Thanks for all the replies, I'll check the links provided. Just to give a summary of the reasons.... As John Gibson pointed out Fourier expansions would be one example.
When solving PDE's we use "ghost cells" to provide boundary conditions. A physical variable, let's say density, could be represented in space by a 3D array, with each spatial index (ix,iy,iz) taking on values like ix=1..nx, iy=1..ny, iz=1..nz etc. If the boundary is, say, reflective, then you need to set the value of the density in the part of space you can't "see", e.g. in the regions ix=-2..0 and ix=nx+1..nx+3 Obviously this can be handled by offsetting each array index by some amount. The problem is mainly that what we have written down on paper, in books and papers on numerical analysis etc are numerical equations which naturally count from 1 to n along some dimension. Couple that to the fact that many codes rely on arrays that consist of mixtures of real space (3D say) and special function expansions, with Fourier expansion being one example. I for example use a 7-dimensional array to describe some problems (3 dimensions for real space, and 3 dimensions for velocity space). Real space is not expanded, so it counts from 1..n naturally, while velocity space has 2 dimensions expanded with one type of series (counting from 0..n) and the other dimension expanded in a different series (counting from -n..n). The final seventh dimension naturally has only 2 indices 0 and 1 (which accounts nicely for the real and imaginary parts of the function). Within each array loop, it is nice to be able to use if statements that correspond to what you have written down on paper, e.g.: if(in>0) then blah if(im<1) then something else or something like: do i=0,1 do im=-mmax,mmax do in=max(im,0),nmax do ir=1,nr do ix=1,nx do iy=1,ny do iz=2,nz-1 blah enddo enddo enddo enddo enddo enddo enddo (incidentally, imagine how many tabs would be required to write the above in python!). Within a code, there may be many such loops and structures with different looping conditions. When you have a code with 20000-40000 lines that you want to update to a new language, having to change all of these to account for offsetting is too much work for anyone to seriously consider. Not to mention the fact you can no longer easily code up the difference equations you have written on paper (and possible spent months creating). That in a nutshell is why nobody is switching from Fortran (even the young guys are writing new codes in Fortran). There are other nice things about Fortran arrays, such as the ability to quickly set all elements of an array to zero with: a=0.0 I hope that sort of makes it clear the type of problems we deal with?! Cheers
