How can I create a nested loop without confusing the indeces?

I have the following problem:

a variable x(i) that represents the payoff and its value changes as other variables cgange WHILE I KEEP FIXED alpha. So I can get it by using a simple loop like that

alpha = 0.3; % between 0 and 1

x = zeros(N,1);

for i=1:N

x(i) = alpha*exp(z(i))+(1-alpha)*exp(u(i));

end

I don't know how to get different paths of x(i) as alpha changes

Answer 1

[DGM]

Let's see if I understand the intent... I don't know what z and u are, so I'm just going to use placeholders.

N = 10;
alpha = [0.2 0.3 0.5]; % a vector of alpha
z = rand(N,1);
u = rand(N,1);
x = alpha.*exp(z) + (1-alpha).*exp(u)

x = 10×3

1.1978 1.2503 1.3553 2.1130 2.0850 2.0290 1.2143 1.2290 1.2583 1.1931 1.2798 1.4532 2.1470 2.0129 1.7446 1.4468 1.5637 1.7975 1.8198 1.7721 1.6766 2.2546 2.1952 2.0765 1.8337 1.7453 1.5686 1.1697 1.1559 1.1285

Note that alpha and the other vectors are orthogonal. Implicit array expansion allows the expression to be evaluated for all values of the parameter alpha (one column each).

[Federica Fubelli]

Exactly, z and u are vectors too. If I proceed in this way, like you showed me, I get that alpha varies while z and u varie too. Instead I want to get at first 10 values of x that I get because z and u varie but by using only the first value of alpha (so alpha=0.2); then other 10 values of x by using alpha=0.3 and so on... in a recursively way. Anyway I think that I have to use two different indeces in the loop (i and j) and then I associate j to alpha and i to other variables

[Image Analyst]

DGM showed you the vectorized way, not recursive. However you can make up a function that takes alpha as in input if you want. However you'd just call it as you need to (with the new alpha) -- you don't need to call the function recursively, and you should not.

[DGM]

That's what the example does. I don't see the functional difference between doing the operations sequentially or simultaneously. For demonstration:

% SETUP
N = 10;
alpha = [0.2 0.3 0.5]; % a vector of alpha
z = rand(N,1);
u = rand(N,1);

% USING LOOPS
x = zeros(N,numel(alpha));
for ia = 1:numel(alpha)
    for ix = 1:N
        x(ix,ia) = alpha(ia)*exp(z(ix)) + (1-alpha(ia))*exp(u(ix));
    end
end

% USING VECTORIZED MATH
x2 = alpha.*exp(z) + (1-alpha).*exp(u);

immse(x,x2) % show that the results are identical

ans = 0

Perhaps instead z and u are larger than you want the output to be, and you only want to sample a portion of them.

% SETUP
N = 10;
alpha = [0.2 0.3 0.5]; % a vector of alpha
z = rand(100,1); % larger than N
u = rand(100,1);

% USING LOOPS
x = zeros(N,numel(alpha));
for ia = 1:numel(alpha)
    for ix = 1:N
        x(ix,ia) = alpha(ia)*exp(z(ix)) + (1-alpha(ia))*exp(u(ix));
    end
end

% USING VECTORIZED MATH
x2 = alpha.*exp(z(1:N)) + (1-alpha).*exp(u(1:N));

immse(x,x2) % show that the results are identical

ans = 0

There is the possibility that you want x to remain a vector, and that each evaluation for alpha should simply be concatenated to the end. In that case, just do this to the result:

x = x(:);
% or
x = reshape(x,[],1);

That will reshape the multicolumn output into a single column vector.