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Re: simpler way to get a particular banded matrix?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98094] Re: simpler way to get a particular banded matrix?
  • From: Raffy <raffy at mac.com>
  • Date: Mon, 30 Mar 2009 04:42:01 -0500 (EST)
  • References: <gqn910$2o$1@smc.vnet.net>

On Mar 29, 12:46 am, rip pelletier <bitbuc... at comcast.net> wrote:
> Hi,
>
> The following command constructs a matrix (typically denoted M0, it
> arises in filter banks in general, in Burrus, Gopinath, & Guo "intro to
> wavelets and wavelet transforms: a primer" in particular).
>
> I'm sure there's a way to do this without typing out all 5 bands. Here's
> what i did:
>
> SparseArray[Band[{1,1}]->H,{6,6}]+
> SparseArray[Band[{2,3}]->H,{6,6}]+
> SparseArray[Band[{3,5}]->H,{6,6}]+
> SparseArray[Band[{-2,-3},{1,1},{-1,-1}]->rH,{6,6}]+
> SparseArray[Band[{-3,-5},{1,1},{-1,-1}]->rH,{6,6}]
>
> where
>
> H={h0,h1,h2,h3,h4,h5};
> rH=Reverse[H];
>
> I get what I want:
>
> h0  0  0  0  0  0
> h2 h1 h0 0  0  0
> h4 h3 h2 h1 h0 0
> 0  h5 h4 h3 h2 h1
> 0  0  0  h5 h4 h3
> 0  0  0  0  0  h5
>
> Any easier ways to get this?
>
> TIA and vale,
>    rip
>
> --
> NB eddress is r i p 1 AT c o m c a s t DOT n e t

To error on the side of readability, I'd probably go with:

mat[n_Integer] := With[
   {vRow = Join[
      ConstantArray[0, n - 1],
      Table[ToExpression["h" <> ToString[i]], {i, n - 1, 0, -1}],
      ConstantArray[0, n - 1]]
    },
   Table[Take[vRow, {2 n + 1, 3 n} - 2 i], {i, n}]
   ];


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