Evaluating symbolic matrix equations

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Nishanth Rao 2021-7-10

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评论： zym 2022-7-27

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

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Answer 1

Nishanth Rao 2021-7-10

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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));

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Walter Roberson 2022-7-23

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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 2022-7-27

Thank you for the clarification. This is very useful

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Answer 2

KSSV 2021-7-10

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Read about double.

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

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KSSV 2021-7-10

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 2021-7-10

编辑：Nishanth Rao 2021-7-10

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?

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