From: Larry Evans <cppljevans@...>
Date: 2011-01-09T04:35:26+09:00
Subject: Re: Nooby question : multidimensional arrays.

On 01/07/11 21:57, Larry Evans wrote:
> On 01/07/11 17:56, Kedar Mhaswade wrote:
>> Is this an okay job of implementing a multidimensional array?
>>
>> https://github.com/kedarmhaswade/datacube/blob/master/data_cube.rb
>>
>> Thank you for any feedback.
>>
>> -Kedar
>>
> There's a book:
> 
>   http://web.engr.oregonstate.edu/~budd/Books/aplc/
> 
> which describes an expansion vector which is a scan of
> the array sizes.  IOW, for:
> 
>   arr = Array.new(s0,s1,...sn)
> 
> the expansion vector for this arr is:
> 
>   arr.ev = [1, s0, s0*s1, s0*s1*s3,..., s0*s1*...*sn]
> 
The expansion vector for DataCube.new(n,m) would be:

  [m**0,m**1,m**2,...,m**n]

IOW, the length of this expansion vector is n+1.

[snip]
> 
>     arr[i0,i1,..., ij, ... in]
> 
> is located:
> 
>     i0*arr.ev[0]+i1*arr.ev[1]+...+in*arr.ev[n]
> 
> elements from the 1st element:
> 
>     arr[0,0,...,0]
> 
> Thus, given the sizes, you can create a member variable
> which is the expansion vector, then use that to access the
> elements by calculating the offset from the initial element
> using the dot product:
> 
>     i0*arr.ev[0]+i1*arr.ev[1]+...+in*arr.ev[n]
> 
However, after looking at:

  https://github.com/kedarmhaswade/datacube/blob/master/data_cube.rb#L48

it's not clear that to_index calculates the same offset because
coefficients[i] corresponds to one of the i0,i1,...,in-1 in the
above formulat, and coefficients[i] is not multiplied by anything.
It's only added to mega_index*n, and mega_index*n involves
multiplication by the dimension, n, instead of ths uniform size, m.


HTH

  -Larry