Splitting a matrix into addition of two same size Matrices

A 12*12 Matrix P is given to us,this matrix has each of it's element as a quadratic expression in symolic variable x3.This Matrix P needs to be made into an addition of 3 different 12*12 matrices A,B,C such that P=A*x3^2+B*x3+C

How can we find these matrices A,B,C in matlab ?

Answer 1

[KSSV]

x3 = rand(12) ; 
A = rand ; 
B = rand ; 
C = rand ; 
P = A*x3.^2+B*x3+C ; 

If A, B, C are matrices

x3 = rand(12) ; 
A = rand(12) ;
B = rand(12) ;
C = rand(12) ; 
P = A.*x3.^2+B.*x3+C ; 

[Sidharth Agarwal]

The matrix P is already defined and needs to be split with x3 as a single symbolic variable.

[KSSV]

Okay..you mean you have P, A, B, C matrices..and you want x3.?

[Sidharth Agarwal]

It is mentioned in the orginal question that I have a 12*12 P matrix which has each of it's element as a quadratic expression in symbolic variable x3.This Matrix P needs to be made into an addition of 3 different 12*12 matrices A,B,C such that P=A*x3^2+B*x3+C

How can we find these matrices A,B,C in matlab ?

Answer 2

[Walter Roberson]

parts_cell = arrayfun(@(s) coeffs(s,x3,'all'), P, 'uniform', 0);
parts_matrices = num2cell(vertcat(parts_cell{:}),1);
A = reshape(parts_matrices{1}, size(P));
B = reshape(parts_matrices{2}, size(P));
C = reshape(parts_matrices{3}, size(P));