Question

Let’s say I have a function that can compute one output from one input, e.g.

function y = sqrt_newton(x)
    y = x ./ 2;
    yo = y;
    y = 0.5.*(y + x ./ y);
    while abs(y - yo) > eps * abs(y)
        yo = y;
        y = 0.5.*(y + x ./ y);
    end
end

I’d like to be able to apply this function to a vector input say sqrt_newton(2:9) like with built-in functions. What is the best way to achieve this with a condition at the beginning of the loop or some if-clause inside? I’d like to avoid writing an extra function as a wrapper just to loop through the input vector, if possible at all.

My current cumbersome solution

What I do up until now is:

• I have to expand first the inputs to the same size (using finargsz from the finance toolbox, but if you know of another core function that does the same, that would be great)

• record the shape using size

• deal the inputs

• loop thru all the input elements

• reshape the output

It seems that the numel function alleviates the need of all this heavy lifting but extra comments would be most welcome.

Answer 1

There’s always arrayfun. You can keep the code you have, putting it into an inner function.

function y = sqrt_newton(z)

    y = arrayfun(@inner, z);

    function y= inner(x)
        y = x ./ 2;
        yo = y;
        y = 0.5.*(y + x ./ y);
        while abs(y - yo) > eps * abs(y)
            yo = y;
            y = 0.5.*(y + x ./ y);
        end
    end
end

Edit: The above solution has the advantage of being trivial to implement after you have it working with a 1×1 input, but the loops in the other answers are way faster for large inputs. For example, on my computer, the code

tic; sqrt_newton(rand(500)); toc

runs in ~1.24 seconds with my code, 0.06 seconds with @Ramashalanka’s code, and 0.28 seconds with @GuntherStruyf’s code.