Re: Matching Equation to Data

[Thomas D. Dean]

On 03/15/13 04:25, Juan Pablo Carbajal wrote:

> 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.

I have been looking at this wrong.  I want to fit an equation to data.

Equation of plane:  a*x + b*y + c*z + d = 0

data:  n rows of [et, x, y, z]
       x, y, and, z depend on et

       Y = data(:,2:3) <== fit a*x + b*y + c*z + d = 0 to these points
       X = data(:,1) <== not applicable to my situation

Criteria: the distance from each point of data to the plane is minimal.
  dist = ptopl(Y,guess), where Y is nx4 and guess is 1x4

I want a least squares fit, so

function [y]=ptopl_sq(x,p)
  abc=p(1:3);  ## check shape
  if (size(abc) == [3,1])
    abc=abc';
  endif;
  y=sum(((x*p').^2)/(abc*abc'));
endfunction;

Y=[A(:,2:4),ones(size(A,1),1)];

and Y*[a,b,c,d]' == 0 if I have an exact fit

I tried
Y=[A(:,2:4),ones(size(A,1),1)];
x=1:size(Y,1);
init=[1,1,1];
p=fmins('ptopl_sq',init, [], [], Y, init);
and, Y*p' has values on the order of mean(Y)!

Tom Dean