Re: List Manipulation

*To*: mathgroup at smc.vnet.net*Subject*: [mg31556] Re: List Manipulation*From*: peter weijnitz <pewei at algonet.se>*Date*: Sun, 11 Nov 2001 00:34:43 -0500 (EST)*References*: <9sgeqm$93v$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

A simple trnsformation seems to work {{A, {0, 0, 0, 5}}, {B, {3, 0, 0, 6}}, {C, {-5, -3, 0,0}}, {D,{7,0, 0,-7}}}/.{ww_,{a_,b_,c_,d_}}->{ ww,{Sign[a],Sign[b],Sign[c],Sign[d]}} gives: {{A,{0,0,0,1}},{B,{1,0,0,1}},{C,{-1,-1,0,0}},{D,{1,0,0,-1}}} Jonathan Woodward wrote: > I am a relatively new user to Mathematica with virutally no > programming experience and need help with a problem: > > Given the following hypothetical eigensystem, a "list of lists" which > has the eigenvalues (A,B,C,D) associated with their corresponding > eigenvectors ({0,0,0,a},{b,0,0,d},{-a,-b,0,0},{c,0,0,-c}): > > {{A,{0,0,0,a}},{B,{b,0,0,d}},{C,{-a,-b,0,0}},{D,{c,0,0,-c}}} > > where the list contains zeros, symbolic expressions, and numbers. > The actual system I have is the eigensystem of a 32x32 symbolic matrix > where the vector components seem to take up hundreds of pages and > are therefore almost useless to me. However, I am interested in the > position of the zero and nonzero components only, not their actual > values. > > So what I want to do is transform the list into another more > useful list in the following way: > > I do not want to change the eigenvalues but want to convert all > eigenvector > components in such a way that I have a list of zeros, ones, and > negative ones. > In other words, divide each eigenvector component by its absolute > value, except for the zeros, to create a new list that might now look > like: > > {{A,{0,0,0,1}},{B,{1,0,0,1}},{C,{-1,-1,0,0}},{D,{1,0,0,-1}}} > > This way I can greatly simplify my problem while keeping the position > of the > zero and nonzero elements of the components unchanged. > > How would I write a code in Mathematica to accomplish this? In > particular, > how would do I tell the program to scan through this list, doing > nothing > to the eigenvalues, but look through the eigenvectors, check to see if > they > are nonzero (if zero, do nothing) and divide each nonzero component by > its > absolute value, and return a new list. I don't want to break the list > apart > and operate just on the vector components themselves because I want to > preserve the eigenvalue-eigenvector association. Also, I need to be > able to tell > the program that symbols of the type {x} are positive and {-x} are > negative > otherwise I might have a list returned like: > > {{A,{0,0,0,a/Abs[a]}},{B,{b/Abs[b],0,0,d/Abs[d]}},{C,{-a/Abs[a],-b/Abs[b],0,0}},{D,{c/Abs[c],0,0,-c/Abs[c]}}} > > which is not simplified to what I need. > > Any help would be greatly appreciated. > > Thanks > > Jonathan Woodward