From: Olivier Saut <osaut@...>
Date: 2012-09-09T01:06:58+09:00
Subject: 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. 

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. 

From 2 2D NArrays describing two scalar fields, dot-product is implemented as :

def dot_product(vec_a, vec_b) 
        dot_product=(vec_a*vec_b">vec_a*vec_b).sum 
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=[]
        (0..sizeX*sizeY">sizeX*sizeY).each { |ind|
            mat << {ind=>1.0}
        }
        mat
end


Matrix vector product is then defined as

def matrix_vector_product(mat, vector) 
        ff=NArray.float(100,100)
        (0..100*100).each { |ind|
            matrix[ind].each do |key,value|
                ff[[ind]]+=value*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? 

Thanks for your help !

-- 
  Olivier Saut
  
osaut@airpost.net
						       	                	- Olivier