Examples for error: Should only be one path from root...

[thorek1]

Hi,

I appreciate the speed of your package but sometimes the package does not provide derivatives (jacobian in my case) while other packages do. This unfortunately prevents me from using it in my work.

Here are two MWEs representative of the issues I encounter:

using FastDifferentiation

𝐗 = make_variables(:𝐗, 31)
𝐘 = make_variables(:𝐘, 9)

eqs = FastDifferentiation.Node[ (((((-((exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30])))) * -(𝐘[1]))) * (1 / 𝐗[11])) * 𝐘[8]) * (𝐗[24] ^ -(𝐘[1]))) * (𝐗[27] ^ 𝐘[1])) * (𝐗[8] * (1 - 𝐘[1])))
            (-(𝐘[8]) * (((exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30])))) * -(𝐘[1])) * ((𝐗[24] ^ (1 - 𝐘[1])) * (𝐗[27] ^ 𝐘[1]))) + (𝐗[27] * -(((1 - 𝐘[7]) * exp(-((𝐘[3] + (𝐘[8] * 𝐗[30])))))))))
            0
            ((-((exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30])))) * -(𝐘[1]))) * 𝐘[8]) * ((𝐗[27] ^ 𝐘[1]) * (𝐗[24] ^ (1 - 𝐘[1])))) ]

jacobian(eqs,𝐘)

sparse_jacobian(eqs,𝐘)

eqs = Node[ (((((-((exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30])))) * -(𝐘[1]))) * (1 / 𝐗[11])) * 𝐘[8]) * (𝐗[24] ^ -(𝐘[1]))) * (𝐗[27] ^ 𝐘[1])) * (𝐗[8] * (1 - 𝐘[1])))
        ((((((-(exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30]))))) * -(𝐘[1])) * (1 / (((𝐗[23] * 𝐗[20]) * 𝐗[3]) * 𝐗[1]))) * 𝐘[8]) * (𝐗[24] ^ (1 - 𝐘[1]))) * (𝐗[27] ^ 𝐘[1])) * ((𝐘[2] * 𝐗[8]) * (1 - 𝐘[1])))
        (-(𝐘[8]) * (((exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30])))) * -(𝐘[1])) * ((𝐗[24] ^ (1 - 𝐘[1])) * (𝐗[27] ^ 𝐘[1]))) + (𝐗[27] * -(((1 - 𝐘[7]) * exp(-((𝐘[3] + (𝐘[8] * 𝐗[30])))))))))
        ((-((exp((-(𝐘[1]) * (𝐘[3] + (𝐘[8] * 𝐗[30])))) * -(𝐘[1]))) * 𝐘[8]) * ((𝐗[27] ^ 𝐘[1]) * (𝐗[24] ^ (1 - 𝐘[1]))))]

jacobian(eqs,𝐘)

sparse_jacobian(eqs,𝐘)

They error with variations of: ERROR: AssertionError: Should only be one path from root ... using FastDifferentiation v0.4.4

I understand you can go equation by equation but that undoes the speed gains from collecting subexpressions.

Any help would be much appreciated.

[brianguenter]

I am looking at this. Can't give you an estimate of time to fix. There is a hard to isolate bug that has a similar error message. If this is caused by that problem it could be a long time. If it's something new then it might be much quicker.

[thorek1]

Thank you for the prompt reply.

If useful I can post more examples here.

[brianguenter]

More examples will be helpful. Even though the error message might be the same the bugs might not be.

[brianguenter]

This is the derivative graph for your first example

Is it possible to make a simpler MWE? This graph goes through many factorization steps which take forever to step through and debug.

[brianguenter]

@thorek1 Do you still want me to work on this? It would help me a lot if you could make an even simpler MWE. If the failure doesn't occur when you reduce the problem size then I'll have to deal with it. But debugging this will be much faster with a smaller problem.

[thorek1]

here is a simpler MWE. I pruned all elements which are not necessary for the code to throw an error from the previous example. I hope this is helpful. thanks for your help

using FastDifferentiation

𝐗 = make_variables(:𝐗, 2)
𝐘 = make_variables(:𝐘, 3)

eqs = FastDifferentiation.Node[ 𝐘[1] * (𝐘[2] + 𝐘[3]) * 𝐘[1] * (1 / 𝐗[1]) * 𝐘[3] * 𝐗[2] ^ 𝐘[1]
                                𝐘[1] * (𝐘[2] + 𝐘[3]) * 𝐘[1] + (𝐘[2] + 𝐘[3])
                                𝐘[1] * (𝐘[2] + 𝐘[3]) * 𝐘[1] * 𝐘[3] * 𝐗[2] ^ 𝐘[1] ]

jacobian(eqs,𝐘)

[brianguenter]

found the bug. Thank you for the simpler example that made it much faster. Still thinking about how to fix it.

[brianguenter]

This is going to take a while to fix. But I am working on it.

[thorek1]

Great. Thanks for your time. Let me know if you need more examples