[thatjoeoverthr]

I actually had a fantastic experience with Fortran lately. I ported a compute kernel from python/numpy to Fortran 2018, partially due to the GIL and partly so I could use Intel's compiler. The performance improvement was tremendous. Several times faster per core, then multiplying further because I could take advantage of threading. In all, the 3 day project increased actual throughput 450x.

(I considered JAX, but the code in question was not amenable to a compute graph. Another option was to thread by fork, and use IPC.)

I liked the language itself more than expected. You have something like "generics" with tensors. Suppose you pass a parameter, N, and you also would like to pass a tensor, and you would like to specify the tensor's shape (N, N). You can do this; the parameter type constraints can reference other parameters.

Tensors and various operations are first-class types, so the compiler can optimise operations easily for the system you're building on. In my case, I got 80% improvement from ifx over gfortran.

Invocation from Python was basically the same as a C library. Both Python and Fortran have facilities for C interop, and Numpy can be asked to lay out tensors in a Fortran compatible way.

Part of what eased the port was that Numpy seems to be a kind of "Fortran wrapper". The ergonomics on tensor addressing, slicing and views is identical.

[prennert]

I did something similar many years ago. I was amazed that Fortran was not more discussed as an option to write performant code within a Python / numpy codebase.

At the time everyone seems to default to using C instead. But Fortran is so much easier! It even has slicing notations for arrays and the code looked so much like Numpy as you say.

[foxglacier]

Yea, Fortran is nice to use for so-called "scientific" computing. It has high performance as well as some handy intrinsic functions like DOT_PRODUCT and TRANSPOSE but the best features to me are colon array slicing syntax like Python/Numpy and arrays being indexed from 1 which makes converting math equations into code more natural without constantly worrying about off-by-one errors.

I wouldn't call multi-dimensional arrays tensors though. That's a bit of a bastardization of the term that seemed to be introduced by ML guys.

It wasn't until I started using Fortran that I realized how similar it is to BASIC which must have been a poor-man's Fortran.

[PaulHoule]

e.g. "tensors" are like "vectors" in they transform in a specific way when the coordinate system changes; what felt so magic about vectors as an undergrad was that they embody "the shape of space" and thus simplify calculations.

If you didn't have vectors, Maxwell's equations would spill all over the place. Tensors on the other hand are used in places like continuum mechanics and general relativity where something more than vectors are called for but you're living in the same space(/time) with the same symmetries.

[Joker_vD]

> If you didn't have vectors, Maxwell's equations would spill all over the place.

What do you mean, "would": they did! :) The original equations had 20 separate equations, although Maxwell himself tried to reformulate them in quaternions. But if you look e.g. at works of Lorentz, or Einstein's famous 1905 paper, you'll see the fully-expanded version of them. The vector form really didn't fully catch until about the middle of the XX century.

[lioeters]

This sounds like an interesting thread to follow. From a cursory search, it seems vector calculus was being used by the early 1900's to reformulate Maxwell's equations, then later with notations like differential, integral, and matrix forms. I'll read more and see if I can understand the gist of each major step of the process over the years, how the notation affected the way mathematicians thought about the equations, and "made them easier to work with".

And how Fortran has unique properties that make converting math equations into code "more natural". Intriguing, I'll to dig deeper for intellectual curiosity.

[foxglacier]

It goes even further. Einstein also simplified the writing of tensor equations involving sums (big sigma sum) with Einstein notation by basically dropping the sigma because it's redundant so undefined indices automatically get summed over all their applicable values. It works with nested sums too to make them deceptively simple looking. Add to that the comma subscript for differentiation and you get formulas with just a couple of terms but huge piles of subscripts. I've seen equations in text books that have both subscripts and superscripts on both the left and right of a variable.

[foxglacier]

Sure, but not all arrays are tensors. In continuum mechanics, you often represent tensors as matrices or vectors to exploit symmetry and then it's really confusing to keep calling them tensors because they don't behave like their tensor equivalent.

[pantsforbirds]

If your problem fits into arrays/matrices/vectors as the only required datastructures, Fortran is a VERY good language.

[sampo]

> Suppose you pass a parameter, N, and you also would like to pass a tensor, and you would like to specify the tensor's shape (N, N).

You can do that, and it might be cleaner and less lines of code that way.

But you don't necessarily need to pass the array dimensions as a parameter, as you can call `size` or `shape` to query it inside your function.

    program main
      implicit none
    
      real :: a(2, 2) = reshape([1., 2., 3., 4.], [2, 2])
    
      call print_array(a)
    
    contains
    
      subroutine print_array(a)
        real, intent(in) :: a(:, :)
        integer :: n, m, i, j
    
        n = size(a, 1) ; m = size(a, 2)
        write(*, '("array dimensions:", 2i3)') [n, m]
        do i = 1, n
          do j = 1, m
            write(*, '(f6.1, 1x)', advance='no') a(i, j)
          end do
          print *
        end do
      end subroutine
    
    end program

[thatjoeoverthr]

True! I just wanted to highlight it. (I had to do this at an interface because the ABI doesn’t pass the shape.)

[3uruiueijjj]

I've never found anything to back this up, but my impression was that both the Python / Numpy and Fortran 90 slicing operations were directly inspired by MATLAB (although most of the ideas go back to at least Algol 68).

It also helps that Fortran compatibility is a must for pretty much anything that expects to use BLAS.

[thatjoeoverthr]

I'm learning just now how old MATLAB is. Wow!

[drnick1]

Any reason why you couldn't do this in C/C++? I use the Eigen matrix library as a replacement for Numpy when I need more performance and the code looks surprisingly very similar.

[thatjoeoverthr]

Of course I could in C.

Intel and Nvidia are both offering both C and Fortran compilers, so I was looking at both. I know C well but I decided to not look at it as a presumed default.

When I used C like this in the past, the intrinsics were very low-level, e.g. wrapping specific Altivec or SSE instructions or whatever. I see see it has OpenMP intrinsics, though, which I’m sure I’ll try later.

If I use a library, I’m breaking up the operations and don’t give the optimizing compiler an opportunity to take operations into account together.

With Fortran, I can give the operations directly to the compiler, tell it the exact chip I’m working with and it deals with it.

It would be fun, when I have some time, to go rewrite it in C and see how it compares.