Re: How to speed up this calculation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg37242] Re: How to speed up this calculation?*From*: "Kevin J. McCann" <kmccann at umbc.edu>*Date*: Fri, 18 Oct 2002 05:17:03 -0400 (EDT)*Organization*: University of Maryland, Baltimore County*References*: <aokc15$agm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Here is a way with symbolic lists. (* Here are some sample lists*) lst1={A,B}; lst2={a,b,c}; (*Join into one list*) list1=Join[lst1,lst2]; (*Do the outer product to get all possible ordered pairs*) list2=Partition[Flatten[Outer[List,list1,list1]],2] {{A, A}, {A, B}, {A, a}, {A, b}, {A, c}, {B, A}, {B, B}, {B, a}, {B, b}, {B, c}, {a, A}, {a, B}, {a, a}, {a, b}, {a, c}, {b, A}, {b, B}, {b, a}, {b, b}, {b, c}, {c, A}, {c, B}, {c, a}, {c, b}, {c, c}} (*Turn the pairs into products*) list3=list2/.{x_,y_}®{x y} {{A^2}, {A*B}, {a*A}, {A*b}, {A*c}, {A*B}, {B^2}, {a*B}, {b*B}, {B*c}, {a*A}, {a*B}, {a^2}, {a*b}, {a*c}, {A*b}, {b*B}, {a*b}, {b^2}, {b*c}, {A*c}, {B*c}, {a*c}, {b*c}, {c^2}} (*Union weeds out repeats*) list4=Union[list3,list3] {{a^2}, {a*A}, {A^2}, {a*b}, {A*b}, {b^2}, {a*B}, {A*B}, {b*B}, {B^2}, {a*c}, {A*c}, {b*c}, {B*c}, {c^2}} (*Now turn the products back into pairs*) (*This is the step the requires symbols*) list5=list4/.{x_^2}®{x,x}/.{x_*y_}®{x,y} {{a, a}, {a, A}, {A, A}, {a, b}, {A, b}, {b, b}, {a, B}, {A, B}, {b, B}, {B, B}, {a, c}, {A, c}, {b, c}, {B, c}, {c, c}} (*List it out*) (*If you have numbers, you can now use a Rule to replace*) Sort[lst]//TableForm -- Kevin J. McCann Joint Center for Earth Systems Technology (JCET) Department of Physics UMBC Baltimore MD 21250 "Cheng Liu" <cliu at lanl.gov> wrote in message news:aokc15$agm$1 at smc.vnet.net... > 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 > ==================================================== > >