design the function function out = x_m(x,m) with input data matrix x of size 𝑁 × 𝑑 in matlab

To design the function out = x_m(x,m), which takes an input data matrix x of size N x d and returns the mth column of x, we can use the following code:

main.m
function out = x_m(x,m)
% This function returns the mth column of matrix x

out = x(:,m);

end
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Here, we define a function x_m that takes two parameters - the matrix x and the integer m. The function then returns the mth column of matrix x using the : operator which selects all rows and the mth column index.

To use the function, simply call it with an input matrix x and the desired column m. For example,

main.m
x = [1 2 3; 4 5 6; 7 8 9];
out = x_m(x, 2);
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This would return the second column of matrix x which is [2; 5; 8].