How can I nest a function in a function?

function AD = AD(n)
    A = zeros(n);
    for i=1:n
        for j=1:n
            A(i,j) = 1/(i+j-1);
        end
    end
    Ainv = A\eye(n);
    Eye = eye(n);
    AD = Eye-Ainv*A;
end
function A = hilbert(n)
    A = zeros(n);
    for i=1:n
        for j=1:n
            A(i,j) = 1/(i+j-1);
        end
    end
end

I want to nest hilbert function in AD function, since hilbert is actually in AD. But I am getting "Unrecognized function or variable 'A'" error. What can I do here?

Answer 1

[Fangjun Jiang]

MyAD=AD(3)

MyAD = 3×3

1.0e-13 * 0 0 0.0089 -0.0711 0 0 0.1421 0.0711 0.0711

function AD = AD(n)
A = hilbert(n);
Ainv = A\eye(n);
Eye = eye(n);
AD = Eye-Ainv*A;
end

function A = hilbert(n)
A = zeros(n);
for i=1:n
    for j=1:n
        A(i,j) = 1/(i+j-1);
    end
end
end

[Barbaros Teoman Kosoglu]

Thank you.

[Fangjun Jiang]

To be clear, hilbert(n) here is a 'local function'. There is no need to make it a 'nested function' based on its content.

See documents for their differences.

I think 'local function' is more suitable in this case.

Answer 2

[John D'Errico]

See that I wrote hilbert differently. Feel free to use doubly nested loops there. But why?

As well, NEVER name a function the same thing as a variable in that function!!!!!!!!! NEVER. NEVER. Having said that three times, it must be true. You named the function AD, then returned a variable named AD. A BAD idea.

ComputeAd(5)

ans = 5×5

1.0e-11 * 0.0171 0 -0.0071 -0.0099 -0.0099 0.0909 0.0455 0.1592 0.1137 0.1137 -0.3638 -0.3638 -0.1819 -0.1819 -0.3638 0.7276 0.3638 0.3638 0.3638 0.5457 -0.1819 -0.0909 -0.0909 -0.1819 -0.2728

It works.

function AD = ComputeAd(n)
  A = hilbert(n);
  Ainv = A\eye(n);
  Eye = eye(n);
  AD = Eye-Ainv*A;
  
  function A = hilbert(n)
    [i,j] = meshgrid(1:n);
    A = 1./(i+j-1);
  end
end

[Barbaros Teoman Kosoglu]

Thank you, but the other answer is better for me I think since, we haven't used meshgrid yet. But I will definitely listen to your naming ideas. By the way I don't know why but when I copy your code it gives Unrecognized function or variable 'ComputeAD' error.

[VBBV]

Check with

ComputeAd(5)

Matlab is case senstive. You might have used

ComputeAD(5)

This is different function and not present in code you copied

[John D'Errico]

Yes. You tried to call ComputeAD, but I named the function ComputeAd. Sorry about my choice of names.

Case sensitivity triumphs there. MATLAB told you it could not find that function, the clue you needed.