have array entries filled depending on their indices?

I want to fill an array

A=zeros(1000,1);

based on another array:

B=linspace(0,100,1000);

Now I want to fill every A(i) with the product of all B(k) with k=1:i-1, I do that alike this:

for i=1:length(A)
    A(i)=prod(B(1:i-1));
end

For large sizes of A this becomes very time intensive. Would there be a way to do it faster? I couldnt find a way to use arrayfun for that.

And suggest I want to fill A(i), but do some more stuff inside the for loop?

Answer 1

[Jan]

The code is strange, because all elements of A are 0 except for the first one. B(1) is zero, so prod(B(1:n)) is zeros also. Maybe you mean:

n = 10000;
B = linspace(1,100,n);  % Not starting at 0

tic
A = zeros(n, 1);
for i = 1:n
    A(i) = prod(B(1:i-1));
end
toc

Elapsed time is 0.106487 seconds.

% Alternative: A naive loop avoiding repeated work:
tic
D = zeros(n, 1);
c = 1;
for i = 1:n
    D(i) = c;
    c    = c * B(i);
end
toc

Elapsed time is 0.006453 seconds.

% Faster:
tic
C = [1, cumprod(B(1:n - 1))].';
toc

Elapsed time is 0.002222 seconds.

Even the loop is much faster than calculating the product from scratch in each iteration again. cumprod is much faster again.