Re: random matrix from row and column sums

• To: mathgroup at smc.vnet.net
• Subject: [mg53581] Re: random matrix from row and column sums
• From: "Astanoff" <astanoff at yahoo.fr>
• Date: Wed, 19 Jan 2005 01:59:32 -0500 (EST)
• References: <csinpt\$njk\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```< Is there an efficient method in Mathematica to generate random tables
< of nonnegative integers from a list of row sums and a list of column
< sums?
< For example for row sums of {7,3,2} and column sums of {2,9,1} the
< following two tables satisfy the constraints:
< {{2, 5, 0}, {0, 2, 1}, {0, 2, 0}}
< and
< {{1, 6, 0}, {1, 2, 0}, {0, 1, 1}}

This is one possible solution :

In[1]:=
rand[sumLin_List, sumCol_List]:=
Module[{n = Length[sumLin],
ones,t},
ones=Table[1,{n}];
While[t=Table[Random[Integer,Min[sumLin[[i]],sumCol[[j]]]],
{i,1,n},
{j,1,n}];
t[[1]]=sumCol-Plus @@ Rest[t];
ok=And @@ Thread[0 <= t[[1]]] &&
And @@ Thread[t[[1]] <= sumCol] &&
t.ones == sumLin &&
ones.t == sumCol;
!ok];
t];

In[2]:=
rand[{7,3,2},{2,9,1}]

Out[2]=
{{1,6,0},{1,1,1},{0,2,0}}

In[3]:=
rand[{7,3,2,4,5},{2,9,1,5,4}]

Out[3]=
{{0,3,0,3,1},{0,3,0,0,0},{0,1,0,0,1},{1,2,0,0,1},{1,0,1,2,1}}

Not very efficient indeed, but it works for small tables of small
numbers.

v.a.

```

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