Using ruby for scientific computing

Hi all,

For pedagogic purposes, I am trying to solve simple partial differential
equations (say a diffusion equation on a regular mesh in 2D) with Ruby.
Using the NArray gem, I have built a satisfactory tool from an interface
(and ease of use) point of view but the performance are suboptimal.=20

I am now wondering what is the right way to improve my code
performance-wise. I am doing a lot of matrix-vector and vector-vector
products.=20

=46rom 2 2D NArrays describing two scalar fields, dot-product is =
implemented as :

def dot_product(vec_a, vec_b)=20
        dot_product=3D(vec_a*vec_b">vec_a*vec_b).sum=20
end

and as I am working with sparse matrices, (for the time being) a matrix
is an Array of Hashes. Each key of the hash contains the index of the
non-vanishing coefficients (the value of this coefficient is the value
of the Hash) of the matrix. For the identity matrix it gives

def identity(sizeX, sizeY)
        mat=3D[]
        (0..sizeX*sizeY">sizeX*sizeY).each { |ind|
            mat << {ind=3D>1.0}
        }
        mat
end


Matrix vector product is then defined as

def matrix_vector_product(mat, vector)=20
        ff=3DNArray.float(100,100)
        (0..100*100).each { |ind|
            matrix[ind].each do |key,value|
                ff[[ind]]+=3Dvalue*vector[[key]][0]
            end
        }
        ff
end

I am wondering what is the best way to tackle this performance problem :
1. Improve the ruby code (and how? :) Should I avoid using hashes?
2. Write an extension to perform these operations in C. BTW is there a
way to access directly NArray data (without copy) from a C extension?
3. Use a wrapper like Ruby-lapack
(
https://rubyforge.org/projects/ruby-lapack/
).

What do you think?=20

Thanks for your help !

--=20
  Olivier Saut
 =20
[e-mail]
						       	                	=
- Olivier