Support for I/O of standard formats

[perazz]

Motivation

As linear algebra support develops, it would be useful to have simple interfaces to access test matrices to/from standard formats into the stdlib formats.

Prior Art

• Matrix Market: https://math.nist.gov/MatrixMarket/ https://math.nist.gov/MatrixMarket/mmio/f/mmiof77.html
• Harwell-Boeing: https://math.nist.gov/MatrixMarket/formats.html#hb-code
• NumPy: https://numpy.org/doc/stable/reference/generated/numpy.load.html
• https://help.imsl.com/java/5.0.1/api/com/imsl/math/SparseMatrixEx2.html
• https://help.imsl.com/c/7.0/html/cmath/default.htm?turl=matrixstoragemodes.htm

Additional Information

cc #749
cc #486
cc @minhqdao

[jalvesz]

For reference, the SciPy IO API: https://docs.scipy.org/doc/scipy/reference/generated/scipy.io.mmwrite.html#scipy.io.mmwrite
the TACO library also offers an API of the sorts for C++ and Python: http://tensor-compiler.org/docs/scientific_computing.html

[ivan-pi]

I've added #486 which is also relevant. I would be keen to have the SciPy .npz format supported, which is also used to pass sparse matrices.

[ivan-pi]

the TACO library also offers an API of the sorts for C++ and Python: http://tensor-compiler.org/docs/scientific_computing.html

The formats supported by TACO are:

• Matrix Market (Coordinate) Format (.mtx)
• Rutherford-Boeing Format (.rb)
• FROSTT Format (.tns)

[ivan-pi]

There is also a naive text format that MATLAB uses, described under

• spconvert
• Importing Sparse Matrices

I've used it in the past, to quickly output a matrix and import it into MATLAB for inspection (spy) and calculating the spectral radius.

[jalvesz]

I've also used the same format locally to then use matplotlib's spy https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.spy.html
So basically take whichever sparse format > transform to COO > dump a file <name>.dat

[ivan-pi]

Can we use the MatrixMarket routines from NIST (potentially, wrapped in a nicer interface)? Or should we do a clean-room design and implementation?

[jalvesz]

It could be good to have them for comparison, but it could be the occasion to make a clean-room design.
Maybe decided on the style for the signature of IO procedures, this could already enable focusing on individual implementations that should respect the decided signature.

I had in mind something like this:

subroutine matrix_<save/load>_<format>( matrix_type , file_name , ...optionals... )
end subroutine

[jvdp1]

Can we use the MatrixMarket routines from NIST (potentially, wrapped in a nicer interface)?

If their licenses permit it, I would say yes. It might be good to contact them, before using their codes (e.g., like it was done for the hash and some sort procedures).

[perazz]

I will ask @minhqdao if he plans to take care of this issue.

[minhqdao]

Thanks, @perazz, for opening this issue and all of you for your input and adding the references. I'll take care of it over the next few weeks.