From: Masahiro TANAKA <masa@...>
Date: 2002-12-01T19:31:14+09:00
Subject: Re: Numerical Ruby

Hi,

>From: Olivier Saut <Olivier.Saut@gmm.insa-tlse.fr>

> My code uses lots of loops as in the following example. 
> 
> def faraday
> for y in 1..(maxY-1)
>  for z in 1..(maxZ-1)   
>   @Bx[y,z]+=-(dt/dy)*(@Ez[y+1,z]-@Ez[y,z])+(dt/dz)*(@Ey[y,z+1]-@Ey[y,z])
>   @By[y,z]+=  - (dt/dz)*(@Ex[y,z+1]-@Ex[y,z])        
>   @Bz[y,z]+=(dt/dy)*(@Ex[y+1,z]-@Ex[y,z])      
>   end
>  end
> end
> 
> I am using NArray from Masahiro Tanaka
> (http://www.ir.isas.ac.jp/~masa/ruby/index-e.html) to represent the
> electromagnetic field.
> 
> Is there any way to speed up this type of computations? (I am not sure
> how a C extension could help in this case.)

If you use NArray, "writing without loop" is the way to speed up.
Your 'faraday' method can be rewritten as:

  def faraday2
    dt,dx,dy,dz = [1.0]*4
    @Bx[1..-2,1..-2] += -(dt/dy)*(@Ez[2..-1,1..-2] - @Ez[1..-2,1..-2]) +
    		         (dt/dz)*(@Ey[1..-2,2..-1] - @Ey[1..-2,1..-2])
    @By[1..-2,1..-2] += -(dt/dz)*(@Ex[1..-2,2..-1] - @Ex[1..-2,1..-2])
    @Bz[1..-2,1..-2] +=  (dt/dy)*(@Ex[2..-1,1..-2] - @Ex[1..-2,1..-2])
  end

For 500x500 array, the result of benchmark on my machine is:

  with loop:    8.69 sec
  without loop: 0.31 sec

Regards,
Masahiro Tanaka