I wrote a multidimensional polyval function, a bit different from the original polyval. May it assist the users:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [a,ErrV]=polyvalN(MatIn,TargetIn)
[n,m]=size(MatIn);
MatOut=sum(pagemtimes(reshape(MatIn',m,1,n),reshape(MatIn',1,m,n)),3);
TargetOut=sum(MatIn.*TargetIn)';
a=MatOut\TargetOut;
ErrV=MatIn*a-TargetIn;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
This function takes in a matrix MatIn which already includes the approximated structure for a linear approximated function (polynom) which the coefficient (a) of the approximated function needs to be found according to the target values TargetIn
for example:
------------
We have 8 points on a box
X=[-1;1;-1;1;-1;1;-1;1];
Y=[-1;-1;1;1;-1;-1;1;1]*2;
Z=[-1;-1;-1;-1;1;1;1;1]*0.5;
The approximated function which we intend to find the coefficients for is:
MatIn=[ones(8,1), X , Y , Z , X.*Y , X.*Z , Y.*Z ];
The value in each point is given. We can use rand or any known values in each point. Just in order to check the function polyvalN, we'll use known a's
intentionally:
TargetIn= 7 + 6*X + 5*Y + 4*Z + 3*X.*Y + 2*X.*Z + 1*Y.*Z;
Now, is we pose MatIn,TargetIn to polyvalN , we expect to get a's
[7;6;5;...1]
-------------
Notes:1. MatIn should be nXm wherein n>=m
TargetIn should be nx1
2. The point represented by X,Y,Z are not necessarily be in a box
structure as in the example. Actually, they can also represent any
single-dimension/multidimensional location, as long as note 1 is kept, and that MatIn includes
the vectors in the approximation.
