Re: Affine transformation


Arno wrote:
> Randy Poe wrote:
> > Either nonlinear least squares or constrained linear least
> > squares is going to require a different algorithm than the
> > one you've been using.
> >
>
> Hi Randy,
>
> thanx for your help !
> I already thought about constrain the linear least square, but I don't
> know how to tell matlab what I want ... I don't know if you are familiar
> with matlab, but it would be great if you could tell me how I can do this !

LSQLIN: Constrained linear least squares.

Unfortunately, a^2 + b^2 = 1 is a quadratic constraint, and
LSQLIN only handles linear constraints.

LSQNONLIN: Nonlinear least squares.

This function is for unconstrained nonlinear least squares,
so you could fit the first form I gave, where the rotation
is given explicitly in terms of sin(theta) and cos(theta)
and the free parameter is theta.

FMINCON: The granddaddy of nonlinear minimization
functions, which handles arbitrary objective functions with
linear and nonlinear constraints. You could use this with
either model. Your objective function that you're minimizing
is the total square error.

I think you'll find LSQNONLIN easiest to adapt.

- Randy

.

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