strange behavior

*To*: mathgroup at smc.vnet.net*Subject*: [mg27158] strange behavior*From*: Otto Linsuain <linsuain+ at andrew.cmu.edu>*Date*: Thu, 8 Feb 2001 04:40:45 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi all. I have a little problem using Thread and MapThread, and although I have found a way around it, I am still unhappy with it being there in the first place. I have a function (call it myF ) that takes as arguments FOUR vectors of equal length (doesn't matter what length) -by vector I mean a List of numbers with the simplest structure possible {x1, x2, ..... xN}- and gives out a number. The only operations involved in getting the number are addition, subtraction, multiplication and division. So I do convolutions of one list with another, and things like that (although I don't use ListConvolve). I want to map this function over a bunch of lists in the following way: For argument #1 I always want the same list xList={x1, x2, .....xN} For argument #2 I have the list: yList={{a1,a2,...aN}, {b1,b2,...bN}} and I want to apply the function first to the x's as argument #1 with the a's as argument #2, and then to the x's as argument #1, with the b's as argument #2. So far so good, and only need to map over the second argument. For argument #3 I have many lists. More exactly, I have a list consisting of two NxN matrices: cList={ { {Ca11,Ca12, ...Ca1N},{Ca21,Ca22, ...Ca2N},...{CaN1,Ca12, ...CaNN} }, { {Cb11,Cb12, ...Cb1N},{Cb21,Cb22, ...Cb2N},...{CbN1,Cb12, ...CbNN} } } similarly for argument #4 lList={ { {La11,La12, ...La1N},{La21,La22, ...La2N},...{LaN1,La12, ...LaNN} }, { {Lb11,Lb12, ...Lb1N},{Lb21,Lb22, ...Lb2N},...{LbN1,Lb12, ...LbNN} } } when I use the a's for argument #2 I want to go through and use the first row in the Ca's for argument #3, and the first row in the La's for argument #4, then the second row of each, etc Notice that I don't want all the combination between the cList and the lList. When I am done with that I go to the b's for argument #2, then I want to use the first rows of Cb and Lb for arguments #3 and #4, then their second rows, etc. This is what I do: MapThread[ myF[xList,#1,#2,#3]&, {yList, cList, lList} ] this uses first the first Parts of yList, cList and lList, and then their second Parts. This produces { myF[ xList, {a1,a2,....aN}, matrix of Ca's, matrix of La's], myF[xlIst, {b1,b2,..bN}, matrix of Cb's, matrix of Lb's]} So far so good. Now I just need to Thread over the last two arguments: Map[ Thread[#, List,-2]&, MapThread[ myF[xList,#1,#2,#3]&, {yList, cList, lList} ] ] This threads the function myF over those arguments just the way I wanted AS LONG AS the function myF has not been defined. The minute I define the function myF to do what I want it to do (to combine the four vectors in a certain way and produce a number) it threads in a different way. Namely it threads as if using the Transpose of the lists cList and lList. One solution is to use the Transpose in the first place, so when they get Transposed again it would be just fine, but this is still puzzling. Any ideas on what is going on and suggestions on how to fix it (Transposing big matrices is a little slow) would be appreciated. Otto Linsuain.