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# vectorized operations on symbolic functions

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Hi, Can we apply vectorized operations on symbolic functions to avoid loops?

syms x1 x2 x3; % symbolic variables

y = x1^3/3 + x2^2/2 - x3; % symbolic function y

X = rand(500,3) % each row representing a combination of x1 x2 x3

I used for loop, but it is taking more time.

y_values = zeros(size(X,1))

for ii = 1:size(X,1)

y_values(ii) = subs(y, [x1, x2, x3], X(ii,:));

end

I have tried following but since there is inconsistency between sizes of old and new it don't work for me.

y_values = subs(y, [x1, x2, x3], X); % Evaluate the function for all combinations in matrix X

Thanks

##### 0 Comments

### Accepted Answer

Hassaan
on 19 Feb 2024

Edited: Hassaan
on 19 Feb 2024

syms x1 x2 x3; % symbolic variables

y = x1^3/3 + x2^2/2 - x3; % symbolic function y

% Generate a random matrix X with 500 rows and 3 columns

X = rand(500, 3); % each row representing a combination of x1 x2 x3

% Evaluate the symbolic function y for each row in X

% Convert the matrix X to a cell array where each row is a separate cell

X_cell = num2cell(X, 2);

% Use cellfun to apply the subs function to each cell (row) of X_cell

y_values = cellfun(@(row) subs(y, [x1, x2, x3], row), X_cell);

% Convert y_values to a double array if needed

y_values = double(y_values);

disp(y_values(1:10))

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##### 2 Comments

Dyuman Joshi
on 21 Apr 2024 at 5:58

Note that using num2cell and subsequently cellfun is not efficient.

### More Answers (5)

Dyuman Joshi
on 19 Feb 2024

Better to use a function handle -

x = rand(500,3);

y = @(x) x(:,1).^3/3 + x(:,2).^2/2 - x(:,3);

out1 = y(x)

For more information, refer to these documentation pages -

##### 2 Comments

Christine Tobler
on 19 Feb 2024

Your best approach then might be to make your input variables have the individual pages already as a third dimension:

x = randn(3, 1, 500);

y = randn(1, 6, 500);

z = x.*y;

size(z)

The formula here is of course completely made up, it would depend on what your formula for this 3x6 matrix is.

Aquatris
on 19 Feb 2024

Edited: Aquatris
on 19 Feb 2024

Yet another method, you can define your symbolic parameter as a matrix symbolic

n = 500;

X = sym('X', [500 3]);

% I assume here you want a element wise power ('.^') instead of matrix power

y = X(:,1).^3/3 + X(:,2).^2/2 - X(:,3); % symbolic function y

X_val = rand(500,3); % each row representing a combination of x1 x2 x3

y_values = double(subs(y, X, X_val)) % Evaluate the function for all combinations in matrix X

size(y_values)

##### 0 Comments

Walter Roberson
on 19 Feb 2024

syms x1 x2 x3; % symbolic variables

y = x1^3/3 + x2^2/2 - x3; % symbolic function y

X = rand(500,3); % each row representing a combination of x1 x2 x3

y_values = double(subs(y, {x1, x2, x3}, {X(:,1), X(:,2), X(:,3)}));

y_values(1:5)

##### 0 Comments

Torsten
on 21 Apr 2024 at 11:48

Edited: Torsten
on 21 Apr 2024 at 11:51

rng("default")

syms x1 x2 x3; % symbolic variables

y = x1^3/3 + x2^2/2 - x3; % symbolic function y

X = rand(500,3) % each row representing a combination of x1 x2 x3

y_values = arrayfun(@(i)double(subs(y,[x1,x2,x3],[X(i,1),X(i,2),X(i,3)])),1:size(X,1))

##### 0 Comments

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