(j3.2006) MATMUL

[Bill Long]

Well, for 3 arguments, I'd use matmul(a1, matmul(a2,a3)).  For 4 
arguments, I would use matmul(matmul(a1,a2),matmul(a3,a4)), etc. 
Personally, I've never seem a case with more than three matrices.

Cheers,
Bill


On 11/30/12 3:43 PM, Van Snyder wrote:
> On Wed, 2012-11-28 at 06:14 +0000, Whitlock, Stan wrote:
>>     1.  MATMUL with more than 2 arguments - why put this in the
>> standard except to force the vendors to do for free what you should
>> buy from some math library company?  If enough customers want it,
>> someone will sell it to you.
>
> I took Stan's advice and started out to write a function with MATMUL's
> functionality -- each argument can independently be any kind of any
> numeric type --  with an arbitrary number of arguments.
>
> I defined an abstract type with a deferred type-bound multiply
> procedure.  I extended that with an "internal" type that has two class
> pointers, and ten "leaf" types that have a rank-1 or rank-2 component of
> default real, double precision, default complex, double complex, and
> default integer.  I didn't use PDTs for the different kinds.  I wrote a
> type-bound multiply procedure for each type.  The module is large.
>
> I know how to compute the optimimum parenthesization, and build an
> evaluation tree from it.
>
> The one remaining problem is writing the function statement.
>
> Fortran doesn't have a "..." dummy argument, and this wouldn't do the
> right thing anyway if all it did was to specify an arbitrary number of
> arguments with the same type, kind, and rank as the last named one.
>
> I briefly contemplated a collection of generic routines, but the number
> of them for three numeric types with two kinds each, plus logical, with
> all arguments of rank 2 or one argument of rank 1, exploded as a
> function of the number of arguments.  For 3..10 arguments, the numbers
> of functions are 867, 6483, 46659, 326595, 2239491, 15116547, 100776963,
> or 665127939, respectively.
>
> I could allow, say, ten arguments of my base class, but that would
> require users to start off with their matrices in one of my extension
> types, or to put the target attribute on their matrices.  I wouldn't get
> compile-time checking that at most one of the arguments was of rank one.
>
> Any other ideas?
>
>
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-- 
Bill Long                                           longb at cray.com
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