Fastor VS ITensors.jl

I'm going to throw in a recommendation for Fastor. It is generally faster than other libraries, is very lightweight, and has a pretty modern syntax.

There are C++ libraries that deal with linear algebra and tensors that are able to produce fully vectorized code without requiring you to mess around with SIMD intrinsics. See, for instance, fastor, blaze, eigen and the huge Trillinos set of packages. C++ is very widely used when it comes to scientific HPC applications. All you need to do is google search or better yet, join r/cpp and r/cpp_questions and start asking away for the things you need. The C++ community is very welcoming and full of experts that will be able to help you.

Picking what size you are targeting is really important, though. Could the matrices you are working with realistically be bigger than say 32x32? BLAS is good for big matrices. It's not as great for small matrices. Eigen or Fastor will do better for these smaller problems. And for various common operations on sizes 2, 3, and 4, hand coded graphics-oriented libraries might outperform those.

Tensorflow, Machine learning: https://www.tensorflow.org/ Fastor, A tensor library: https://github.com/romeric/Fastor GNU Scientific Library(GSL): https://www.gnu.org/software/gsl/ Boost. FEniCS, A finite element library: https://fenicsproject.org/ Intel MKL, a BLAS+LAPACK+other goodies library: https://software.intel.com/content/www/us/en/develop/tools/math-kernel-library.html SuiteSparse, A sparse linear algebra library: http://faculty.cse.tamu.edu/davis/suitesparse.html Sundials, Nonlinear solvers: https://computing.llnl.gov/projects/sundials

DMRG packages are available in Julia and C++ and Python. (Don't use Fortran. But here is a Fortran library if you insist.)

As one example, one of the leading libraries for tensor network simulations (https://itensor.org) has recently been rewritten in Julia (previously was c++) and the flatiron institute who develops it (which is certainly one of the leading Computational physics institutions in the world) is advising new users to use the Julia version. I also know some other computational groups which use Julia, even for things like quantum Monte Carlo (where I personally would have believed c++ to have an edge but people tell me different)! I think when even leading computational groups switch, Julia is almost always the much better option for the average user if you write your code from scratch (a situation not so rare in condensed matter). If you need to use some libraries or legacy code, this obviously changes the situation.

> One thing that supports this view is that there are several Julia packages that are wrappers around existing C/Fortran/C++ libraries, and basically no examples (that I know) of people porting existing libraries to Julia.

As with the others, I'll strongly disagree and chime in with a few examples off the top of my head:

* ITensors.jl : They started moving from a C++ to Julia a couple years ago and now their webpage doesn't even mention their original C++ implementation on its homepage anymore https://itensor.org/

* DifferentialEquations.jl : This has many state of the art differentiatial equation solving facilities in it, many of which are improvements over old Fortran libraries.

* SpecialFunctions.jl, Julia's own libm, Bessels.jl, SLEEFPirates.jl : Many core math functions have ancient Fortran or C implementations from OpenLibm or whatever, and they're being progressively replaced with better, faster versions written in pure julia that outperform the old versions.

Otherwise, maybe check ITensors.jl or look for packages that want to do the same thing?