The editor shows you 12 valuable hints already: Letting an array grow iteratively is very expensive. See this example:
x = [];
for k = 1:1e6
x(k) = rand;
end
The final array x need 8 MB only (8 bytes per element). But Matlab has to create a new vector in each iteration and copy the former contents to it. Theredfore Matlab has to request sum(1:1e6)*8 Bytes and copy sum(1:1e6-1)*8 Bytes. This is more than 4 Terabyte! Of course, this slows doen the procesing massively.
The solution is easy: Pre-allocation:
x = zeros(1, 1e6);
for k = 1:1e6
x(k) = rand;
end
Now Matlab allocates the final array with 8MB only and no further allocations or copies are required.
If you do not know the final size of your array, allocate the maximum posible size, if this matchs in your RAM and crop the array afterwards.
Another option is to allocate in chunks:
chunk = 1e3;
ix = 0;
nx = 0;
x = [];
for k = 1:1e6 * rand
ix = ix + 1;
if ix > nx
nx = nx + chunk;
x(nx) = 0; % Expands the array implicitly
end
x(ix) = rand;
end
x(ix + 1:nx) = []; % Crop unused memory
Prefer larger chunk sizes.
while nume/deno > octaveRatio
deno = deno*2;
end
while nume/deno > octaveRatio
deno = deno*currentPrime;
end
Seriously? There ius no need to do this in a loop.
This has a lot of overhead:
if ismember(fRatio,fRatioArray) == 0
Faster and nicer:
if ~any(fRatio == fRatioArray)
With replacing ismember by any(a==b), the code runs in 7.5 instead of 8.5 seconds in my Matlab R2018b.
Now use the profiler to find the bottleneck: gcd(). You can create a much faster tool omitting the smart features as array input, special treatment of integer types and so on:
function u = myGCD(a, b)
u = max(a, b);
v = min(a, b);
while v > 0
t = rem(u, v);
u = v;
v = t;
end
end
Using this instead of of Matlab's gcd() reduces the tun time to 2.4 seconds.
I do not understand the pile of tocs. You measure the time from the last start of the first loop, where tic is called. Is this really the correct timing for the output file?
