       Re: random matrix from row and column sums

• To: mathgroup at smc.vnet.net
• Subject: [mg53727] Re: random matrix from row and column sums
• From: "Simons, F.H." <F.H.Simons at tue.nl>
• Date: Tue, 25 Jan 2005 05:03:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Here is (another) very fast function for finding a matrix of non
negative integers with given row and column sums. We start with a random
matrix of non negative integers. Then we redefine the first row and the
first column in such a way that the matrix has the desired row and
column sums, as done by Astanoff in his second posting on this topic. As
a consequence, some of the elements on the first row or first column now
can be negative. To overcome this, we manipulate the matrix in such a
way that the row and column sums do not change and negative entries
become at least 0.

randommatrix[rowSums_, colSums_] := Module[{mat, neg, a,b},
mat =Table[
Random[Integer,Min[rowSums[[i]],colSums[[j]]]], {i,1,
Length[rowSums]},{j,1,Length[colSums]}];
mat[[All, 1]]=rowSums- Total /@ Rest /@ mat;
mat[]=colSums-Plus @@ Rest[mat];
neg=Position[mat, _?Negative];
While[Length[neg]>0,
{a,b}=neg[];neg=Rest[neg];
Do[If[mat[[a,b]]\[GreaterEqual]0, Return[]];
If[(d = Min[{mat[[a,j]], mat[[i,b]]}])>0,
{mat[[a,b]],mat[[a,j]], mat[[i,j]],
mat[[i,b]]}={mat[[a,b]],mat[[a,j]], mat[[i,j]],
mat[[i,b]]}+{d,-d,d,-d}],
{i,1, Length[rowSums]}, {j,1,Length[colSums]}]];
mat]

Because of we start with a random matrix, we cannot predict what the
resulting matrix will be. But, as Bobby already remarked, it is not at
all clear how random the result is.

Fred Simons
Eindhoven University of Technology

```

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