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Evaluation Control of a recursive function inside Piecewise

Andre Luiz Rocha Alves
Posted 2 years ago

Please, How to do Evaluation Control in order to let a function "FC[t]" be evaluated recursively to define a Piecewise function, BUT, after this evaluation, save the new Piecewise function "pwtemp", so that, each time "pwtemp" are called, "FC[t]" are NOT evaluated again?

Please see notebook below. When I tried to define "pwtemp" as the Piecewise function with the "FC[t]" inside, it was not possible to Plot what I wanted. But, when I used the Plot function directely with the Piecewise construction, it was possible to Plot the function I want.

I want to define "pwtemp" in function of "t" and easily evaluate this function resulting in the values shown in the second Plot result (vertical axis). When I tried to evaluate "pwtemp" using the code below, it returned 0, and it is not what I wanted.
POSTED BY: Andre Luiz Rocha Alves
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Rohit Namjoshi
Rohit Namjoshi
Posted 2 years ago

Hi Andre,

I think Gianluca is right about the definition of pwtemp

ClearAll@pwtemp;
pwtemp[t_] := 
  Piecewise[{{0, t < Vscc}, {FC1[t], Vscc ⩽ t < 2 Vscc}, {FC2[t], 2 Vscc ⩽ t < m}}];

Plot[pwtemp[t], {t, 0, m},
 PlotRange -> Full,
 Filling -> Axis,
 PlotTheme -> "Detailed",
 PlotLegends -> Definition@pwtemp]

enter image description here
POSTED BY: Rohit Namjoshi

Thanks Rohit, This worked for "pwtemp" plot, but the only problem is that when I try to create another function that is a multiplication of another Piecewise function with this new pwtempt], the Integrate function seems not to understand tthat the variable "t" is for the two. See this another question that I have posted >>[here<<.
POSTED BY: Andre Luiz Rocha Alves

You should give the variable t to pwtemp[t_]:=....

Instead of Count, which does not play well with calculus, you may try an integral of DiracDelta:

With[{vti = Range[10], Vscc = 3/2},
  Integrate[Sum[DiracDelta[x - pt], {pt, vti}], {x, t - Vscc, t}, 
   Assumptions -> Element[t, Reals]]] /. HeavisideTheta -> UnitStep
% // PiecewiseExpand
POSTED BY: Gianluca Gorni

Thank you Gianluca, but let me explain the intention:

  1. I have a list with the times that some events occurred in a timeline from 0 to 10 years: vti = {0.5, 1.5, 2.4, 3, 4.1...};
  2. Considering a moving time window with fixed width (w=1.5), I want to sum the total nr. of events inside the time window, in function of time t;
POSTED BY: Andre Luiz Rocha Alves
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