[SciPy-User] bug in signal.lsim2

josef.pktd at gmail.com josef.pktd at gmail.com
Sun Feb 14 21:43:22 EST 2010 

On Sun, Feb 14, 2010 at 8:02 PM, Warren Weckesser
<warren.weckesser at enthought.com> wrote:
> I added a patch to ticket #1112.  In addition to adding the suggested
> change to pass keyword args to odeint, I also added a new funciton,
> impulse2(), that computes the impulse response by using odeint.  See
> this thread for details:
>
>    http://mail.scipy.org/pipermail/scipy-user/2009-November/023416.html

Thanks, the test examples look nice and serve also as some
documentation for ltisys. The lsim2 test05 is interesting, I was
convinced last year (and there were some previous threads) that ltisys
cannot handle multi-input systems. I always got shape errors when I
tried and without documentation it's difficult to figure out what is
supposed to work and what not. (I will look at it more closely when I
have more time.)

I think the changes are reasonable including turning u and t into
keywords instead of required arguments. Maybe Ryan or someone who is
using this functions can comment on this.

Just one improvement to the tests, assert_almost_equal takes a decimal
argument. If you know the precision of your tests, then it would be
useful to increase it from the default decimal=7.

Josef


>
> Warren
>
>
> Ryan Krauss wrote:
>> Yeah, **kwds is a little harder to understand and slightly less user
>> friendly, but it is easier to maintain and less work for the patch
>> writer.  And it is more future proof if the integrator ever changes.
>>
>> On Tue, Feb 9, 2010 at 12:17 PM, Warren Weckesser
>> <warren.weckesser at enthought.com> wrote:
>>
>>> josef.pktd at gmail.com wrote:
>>>
>>>> On Wed, Feb 3, 2010 at 9:00 AM, Ryan Krauss <ryanlists at gmail.com> wrote:
>>>>
>>>>
>>>>> FYI, I am quite happy with passing in an hmax value.  I basically
>>>>> copied and pasted lsim2 from signal.ltisys and adapted it just a
>>>>> little to make it a method of my derived class.  Then I added the hmas
>>>>> kwarg that gets passed to odeint.
>>>>>
>>>>> Is there any reason not to allow the user to pass in a kwargs to lsim2
>>>>> that gets passed to odeint?
>>>>>
>>>>>
>>>> I don't see a reason why we cannot add a **kwargs, it should be
>>>> completely backwards compatible.
>>>> Can you file a ticket and add your adjusted version or a patch? And
>>>> even better, add your original example as a test case?
>>>>
>>>>
>>>>
>>> Josef,
>>>
>>> I just created ticket #1112 for this.  Unless Ryan wants to adapt his
>>> change to lsim2, I can make a patch this week to implement the enhancement.
>>>
>>> Warren
>>>
>>>
>>>
>>>> Josef
>>>>
>>>>
>>>>
>>>>
>>>>> On Fri, Jan 29, 2010 at 6:44 AM, Ryan Krauss <ryanlists at gmail.com> wrote:
>>>>>
>>>>>
>>>>>> Thanks to Warren and Josef for their time and thoughts.  I feel like I
>>>>>> now understand the underlying problem and have some good options to
>>>>>> solve my short term issues (I assigned the project last night and they
>>>>>> need to be able to start working on it immediately).  I actually use a
>>>>>> TransferFunction class that derives from ltisys.  I could override its
>>>>>> lsim2 method to try out some of these solutions quickly and fairly
>>>>>> easily.
>>>>>>
>>>>>> Ryan
>>>>>>
>>>>>> On Thu, Jan 28, 2010 at 10:00 PM,  <josef.pktd at gmail.com> wrote:
>>>>>>
>>>>>>
>>>>>>> On Thu, Jan 28, 2010 at 10:33 PM, Warren Weckesser
>>>>>>> <warren.weckesser at enthought.com> wrote:
>>>>>>>
>>>>>>>
>>>>>>>> josef.pktd at gmail.com wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>> On Thu, Jan 28, 2010 at 8:50 PM, Warren Weckesser
>>>>>>>>> <warren.weckesser at enthought.com> wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> 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.)
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> It's something what I suspected. I don't know much about odeint, but
>>>>>>>>> do you think it would be useful to let lsim2 pass through some
