Talk:Multi-dimensional array: Difference between revisions

:Well, anyone unfamiliar with Fortran's array ordering who is intent on matrix arithmetic is going to be puzzled. Taking two-dimensional arrays A and B as obviously equivalent to matrices A and B, one can prepare a test prog. that has READ A, and READ B (or equivalently, uses a DATA statement to initialise the arrays), and prepare the layout

1, 2,

3, 4

:And indeed, such an input as that will appear as expected with output via WRITE A, and WRITE B. But when the result of MATMUL(A,B) is printed there will be confusion. Yes, a matrix is a matrix, and also, an array is an array. And an array can be regarded as a matrix or a matrix an array. But if you don't know the difference between the mathematician's "row major" order for a matrix and Fortran's "column major" for an array, you won't get far.

:That arrays were stored backwards in memory is a feature of the old style and relevant to assembler programming on say the IBM1130, but this wasn't done on the B6700 for example. Thus, "storage order" doesn't really apply to reverse memory order. Perhaps it would be better to omit "storage order" in favour of emphasis on the consecutive order of input and output. I was thinking of equivalencing a two-dimensional array to a single-dimensional array. For systems using memory backwards, both arrays would be in memory backwards but one would still regard the single-dimensional array as having a natural sequence 1, 2, 3, ... etc. I have never seen an explanation for this reverse-memory order. Perhaps with index bound violations and COMMON storage starting at high memory a large index would attack lower memory, most probably the user's code area rather than assault the system area in low memory addresses (the skeleton supervisor on the IBM1130 for example) via negative indices which presumably would be less likely. But this is guesswork.

:Similarly with arrays of matrices. Suppose you had an array A(3,2) which you regarded as a matrix, and then you wanted a collection of such matrices: AHORDE(3,2,100) would give you a hundred such while AHORDE(100,3,2) would give you confusion. But explaining this and schemes for passing a part of such a 3-D array to a subroutine expecting a 2-D array I thought too tricky. On the other hand, not explaining that matrices are normally considered as "row major" in mathematics, ''and that Fortran's MATMUL uses that interpretation'' despite its arrays being the reverse leaves a gap. I have never seen an explanation for this Fortran choice, which it seems to me has only introduced trouble. [[User:Dinosaur|Dinosaur]] ([[User talk:Dinosaur|talk]]) 08:36, 25 October 2016 (UTC)