Re: vector ordering problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg126713] Re: vector ordering problem*From*: Ray Koopman <koopman at sfu.ca>*Date*: Sat, 2 Jun 2012 05:41:28 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jq74k3$qkn$1@smc.vnet.net>

On May 30, 11:54 pm, Marco Lazzaretti <marco.lazzarett... at gmail.com> wrote: > Hi, > I have these two vectors, vector1 and vector2. > I need to have vector2 sorted by a positions vector, > given by a vector1. > e.g. > vector1 ={32,4,28,11,20} > position_vector1= Ordering[vector1] > position_vector1 = {5,1,4,2,3} > > vector2 = {78,12,95,14,35} > > requested output > {35,78,14,12,95} > > that is, I have this position vector, as an output from another > calculation; then i need my input vector to be sorted as the > position vector says. > Obviously, my real input vector is quite bigger so i can't sort it > manually... I hope the small example can explain my problem better > than my words... "Position vector" is an ambiguous term. You need to distinguish between "to" lists and "from" lists. The list of indices returned by Ordering is a "from" list: the k'th element specifies where in the original list the k'th element in the reordered list came *from*. However, your position_vector1 seems to be a "to" list: the k'th element specifies the position in the new list that the k'th element in the old list should go *to*. Ordering toggles between the two kinds of lists. In[1]:= v1 = {32,4,28,11,20}; In[2]:= o1 = Ordering@v1 p1 = Ordering@o1 o1 === Ordering@p1 Out[2]= {2,4,5,3,1} Out[3]= {5,1,4,2,3} Out[4]= True In[5]:= v2 = {78,12,95,14,35}; In[6]:= v2[[o1]] v2[[p1]] Out[6]= {12,14,35,95,78} Out[7]= {35,78,14,12,95}