       Re: DirectSum (feature request)

• To: mathgroup at smc.vnet.net
• Subject: [mg97827] Re: DirectSum (feature request)
• From: ADL <alberto.dilullo at tiscali.it>
• Date: Mon, 23 Mar 2009 04:02:09 -0500 (EST)
• References: <gq2eu9\$ech\$1@smc.vnet.net>

```Maris, from Raffy clever analysis, I would do this:

Unprotect[DiagonalMatrix];
DiagonalMatrix[vComp_?(VectorQ[#, MatrixQ] &)] :=
ArrayFlatten@ReleaseHold@DiagonalMatrix[Hold /@ vComp];
Protect[DiagonalMatrix];

This might be the "permanent" fix (and the fastest one) you were
looking for, waiting for a kind develper to implement it natively.

On 21 Mar, 11:18, Maris Ozols <maroz... at gmail.com> wrote:
> Taking a direct sum of a given list of matrices is a very common task
> (unless you are a quantum physicist and use only KroneckerProduct).
> Unfortunately there is no built-in function (that I know of) for doing
> this in Mathematica. The closest thing we have is ArrayFlatten. So I
> usually do something like this to compute a direct sum:
>
> DirectSum[Ms_] := Module[{n = Length[Ms], z, i},
>   z = ConstantArray[0, n];
>   ArrayFlatten@Table[ReplacePart[z, i -> Ms[[i]]], {i, 1, n}]
> ];
>
> Is there a better way of doing this?
>
> Note: A nice way to implement it would be
>
> DirectSum[Ms_] := ArrayFlatten@DiagonalMatrix[Ms];
>
> Unfortunately this gives "DiagonalMatrix::vector" error, since
> DiagonalMatrix is not flexible enough to accept a list of matrices.
> The way DiagonalMatrix is used in the above code might cause some
> confusion for beginners, but in general I don't see why DiagonalMatrix
> should be limited in this way.
>
> ~Maris Ozols~

```

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