Re: DirectSum (feature request)
- To: mathgroup at smc.vnet.net
- Subject: [mg97830] Re: DirectSum (feature request)
- From: Ray Koopman <koopman at sfu.ca>
- Date: Mon, 23 Mar 2009 04:02:42 -0500 (EST)
- References: <gq2eu9$ech$1@smc.vnet.net>
If Ms is a list of matrices then this should give their direct sum:
dirsum[Ms_] := Module[{c = FoldList[Plus,0,Length/@First/@Ms]},Join@@
MapThread[PadRight[#1,{Length@#1,Last@c},0,{0,#2}]&,{Ms,Most@c}]]
On Mar 21, 3:18 am, 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~