RE: RE: RE: Define a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg34700] RE: [mg34650] RE: [mg34595] RE: [mg34556] Define a function*From*: "DrBob" <majort at cox-internet.com>*Date*: Sat, 1 Jun 2002 04:29:10 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

>>the employed time to carry out the calculations is smaller. Really? We should test that theory. Here are timings for six equivalent functions: f[x_] := x UnitStep[x - 10] - x/2UnitStep[x - 20] g[x_] := Which[x < 10, 0, x < 20, x, True, x/2] h[x_] := x (UnitStep[x - 10] - UnitStep[x - 20]) + x/2 UnitStep[x - 20] i = #UnitStep[# - 10] - #/2UnitStep[# - 20]; j[x_] /; x < 10 := 0 j[x_] /; x < 20 := x j[x_] := x/2 k := Which[# < 10, 0, # < 20, #, True, #/2] & Timing[f /@ Range[10^5];] Timing[g /@ Range[10^5];] Timing[h /@ Range[10^5];] Timing[i /@ Range[10^5];] Timing[j /@ Range[10^5];] Timing[k /@ Range[10^5];] {2.047 Second, Null} {1.25 Second, Null} {2.219 Second, Null} {1.86 Second, Null} {1.328 Second, Null} {1.063 Second, Null} Bobby -----Original Message----- From: Juan Egea Garcia [mailto:jeg at um.es] To: mathgroup at smc.vnet.net Subject: [mg34700] [mg34650] RE: [mg34595] RE: [mg34556] Define a function Yes, I think the same thing if what we want is to integrate the function, but if what we want is to carry out a great number of calculations that involve (or not) complicated functions is better definig piecewise functions using bifurcation sentences because the employed time to carry out the calculations is smaller. ============================ Juan Egea Garcia Atica - Dpto. Matematica Aplicada Universidad de Murcia - http://www.um.es España +34 968367144 -----Mensaje original----- De: David Park [mailto:djmp at earthlink.net] Enviado el: miércoles, 29 de mayo de 2002 8:45 Para: mathgroup at smc.vnet.net Asunto: [mg34595] RE: [mg34556] Define a function Michael, The best method for defining piecewise functions is to use UnitStep. f[x_] := x(UnitStep[x - 10] - UnitStep[x - 20]) + x/2UnitStep[x - 20] This will not only plot... Plot[f[x], {x, 0, 30}]; but you can also do things like integrate. g[x_] = Integrate[f[x], x] (-(1/4))*(-400 + x^2)*UnitStep[-20 + x] + (-50 + x^2/2)*UnitStep[-10 + x] Plot[g[x], {x, 0, 30}]; The Mathematica Book, which has not really been updated properly to reflect the UnitStep function often leads users to using conditional definitions. Clear[f] f[x_] /; x < 10 := 0; f[x_] /; 10 <= x <= 20 := x; f[x_] /; 20 < x := x/2; This works for plotting... Plot[f[x], {x, 0, 30}]; but won't integrate or perform other calculus functions. Integrate[f[x], x] Integrate[f[x], x] So, the UnitStep method is far superior. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > -----Original Message----- > From: Michael Popp [mailto:popp.michael at gmx.at] To: mathgroup at smc.vnet.net > Sent: Monday, May 27, 2002 1:17 AM > Subject: [mg34700] [mg34650] [mg34595] [mg34556] Define a function > > > Hello > > I want to define a function in Mathematica. But just f[x_]:=... does not > work, because I have to define different functions for different ranges of > the variable x. > For example: > > x < 10: f(x) = 0 > 10 < x < 20: f(x) = x > 20 < x: f(x) = x/2 > > How to do this? > > Thanks, greetings > Michael > > > >