A Summary of Fortran [pdf] (1992)
math.utah.edu
math.utah.edu
For current information on Fortran one should visit https://fortran-lang.org/ .
Let's wait until 2050s and see, whatever Fortran 2050 will be like, if CS people will still joke about Fortran as if it was FORTRAN 77.
Not that other languages which have widespread support also have similar historical mistake leakage. Null vs Optional in Java comes to mind. The python 2 -> 3 debacle was a similar sort of "historical mistake correction" but the breakage of backwards compatibility lead to quite some polarization. Actually, in python 2 -> 3, the python core developers tried to fix a historical defect that fortran still has: print as a keyword vs a function.
A small price to pay for being able to run code from 60 years ago. And no, there is no such requirement as such.
<need to specify the "leading dimension of A">
A very clever way of applying your algo to a submatrix from the days of sequence association and no array expressions. Nothing to do with dynamic memory allocation and you know the compiler will have no excuse to copy data.
Why is it a defect that I/O needs keyword? Fortran has doubled-down on that "defect" by making coarray references through syntax [] and not an MPI-like procedure call. I don't think it's a defect at all, it's a strength.
> A very clever way of applying your algo to a submatrix from the days of sequence association and no array expressions.
This isn't why you specify the leading dimension, it is just a useful feature of the leftover artifact of the lack of dynamic allocation. If the algorithms were written today, the array slicing notation would simply be used to achieve that.
Back in Fortran 66 days, you would compile a large 2d array to solve the biggest problem you wanted to solve because you couldn't dynamically allocate. The alternative would be to change the source code and compile, but that was untenable. Then you would set your array elements with ordinary matrix notation but you would need to specify the stride to the solver to work with that: thus yes, it was solving a block, but it is only capable of solving the upper block. So clearly not intended for general submatrix solving: it is meant for using the upper block of a matrix in lieu of dynamically allocating the matrix to the correct size. Alternatively they could have required people to work with 1d arrays and manually handle the matrix indexing, but that would have been unfriendly.
Nope, you can solve any submatrix by passing the address of some other element than the upper left corner as the address of the array.
Anyways, from the original guide of fortran (maybe I am mischaracterizing their rationale, but from the horse's mouth):
> However an assumed-size array declaration has been used in the software, in order to overcome some limitations in the Fortran 77 standard. [LAPACK Users' Guide Third Edition]
It doesn't matter what the real reason is. The interface to matrix solving algorithms is archaic feeling:
DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO )
x, _ = A.solve(b)
There's that LDB, and it certainly has nothing to do with a sub-block of the matrix since it has to do with the storage of the right hand side and enabling a single call to provide multiple solutions while assuming a particular array layout.
Anyways, nobody is really engaging with the real point: that it is obvious with use that Fortran is an old language because there are all kinds of these historical artifacts laying around. As I said, everyone knows it, everyone who interacts with it will feel it. But by now fortran isn't alone in this camp. Moreoever, so what? You should be able to admit to yourself that Fortran is an old language (that is simply a fact), that it gives the impression to most people of being an old language (that is again, simply a fact and why shouldn't it?), yet it has many modern features and people can be quite productive in it for some problem domains. Adding modern features isn't going to win people over that are prejudiced against Fortran.
"pointer arithmetic" is not Fortran. The Fortran POINTER should not be confused with a C pointer (POINTER has more information). You cannot do arithmetic with a TYPE(C_PTR), either.
LDB allows you to solve the 3rd and 5th RHSs only, when B is dimensioned (1000,100): call with NRHS=2, B=B(1,3) and LDB=2000
You can write a type-bound procedure call
x = A%solve(b)
with today's Fortran. LAPACK calls can be hidden from the casual user. I doubt that a casual user of C++ would enjoy looking at the implementation of its standard library, either.
Yes, 29 year-old code written to a 43-year old standard looks old. How is that a Fortran issue? Would it look any newer if it was written in another 40-year old language? The fact that this code is still the mainstay of scientific computation is evidence of the strength of its design and the design of the programming language.
It was “array slicing” (array expressions) that was missing in F77. That’s what sequence association was meant to help with. You pass a scalar that is an element of an array and the corresponding dummy is an array. The dummy gets associated with an array that starts at that element and then continues with all the other elements of the actual argument array in array element order. You then use the LDA argument to give a 2d view of the same array in the dummy so you can step to the next column (or every other column if you want, just double the LDA) no matter where you started from.
Programs back then had no need for dynamic memory, they were the only thing running on the machine, no kernel, no other processes or users, why not just grab the entire memory? They booted in a blink of an eye, too. Now, not even our supercomputers run like that. You never know who else is using the resources of the machine.
Everytime someone tries to interact with DGETRF for the first time, they look up the API (at http://www.math.utah.edu/software/lapack/lapack-d/dgetrf.htm... maybe) and read, "The leading dimension of the array A. LDA >= max(1,M)." Which tells them nothing, so they keep digging through the documentation. Maybe they check the user's guide, https://www.netlib.org/lapack/lug/node116.html and they read "However an assumed-size array declaration has been used in the software, in order to overcome some limitations in the Fortran 77 standard." but sadly their journey is still not over because none of these source have characterized it as you are (as an array stride due to memory layout). Nor named it appropriately. They still have to keep digging to understand it as a stride.
