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Re: VectorToMatrix
*To*: mathgroup at smc.vnet.net
*Subject*: [mg4373] Re: VectorToMatrix
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Mon, 15 Jul 1996 07:01:10 -0400
*Organization*: University of Western Australia
*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.)
See The Mathematica Journal 4(1):34. That example converts a vector
into a symmetric matrix. It is easy to modify this example to meet
your needs:
To convert a vector into a symmetric matrix, note that an m x m
symmetric matrix corresponds to a vector of length m(m+1)/2 (a so-
called traingular number). Inverting this formula:
In[1]:= dim[n_] = (m /. Solve[m(m+1)/2 == n, m] // Last)
Out[1]= -1 + Sqrt[1 + 8 n]
------------------
2
In[2]:= vec = {a,b,c,d,e,f,g,h,i,j};
In[3]:= dim[Length[vec]]
Out[3]= 4
This is fast so you might as well compute it.
In[4]:= VectorToMatrix[vec_ /; IntegerQ[dim[Length[vec]]]] :=
Module[{m = dim[Length[vec]],i,j},
Table[If[i>=j,0,vec[[j + (i-1)(m-i/2)-1]]],
{i, m}, {j, m+1} ]]
In[5]:= VectorToMatrix[vec] // MatrixForm
Out[17]//MatrixForm=
0 a b c d
0 0 e f g
0 0 0 h i
0 0 0 0 j
Cheers,
Paul
_________________________________________________________________
Paul Abbott
Department of Physics Phone: +61-9-380-2734
The University of Western Australia Fax: +61-9-380-1014
Nedlands WA 6907 paul at physics.uwa.edu.au
AUSTRALIA http://www.pd.uwa.edu.au/Paul
_________________________________________________________________
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