[SciPy-User] bug in signal.lsim2

[Warren Weckesser]

Ryan,

The problem is that the ODE solver used by lsim2 is too good. :)

It uses scipy.integrate.odeint, which in turn uses the Fortran library 
LSODA.  Like any good solver, LSODA is an adaptive solver--it adjusts 
its step size to be as large as possible while keeping estimates of the 
error bounded.  For the problem you are solving, with initial condition 
0, the exact solution is initially exactly 0.  This is such a nice 
smooth solution that the solver's step size quickly grows--so big, in 
fact, that it skips right over your pulse and never sees it.

So how does it create all those intermediate points at the requested 
time values?  It uses interpolation between the steps that it computed 
to create the solution values at the times that you requested.  So using 
a finer grid of time values won't help.  (If lsim2 gave you a hook into 
the parameters passed to odeint, you could set odeint's 'hmax' to a 
value smaller than your pulse width, which would force the solver to see 
the pulse.  But there is no way to set that parameter from lsim2.)

The basic problem is you are passing in a discontinuous function to a 
solver that expects a smooth function.  A better way to solve this 
problem is to explicitly account for the discontinuity. One possibility 
is the attached script.

This is an excellent "learning opportunity" for your students on the 
hazards of numerical computing!

Warren


Ryan Krauss wrote:
> I believe I have discovered a bug in signal.lsim2.  I believe the
> short attached script illustrates the problem.  I was trying to
> predict the response of a transfer function with a pure integrator:
>
>              g
> G = -------------
>          s(s+p)
>
> to a finite width pulse.  lsim2 seems to handle the step response just
> fine, but says that the pulse response is exactly 0.0 for the entire
> time of the simulation.  Obviously, this isn't the right answer.
>
> I am running scipy 0.7.0 and numpy 1.2.1 on Ubuntu 9.04, but I also
> have the same problem on Windows running 0.7.1 and 1.4.0.
>
> Thanks,
>
> Ryan
>   
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