Define Piecewise Functions in Julia

Question

I have an application in which I need to define a piecewise function, IE, f(x) = g(x) for [x in some range], f(x)=h(x) for [x in some other range], ... etc.

Is there a nice way to do this in Julia? I'd rather not use if-else because it seems that I'd have to check every range for large values of x. The way that I was thinking was to construct an array of functions and an array of bounds/ranges, then when f(x) is called, do a binary search on the ranges to find the appropriate index and use the corresponding function (IE, h(x), g(x), etc.

It seems as though such a mathematically friendly language might have some functionality for this, but the documentation doesn't mention piecewise in this manner. Hopefully someone else has given this some thought, thanks!

Answer 1

with a Heaviside function you can do a interval function:

function heaviside(t)
   0.5 * (sign(t) + 1)
end

and

function interval(t, a, b)
   heaviside(t-a) - heaviside(t-b)
end

function piecewise(t)
   sinc(t) .* interval(t,-3,3) + cos(t) .* interval(t, 4,7)
end

and I think it could also implement a subtype Interval, it would be much more elegant