Re: Vectorize a function that depends on previous function value

[Kai Torben Ohlhus]

On Mon, May 19, 2014 at 1:08 PM, gergo <address@hidden> wrote:

Dear list members!

I have have a discrete time dynamical system:

function [a,b] = dynamicalSystmem(data, params)
a(n) = a(n-1) + data(n) + b(n-1) + someNonLinearFunction(a(n-1))
b(n) = b(n-1) + someOtherNonlinearFctn(a(n-1))

To fit the model to my data, I'm minimizing a simple cost function, which
requires me to iterate the dynamical system function. Currently this is done
by a simple for-loop, which makes the optimization very slow, because this
is done in every optimization step.

However I couldn't find a way to vectorize this for loop. Has anybody of you
an idea how to solve this?

Thank you very much in advance!

Gerald



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Hello Gerald,

From your code snippet I conclude, that you don't have data dependencies from the left hand side (lhs) to the rhs, like a(n) = a(n) + a(n -1), right? In your loop, your previous a(n) will be dropped and a(1) is generated by a different rule, still right? And someNonLinearFunction() is vectorized, too? In this case you should be able to do something like this:

n = 10;

a = rand (1,n);

b = rand (1,n);

data = "" (1,n);

a(2:end) = a(1:end - 1) + data(2:end) + b(1:end - 1) + sin(a(1:end - 1));

a(1) = rand;

HTH,

Kai