Re: matrices with arbitrary dimensionality

• To: mathgroup at smc.vnet.net
• Subject: [mg76739] Re: matrices with arbitrary dimensionality
• From: Ray Koopman <koopman at sfu.ca>
• Date: Sat, 26 May 2007 04:46:20 -0400 (EDT)
• References: <f36ea9\$7tn\$1@smc.vnet.net>

```On May 25, 3:38 am, "alexxx.ma... at gmail.com" <alexxx.ma... at gmail.com>
wrote:
> Hi there,
> with V.6.0 I keep on with my experiment in translating a large C++
> spin simulation program.
>
> What I'm bouncing my head against today is the following:
>
> there is a way in M to describe objects (matrices) having an arbitrary
> number of dimensions, defined just at runtime?
>
> In detail, I work on an orthogonal lattice where my spins are defined,
> but the simulations require sometimes to deal with 1d (arrays),
> sometimes more.
>
> Yet I'd like to write the most general code it is possible, e.g. when
> writing a procedure that - given a location in the lattice at the
> coordinates {i,j,...} - returns a list of locations of the nearest
> neighbors
> (in 1d: {{i-1},{i+1}}; in 2d: {{i-1,j},{i+1,j},{i,j-1},{i,j+1}} and so
> on...)
>
> thanks for any hint...
>
> Alessandro Magni

neighbors[v_List?VectorQ] := Flatten[{v-#,v+#}& /@
IdentityMatrix@Length@v,1]
neighbors[{x,y,z}]

{{-1+x,y,z},
{1+x,y,z},
{x,-1+y,z},
{x,1+y,z},
{x,y,-1+z},
{x,y,1+z}}

```

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