# function handle as array

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Wout Laeremans on 2 Dec 2022
Edited: Torsten on 2 Dec 2022
I define a function handle as
P = @(t) mtimes(expm(t.*M),P_initial);
Where P_initial is a 4x1 array and M a 4x4 matrix. This works fine, but now I have a function with for every t a 4x1 answer, for example at t = 0 I get:
P(0)
ans =
0.0000
0.0000
0.0011
0.9988
What I want is to get this first element as a separate function of time, so I want a P_1(t) as a function handle, but I do not know how to do so.
Thanks already! :)
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### Accepted Answer

Torsten on 2 Dec 2022
M = rand(4,4);
P_initial = rand(4,1);
P = @(t) mtimes(expm(t.*M),P_initial);
P(0)
g = @(a,x)a(x);
g(P(0),1)
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Wout Laeremans on 2 Dec 2022
Hi Torsten, this comes close to what I want thank you! Do you also know how I can plot g(P(t),1) for a general t?
Torsten on 2 Dec 2022
Edited: Torsten on 2 Dec 2022
M = rand(4,4);
P_initial = rand(4,1);
P = @(t) mtimes(expm(t.*M),P_initial);
g = @(a,x)a(x);
t = 0:0.01:1;
plot(t,arrayfun(@(t)g(P(t),1),t))

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### More Answers (1)

Davide Masiello on 2 Dec 2022
Edited: Davide Masiello on 2 Dec 2022
That's because mtimes(a,b) = a*b, and if a is 4x4 and b is 4x1 than the operation yields a 4x1 array.
I think what you might want to do is
P = @(t) expm(t.*M).*P_initial;
Which will yield a 4x4 matrix where each column is .
But I am not completely sure I interpreted this correctly.
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Davide Masiello on 2 Dec 2022
Edited: Davide Masiello on 2 Dec 2022
you can define a cell array of functions
M = rand(4,4);
P_initial = rand(1,4);
for i = 1:length(M)
P{i} = @(t)mtimes(expm(t.*M),P_initial);
end
P
P = 1×4 cell array
{@(t)mtimes(expm(t.*M),P_initial)} {@(t)mtimes(expm(t.*M),P_initial)} {@(t)mtimes(expm(t.*M),P_initial)} {@(t)mtimes(expm(t.*M),P_initial)}
With your formulation, however, they are all the same.
Are you sure you must use expm and mtimes?
I think the problem might be ill-posed in that aspect.
Wout Laeremans on 2 Dec 2022
Yes, I want the solution of:
The general solution is given by:
Where I call P = [P_O; P_3; P_2; P_1] and M the transition matrix. I know I can also solve this using an ode solver or just define a time array with a small time increment. However I really want P_O(t) as a function handle.

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