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Re: VectorToMatrix
*To*: mathgroup at smc.vnet.net
*Subject*: [mg4343] Re: VectorToMatrix
*From*: tlm at ameslab.gov (Dr. T. L. Marchioro II)
*Date*: Thu, 11 Jul 1996 00:59:39 -0400
*Organization*: Iowa State University, Ames, Iowa
*Sender*: owner-wri-mathgroup at wolfram.com
Robert Pratt wrote:
> I want to define a function VectorToMatrix[list_, n_] that behaves as
> follows:
>
> VectorToMatrix[{a,b,c,d,e,f,g,h,i,j}, 4]//MatrixForm
>
> 0 a b c d
> 0 0 e f g
> 0 0 0 h i
> 0 0 0 0 j
>
> Now n can be determined from Length[list], which will always be equal
to
> n choose 2 for some n. But I would rather input n to save that
> computation. (I will be doing this for a lot of vectors.)
>
> Any ideas?
This proved a little more difficult than I had thought... but I think
the following is what you want to convert a vector into the elements of
an upper triangular matrix. I am a little surprised your example is not
nXn, but assume that is what you want. If not, the following should be
easy to adapt. No doubt some guru can present a more efficient method :)
vectorToUTMatrix[l_List, n_Integer]:=
Module[{temp, temp1},
(*make the first row *)
temp=RotateRight[Join[l, Table[0, {n}]]];
temp1=Take[temp, n+1];
(* now form other rows and join them to first *)
Do[(
temp=Drop[temp, {iter+1, n+1}];
temp=RotateRight[temp];
temp1=Join[temp1, Take[temp, n+1]];),
{iter, 1, n-1}];
(* Partition list of elements into matrix of proper shape *)
Partition[temp1,n+1]
]
For me this yields:
l={a, b, c, d, e, f, g, h, i, j};
vectorToUTMatrix[l,4]//MatrixForm
0 a b c d
0 0 e f g
0 0 0 h i
0 0 0 0 j
l=Join[l, {k, el, m, n, o}];
vectorToUTMatrix[l,5]//MatrixForm
0 a b c d e
0 0 f g h i
0 0 0 j k el
0 0 0 0 m n
0 0 0 0 0 o
l=Join[l, {p,q, r, s, t, u}];
vectorToUTMatrix[l,6]//MatrixForm
0 a b c d e f
0 0 g h i j k
0 0 0 el m n o
0 0 0 0 p q r
0 0 0 0 0 s t
0 0 0 0 0 0 u
etc. I hope this is what you were after.
TLM
--
Dr. Thomas L. Marchioro II Two-wheeled theoretical physicist
Applied Mathematical Sciences 515-294-9779
Ames Laboratory 515-432-9142 (home)
Ames, Iowa 50011 tlm at ameslab.gov
Project Coordinator: Undergraduate Computational Engineering and Sciences
http://uces.ameslab.gov/
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