>>>>>>>>> parameters to odeint?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>> Sounds useful to me.  A simple implementation is an optional keyword
>>>>>>>> argument that is a dict of odeint arguments.   But this would almost
>>>>>>>> certainly break if lsim2 were ever reimplemented with a different
>>>>>>>> solver.  So perhaps it should allow a common set of ODE solver
>>>>>>>> parameters (e.g. absolute and relative error tolerances, max and min
>>>>>>>> step sizes, others?).
>>>>>>>>
>>>>>>>> Perhaps this should wait until after the ODE solver redesign that is
>>>>>>>> occasionally discussed:
>>>>>>>>    http://projects.scipy.org/scipy/wiki/OdeintRedesign
>>>>>>>> Then the solver itself could be an optional argument to lsim2.
>>>>>>>>
>>>>>>>>
>>>>>>> I was just thinking of adding to the argument list a **kwds argument
>>>>>>> that is directly passed on to whatever ODE solver is used. This should
>>>>>>> be pretty flexible for any changes and be backwards compatible.
>>>>>>>
>>>>>>> I've seen and used it in a similar way for calls to optimization
>>>>>>> routines, e.g. also optimize.curve_fit, does it. What are actually
>>>>>>> valid keywords would depend on which function is called.
>>>>>>>
>>>>>>> (But I'm not a user of lsim, I'm just stealing some ideas from lti and
>>>>>>> friends for time series analysis.)
>>>>>>>
>>>>>>> Josef
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>> Warren
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>> Josef
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> 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
>>>>>>>>>>>  ------------------------------------------------------------------------
>>>>>>>>>>>
>>>>>>>>>>> _______________________________________________
>>>>>>>>>>> SciPy-User mailing list
>>>>>>>>>>> SciPy-User at scipy.org
>>>>>>>>>>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>> from pylab import *
>>>>>>>>>> from scipy import signal
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> g = 100.0
>>>>>>>>>> p = 15.0
>>>>>>>>>> G = signal.ltisys.lti(g, [1,p,0])
>>>>>>>>>>
>>>>>>>>>> t = arange(0, 1.0, 0.002)
>>>>>>>>>> N = len(t)
>>>>>>>>>>
>>>>>>>>>> # u for the whole interval (not used in lsim2, only for plotting later).
>>>>>>>>>> amp = 50.0
>>>>>>>>>> u = zeros(N)
>>>>>>>>>> k1 = 50
>>>>>>>>>> k2 = 100
>>>>>>>>>> u[k1:k2] = amp
>>>>>>>>>>
>>>>>>>>>> # Create input functions for each smooth interval. (This could be simpler,
>>>>>>>>>> since u
>>>>>>>>>> # is constant on each interval.)
>>>>>>>>>> a = float(k1)/N
>>>>>>>>>> b = float(k2)/N
>>>>>>>>>> T1 = linspace(0, a, 201)
>>>>>>>>>> u1 = zeros_like(T1)
>>>>>>>>>> T2 = linspace(a, b, 201)
>>>>>>>>>> u2 = amp*ones_like(T2)
>>>>>>>>>> T3 = linspace(b, 1.0, 201)
>>>>>>>>>> u3 = zeros_like(T3)
>>>>>>>>>>
>>>>>>>>>> # Solve on each interval; use the final value of one solution as the
>>>>>>>>>> starting
>>>>>>>>>> # point of the next solution.
>>>>>>>>>> # (We could skip the first calculation, since we know the solution will be
>>>>>>>>>> 0.)
>>>>>>>>>> (t1, y1, x1) = signal.lsim2(G,u1,T1)
>>>>>>>>>> (t2, y2, x2) = signal.lsim2(G, u2, T2, X0=x1[-1])
>>>>>>>>>> (t3, y3, x3) = signal.lsim2(G, u3, T3, X0=x2[-1])
>>>>>>>>>>
>>>>>>>>>> figure(1)
>>>>>>>>>> clf()
>>>>>>>>>> plot(t, u, 'k', linewidth=3)
>>>>>>>>>> plot(t1, y1, 'y', linewidth=3)
>>>>>>>>>> plot(t2, y2, 'b', linewidth=3)
>>>>>>>>>> plot(t3, y3, 'g', linewidth=3)
>>>>>>>>>>
>>>>>>>>>> show()
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> SciPy-User mailing list
>>>>>>>>>> SciPy-User at scipy.org
>>>>>>>>>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> SciPy-User mailing list
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>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
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>>>>>>>> SciPy-User mailing list
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>>>>>>>>
>>>>>>>>
>>>>>>>>
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>>>>>>>
>>>>>>>
>>>>>>>
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>>>>>
>>>>>
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