div by zero error in scikit-fmm extension velocity

[conqueror5]

I am testing this package with random data and got this error message below:

terminate called after throwing an instance of 'std::runtime_error'
what(): div by zero error in scikit-fmm extension velocity

I am not sure whether there is any bugs or limitations of fast marching method. I attached my code.

Thanks
Code.zip

[jkfurtney]

Thanks for getting in touch and for your testing effort. I have not seen this error before. It looks like a point which is exactly on the front is being finalized and the extension velocity cannot be calculated. I am not sure why this is happening, I will investigate in more detail. For now, this work around seems OK, could you test it?

In extension_velocity_marcher.cpp replace

  if (denominator != 0.0)
  {
    f_ext_[i] = numerator/denominator;
  }
  else
  {
    throw std::runtime_error(
          "div by zero error in scikit-fmm extension velocity");
  }

with

  if (denominator != 0.0)
  {
    f_ext_[i] = numerator/denominator;
  }
  else
  {
    double maxMagSpeed = 0;
    for (int dim=0; dim<dim_; dim++) {
      if (fabs(lspeed[dim]) > maxMagSpeed) {
        maxMagSpeed = lspeed[dim];
      }
    }
    f_ext_[i] = maxMagSpeed;
  }

The Adalsteinsson and Sethian paper has the details on this algorithm.

[conqueror5]

It works for this example. Thank your for your help.

[jkfurtney]

Here is the example that is not working:

data = {
	"phi": [
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	"speed": [
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	],
	"dx": 0.05
}
import skfmm
skfmm.extension_velocities(data["phi"], data["speed"], dx=data["dx"])

[jkfurtney]

Interestingly, if you omit the dx keyword argument and let it default to 1.0 there is no crash??

[jkfurtney]

Here is a simplified case that shows the problem:

import numpy as np
import skfmm

phi = np.array([[  0.00000000e+00],
       [  5.00000000e-02],
       [  1.00000000e-01],
       [  1.50000000e-01],
       [  1.50000000e-01],
       [  1.00000000e-01],
       [  5.00000000e-02],
       [ -1.38777878e-17]])

speed = np.array([[ 0.2704946 ],
       [-0.04084191],
       [-0.04704457],
       [-0.04706646],
       [-0.04706324],
       [-0.04703607],
       [-0.03551645],
       [ 0.66778351]])
dx = 0.05
d, f_ext = skfmm.extension_velocities(phi, speed, dx=dx)

• If dx = 1.0, the crash does not happen
• phi and speed here are 2D arrays but only have one column of data. If you run it as a 1D problem it works
• Possibly the negative speed values are a problem?

[murraycutforth]

Hi, I've also encountered a div by zero error in extension_velocities. I'm pretty sure that it's the same problem as described here. I looked into the exact values of phi in surrounding cells at the point when the error occurred in my case, and found that it reduced to the following 1D problem as the neighbouring cells in the other two dimensions were not frozen:

The issue is happening when the wave front propagating outward arrives at a point at the same time from both directions, so d, and ldistance[dim] are set to zero.

scikit-fmm/skfmm/extension_velocity_marcher.cpp

Lines 107 to 126 in ff8a467

	for (int dim=0; dim<dim_; dim++)
	{
	lspeed[dim]=0;
	ldistance[dim]=0;
	for (int j=-1; j<2; j+=2) // each direction
	{
	int naddr = _getN(i,dim,j,Mask);
	if (naddr!=-1 && flag_[naddr]==Frozen)
	{
	//determine which direction, in this dimension, is nearest to
	//the front. Calculate the distance to front in this direction
	double d = distance_[i] - distance_[naddr];
	if (ldistance[dim]==0 || ldistance[dim]>d)
	{
	ldistance[dim] = d;
	lspeed[dim] = f_ext_[naddr];
	}
	}
	} // for each direction
	} // for each dimension

I think a viable fix is just to check that d is not zero before updating ldistance and lspeed, like this:

https://github.com/murraycutforth/scikit-fmm/blob/b1cf74c5ed14a30c3b1432c9cec38399ebb531ff/skfmm/extension_velocity_marcher.cpp#L122-L126

This runs successfully on my case, as well as on the simplified test case posted above. The extension velocity example script also remains correct. This fix means that the velocity is extended from the neighbouring cell which phi was calculated from, so the extension velocity and phi are consistent with each other (e.g. in my hand-drawn example above, v is extended from the cell on the right hand side, rather than the left hand side).

Do you think this is the right approach @jkfurtney ?

[jkfurtney]

Thanks for your investigation here and for your intuitive explanation. What you describe makes sense, could you put this in a PR? I will merge it and give it a few more tests.

[jkfurtney]

Is that fountain pen ink?

[murraycutforth]

Sure, just sent the PR. I don't think it should change the result of the function since any d > eps is treated the same as before, but would be great if you can run some regression tests to double check.

Haha yeah almost, I used to use a fountain pen but switched to one of those uni-ball pens now.