Fast Element-Wise power to non-integer value
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I am working on a non-linear optimization problem using fmincon. My current setup delivers the best results so far in simulations.
Now I am working on optimizing my code and I have a bottle-neck in computation time in the expression:
(1-(1-x.^a).^b);
where 'x' is a vector of Nx1 observations, with N "medium-large" (> 30000 rows). Moreover, 'a' and 'b' are non-integer parameters > 0 (to be fitted)
f is the function that I am minimizing, thus, it's called by the optimizer several times (90000 in my current setting) resulting in a significant bottleneck in the overall procedure.
Are there any ways to improve the speed of this calculation? According to the code, profiler, this line is responsible for 25% of the total computation time in seconds. A replicable example is shown below:
%Example
N = 30000;
x = linspace(0,1,N)'; %vector of N x 1
a = 1.2; %positive non-integer power
b = 0.3; %positive non-integer power
f3 = @() (1-(1-x.^a).^b);
timeit(f3)
Although it seems fast, if the function is called by the optimization procedure 90000 times, then the total time is around 0.0029*90000 = 261 seconds
Question:
Is there any way to make this computation faster? So far, I've tried
- bsxfun, however it's included in the .^ command for newer releases
- Increase maxNumCompThreads to 8
- Relax optimization Tolerance levels
- Tried other optimizers (such as lsqnonlin) but deliver worst estimates
- write the expression as logarithm and then take exponential (it seems slower in preliminar trials)
Thank you for your comments
All best!
4 个评论
Walter Roberson
2023-2-23
[I was wondering whether it would be effective to taylor f3 to a reasonable number of terms. I experimented with taylor around b = 0.5 (midpoint of the range), tested at 0.1 0.2 0.3 0.4... and the results for order 10 or order 20 were not encouraging.
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