How can I define a function handle with 50 very similar functions?

Hello!

I am trying to solve a DDE with ODE45, by rewriting it as a coupled system of ODEs, to do that I need a function handle with i=1...N functions like this f=@u[u(1)-u(2);u(2)-u(3)....;u(N-1)-u(N)] (there are some extra rows in it but those are irrelevant right now).

Is there a way to do this with a foor loop?

Answer 1

[Steven Lord]

You can't use a for loop in an anonymous function, but the good news is you don't need to. The diff function returns the difference between each element and its predecessor; to get the difference between each element and its successor just multiply by -1.

f = @(x) -diff(x)

f = function_handle with value:
    @(x)-diff(x)

x = 1:10;
y = x.^2

y = 1×10

1 4 9 16 25 36 49 64 81 100

differences = f(y)

differences = 1×9

-3 -5 -7 -9 -11 -13 -15 -17 -19

We can spot check by looking at the results for the fifth element:

[y(5)-y(6); differences(5)]

ans = 2×1

-11 -11

Note that differences is one element shorter than y so you'll likely need to add an element at the start or at the end of differences.

g = @(x) [NaN, f(x)]

g = function_handle with value:
    @(x)[NaN,f(x)]

[y; g(y)]

ans = 2×10

1 4 9 16 25 36 49 64 81 100 NaN -3 -5 -7 -9 -11 -13 -15 -17 -19