Element-wise raise an array to an integer power
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Hi everybody,
I found that the element-wise multiplication of a large array (a.*a.*a) is much faster than the equivalent element-wise power function (a.^3). It seems that the only exception is squaring:
>> a = rand(300,300,300);
>> tic,a.^2;toc
Elapsed time is 0.125585 seconds.
>> tic,a.^3;toc
Elapsed time is 2.304034 seconds.
>> tic,a.^12;toc
Elapsed time is 2.328101 seconds.
while:
>> tic,a.*a;toc
Elapsed time is 0.147440 seconds.
>> tic,a.*a.*a;toc
Elapsed time is 0.214431 seconds.
>> tic,(a.*a.*a).^2.^2;toc
Elapsed time is 0.505067 seconds.
Is there an alternative Matlab element-wise power function which factorizes integer exponents and performs element-wise multiplications instead of exponentiations, whenever preferable?
Thanks a lot
Bernhard
3 个评论
dpb
2018-3-24
That is disappointing, indeed.
Appears no optimization has been implemented and AFACT there's no alternative builtin in that does.
Looks like "roll your own" time; might check the File Exchange and see if somebody has already done the heavy lifting.
Walter Roberson
2018-3-24
Pretty sure there is appropriate logic in the file exchange
dpb
2018-3-24
Another of those bizarre mysteries why TMW wouldn't have done when first wrote the function for such a fundamental operation with the solution so well known. Generally runtime libraries of compilers do; seems as though would get "for free" if just used called it in the bowels.
采纳的回答
What about:
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Walter Roberson
2018-3-24
On my system, with R2018a, timeit shows less discrepancy:
>> a = rand(300,300,300);
>> timeit(@() a.^2, 0)
ans =
0.060887501623
>> timeit(@() a.^3, 0)
ans =
0.544000124623
>> timeit(@() a.^12, 0)
ans =
0.535817926623
>> timeit(@() (a.*a.*a).^2.^2, 0)
ans =
0.135812291623
Now, the A.^B operation is defined in terms of exp(log(A)*B) (somewhere... I don't see the reference right this moment.) So I tested max(max(max(abs(exp(log(a)*12) - a.^12)))) -- and it isn't 0, it is eps/2 . So whatever MATLAB is doing internally is not the log implementation, and from the timings is not an integer factorization based implementation either. (I also created a random complex matrix and tested the results of various factorizations, and none of them match bit for bit.)
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