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Re: Using implicit information about row indices


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


Not pretty, but...

info = {
   {{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}}};

In[19]:= Normal[Apply[SparseArray,{Flatten[
   MapIndexed[Map[Function[{x},{#2[[1]],x[[1]]}->x[[2]]],#]&, info]]}]]

Out[19]= {{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}}

There is probably a cleaner way to do the MapIndexed[Map[...]] part.

Daniel Lichtblau
Wolfram Research


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