Re: Matching Equation to Data

[Juan Pablo Carbajal]

On Fri, Mar 15, 2013 at 3:34 AM, Thomas D. Dean <address@hidden> wrote:
> I have a problem with matching an equation to data.
>
> I have JPL's de405 and created an oct file to interface to it.  I can
> extract data from de405 and with scatter3(), the plot looks exactly like
> what you would expect.  The orbit of Earth, or any other selected body.  The
> source for the oct file is available if anyone is interested.
>
> I calculated the angle to the ecliptic and got 23.457 degrees, exactly what
> it should be.
>
> I have an array with 1000 data points, D=[et,x,y,z,dx,dy,dz];  I want to get
> an equation for the plane that contains the earth's orbit.
>   a*x + b*y + c*z + d = 0
> so the vector x=[a, b, c, d] and,
>   [D(:,2:4),ones(size(D,1),1)]*x'
> is near zero for all values in D(:,2:4).
>
> I tried looking at optim but, cannot get my head produce the correct
> arguments to the functions.
>
> How do I do this?
>
> Tom Dean
> _______________________________________________
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> address@hidden
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Hi Tom,

Almost all optimizers required code that looks more or less like this:
Assume "data" has your (x,y,z,1) points, one **column** per point.
Assume p is the vector of parameters to find, is given as a 1x4 row vector.
The following function gives the total square error:

function rhs = myfunc (p, data)
  rhs = sum((p*data).^2);
endfunction

When you call the optimizer you create a handle to that function and
pass the data at construction time (you can also use global variables
or even persistent variables with a load command)

errfun = @(p) myfun(p,mydata)

You will have to provide a firts guess p0 and call the optimizer of
your choice like

p = optimizer (errfun, p0)

Now, since you are doing linear regression on the data I would
recommend to look at functions regress and regress_gp in the
statistics package.

Hope this helps.

JPi