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!

You might want to look at the implementation of [NumPy's `piecewise` function](http://docs.scipy.org/doc/numpy/reference/generated/numpy.piecewise.html). — jub0bs, Dec 27 '14 at 17:58

score 5 · Answer 1 · answered Dec 28 '14 at 14:56

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

score 2 · Answer 2 · answered Nov 01 '15 at 09:51

I tried to implement a piecewise function for Julia, and this is the result:

function piecewise(x::Symbol,c::Expr,f::Expr)
  n=length(f.args)
  @assert n==length(c.args)
  @assert c.head==:vect
  @assert f.head==:vect
  vf=Vector{Function}(n)
  for i in 1:n
    vf[i]=@eval $x->$(f.args[i])
  end
  return @eval ($x)->($(vf)[findfirst($c)])($x) 
end
pf=piecewise(:x,:([x>0, x==0, x<0]),:([2*x,-1,-x]))
pf(1) # => 2
pf(-2) # => 2
pf(0) # => -1

score 1 · Answer 3 · answered Apr 02 '16 at 17:30

Why not something like this?

function piecewise(x::Float64, breakpts::Vector{Float64}, f::Vector{Function})
       @assert(issorted(breakpts))
       @assert(length(breakpts) == length(f)+1)
       b = searchsortedfirst(breakpts, x)
       return f[b](x)
end

piecewise(X::Vector{Float64}, bpts, f) = [ piecewise(x,bpts,f) for x in X ]

Here you have a list of (sorted) breakpoints, and you can use the optimized searchsortedfirst to find the first breakpoint b greater than x. The edge case when no breakpoint is greater than x is also handled appropriately since length(breakpts)+1 is returned, so b is the correct index into the vector of functions f.

Define Piecewise Functions in Julia

3 Answers3