Error in calculating the null space values

[Siegfriedchao]

When running the programme, using DragForce.nt, we obtain the following Kernel 0 value.

Kernel 0 is a new unique kernel

1.1259e+151.1259e+15  -0

   11.1259e+15-1.1259e+15

-2.2518e+15-1.1259e+15   0

1.1259e+15   0   0

   01.1259e+15   0

   0   01.1259e+15

Which is clearly not correct. The other kernels are fine.
An issue with the operation in multiplying by reciprocal of smallest coefficient, around Line 511 in newton-eigenLibraryInterface.cpp

When not performing the smallest coefficient multiplication, we have the following Kernel 0

 1   1  -0
8.88178e-16   1  -1
-2  -1   0
 1   0   0
 0   1   0
 0   0   1

Where a very small 8.88178e-16 exists, clearly affecting the finding the smallest coefficient operation.

[phillipstanleymarbell]

This is important to fix but is not a critical blocker at this point.

[phillipstanleymarbell]

To elaborate further on my comment: to fix this issue correctly, we would need to be computing the RREF symbolically rather than numerically. If we are computing it numerically, it is not trivial to address correctly and will require someone with a better grasp of numerical analysis than I have. Some pointers:

• Symbolic math libraries, e.g., https://github.com/gap-system/gap or https://github.com/sympy/sympy
• Numerical stability of Gaussian elimination: https://people.maths.ox.ac.uk/trefethen/nov12.pdf
• Using higher precision to counteract numerical instability: see, e.g., https://www.nersc.gov/assets/pubs_presos/HPAJSC.pdf, https://ieeexplore.ieee.org/document/1425396/, and https://dl.acm.org/citation.cfm?id=2737959