Re: piecewise function

*To*: mathgroup at smc.vnet.net*Subject*: [mg109196] Re: piecewise function*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 16 Apr 2010 05:52:57 -0400 (EDT)*References*: <hq61qs$3j0$1@smc.vnet.net>

On Apr 14, 8:40 pm, mircea <mircea.da... at gmail.com> wrote: > I want a define a piecewise constant function on an interval [a,b]. > What I did is: > > s[x_] := Module[{out}, out = 0; > For[i = 1, i <= N, i++, > If[mesh[[i]] <= x < mesh[[i + 1]], > out = (mesh[[i]] + mesh[[i + 1]])/2; Break[]]]; out]; > > where: > > mesh = {x_1,x_2,..,x_{N+1} }, a = x_1 < x_2 < .. < x_{N+1} = b > > However > > PiecewiseExpand /@ s[x] > > gives me 0..... > > Can you please help me? > Thanks, > Mirela Here is a translation of your procedural s[x] into functional code: s1[x_] := First[ Cases[ Transpose@{Most@mesh,Rest@mesh}, {a_,b_} /; a <= x < b :> (a+b)/2, {1}, 1] /. {} -> {0} ] If you want it to use Piecewise then this will do it: makefunc[mesh_] := ToExpression["Function[x, Piecewise[" <> Block[{x}, ToString[{Mean@#, #[[1]] <= x < #[[2]]}& /@ Transpose@{Most@mesh,Rest@mesh}]] <> "]]" ] mesh = Sort@RandomReal[{0,1},10] {0.0731222,0.0955697,0.184462,0.369542,0.476, 0.568679,0.725734,0.784328,0.860571,0.901895} s2 = makefunc[mesh] Function[x, Piecewise[{ {0.084346, 0.0731222 <= x < 0.0955697}, {0.140016, 0.0955697 <= x < 0.184462 }, {0.277002, 0.184462 <= x < 0.369542`}, {0.422771, 0.369542 <= x < 0.476 }, {0.52234, 0.476 <= x < 0.568679 }, {0.647207, 0.568679 <= x < 0.725734 }, {0.755031, 0.725734 <= x < 0.784328 }, {0.822449, 0.784328 <= x < 0.860571 }, {0.881233, 0.860571 <= x < 0.901895 }}]]