Integrating complex functions about cubature.jl HOT 7 OPEN

No, unfortunately, Julia doesn't have arrow types.

from cubature.jl.

I don't want a whole other set of cubature functions. I guess we could have a wrapper

complexfunc(f) = (x,v) -> let c = f(x); v[1] = real(c); v[2] = imag(c); end
vec2complex(v) = Complex(v[1],v[2])

So that they you could do e.g. vec2complex(hquadrature(2, complexfunc(f), ...)[1]).

from cubature.jl.

I suppose there is no way to do a clever dispatch based on what f returns (or even the type of arguments it takes).

from cubature.jl.

That's very neat, I have never seen the concept expressed like that, thank you. Also on an off topic note, I must thank you for your online maths resources, which I have found useful on several occasions (namely your PML tutorial and differentiation by FFT).

from cubature.jl.

Here's a slight generalisation of the wrapper which also allows for complex intervals of integration:

complexfunc(f) = (x,v) -> let c = f(x); v[1] = real(c); v[2] = imag(c); end;
vec2complex(v) = Complex(v[1],v[2]);
hquadratureCOMPLEX(f,a,b) = vec2complex(hquadrature(2, complexfunc(t -> f(a+t*(b-a))*(b-a)),0,1,abstol=1e-8)[1]);

It must be possible to improve this so that the named argument abstol can be passed to hquadratureCOMPLEX rather than set in the wrapper itself, but I'm new to Julia. I'll update if I figure it out.

from cubature.jl.

Ultimately, the right way to solve this is to rewrite in pure Julia.

from cubature.jl.

See https://github.com/stevengj/HCubature.jl for a pure-Julia re-implementation of hcubature that handles complex integrands, etc.

from cubature.jl.