4 ms·

There are tons of solvers, there're a lot of libraries and SciPy, Fenics, most likely even MATLAB, Octave, FreeFEM++ all of them use LAPACK and BLAS (at least i

There are tons of solvers, there're a lot of libraries and SciPy, Fenics, most likely even MATLAB, Octave, FreeFEM++ all of them use LAPACK and BLAS (at least in their most performant flavours), all calling eventually the FORTRAN subroutines written decades ago. And yes, the tricky parts of this is also that how Fortran and C store 2D arrays, https://en.wikipedia.org/wiki/Row-_and_column-major_order https://en.wikipedia.org/wiki/Row-_and_column-major_order. So no one re-writes their own stuff, unless for academic purposes. I was on the verge of trying to extend the SciPy library to support block matrices 4 years ago for my thesis, but was able to work around it because duck-typing had generalised quite enough to encapsulate even that. Sparse and Full matrices have a totally different data structure. hence the difference in the solvers. Engineers and Mathematicians that want more performant solving, rely more on the modelling of the problem (physically or mathematically) than improving the solvers.The other option is hardware-assisted optimization. For full solvers, I suppose the AI/ML folk have come up with TPUs, also because they have different tolerances for floating point calculations in classifying an image compared with launching a satellite on Mars.

dwohnitmok 7y ago
The most performant BLAS implementations are actually generally written in C and Assembly these days with a Fortran wrapper. So you can have a weird sandwich of C -> Fortran interface -> C in your code.
alimw 7y ago
> So no one re-writes their own stuff I have (unwillingly) had to do this. I did look at off-the-shelf solvers but they all seemed to restrict themselves to nice domains in low dimensions. Edit: Perhaps you are only talking about the linear algebra "stuff". I did use SciPy for that.

4 ms·

There are tons of solvers, there're a lot of libraries and SciPy, Fenics, most likely even MATLAB, Octave, FreeFEM++ all of them use LAPACK and BLAS (at least i

by InfinityByTen 7y ago

dwohnitmok 7y ago
The most performant BLAS implementations are actually generally written in C and Assembly these days with a Fortran wrapper. So you can have a weird sandwich of C -> Fortran interface -> C in your code.
alimw 7y ago
> So no one re-writes their own stuff I have (unwillingly) had to do this. I did look at off-the-shelf solvers but they all seemed to restrict themselves to nice domains in low dimensions. Edit: Perhaps you are only talking about the linear algebra "stuff". I did use SciPy for that.