Re: Does Ada need elemental functions to make it suitable for scientific work?

[Robin Vowels <robin.vowels@gmail.com>]

On Jul 12, 5:12 pm, "Dmitry A. Kazakov" <mail...@dmitry-kazakov.de>
wrote:
> On Wed, 11 Jul 2012 17:31:33 -0700 (PDT), rrrrrrr@gmail.com wrote:
> >> It is ill-defined. E.g. exp(A), where A is a matrix. Is exp(A) a matrix of
> >> exponents or exponent matrix?
>
> > In languages that provide whole array operations (i.e.,
> > element-by-element operations -- such as PL/I and Fortran),
> > it is the former.
>
> > BTW., I think you mean matrix exponential, which is a far
> > less common operation than exp(A) or e**A(i) for i = 1 to n,
>
> In linear algebra, provided matrices mean matrices, per-element operation
> just does not make any sense.

Element-by-element operations are required routinely in numerical
work.  They have been demanded and have been available since
at least 1955.

> Exp(A), as well as power series are fairly
> common in spectral analysis.
>
> > and would be written MATRIX_EXPONENTIAL or some such,
> > just as matrix multiplication would be written MATRIX_MULT
> > or some such, to distinguish it from the more common
> > element-by-element product.
>
> My FORTRAN and PL/1 are quite rusty, but even these incredibly poor
> languages did not define multiplication for matrices that way.

PL/I defined multiplication for matrices as an element-by-element
product, as I said before.
Back then, FORTRAN did not offer such operations on matrices,
however it now does, and has done so since Fortran 90.

> In fact they
> just had no matrices last time I used either.

Back then, both PL/I and FORTRAN offered matrices (and still do).
For that matter, both offered multi-dimensional arrays (and still do).

> I remember one library for sparse matrices in FORTRAN-IV, doing LU
> decomposition and other stuff. It was quite fun. The library was in fact
> very well-designed, but since FORTRAN-IV lacked even elementary data types,

FORTRAN always has had elementary data types.

> they did all memory management required using INTEGER*4 as an index in one
> huge REAL*4 array, serving as a memory pool.

That's because FORTRAN IV did not have dynamic arrays.
PL/I did, of course, from the first compilers in c. 1966.