matlab inline function with special handling for zero

Question

I have a function that has a singularity at zero. The resulting value should be at that point 1.

However I fails to understand how to create an inline function that has a special treatment for values of x and y at x or y = 0.

The function could for example be

f = @(x,y) ( 1./x + 1./y ); 

Answer 1

To answer your question with a counter-question: why do you want it to be inline?

As a general rule, keep inline functions simple. If more functionality is needed, use a dedicated function:

function val = f(x,y)

    if ~all(size(x)==size(y))
        error('sizes must match');

    val = zeros(size(x));

    zero_x = x==0;
    zero_y = y==0;

    not_zero = ~zero_x & ~zero_y;
    zero = ~not_zero;

    val(not_zero) = 1./x(not_zero) + 1./y(not_zero);
    val(zero) = 1;           

end

Having said that, there are of course ways to do it inline (see other answers).

But as you indicated, your actual function is more complex, so...why inline?

Answer 2

Create the following iif.m function file, residing in your working folder, or even as a subfunction if you're using it in other functions (scripts of course can not contain subfunctions):

function val = iif(expr, truepart, falsepart)
    if isscalar(truepart)
        truepart=truepart(ones(size(expr)));
    end
    if isscalar(falsepart)
       falsepart=falsepart(ones(size(expr))); 
    end
    val = arrayfun(@iif_scalar, expr, truepart, falsepart);
end
function val = iif_scalar(expr,truepart,falsepart)
    if expr
        val = truepart;
    else
        val = falsepart;
    end
end

and use it as follows:

f = @(x,y) iif(x==0 | y==0, 1, 1./x + 1./y );

I kept the iif function as general as possible, you can use it on vectors, scalars, mixed scalar and vectors, or even matrices. For example, in the above I used 2 vectors and a scalar:

iif( ...
     x==0 | y==0 ,... % expression if x or y are 0 => vector
     1 , ...          % scalar obviously
     1./x + 1./y ...  % function of x and y => vector
   )