function handle as array

Question

Wout Laeremans 2022-12-2

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https://ww2.mathworks.cn/matlabcentral/answers/1869232-function-handle-as-array

编辑： Torsten 2022-12-2

采纳的回答： Torsten

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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:

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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Answer 1

Torsten 2022-12-2

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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 2022-12-2

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 2022-12-2

编辑：Torsten 2022-12-2

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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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Answer 2

Davide Masiello 2022-12-2

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编辑：Davide Masiello 2022-12-2

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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 2022-12-2

编辑：Davide Masiello 2022-12-2

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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 2022-12-2

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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