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Topic: Creating a Piecewise function with imported list of arbitrary length
Replies: 1   Last Post: Dec 6, 2012 4:57 AM

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Ray Koopman

Posts: 3,383
Registered: 12/7/04
Re: Creating a Piecewise function with imported list of arbitrary length
Posted: Dec 6, 2012 4:57 AM
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On Dec 4, 1:09 am, Nick Broderick <crazychess...@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]




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