Re: Fastest way to check inequality

*To*: mathgroup at smc.vnet.net*Subject*: [mg91380] Re: [mg91361] Fastest way to check inequality*From*: DrMajorBob <drmajorbob at att.net>*Date*: Tue, 19 Aug 2008 07:15:01 -0400 (EDT)*References*: <4130912.1219083186830.JavaMail.root@m08>*Reply-to*: drmajorbob at longhorns.com

> (And @@ NonPositive[constrMat . # ]) & /@ x; That's a very fast way to do nothing, since "constrMat" is undefined. A.x also makes no sense, since A and x don't have compatible dimensions. There are a couple of ways to "make" them compatible, namely a = RandomReal[{0, 1}, {3500, 3}]; x = RandomReal[{0, 1}, {2000, 3}]; a.Transpose[x] // Dimensions {3500, 2000} x.Transpose[a] // Dimensions {2000, 3500} (I shrank the dimensions so that I didn't get old waiting for results.) Now the question is whether you intend 35000 inequalities, 20000, or 35000*20000. I'm guessing the latter. That is, ALL entries must be non-positive in EITHER of the dot products above. If that guess is correct, we can speed things up by stopping when we reach a failure. Since Dot is a special case of Inner, we can do it this way: Catch[Inner[Times, a, Transpose@x, (Plus[##] > 0 && Throw[False]) &]; True] Here are a couple of examples with obvious answers: a = RandomReal[{-1, 0}, {35, 3}]; x = RandomReal[{0, 1}, {20, 3}]; Catch[Inner[Times, a, Transpose@x, (Plus[##] > 0 && Throw[False]) &]; True] True a = RandomReal[{0, 1}, {35, 3}]; x = RandomReal[{0, 1}, {20, 3}]; Catch[Inner[Times, a, Transpose@x, (Plus[##] > 0 && Throw[False]) &]; True] False Bobby On Mon, 18 Aug 2008 02:36:52 -0500, Ravi Balasubramanian <bravi at cs.washington.edu> wrote: > Hello Math-groupers, > > I need to test the inequality > > A . x <= 0, where > > x is a three-D vector. > A is a 35000x3 matrix. > > I need to test this for 20000 points. > > So I set this up as follows: > > A = RandomReal[{0,1},{35000,3}]; > > x = RandomReal[{0,1},{20000,3}]; > > (And @@ NonPositive[constrMat . # ]) & /@ x; > > Is this the fastest way? > > Ravi > The University of Washington > Seattle, WA > > > -- DrMajorBob at longhorns.com