Evaluating symbolic matrix equations

I have a symbolic matrix of size 20x3, which I have created using the sym() function. I have another matrix B which is calculated using certain rows of A, or in general the matrix B is a function of A i.e., . Once I obtain all the numerical entries of A, how can I evaluate B after substituting A with the obtained numerical values?

A = sym('a', [20, 3]);  % Create a 20x3 symbolic matrix

% Create a matrix B whose values depend on some function of A's elements
B(1, :) = cross(A(1, :), A(3, :));
B(2, :) = A(5, :) .* A(10, :) .* A(20, :);

% Substitute A with numerical values
A = subs(A, A, rand(20, 3));    % Now, A is a 20x3 matrix with random entries

% How do I evaluate the matrix B?
subs(B) ?
subs(B, A) ? % Both commands aren't working

Answer 1

[Nishanth Rao]

After some hit and trials, I found the solution:

A = sym('a', [20, 3]);  % Create a 20x3 symbolic matrix

% Create a matrix B whose values depend on some function of A's elements
B(1, :) = cross(A(1, :), A(3, :));
B(2, :) = A(5, :) .* A(10, :) .* A(20, :);

% Substitute B with A, where A is substitued with 20x3 numerical entries:
B = subs(B, A, rand(20, 3));

[Nishanth Rao]

You can use eval(B) later to simplify the entries of B

[Walter Roberson]

eval() of a symbolic expression can give you error messages or can give you unexpected results. eval() of a symbolic expression is the same as eval(char()) of the expression, but char() of a symbolic expression is in a language that is not MATLAB and is not the internal symbolic language, MuPAD.

You can simplify() or vpa() (or sometimes, double()) symbolic expressions, but eval() is risky.

[Nishanth Rao]

Oh.. I see. Thanks a lot for the information.

[zym]

Thanks for this! I was just wondering if you happen to know why subs does not work with multiple matrices? It seems I need to use subs twice to evaluate the expression

clear;
A = sym('a', [2, 2]);
B = sym('b', [2, 2]);
C=A*B;

%this does not works
subs(C, {A, B}, {rand(2, 2), rand(2, 2)})

%this works
Ceval1 = subs(C, A, rand(2, 2))
Ceval3 = subs(Ceval1, B, rand(2, 2))

[Torsten]

Works.

A = sym('a', [2, 2]);
B = sym('b', [2, 2]);
C=A*B;
%this does not works
subs(C, [A, B], [rand(2, 2), rand(2, 2)])

ans = 

[Walter Roberson]

It is a syntax restriction. When you use the {} form of subs(), the second parameter must be a cell array in which each entry is a scalar symbolic variable, and the third parameter must be a cell array the same size as the second parameter

A = sym('a', [2, 2]);
B = sym('b', [2, 2]);
C=A*B;

Anum = rand(2,2);
Bnum = rand(2,2);

Ac = num2cell(A);
Bc = num2cell(B);
Anc = num2cell(Anum);
Bnc = num2cell(Bnum);

subs(C, [Ac, Bc], [Anc, Bnc])

ans = 

note here that [Ac, Bc] is a cell array, and [Anc, Bnc] is a cell array the same size

[zym]

Thank you for the clarification. This is very useful

Answer 2

[KSSV]

Read about double.

A = subs(A, A, rand(20, 3));
A = double(A) ; 

[Nishanth Rao]

Please go through the question, I am asking how to evaluate matrix B, and not A

[KSSV]

subs(B) what you want to substitute here? In the above line you have substituted in A. Also the dimensions of A and B are different. How you want to substitute?

[Nishanth Rao]

Please look at the accepted answer. I am sorry if the question isn't clear. For your convenience, I'll explain it here.

I have a symbolic matrix A. Now the matrix B (may have different size than A), is some function of the matrix A. Or to be even clearer, the matrix B depends on some of the elements of A. In general, I can write it mathematically as . Now, lets say from say sensor measurements (for eg.,), I will get all the numerical entries of A. How do I calculate the matrix B?