Re: Cartesian product of n sets of lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg5906] Re: [mg5860] Cartesian product of n sets of lists*From*: "w.meeussen" <w.meeussen at solair4b.eunet.be>*Date*: Tue, 4 Feb 1997 00:03:24 -0500*Sender*: owner-wri-mathgroup at wolfram.com

At 01:30 2-02-97 -0500, you wrote: > >PLEASE: be kind to mail answers to <jchd at worldnet.fr> as well. >I do _not_ receive this list at all here (I wonder why, since I got the >welcome automated message) and the feed for the Mma newsgroup is utterly >unreliable at this end, sigh! Sorry for that unconvenience. > > >Using Mma v2.x, I never found the proper way to get the cartesian >product of several sets whose elements are themselves Lists. > >In other terms, I would like to write something like this (using List as >operator): > >p =3D CartProd[List, { {a, b, c}, {1, 2, 3} }, > { {d, e, f}, {4, 5, 6} }] > >and obtain four matrices: > > a b c a b c d e f d e f > 1 2 3 4 5 6 1 2 3 4 5 6 > > >Outer is of little use since it acts beyond level 1 of its arguments, e.g= >.: > >Outer[List, { {a, b}, {1, 2} }, > { {c, d}, {3, 4} }] > >{{{{{a, c}, {a, d}}, {{a, 3}, {a, 4}}}, {{{b, c}, {b, d}}, {{b, 3}, {b, >4}}}},=20 > {{{{1, c}, {1, d}}, {{1, 3}, {1, 4}}}, {{{2, c}, {2, d}}, {{2, 3}, {2, >4}}}}} > > >Of course, it's possible to define a bunch of functions (one taking 2 >sets, one taking 3 sets, ...) like: > >CartProd[f_, s1_List, S2_List] :=3D Block[{ii,jj}, > Flatten[ Table[ f[s1[[ii]], s2[[jj]] ], > {ii,Length[s1]}, {jj,Length[s2]} ], 1]] > >but I find it a little ugly. > > >Thank you for your hints. >-- > jchd at worldnet.fr | Jean-Chistophe Deschamps > | 14, rue Hermel > T=E9l.: (33) 01 42 55 01 93 | 75018 Paris > > > > hi, In Mma 3.0, your usage of Outer[] has been included: ?Outer "Outer[f, list1, list2, ... ] gives the generalized outer product of the listi, forming all possible combinations of the lowest-level elements in each of them. Outer[f, list1, list2, ... , n] treats as separate elements only sublists at level n in the listi. Outer[f, list1, list2, ... , n1, n2, ... ] treats as separate elements only sublists at level ni in the corresponding listi." In Mma 2.2.3, I would use a simple inert wrapping function like dummy[] to protect the innermost list: li1={ {a, b, c}, {1, 2, 3} } {{a, b, c}, {1, 2, 3}} li2={ {d, e, f}, {4, 5, 6} } {{d, e, f}, {4, 5, 6}} {it1,it2}= Transpose at {li1,li2} it1 {{a, b, c}, {d, e, f}} it2 {{1, 2, 3}, {4, 5, 6}} Outer[List,dummy@@it1,dummy@@it2]/.dummy->List {{{{a, b, c}, {1, 2, 3}}, {{a, b, c}, {4, 5, 6}}}, {{{d, e, f}, {1, 2, 3}}, {{d, e, f}, {4, 5, 6}}}} %//TableForm a b c a b c 1 2 3 4 5 6 d e f d e f 1 2 3 4 5 6 If you want the four smaller lists sequentially, then do Flatten[Outer[List,my@@it1,my@@it2]/.my->List,1] I hope this is what you meant. Dr. Wouter L. J. MEEUSSEN w.meeussen at solair4b.eunet.be