Issue #8223 has been updated by boris_stitnicky (Boris Stitnicky).


So with another apology, I will use this space to write down a few more remarks so that I do not forget about them. My line of thinking was as follows: The first step to the systematic solution of this problem would be to generalize zero. It means that the matrix elements would be required to be of a class that has #zero method defined. As for Matrix.zero and Matrix.empty, I think that there should be an option to tell them what this zero is (or tell them the class that has #zero defined). Or perhaps we could play the abstract algebra terminology and call it "additive_identity_element" instead of "zero". That would mean that Matrix would require its elements to comply with at least monoid definition for matrix addition and multiplication, and monoids necessarily need to have the additive identity element defined.
----------------------------------------
Feature #8223: Make Matrix more omnivorous.
https://bugs.ruby-lang.org/issues/8223#change-38316

Author: boris_stitnicky (Boris Stitnicky)
Status: Open
Priority: Normal
Assignee: 
Category: 
Target version: 


Let's imagine a class Metre, whose instances represent physical magnitudes in metres.

    class Metre
      attr_reader :magnitude
      def initialize magnitude; @magnitude = magnitude end
      def to_s; magnitude.to_s + ".m" end
    end

Let's say that metres can be multiplied by a number:

    class Metre
      def * multiplicand
        case multiplicand
        when Numeric then Metre.new( magnitude * multiplicand )
        else
          raise "Metres can only be multiplied by numbers, multiplication by #{multiplicand.class} attempted!"
        end
      end
    end

And that they can be summed up with other magnitudes in metres, but, as a feature,
not with numbers (apples, pears, seconds, kelvins...).

    class Metre
      def + summand
        case summand
        when Metre then Metre.new( magnitude + summand.magnitude )
        else
          raise "Metres can only be summed with metres, summation with #{summand.class} attempted!"
        end
      end
    end

Now with one more convenience constructor Numeric#m:

    class Numeric
      def m; Metre.new self end
    end

We can write expressions such as

    3.m + 5.m
    #=> 8.m
    3.m * 2
    #=> 6.m

And with defined #coerce:

    class Metre
      def coerce other; [ self, other ] end
    end

Also this expression is valid:

    2 * 3.m
    #=> 6.m

Before long, the user will want to make a matrix of magnitudes:

    require 'matrix'
    mx = Matrix.build 2, 2 do 1.m end
    #=> Matrix[[1.m, 1.m], [1.m, 1.m]]

It works, but the joy does not last long. The user will fail miserably if ze wants to perform matrix multiplication:

    cv = Matrix.column_vector [1, 1]
    mx * cv
    #=> RuntimeError: Metres can only be summed with metres, summation with Fixnum attempted!
    # where 2.m would be expected

In theory, everything should be O.K., since Metre class has both metre summation and multiplication by a number defined. The failure happens due to the internal workings of the Matrix class, which assumes that the elements can be summed together with numeric 0. But it is a feature of metres, that they are picky and allow themselves to be summed only with other Metre instances.

In my real physical units library that I have written, I have solved this problem by
defining an über zero object that produces the expected result, when summed with objects, that would otherwise not lend themselves to summation with ordinary numeric 0,
and patching the Matrix class so that it uses this über zero instead of the ordinary one.

But this is not a very systematic solution. Actually, I think that the Matrix class would be more flexible, if, instead of simply using 0, it asked the elements of the matrix what their zero is, as in:

    class << Metre
      def zero; new 0 end
    end

But of course, that would also require that ordinary numeric classes can tell what their zero is, as in:

    def Integer.zero; 0 end
    def Float.zero; 0.0 end
    def Complex.zero; Complex 0.0, 0.0 end
    # etc.

I think that this way of doing things (that is, having #zero methods in numeric classes and making Matrix actually require the class of the objects in it to have public class method #zero defined) would make everything more consistent and more algebra-like. I am having this problem for already almost half a year, but I only gathered courage today to encumber you guys with this proposal. Please don't judge me harshly for it. I have actually already seen something like this, in particular with bigdecimal's Jacobian (http://ruby-doc.org/stdlib-2.0/libdoc/bigdecimal/rdoc/Jacobian.html), which requires that the object from which the Jacobian is computed implements methods #zero, #one, #two etc. Sorry again.


-- 
http://bugs.ruby-lang.org/