laplace transformation for array

hello every one

I try to do laplace transformation for this array

M = [exp(x) 1; sin(y) i*z];

i do "laplace(M)" but the answer is not correct

I read the help

"syms a b c d w x y z

M = [exp(x) 1; sin(y) i*z];

vars = [w x; y z];

transVars = [a b; c d];

laplace(M,vars,transVars)" but I get error

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??? Error using ==> sym.maple at 87

Error, (in laplace) invalid input: laplace expects its 2nd argument, t, to be of type name, but

received array(1 .. 2, 1 .. 2,[(1, 1)=w,(2, 1)=y,(1, 2)=x,(2, 2)=z])

Error in ==> sym.laplace at 79

L = maple('map','laplace',F,t,s);

Error in ==> laplace at 5

laplace(M,vars,transVars)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

please help me

Answer 1

[Dev]

Hi @mouh nyquist,

To perform the Laplace transformation for the array M = [exp(x) 1; sin(y) i*z], we first need to define symbolic variables to represent mathematical symbols rather than specific numerical values. This step is essential to perform transformations like the Laplace. To do so, we can use the ‘Symbolic Math Toolbox’ provided in MATLAB to create symbolic variables using the ‘syms’ function and then define the required matrix. Both the steps are represented in the code snippet below-

% Define symbolic variables
syms x y z s

% Define the matrix
M = [exp(x), 1; sin(y), 1i*z];

Next, we can use the ‘arrayfun’ function in MATLAB to perform the Laplace transformation on each element of the matrix M. To do so, we can use the ‘laplace’ function in the Symbolic Math Toolbox. I have added an example code snippet below which does the same.

% Perform Laplace transform on each element of the matrix
L = arrayfun(@(element) laplace(element, s), M);

Finally, we can display ‘L’ which prints the Laplace transformation performed on M. I have also attached the output for your reference below.

For more information regarding the functions used above, kindly refer to the documentation links below-

Symbolic Math Toolbox- https://www.mathworks.com/products/symbolic.html

syms- https://www.mathworks.com/help/releases/R2024b/symbolic/syms.html

arrayfun- https://www.mathworks.com/help/releases/R2024b/matlab/ref/arrayfun.html

laplace- https://www.mathworks.com/help/releases/R2024b/symbolic/sym.laplace.html

I hope the above explanation resolves the question.