Re: [Maxima-discuss] Integrating piecewise defined functions

[Eduardo O. <edu...@gm...>]

Hi list,

I tried to replace the `integrate' of my last question with a variant
that calls `quad_qagi':

  integrate_qagi(f,x,a,b) := quad_qagi(f,x,a,b)[1]$

  f(x) := if     x<0 then 0
          elseif x<1 then 1
          else            0;
  g(x) := if     x<0 then 0
          elseif x<1 then x
          else            0;
  h(x) := integrate_qagi(f(t)*g(x-t), t, minf, inf);

  draw2d(xrange=[-4,4],
         yrange=[-4,4],
         proportional_axes=xy,
         explicit(h(w),w,-4,4));

Now calculating h(x) at specific points works:

  h(0.0042906454260024365);
  h(0.5);
  h(0.1);
  h(-1);
  h(-2);
  h(-3);

but the draw2d above fails with this error...

  quad_qagi: Numerical evaluation of (if t < 0 then 0 elseif t < 1 then 1
else 0)
   (if w - t < 0 then 0 elseif w - t < 1 then w - t else 0) at
  0.0042906454260024365 is not a float or is not defined

Is that a bug?
Thanks in advance!
  Eduardo Ochs

On Wed, 27 Nov 2024 at 18:56, Eduardo Ochs <edu...@gm...> wrote:

> Hi list,
>
> what is the recommended way to integrate piecewise defined
> functions? I tried this,
>
>   f(x) := if     x<0 then 0
>           elseif x<1 then 1
>           else            0;
>   g(x) := if     x<0 then 0
>           elseif x<1 then x
>           else            0;
>   h(x) := integrate(f(t)*g(x-t), t, -2, +2);
>
> and I couldn't find a way to make Maxima calculate this
> integral...
>
>         integrate(f(x), x, -2, 4);
>   float(integrate(f(x), x, -2, 4));
>
> The convolution left Maxima even more confused, obviously...
> Thanks in advance!
>   Eduardo Ochs
>   http://anggtwu.net/eev-maxima.html
>   http://anggtwu.net/eev-qdraw.html
>