Re: New User - Programming

*To*: mathgroup at smc.vnet.net*Subject*: [mg52535] Re: [mg52507] New User - Programming*From*: "David Park" <djmp at earthlink.net>*Date*: Wed, 1 Dec 2004 05:57:55 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Dean, This looks like a great application for functional programming in Mathematica. a = {5, 6, 3, 2, 8, 2}; b = {5, 4, 1, 3, 9, 4}; If you want to combine two equal length lists to make a new list, a good command to use is Inner. signal = Inner[Sign[#1 - #2] &, a, b, List] {0, 1, 1, -1, -1, -1} The Sign function is used on the difference of the elements in the a and b lists. We want the whole operation to return a new List so that is the last argument. If you wanted to go with your first specification and sum all the signal elements you could use... Inner[Sign[#1 - #2] &, a, b, Plus] -1 If you want to sum the signal elements but clamp the cumulative sum between -1 and +1 then you can use another functional command, FoldList on the signal elements, FoldList[Max[-1, Min[1, #1 + #2]] &, 0, signal] {0, 0, 1, 1, 0, -1, -1} That has the starting value, 0, at the beginning of the list, which you could get rid of by using the Drop command. If you want to sum this new series you can Apply Plus to the intermediate result. Plus @@ FoldList[Max[-1, Min[1, #1 + #2]] &, 0, signal] 0 David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Dean Williams [mailto:deanwilliams at mac.com] To: mathgroup at smc.vnet.net I am a new user who is well and truly stuck. Any help would be greatly appreciated. I have two lists, a and b, that when compared, will produce a third list of signals. This third list is then summed to get a cumulative total of the signals. The rules are fairly simple. If a = b, the signal is 0, if a > b, the signal is 1 and finally, if a < b, then the signal is ?1. a={5,6,3,2,8,2}; b={5,4,1,3,9,4}; c={a,b}; p=0; Fun[t_,u_]/;t==u :=0; Fun[t_,u_]/;t>u:=1; Fun[t_,u_]/;t<u:=-1; signal=Map[ (Fun[#[[1]],#[[2]]])&,Transpose[c]]; c4={signal}; cumTotal=Flatten[Map[p+={Last[#]} &,Transpose[c4]]]; TableForm[{a,b,signal,total},TableDirections->Row, TableHeadings->{{"a","b","Signal","Cumm.Total"},None}, TableSpacing->{4,4,4,4,4}] a b Signal Cum.Total 5 5 0 0 6 4 1 1 3 1 1 2 2 3 -1 1 8 9 -1 0 2 4 -1 -1 I want to modify slightly how the signal is generated. The rules are the same except that if the cumulative total is already 1 or -1, then no new signal is generated unless the new signal would make the cumulative total move back towards zero. Ideally, I am looking to modify my code, so it produces, signal = {0,1,0,-1,-1,0} and cumTotal = {0,1,1,0,-1,-1}.The maximum size of the cumulative total need not be 1, but rather any value that is chosen as a limit. This has been causing me a great deal of grief and I would greatly welcome any help and suggestions. Given my lack of experience, I am sure that there is a more efficient way to tackle this type of problem, especially as I am dealing with many large lists. Regards Dean Williams