Re: simulating dynamical systems with arbitrary external inputs using lsode

[Scott Kuntze]

John W. Eaton wrote:
> What do you mean by "exact input"?  You have data at points.  You need
> to be able to get values at any time T.  What sort of approximation do
> you want for the times in between the data points?  Zero order hold? 
> Linear interpolation?  Polynomial fit?  It's up to you.  I don't think
> it's exceptionally hard to write code for any of these.
>   

By "exact input" I mean the set of data points collected at a known 
sampling frequency.

> Would it have helped if I had written something like
>
>   function retval = u (t)
>     ## This is a zero-order hold function.  TVALS are the switching
>     ## times, UVALS are the values of U up until the corresponing
>     ## element of tval.
>     tvals = [5, 10, 15, Inf];
>     uvals = [1, -1, 1, 0];
>     idx = find (t < tvals, 1, "first");
>     retval = uvals (idx);
>   endfunction
>
> instead of using if/elseif/else/endif?
>   

I understand what this function does, but lsode doesn't like something 
about it... I believe that 'find' is causing troubles, otherwise I would 
have used the solution I suggested in my first posting i.e.

function retval = u(t)
   tvals = some array
   uvals = some array
   idx = find(t == tvals)
   retval = uvals(idx)
endfunction

I'm not sure we're seeing eye-to-eye here -- let me try another 
example...  If my waveform consisted of a sinusoid, I could write

function retval = u(t)
   retval = sin(w*t)
endfunction

and I could call u(t) directly from the function I'm integrating with lsode.

However, the waveform is arbitrary and comes from a datafile, captured 
with a known sampling frequency...

I'd like to set t equal to the set of times at which the waveform was 
captured, and pump the waveform into the function integrated by lsode.  
There is no interpolation necessary if t corresponds to the times at 
which 'waveform' was captured.

The waveform might contain many thousands of samples and be entirely 
arbitrary.

In essence, I want

function retval = u(t)
   retval = waveform(index of t)
endfunction

Again, 'find' is problematic here (or at least it appears to be).

Is that more clear?