Dear all,
I am trying to continue a NS point. However I repeatedly receive get the error message below. I tried to recompute the NS point wherefrom I would like to start my continuation with more accuracy, setting smaller MinStepSize/MaxStepSize/StepSize, but this unfortunately did not help.
Hi, Maurizio. First of all, PyCont can't continue NS points yet for limit cycle curves, although it CAN continue NS points for maps. Are you doing this for a map?
In general, however, when initdirec is not specified, PyCont attempts to find a tangent vector to the curve (this is the portion of the code that is throwing the exception). Sometimes this can fail, in particular since the routine that it uses has an initial guess that is the unit vector along the first coordinate. This particular choice might lead to a singular matrix (which is what is happening here).
If you are indeed trying to continue an NS curve for maps, you might try specifying an initial direction and see what happens. You don't have to pick the actual tangent vector to the curve, just an initial guess should suffice. That would be the first thing I would try. Let me know how that goes and we'll go from there.
Drew
Last edit: Drew LaMar 2014-08-23
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Hi Drew,
thanks for the clarification.
Yet indeed, I missed the part that NS-C could only be started from maps and not from LC-C since this latter is my case.
Sorry about it.
M
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Hi Drew,
I assume that the FP-C also works only on maps so far, am I correct on this?
I mean, I have some PDs on my continued curve in a continuous system, that in (XPP)AUTO I could attempt to further continue by "Run>Doubling". In PyCont the only curve type that could fit these criteria would be FP-C but unfortunately I get the same error I was obtaining for NS-C.
So, I am only able to see where my original limit cycle looses or gain stability by the PD bifurcation, but I cannot have any information on the actual envelopes (max-mins) of the period-2 orbits. Is there any chance that this possibility could be implemented soon in PyCont? It would be extremely useful.
M
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Hi, Maurizio. Let me look into the PD issue. It sounds like you want to simply double the period and continue the resulting limit cycle? This should still be a LC-C and shouldn't require implementing anything new. I don't think it is currently implemented, however, as branch points have been hard coded to be "off" (PD points signify a branch point).
However, I am planning on diving into AUTO soon to attempt to wrap codim-1 bifurcation curves for limit cycles, so that you can continue PD and NS points. I will the ability to follow period doubling limit cycles as well to the list.
Drew
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear all,
I am trying to continue a NS point. However I repeatedly receive get the error message below. I tried to recompute the NS point wherefrom I would like to start my continuation with more accuracy, setting smaller MinStepSize/MaxStepSize/StepSize, but this unfortunately did not help.
Could this be a bug or am I missing something?
Cheers,
Maurizio
PyDSTool_ExistError Traceback (most recent call last)
<ipython-input-100-fad6a905e330> in <module>()
10
11 PC.newCurve(PCargs)
---> 12 PC['NS1'].forward()</module></ipython-input-100-fad6a905e330>
/home/maurizio/Downloads/PyDSTool/PyCont/Continuation.pyc in forward(self)
1241 self.CurveInfo = PointInfo()
1242 if self.sol is None:
-> 1243 self._compute(v0=self.initdirec)
1244 self.sol = self._curveToPointset()
1245
/home/maurizio/Downloads/PyDSTool/PyCont/Continuation.pyc in compute(self, x0, v0, direc)
1045
1046 if singular:
-> 1047 raise PyDSTool_ExistError("Problem in _compute: Failed to compute tangent vector.")
1048 # v0 = zeros(self.dim, float)
1049 # v0 = linalg.solve(r[c_[J_coords, J_params],
PyDSTool_ExistError: 'Problem in _compute: Failed to compute tangent vector.'
Hi, Maurizio. First of all, PyCont can't continue NS points yet for limit cycle curves, although it CAN continue NS points for maps. Are you doing this for a map?
In general, however, when initdirec is not specified, PyCont attempts to find a tangent vector to the curve (this is the portion of the code that is throwing the exception). Sometimes this can fail, in particular since the routine that it uses has an initial guess that is the unit vector along the first coordinate. This particular choice might lead to a singular matrix (which is what is happening here).
If you are indeed trying to continue an NS curve for maps, you might try specifying an initial direction and see what happens. You don't have to pick the actual tangent vector to the curve, just an initial guess should suffice. That would be the first thing I would try. Let me know how that goes and we'll go from there.
Drew
Last edit: Drew LaMar 2014-08-23
Hi Drew,
thanks for the clarification.
Yet indeed, I missed the part that NS-C could only be started from maps and not from LC-C since this latter is my case.
Sorry about it.
M
Hi Drew,
I assume that the FP-C also works only on maps so far, am I correct on this?
I mean, I have some PDs on my continued curve in a continuous system, that in (XPP)AUTO I could attempt to further continue by "Run>Doubling". In PyCont the only curve type that could fit these criteria would be FP-C but unfortunately I get the same error I was obtaining for NS-C.
So, I am only able to see where my original limit cycle looses or gain stability by the PD bifurcation, but I cannot have any information on the actual envelopes (max-mins) of the period-2 orbits. Is there any chance that this possibility could be implemented soon in PyCont? It would be extremely useful.
M
Hi, Maurizio. Let me look into the PD issue. It sounds like you want to simply double the period and continue the resulting limit cycle? This should still be a LC-C and shouldn't require implementing anything new. I don't think it is currently implemented, however, as branch points have been hard coded to be "off" (PD points signify a branch point).
However, I am planning on diving into AUTO soon to attempt to wrap codim-1 bifurcation curves for limit cycles, so that you can continue PD and NS points. I will the ability to follow period doubling limit cycles as well to the list.
Drew
Hi Drew,
yes precisely. I look forward your updates then!
Thanks for it.
M