error coming during solving steady state density matrix

[ANUSHREE DEY‏]

Dear all,

            I am getting an error as 'Zero pivot, numerical factorization or iterative refinement problem', while solving the steady state density matrix. Please suggest me how to solve the problem. I have also attached my code.

[Simon Cross‏]

Hi Anushee,

I don't see the "Zero pivot, ..." error in your notebook.

Yours sincerely,
Simon Cross

[Neill Lambert‏]

 For what it's worth, my colleague recently had a similar issue where some particular steadystate problem would sometimes generate pivot errors which I could not reproduce.  

He resolved it by a fresh python install + update to the latest packages,  though even if I downgraded to the versions of scipy and qutip he was using with the problem I couldn't reproduce the error.  Bit of a mystery.

thanks

neill

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[ANUSHREE DEY‏]

Dear Simon and Neil,

                    Thanks for the response, but its still not clear why I am getting the problem in even 2 p.cs in my lab, while running the same code. Hope to fix the problem soon, thanks for your help.

Best

Anushree

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[Simon Cross‏]

Hi Anushree,

Thanks for reporting this. Let us know if you discover anything.

Yours sincerely,
Simon Cross

[Neill Lambert‏]

Dear Anushree,

Just wanted to follow up on this.   I had a play around a little, and I noticed that in older versions of qutip, these pivot errors would sometimes arise for master equations which have ill-defined steady states, multiple possible steady states, and things like that.  I recall that the errors were actually kind of useful, as they sometimes gave you an indication that your model might have dissipationless dark states in it or something. I had a play with qutip 4.3.1, and I can construct some examples where the errors appear but where they do not appear in the latest version of qutip (instead, in the latest version, steadystate always seems to return a result, but it may well be nonsense in some of these cases.  Other solver options, like iterative-lgmres or power, seem to deal with this a little better, in that they are more likely to give reasonable results for the system properties in these slightly pathological cases).

Your example is a little complicated to deconstruct, so I am not sure if this is precisely the case there, but just fyi.

I guess the error doesn't appear anymore due to some change in scipy, and it is a bit of a shame, it is usually better to get an error than get an entirely incorrect result without realizing it!  Though in the past the error wasn't always consistent, when it did appear it would give some indication that one's model had some issues.

I am not sure there is any easy way to include checks in steadystate() for this kind of thing. It's possible to look at the eigenvalues in the Liouvillian and see if there are multiple values near zero, but that is quite numerically costly in many cases.

all the best

neill

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[ANUSHREE DEY‏]

Dear Neil,

               It is indeed blissful to hear from you about the possible reason for the problem. Meanwhile, I noticed that the two p.cs in our lab are showing that "zero pivot" error, and you are absolutely right that the error is not always reproducible. For example, sometimes the error is showing up for the loop variable spanning, say (0-3), sometimes for (0-5), which appeared kind of spooky for me. I started to find the error in my model, but could not find any major problem. Then I run the same code on my laptop, which is new, and found no error, rightly pointed by Simon Cross. Now, what I can conclude, to the best of my knowledge is that the version of the qutip may be the possible reason of this error. I tried to update qutip in my lab p.c, but could not do it, so I am totally dependent on my laptop now.

Thank you

Best wishes

Anushree

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