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From Christoph Höger <christoph.hoe...@tu-berlin.de>
Subject Re: [math] Total derivative of a MultivariateVectorFunction
Date Thu, 23 May 2013 08:39:08 GMT
```Am 22.05.2013 22:50, schrieb Luc Maisonobe:

> I am not sure I understood your use case properly. I'll look at it further in the next
few days.
>
> A first very quick answer is that the interface as it is defined does not seem to correspond
> In the current interface, the meaning of the two "value" method is the same. So the various
elements in
> The point array should be the same. In your case, I think you already use the array to
represent derivatives
> of the first element, so I think you expanded the content of what should be a single
DerivativeStructure instance as a double array.
>
> Are you sure you should not use a univariate function ? The DerivativeStructure argument
you would get
> would contain all the partial derivatives already.
>
> Once again, I'm not sure I understood your example properly as I did not find the time
to think about it for now.
>
> Best regards,
> Luc

Hi Luc,

I am trying to motivate the problem:

Consider the simple pendulum equation

x² + y² - L² = 0

I could use DerivativeStructure to solve for that equation by using e.g.
NewtonRaphson.

But in a model, x and y are actually depending on the free variable t,
so I may require the total derivative of the above equation, e.g.:

2*x*dx + 2*y*dy = 0

Again, I want to be able to solve for that equation by using an
iterative method. The thing is: This total derivative has now more
parameters than the original equation (namely dx and dy).

If I model it that way, I can pass the x and y parameters to the base
function, evaluate the partial derivatives (2x and 2y) and multiply them
with the total derivatives dx and dy. The problem here is that the
base-equations partial derivatives are not constant (the second order
partial derivatives are, though). So I somehow need to reflect that for
the numerical solver. That's why I thought, I should make the derivative
also a MultivariateDifferentialFunction.

--
Christoph Höger

Technische Universität Berlin
Fakultät IV - Elektrotechnik und Informatik
Übersetzerbau und Programmiersprachen

Sekr. TEL12-2, Ernst-Reuter-Platz 7, 10587 Berlin

Tel.: +49 (30) 314-24890
E-Mail: christoph.hoeger@tu-berlin.de

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