Substitute multiple elements of multiple arrays with vectors

Hello. From solving the following matrix equation (with matrices of arbitrary size NxN) I obtain the solution to my problem functions cepsepssym:

syms cepsepssym [nvars nvars]

syms cBeps [nvars nvars]

syms cepsB [nvars nvars]

syms Bautocorr

equations = -cepsepssym*transpose(matrizGamma)-matrizGamma*cepsepssym+cepsB+cBeps+diag(vecsigmas)*Bautocorr==0;

sol=solve(equations,cepsepssym);

solvec=reshape(transpose(sol),1,[]);

But now I want to substitute each of the other variables (i.e., each element of the matrixes cBeps and cepsB, and Bautocorr) by a vector (given by known time dependent functions). Is there an easy way to do that?

Thank you very much in advance

Answer 1

[Varun]

Hello!

You can use the “subs” function in MATLAB to substitute each of the variables by a vector. For example, for a simple matrix product equation, we have

syms X Y [2 2] matrix
sM = X*Y

sM = 

S = subs(sM,{X,Y},{[0 sqrt(sym(2)); sqrt(sym(2)) 0], [1 -1; -2 1]})

S = 

Ssym = symmatrix2sym(S)

Ssym = 

You may refer to this documentation for more information:

“subs”: https://www.mathworks.com/help/symbolic/subs.html#mw_12726007-2cf5-4537-a248-7230abd1174f

[RODRIGO CRESPO MIGUEL]

The problem is that I want to substitute entire time dependant vectors in each element of the matrix.

For example, let A be a 2x2 matrix. I want each of those four elements substituted by a different (let's say 1:100) vector. Can I do that with subs?

[Dyuman Joshi]

You can do that, but note that you won't obtain every unique combination in output, just one-to-one combination.

syms x y z q
A = [sin(x) cos(y); exp(z) q]

A = 

subs(A,{x,y,z,q},{1:10,1:10,1:10,1:10})

ans =