Again, How to speed up this calculation? and more

*To*: mathgroup at smc.vnet.net*Subject*: [mg37246] Again, How to speed up this calculation? and more*From*: Cheng Liu <cliu at lanl.gov>*Date*: Fri, 18 Oct 2002 05:17:22 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Dear group, Thank you all for the responses. I might not make my question very clear. Suppose that I have a list of points {p1,p2, ..., pn}, I try to find all possible pairs of them. The pairs may include {pi,pi}, but {pi,pj} and {pj,pi} are considered the same and only one is counted. That said. After some try and error, I came to the following way: h=4;w=5; points=Flatten[Outer[List,Range[w],Range[h]],1]; pairs=Flatten[Map[Outer[List,{#},Drop[points,Position[points,#][[1,1]]-1],1][[1]]&,points],1]; The speed of the above calculation is reasonably fast. But I run into the memory problem. For example, for h=64 and w=64, the length of the list pairs will be w*h (w*h+1)/2 = 8,390,656. In my case, The numbers for h and w will be a lot larger than 64. How can I get around this memory problem or that's the dead end for my calculation (I do have 1 GB physical mem in my machine)? Thanks a lot. Cheng At 12:26 PM 10/16/2002, you wrote: >Dear group, > > I have the following question regarding a lengthy calculation >using Mathematica: > >For given w points in x direction and h points in y direction, I can >construct all the points using > > h=10; w=8; > points=Flatten[Transpose[Outer[List,Range[w],Range[h]]],1] > >Next, I need to find all the possible pairs of point including points >themselves, i.e., pair AA. I can use > > pairs=Outer[List,points,points,1] > >Then, I have to clear those pairs that repeat themselves, i.e., pair AB and >pair BA. Also, when w and h are of the order of 1000s, the computation >takes a very long time. Is there a better way of doing the second part of >the computation? Thanks in advance. > >Sincerely > >Cheng > > >==================================================== >Cheng Liu, Ph.D. >MST-8, Structure/Property Relations >Materials Science and Technology Division >Los Alamos National Laboratory >Los Alamos, New Mexico 87545 > >Phone: 505-665-6892 (office), 505-667-9950 (lab) >Fax: 505-667-8021 >email: cliu at lanl.gov >==================================================== ==================================================== Cheng Liu, Ph.D. MST-8, Structure/Property Relations Materials Science and Technology Division Los Alamos National Laboratory Los Alamos, New Mexico 87545 Phone: 505-665-6892 (office), 505-667-9950 (lab) Fax: 505-667-8021 email: cliu at lanl.gov ====================================================