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MathGroup Archive 2006

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Re: Using implicit information about row indices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68310] Re: [mg68254] Using implicit information about row indices
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 1 Aug 2006 06:59:35 -0400 (EDT)
  • References: <200607310745.DAA26729@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 31 Jul 2006, at 09:45, Diamond, Mark wrote:

> I am wanting to fill a square matrix M (say, r by r)  using  
> information from
> a list, L.
>  The list L is also of length r, but is not a square matrix. It  
> contains
> lists of ordered pairs {col, num}
> It typically looks something like this; I have arranged it into  
> rows so that
> it is more obvious
> {
>   {{1, a}, {2, b}},
>
>   {{1, c}, {2, d}, {3, e}, {4, f}},
>
>  {{2, g}, {3, h}, {4, i}},
>
>  {{3, k}, {4, l}, {5,m}},
>
>  {{4, n}, {5, p}}
>
> }
>
> Now what I am trying to do is, for example, set M[[1,1]]=a, M[[1,2]] 
> =b,
> M[[2,1]]=c, M[[2.2]]=d, M[[2,3]]=e and so forth, and leave (or set)  
> all the
> other entries in M to zero. The row information for M is implicit  
> in the
> structure of the list L; additionally, the column indices as they  
> appear
> within sublist of L are guraranteed to be sequential. It seems with  
> all this
> info, there should be an easy way to fill M correctly, but I have  
> struggled
> without success to do anything other than an iterative process with  
> Do[]. I
> would appreciate any guidance you might have.
>
> Thank you.
>
> Mark Diamond
>
>
>
>


One way:

P={{{1, a}, {2, b}}, {{1, c}, {2, d}, {3, e}, {4, f}},
   {{2, g}, {3, h}, {4, i}}, {{3, k}, {4, l}, {5, m}},
   {{4, n}, {5, p}}}


Normal[SparseArray[Flatten[MapIndexed[
      Function[x, {First[#2], x[[1]]} -> x[[2]]] /@ #1 & ,
      P]]]]


{{a, b, 0, 0, 0}, {c, d, e, f, 0}, {0, g, h, i, 0},
   {0, 0, k, l, m}, {0, 0, 0, n, p}}

Andrzej Kozlowski


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