looking for a faster way

*To*: mathgroup at smc.vnet.net*Subject*: [mg24998] looking for a faster way*From*: Otto Linsuain <linsuain+ at andrew.cmu.edu>*Date*: Fri, 1 Sep 2000 01:09:31 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi to all. I am looking for a faster way to achieve the following: Have two lists with the formats: xlist = { x1, x2, x3, ....... xN } flist = { f1, f2, f3, ....... fN } the x's and f's are just numbers. Want the matrix: myMatrix [[ i, j ]] = ( fi - fj ) / ( xi- xj ) There are probably a thousand ways to avoid the Indeterminate along the diagonal. Any of them is fine, as long as the off-diagonal part is not touched. Speed is the real problem. My solution so far is: myMatrix[ xlist_, flist_ ] := Outer[Subtract, flist, flist] / ( Outer[Subtract, xlist, xlist] + IdentityMatrix[Length[xlist]]) the IdentityMatrix makes the diagonal zero, rather than Indeterminate. This solution is not very fast because it involves 2 Outers, so that the speed goes roughly as 2 N^2. If I could avoid one of them I would have just one N^2, possibly + something-linear-in-N. I have tried myMatrix[ xlist_, flist_ ] := Outer[myFunction, Transpose[{flist,xlist}], Transpose[{flist,xlist}], 2] this uses one Outer. This produces: myMatrix [[ i, j ]] = myFunction[ {fi, xi}, {fj, xj} ] myFuction is of course chosen to produce the desired combination of f's and x's. For lists in the length range I am interested in ( from 200 to 1000 elements ) the second solution is slower than the first, despite the fact that it uses only one Outer. If anyone can think of something faster than the first solution I would really appreciate it. Otto Linsuain.