RE : Solving equation containing sum over list of vectors

Hi,

I thing you have to declare sum to be linear with: declare(sum, linear)
And maybe set simpsum to true.

Regards.


> -----Message d'origine-----
> De?: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] De la part de
> Matthias Bindernagel
> Envoy??: mardi 23 ao?t 2011 15:00
> ??: maxima at math.utexas.edu
> Objet?: [Maxima] Solving equation containing sum over list of vectors
> 
> Hi,
> 
> I'm trying to investigate a problem containing the root mean square
> distance of a set of vectors to a set of transformed vectors. The
> transformation is parameterized by some scalar values.
> 
> Now I want to minimize the rms distance under variation of the
> transformation parameters by finding the roots of the derivative.
> This is where I am stuck right now.
> 
> I tried this approach:
> 
> v: matrix([vx[i]], [vy[i]], [vz[i]], [1]);
> u: matrix([ux[i]], [uy[i]], [uz[i]], [1]);
> 
> Rot: matrix(
>    [cos(phi),-sin(phi), 0, 0],
>    [sin(phi), cos(phi), 0, 0],
>    [       0,        0, 1, 0],
>    [       0,        0, 0, 1]);
> 
> Transl: matrix(
>    [1, 0, 0, l*tx],
>    [0, 1, 0, l*ty],
>    [0, 0, 1, 0],
>    [0, 0, 0, 1]);
> 
> Center: matrix(
>    [1, 0, 0, cx],
>    [0, 1, 0, cy],
>    [0, 0, 1, 0],
>    [0, 0, 0, 1]);
> 
> T: invert(Center) . Rot . Center . Transl;
> 
> d_rms(phi,l):=
>    sum(
>      transpose(T . v - u) . (T . v - u) * w[i],
>      i,1,n);
> 
> d_rms_l: diff(d_rms(phi,l), l);
> 
> solve(d_rms_l = 0, l);
> 
> The above code does not actually solve for l, which is what I want. And
> which I could perform by hand. (Note: for the last statement we can
> assume everything as constant except for l.)
> 
> It may be related to the vector lists v and u and the scalar weight list
> w - I don't know how to declare them as list of vectors and scalars (I
> actually tried declare(v, nonscalar) etc., but it didn't work out).
> 
> I would appreciate any help.
> Regards,
> Matze
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