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MathGroup Archive 1995

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Re: Piecewise function generator

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1155] Re: Piecewise function generator
  • From: pasquale Nardone <pnardon at ulb.ac.be>
  • Date: Sat, 20 May 1995 01:03:20 -0400
  • Organization: Universite' Libre de Bruxelles

You can define a function that compute the coefficient a and b in the 
linear expression a*x+b and the segment where this hold 

fff[{pt1_,pt2_}]:={
LessEqual[pt1[[1]],x,pt2[[1]]],
Apply[Divide,Reverse[pt2-pt1]]*x-Det[{pt1,pt2}]/Apply[Plus,(pt2-pt1)*{1,0}]
};

then you can use recursive tricks
fff[{pt1_,pt2_,restOfpts__}]:=Join[fff[{pt1,pt2}],fff[{pt2,restOfpts}]];

and it will work
pts={{20,0.08},{50,0.8},{250,0.8},{5000,0.004}};
g[x_]=Apply[Which,fff[pts]];


nb: of course fff could be define more easily using explicit 
representation:

hhh[{{x1_,y1_},{x2_,y2_}}]:={
LessEqual[x1,x,x2],
((y2-y1)*x+y1*x2-y2*x1)/(x2-x1)};

hhh[{pt1_,pt2_,restOfpts__}]:=Join[hhh[{pt1,pt2}],hhh[{pt2,restOfpts}]]

g[x_]=Apply[Which,hhh[pts]]

Out[]
Which[20 <= x <= 50, (-12. + 0.72*x)/30, 50 <= x <= 250, (160. + 0.*x)/200, 
250 <= x <= 5000, (3999. - 0.796*x)/4750]

and if you want to have the possibility to define your variable name :

qqq[{{x1_, y1_}, {x2_, y2_}}, var_] := {x1 <= x <= x2, ((y2 - y1)*var + 
y1*x2 - y2*x1)/(x2 - x1)};
 
qqq[{pt1_, pt2_, restOfpts__}, var_] := Join[qqq[{pt1, pt2}, var], 
qqq[{pt2, restOfpts}, var]];

gnew[t_]:=Apply[Which,qqq[pts,t]]

gnew[X]
Out[]
Which[20 <= x <= 50, (-12. + 0.72*X)/30, 50 <= x <= 250, (160. + 0.*X)/200, 
250 <= x <= 5000, (3999. - 0.796*X)/4750]

I hope this could help

P. Nardone




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