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help with minimisation, from a data set

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CLARK KENDRICK GO
编辑： Matt J 2018-7-9
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.

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Alan Weiss
Alan Weiss 2018-7-6
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
  2 个评论
CLARK KENDRICK GO
CLARK KENDRICK GO 2018-7-9
I didn't know! That is a lot easier than I anticipated!
Matt J
Matt J 2018-7-9
编辑：Matt J 2018-7-9
Clark,
Since it addressed your question, you should Accept-click Alan's answer. You should do likewise in all of your open threads.

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