Its name reflects the fact that it was common to oversize the allocation of the memory for the matrix and then LDA > M of course, because in fact LDA = M_MAX. The leading dimension of the matrix in memory (the stride if you were dealing with a 1-d array). If they are lucky (as I was), they will have access to some of the older software that was doing this and they can see what the purpose of the argument and the rationale of the name is. That this also enables one to focus on a sub-block of A and give a stride value. But certainly that isn't the "leading dimension of A". It is the leading dimension of A precisely when A is a bigger matrix and you are focused only on the upper block because of static allocation of A.
To summarise: F77 has no array expressions so the only way to pass a subobject of an array is through sequence association, as described.
If it had dynamic allocation and no array expressions, sequence association would still be needed. In fact, most F77 compilers supported dynamic allocation as a non-standard extension and STILL used sequence association to pass subobjects of arrays.
Whether you pass a whole array or use sequence association, the meaning of LDA is clear: it determines how sequence association will work between rank-2 dummy and actual array. And, yes, you can use different LDAs (as long as you don't step over the bounds) to effectively walk the diagonal or skip columns.
Yes, what you are saying is correct about the technical capabilities of the parameter; I have agreed with you 3 times already, but it is irrelevant. You keep ignoring the actual point: an answer of what you can use the parameter for is not the same as an answer to why that parameter is there. You can be quite right about what the parameter allows you to do and quite wrong about why it was added in the first place.
The origin of LDA as an argument traces all the way back to LINPACK. Just read chapter 1 of the LINPACK user's guide, https://doi.org/10.1137/1.9781611971811.ch1 and see them using the parameter as I describe. It is used precisely to over allocate an array in a program so that it can be dynamically sized at runtime. The allocate an array A of size 50 x 50, specify LDA to be 50, then assign N to some value and use 2d array notation to set a block of the array A to a matrix. My assertion is that is precisely the use case they designed that parameter to be used for. That usage is why algorithms with LDA are first class and there are no variants (and they offer many variants) without it: because they knew that people would compile programs with overallocated arrays and require it.
LINPACK predates even fortran 77, tracing back into subroutines developed by Wilkinson this sort of use arises from fortran 66. I'm having a hard time finding technical notes describing those routines though. I'm curious if LDA shows up in the ALGOL 60 versions. In any case all this history was relayed to me by my supervisor who worked worked much closer to this history than me so I trust that quite implicitly.
For you, maybe it was enough to see that the parameter was a stride and stop digging. For me, I saw that, saw it always being set equal to N (and M = N) in all actual uses in the modern code I was working with and I was curious why it wasn't abstracted away because even at Fortran 77 is was easy to hide it behind a zero cost abstraction. So I went down the historical rabbit hole. Maybe I should have just pointed out that the names of the subroutines are limited to 6 characters because of history and you would have agreed that use of LAPACK is a trigger for most people to realize that fortran is filled with historical artifacts.
describes use of Fortran dummy arrays before Fortran IV. No LDA/B/C in the example provided. But I find it hard to believe that once a compiler existed that would compile that example, people took more than a week to realize that by adding LDA/B/C you can write a general DGEMM that can multiply submatrices.
We need to remember that first there was a compiler implementation and the language was secondary to that. Language extensions that the compiler could do "easily" get implemented quickly. Sequence association was one of those things and I still maintain that it would be needed (in the absence of array expressions) even if there was dynamic allocation in Fortran I.
Consider a subroutine that is expected to take the 1st column and the last column of an array, sum them, and put the result in the 1st column. You want to write
allocate(a(3,5),source=b); call sub(a) deallocate(a) allocate(a(2,4),source=c); call sub(a)
Can you reuse sub to only sum the bottom half of the columns? Not without allocating a new array and copying before passing the copy to sub. With sequence association, LDA and adjustable or assumed-size arrays and extra integer arguments, you can and it will work for any rank.
The alternative coding that I have seen (and abhor), is putting an LDA in a COMMON and then all your subroutines pick up an LDA from there. Such codes are usually riddled with errors.
Or C like K&R C book was just published yesterday.
People don’t modernize their codes because the Fortran compilers allow them to, and the Standard is reluctant to delete old features (and compilers would not delete them anyway).
Unfortunately, that means that old bugs can lie undetected. I don’t think any other language/compilers have squared that circle.
And there’s plenty of new projects started in Fortran.
-But we can build with concrete and steel and plastics and all sorts now.
-Most people use bricks though. And people are not tearing their brick houses down to rebuild them in steel. See? Building is old fashioned, antiquated!
In fact, nobody now starts a new project in F77. There’s a lot of F77 brick code around, yes. And it still does the job it was asked to do even though it gets moved to a new district every ten years.
! MARK 1 RELEASE. NAG COPYRIGHT 1971.
It has been revised since then to use free form, structured programming, MODULEs, KINDs, INTENTs and IMPLICIT NONE.
If we can do it, everybody can. I have already mentioned some reasons that people don't do it. None of the reasons I have heard are "Fortran is too old and clunky".
As for which version is used in the wild, it's the same as with many other languages that have stuck around for a long time. Plenty of legacy code which might still be F77, but practically all new projects, or extensive modernization of legacy code, will make use of the modern features.
I suspect Fortran's reputation is largely due to many of the foundational libraries of numerical computing like BLAS and LAPACK, are F77 (LAPACK uses a small number of 'modern' features, but largely it's still a F77 codebase). This is the kind of Fortran that non-Fortran programmers might come into contact with. But the Fortran that Fortran programmers write today is definitely much more modern.