Convolution of function handles

I'm doing some nonlinear fitting in MATLAB.

With most details stripped away, I have two function handles, f = @(x) and g = @(A,x) , where A is some parameter vector.

I'd really like to make a new function handle C = @(A,x), which is the convolution of f with g using parameter A.

Naively, that would be..

c = @(A,x) integral ( @(s) f(s).*g(A,x-s),-inf,inf);

This works for single values--e.g. c(1,1), but c isn't a well behaved function handle -- it throws errors for c(1,[1,2])*, which renders c unusable in non-linear fit algorithms. I think that's because the integral function is vectorized, so when x is a singleton, it can put in whatever size array it wishes for s, but when x is a vector, it snags on that step. In theory I could use some kind of repmat to fix this problem, but that seems awfully sloppy.

For a few more details:

f = @(x) is a piecewise combination of a few different exponentials and input functions.

g is actually just an exponential decay -- g = @(A,x) exp(-A*x);

I could probably compute these things explicitely and that might end up being fastest anyways but f may not always be such a nice function in practice.

*error here:

>> c(1,[1, 1])

Matrix dimensions must agree.

Error in @(s)f(s).*g(A,x-s)

Error in integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

Error in @(A,x)integral(@(s)f(s).*g(A,x-s),0,180)

Answer 1

[Steven Lord]

Use the 'ArrayValued', true name-value pair argument as shown in the "Vector-Valued Function" example on the documentation page for the integral function.

[qfn]

This fixes the problems stated. Thank you!