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numerical-mathematics / extrapolation

Parallel extrapolation for ODEs
MIT License
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Divide by 0 in regression tests #6

Closed mcr222 closed 8 years ago

mcr222 commented 9 years ago

In the 2nd test in regression test, although the test passes, this exception is shown:

divide by zero encountered in double_scalars H_k = lambda h, k, err_k: h0.94(0.65/errk)*(1/(2_k-1))

HumamAlwassel commented 9 years ago

In function H_k, the input k is an integer >= 3. So this would happen only when err_k is 0, which means that our estimated solution at that step happened to have no error. I found that this can happen on certain problems and initial conditions when I was testing the code and developing the test cases.

mcr222 commented 9 years ago

Understood.

But digging deeper I am seeing that this turns out to return (in these cases) the h_new=inf and then the line: h = min(h_new, t_max - t_curr) chooses the new step as t_max - t_curr, which means that we will take only one step more (doesn't sound right if t_curr is still far from t_max).

The test cases I am seeing that have this problem are always on the last step (t_curr=t_max) therefore it doesn't affect the solution (and tests pass). Maybe this should be treated more carefully.

ketch commented 9 years ago

I think the usual approach is to add a small epsilon to the denominator. The trouble is that it seems like an appropriate size for epsilon would be problem dependent. There is probably something in H&W on this.

mcr222 commented 8 years ago

In my branch I left the current approach, it takes the step as big as possible (until the final time), which would be like taking a very small epsilon.

We can discuss further.

mcr222 commented 8 years ago

A related issue is sometimes also shown: RuntimeWarning: divide by zero encountered in double_scalars hint = H((1/errint)_*(1/(u+4)))

This one is raised when errint=0 (interpolation error). This one doesn't affect the execution (if errint==0 then h_int is not used).

mcr222 commented 8 years ago

Solved with last commit to mcr-implicit branch.

Added a factor that limits the relative increase or decrease of the new estimated step (relative to the last step).