Re: Creating a symmetric matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg46986] Re: Creating a symmetric matrix
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 18 Mar 2004 04:38:01 -0500 (EST)
• Organization: The University of Western Australia
• References: <c2p9ld\$dns\$1@smc.vnet.net> <200403130440.XAA15145@smc.vnet.net> <A8166766-7689-11D8-A63D-0003938BF55C@jeol.com> <c36baq\$s26\$1@smc.vnet.net> <c3bfgk\$7i5\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <c3bfgk\$7i5\$1 at smc.vnet.net>,
Paul Abbott <paul at physics.uwa.edu.au> wrote:

> In article <c36baq\$s26\$1 at smc.vnet.net>, DrBob <drbob at bigfoot.com>
> wrote:
>
> > Building a matrix that large (2000x2000), when half the information is
> > redundant, is probably a bad idea in the first place; and that applies to
> > the upper-triangular matrix you're taking it from as well.
> >
> > Instead, you should write code that uses the necessary information more
> > efficiently.
> >
> > SparseArray also may be of help.
>
> Perhaps something like
>
>   Flatten[Table[{i,j} -> a[i,j],{j, 1, 4}, {i, 1, j}]];
>
>   % /. ({i_, j_} -> a_) :> {j, i} -> a;
>
>   Normal[SparseArray[Join[%, %%]]]

or maybe

tri = Flatten[Table[{i, j} -> a[i, j], {j, 1, 4}, {i, 1, j}]]

diag = Cases[tri, c:({i_, i_} -> a_) -> c]

tri = SparseArray[tri]

diag = SparseArray[diag]

tri + Transpose[tri] - diag

Normal[%]

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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