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~