Reference-LAPACK
DGELSD: SVD fails to converge for some matrices
Description
I have found that DGELSD sometimes fails for certain matrices, even though the matrix is well-conditioned and does not contain any unreasonably large or small values. I have attached a 1602x1062 bidiagonal matrix that triggers the problem as an example (this is the smallest test case I have been able to find so far).
Minimal example
This includes a minimal Fortran example that triggers the problem, and the required data files with matrix data. example.zip
When the problem occurs, this example will produce the following error:
Error: DGELSD failed with info = 1
Note: The following floating-point exceptions are signalling: IEEE_UNDERFLOW_FLAG IEEE_DENORMAL
Tested with the latest reference blas+lapack as well as various older versions, on Linux (RHEL8) with gcc/gfortran 8.5.0. Originally found in OpenBLAS: https://github.com/OpenMathLib/OpenBLAS/issues/5333
Checklist
- [x] I've included a minimal example to reproduce the issue
- [x] I'd be willing to make a PR to solve this issue
