Re: Specifying arguments inside nested functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg46130] Re: Specifying arguments inside nested functions*From*: drbob at bigfoot.com (Bobby R. Treat)*Date*: Sat, 7 Feb 2004 04:02:15 -0500 (EST)*References*: <bvvnse$j7v$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

First a couple of test matrices. mA = {{a, b, c}, {d, e, f}, {g, h, i}}; mB = {{a, x, y}, {o, e, g}, {q, r, s}}; First solution, not far from what you had in mind: ClearAll[match, not, matchNone, unmatched] not = If[#1, False, True, True] &; match[a_List, b_List] := Or @@ Thread[Equal[a, b]] matchNone[a_List, b_?MatrixQ] := not[Or @@ (match[a, #] & /@ b)] unmatched[a_?MatrixQ, b_?MatrixQ] := Select[a, matchNone[#, b] &] matchNone[#, mB] & /@ mA unmatched[mA, mB] Testing: (matchNone[#1, mB] & ) /@ mA unmatched[mA, mB] {False, False, True} {{g, h, i}} Here's a second solution, probably more efficient: ClearAll[matchNone, unmatched] matchNone[a_List, b_?MatrixQ] := Module[{f}, Nor @@ (Thread[f[Transpose@b, a]] /. f -> MemberQ) ] unmatched[a_?MatrixQ, b_?MatrixQ] := Select[a, matchNone[#, b] &] I wonder whether, if mB has a LOT of rows, it would be better to replace Transpose@b with Union/@Transpose@b or, better yet, UnsortedUnion (see the Help examples for Union. Also, since Nor will stop at the first column where there's a match, it's better for large problems if the columns are in an order that makes that happen early, most of the time -- if possible. I didn't do any testing like that, however. The same test: (matchNone[#1, mB] & ) /@ mA unmatched[mA, mB] {False, False, True} {{g, h, i}} Here's the same solution, if you don't have a global called memberQ: ClearAll[matchNone, unmatched] matchNone[a_List, b_?MatrixQ] := Nor @@ (Thread[memberQ[Transpose@b, a]] /. memberQ -> MemberQ) unmatched[a_?MatrixQ, b_?MatrixQ] := Select[a, matchNone[#, b] &] or, even niftier: ClearAll[matchNone, unmatched] matchNone[a_List, b_?MatrixQ] := Block[{MemberQ}, Nor @@ (Thread[MemberQ[Transpose@b, a]])] unmatched[a_?MatrixQ, b_?MatrixQ] := Select[a, matchNone[#, b] &] Bobby koopman at sfu.ca (Ray Koopman) wrote in message news:<bvvnse$j7v$1 at smc.vnet.net>... > I have two matrices, A and B, that have the same number of columns. > I want to select the rows of A that differ in every position from > every row of B. So I write > > Select[A, And@@Map[Inner[Unequal,#1,#2,And]&, B]& ] > > But that won't work, because I have no way to tell Inner that one of > its arguments should be the row of A that is being tested by Select, > and the other argument should be the row of B from Map. > > Now, I realize that there are ways around the problem in this > particular case. For instance, the Select test could be > > And@@Map[FreeQ[Rest[#],First[#]]&, Transpose@Prepend[B,#]]& > > which checks B a column at a time and might well be more efficient. > However, this is not the first time I've run into the problem of > specifying arguments inside nested functions, and I wonder how other > people handle it. Is there a general solution, or must I always > ad hoc it?