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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 }}]]


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