From: "M. Edward (Ed) Borasky" <znmeb@...>
Date: 2006-09-11T21:37:50+09:00
Subject: Re: Matrix

Paul Lutus wrote:
> MonkeeSage wrote:
> 
>> Dave Burt wrote:
>>> It's by design. A Matrix is immutable, like Ruby's other numbers
>>> (Fixnum, Rational, Complex...)
>> Why should a Matrix be immutable? It's not a type like a Fixnum, it's a
>> data structure, like an Array or Hash. What is gained by creating a new
>> Matrix from a changing data stream, rather than updating an existing
>> one?
> 
> In mathematics, matrices of various kinds are regarded as a unit, usually
> indivisible. For example, they're used a lot in computer graphics
> processing to hold rotation matrices.
> 
> The rotation matrices are loaded with specific values that accomplish
> rotations and translations, and until the computed viewpoint changes, the
> entire matrix is used to process all the image vertices.
> 
> Then, when the viewpoint changes, the entire matrix is recomputed, and a new
> immutable matrix is created. The point I am making is that the matrix can't
> function if it is thought of as nine scalar values rather than a 3x3 square
> matrix.

The immutability of a Matrix violates Whoever's Law, which states

It is possible to write Fortran programs in any language.

<ducking>

Seriously, though, I agree with the poster who said some mathematicians
want to be able to compute and change elements of a matrix. I happen to
be one of those, and the subclass trick someone posted is one I'll need
to use if I use the "Matrix" concept in my Ruby code. Given how slow it
is, though, that seems unlikely.