff(z) = (conjugate(f)*f.diff(z) + f*conjugate(f).diff(z)) /
(2*abs(f))
>>>
>>
>>>
>>> Let me know if you found any issue with this.
>>>
I implemented this in FriCAS and tried a few examples, e.g.
(4) -> D(abs(f(z,conjugate(z))),z)
_ _ _ _
f(z,z)f (z,z) + f(z,z)f (z,z)
,2 ,1
(4) -------------------------------
_
2abs(f(z,z))
Type:
Expression(Integer)
where the ,1 and ,2 notation represents the derivative with respect the the
first and second variable of f, respectively.
Then I noticed that if we have f=z we get
conjugate(z).diff(z)
which is 0. So the 2nd term is 0 and the result is just the first
Wirtinger derivative.
Perhaps I am misinterpreting something?
Bill.
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
