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Stepwise Function Mathematica

  1. Aug 1, 2007 #1
    How do I define a stepwise function in Mathematica? I am trying to model the behavior of a detector up in the atmosphere. For instance, the detector might experience temperature drops in the atmosphere over a 24 hour period. I would like to know if there's any way of using a step function in Mathematica to do that. Thanks.
     
  2. jcsd
  3. Aug 2, 2007 #2

    George Jones

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    Yes, you can use the Heavisde step function to do this. For exmple,

    [tex]\left( Heaviside \Heaviside \left( x-1 \right) - Heaviside \left( x-3 \right) \right) x^2[/tex]

    is the the function [itex]x^2[/itex] for [itex]1 < x < 3[/itex], and zero elsewhere.

    Heaviside is a Maple function, but Mathematica will have a similar function, with maybe a different name.
     
  4. Aug 2, 2007 #3

    CompuChip

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    Which version of Mathematica are you using?

    As George suggested, you can use the Heaviside function
    Code (Text):

    ( HeavisideTheta[x - 1] - HeavisideTheta[x - 3] ) x^2
     
    You can do
    Code (Text):

    f[x_] := 0;
    f[x_] := x^2 /; (x > 1 && x < 3)
     
    which is ugly but works.

    You can use Which
    Code (Text):

    g[x_] := Which[x < 1, 0, x > 3, 0, True, x^2];
     
    which is better, but has the unfortunate property that it Hold[]s its arguments, so this won't do if you want to apply functions and replacements to this.

    The most elegant way, in my opinion, is using the Piecewise function
    Code (Text):

    h[x_] := Piecewise[{{x^2, 1 < x < 3}}, 0]
     
    but this function was implemented in 5.1 so that won't help you if you have an older version.
     
    Last edited: Aug 2, 2007
  5. Aug 3, 2007 #4
    I am using version 6.0.

    I actually tried to do a piecewise function but it didn't quite work out. Instead, I just plot the points and connected it so that it looks like a stepwise function. I have attached the plot I want to this post. However, I need to learn how to do achieve this shape the right way with a stepwise function and not just points, because in the future I will need to replace this function instead of a sine function into two differential equations to solve it.

    The points I am using are for the attached plot are
    The x values are fixed. The y values can change but the same shape needs to be achieved. If this is impossible to do with a step function, is it possible to model this using a cubic spline function with the same general shape as the step function?
    I would appreciate any help.
     

    Attached Files:

    Last edited: Aug 3, 2007
  6. Aug 4, 2007 #5

    CompuChip

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    Code (Text):

    Plot[Piecewise[{{1, x < 3.5}, {2, x < 5.5}, {1.5, x < 9.5}, {2,
        x < 15}}, 1], {x, 0, 25}, PlotRange -> {0, 2}]
     
    worked fine here (Mathematica 6.0), without the vertical lines (they finally fixed that bug :smile:).

    But if you insist on the vertical lines, you can use
    Code (Text):

    Plot[Which[x < 3.5, 1, x < 5.5, 2, x < 9.5, 1.5, x < 15, 2, True,
      1], {x, 0, 25}, PlotRange -> {0, 2}]
     
     
  7. Aug 4, 2007 #6
    For the vertical lines, you can also use the Exclusions option:

    Code (Text):
    Plot[Piecewise[{{1, x < 3.5}, {2, x < 5.5}, {1.5, x < 9.5}, {2,
        x < 15}}, 1], {x, 0, 25}, PlotRange -> {0, 2}, Exclusions -> None]
     
  8. Aug 7, 2007 #7
    Thanks for your help. :smile:
     
  9. Aug 7, 2007 #8
    Thanks. :smile: I am still trying to get adjusted to Mathematica.
     
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