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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Larger matrices
Newsgroups: comp.lang.ada
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Date: Fri, 8 Aug 2008 12:38:09 +0200
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Date: 2008-08-08T12:38:09+02:00
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On Fri, 8 Aug 2008 02:59:56 -0700 (PDT), amado.alves@gmail.com wrote:

>>> And Ada got in the way: slicing restricted to one-dimensional arrays!
>>
>> Compared to other languages that have no slicing at all?
> 
> There are languages better than Ada at array indexing, including
> slicing. If there aren't, there should be!
> 
> A bidimensional array like the standard Real_Matrix should be
> compatible with a unidimensional array like Real_Vector.
> One row (or one column) of a matrix is a vector.
> In fact aggregate notation reflects this
> 
> Matrix := ( (a, b, c) ,
>             (d, e, f) ,
>             (g, h, i) );
> 
> Vector := (x, y, x);
> 
> but then the obvious are illegal:
> 
> Vector := Matrix (1); -- (a, b, c)
>
> or
> 
> Band_Matrix := Matrix (1 .. 2); -- ( (a, b, c) ,
>                                 --   (d, e, f) )
> 
> A good language should even permit
> 
> Vertical_Band_Matrix := Matrix (Matrix'Range, 1 .. 2); -- ( (a, b) ,
>                                                             (d, e) ,
>                                                        --   (g, h) )
> or
> 
> Block := Matrix (1 .. 2, 1 .. 2); -- ( (a, b) ,
>                                   --   (d, e) )

A good language should support keyed notation of array indices:

Vector := Matrix (Column => 1);  -- (a, d, g)

   type Matrix is array (Row, Column : Positive range <>) of Float;

It also should provide index types:

   type Square is index (Row, Column : Positive range <>);
   type Matrix is array (Square) of Float;

and

   type Matrix is array (Row, Column : Positive range <>) of Float;
   subtype Square is Matrix'Index;

and iteration

   for I in M'Index loop -- Zeroes all matrix
      M (I) := 0.0;
   end loop;

and enumeration

   case A'Index is
      when (1,1) | (2,2) => ...
      when others => ...
   end case;

and array aggregates

   ((1,1)=>0.0, (1,2)=>...); -- Flat notation

The value of an index type is a tuple. Elements of the tuple are ranges and
individual indices.

All operations you mentioned above are compositions of the corresponding
slicing of the index type and then indexing the array by the index. The
result of indexing depends on the index type:

   A (1, 2) -- Element, dimension 0
   A (1..1, 2) -- Vector, dimension 1
   A (1..1, 2..2) -- Matrix, dimension 2

There also has to be range types and range values.

Last but not least, a good language should allow reasonable array renaming
with bounds slicing. Array renaming in Ada is bogus.

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