Thread Subject: polyfit in 3D

I'm looking for a function that finds the coefficients of a
polynomial of degree n that fits the data of a three
dimensional set of variables. I have X, Y and Z vectors and
I want to fit a plan (not a curve)on XY plan ?

How can I proceed ?


Thx

Nicolas Guillemette

"Nicolas Guillemette" <nico_guillemette@hotmail.com> wrote
in message <fvl1q3$8sv$1@fred.mathworks.com>...
>
> I'm looking for a function that finds the coefficients of a
> polynomial of degree n that fits the data of a three
> dimensional set of variables. I have X, Y and Z vectors and
> I want to fit a plan (not a curve)on XY plan ?
>
> How can I proceed ?
>

[X(:) Y(:) ones(numel(z),1)] \ Z(:)

provides you (a,b,c) of the fitted plane z=ax+by+c

Bruno

Sorry for the typo (uppercase z)
>
>
> [X(:) Y(:) ones(numel(Z),1)] \ Z(:)
>
>

Here's an example. Also: help inline, help fminsearch, ecc....
Regards

Ale



% make some data

p=randn(1,6);

[x,y]=ndgrid([0:.1:1],[0:.1:1]);

z=polyval(p(1:3),x)+polyval(p(4:6),y)+.1*randn(size(x));

plot3(x(:),y(:),z(:),'+')


hold on

disp(p)

clear('p')



%fit

fun='polyval(p(1:3),x)+polyval(p(4:6),y)';

chi=inline(['sum((' fun '-z).^2)'],'p','x','y','z');

h=@(p)chi(p,x(:),y(:),z(:));


options =
optimset('display','on','MaxIter',1d4,'TolFun',1d-49,'TolX',1d-49,'maxfuneval',1d4);

p=fminsearch(h,randn(1,6),options);


zf=feval(inline(fun,'p','x','y'),p,x,y);

surf(x,y,zf)

disp(p)


--
Alessandro Mura
Istituto Nazionale di Astrofisica - IFSI
http://pptt4.ifsi-roma.inaf.it/~mura/index.html
http://www.alessandromura.it

"Nicolas Guillemette" <nico_guillemette@hotmail.com> wrote in message
<fvl1q3$8sv$1@fred.mathworks.com>...
>
> I'm looking for a function that finds the coefficients of a
> polynomial of degree n that fits the data of a three
> dimensional set of variables. I have X, Y and Z vectors and
> I want to fit a plan (not a curve)on XY plan ?
>
> How can I proceed ?
> Thx
> Nicolas Guillemette
------------
  It isn't clear what you are asking, Nicolas. It doesn't require a polynomial of
degree higher than 1 to define a plane, which is what you seem to be asking
for. With only degree 2 in x, y, and z, you would be in the realm of ellipsoids,
hyperboloids, paraboloids, and the like.

  Also you haven't told us what you regard as your criterion for best fit here.
In the case of a plane you might want to minimize the mean square deviation
of the points' z coordinates from that of the plane, or you might want to
minimize their mean square orthogonal distances from the plane. Matlab
provides methods for solving either kind of problem. Similar questions apply
to higher degree polynomial surfaces.

Roger Stafford