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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Newsgroups: comp.lang.ada
Subject: Re: Does Ada need elemental functions to make it suitable for
 scientific work?
Date: Thu, 12 Jul 2012 09:12:41 +0200
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Date: 2012-07-12T09:12:41+02:00
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On Wed, 11 Jul 2012 17:31:33 -0700 (PDT), robin.vowels@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. 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. In fact they
just had no matrices last time I used either.

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

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de