help with minimisation, from a data set

I have a data set of the positions (in x,y coordinates) of n particles per time step. I will call this matrix P which has dimensions n by 2 by t.

I also have a linear combination of 8 forces (each in two dimensions) of n particles per time step. So the forces F would have dimensions n by 16 by t. (It is 16 because there are 8 forces and two dimensions each.) We can get data from here.

Since this is a linear combination, I have a set of 8 constants, C, one for each force.

My question is, so we have the equation P = FC, and I want to find C so that P-FC is minimised. I do not know how to perform this given all these matrix dimensions.

Answer 1

[Alan Weiss]

If you are using matrix multiplication (and it seems to me that you are), you have the equation

F*C = P

and you are trying to solve for C, in the least-squares sense. The MATLAB command for this is

C = F\P

See the documentation on solving linear systems of equations.

Alan Weiss

MATLAB mathematical toolbox documentation

[CLARK KENDRICK GO]

I didn't know! That is a lot easier than I anticipated!

[Matt J]

Clark,

Since it addressed your question, you should Accept-click Alan's answer. You should do likewise in all of your open threads.