Re: Creating a Piecewise function with imported list of arbitrary length

*To*: mathgroup at smc.vnet.net*Subject*: [mg128977] Re: Creating a Piecewise function with imported list of arbitrary length*From*: Ray Koopman <koopman at sfu.ca>*Date*: Thu, 6 Dec 2012 05:00:33 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k9kek2$681$1@smc.vnet.net>

On Dec 4, 1:09 am, Nick Broderick <crazychess... at msn.com> wrote: > Apologies if this seems like a simple question, but I'm not > familiar enough with Mathematica syntax to know how to do this. > Essentially I have an arbitrary list (length n) of pairs -- taken > from an input file -- from which I need to define a Piecewise > function. The pairs (x_i,y_i) define the left-sided endpoints > for each portion of the function, and the last point defines > the value y_n of the function for x > x_n. For example: > > {{0,1},{300,2},{600,3}} > > defines a Piecewise function: > > f(x)= {{1, 0 <= x <300},{2, 300 <= x <600}, {3, x > 600}, {0, True}} > > But I'm not sure how to go about creating a arbitrary list of > conditions from my list of pairs. Any help would be appreciated. Here's another version, that I think is a little easier to follow. In general, I use Apply (@@ and @@@) instead of Map (/@) whenever it will let me use numbered arguments instead of indexed arguments; e.g., #2 instead of #[[2]]. f[x_] = Piecewise @ Append[ {#2, #1 <= x < #3}& @@@ Partition[Flatten@data,3,2], {#2, x >= #1}& @@ Last@data]