# Much slower valid convolution using complementary size of kernels.

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Shen Zhao on 13 Dec 2020
Edited: Shen Zhao on 24 Dec 2020
I am using the valid convolution using convn( T, a, 'valid').
I have run the code below:
T = randn(384,384,8);
a = randn(5,5,8);
b = randn(380,380,1);
tic; convn(T,a,'valid'); toc
tic; convn(T,b,'valid'); toc
The reuslt in my computer is
Elapsed time is 0.002837 seconds.
Elapsed time is 0.016301 seconds.
Thus the the latter is much slower compared to fomer one.
However, in terms of flops, or only in terms of multiplications
convn(T,a,'valid')
takes 5*5*8*(384-5+1)*(384-5+1)*(8-8+1) = 28880000 multiplications
convn(T,b,'valid')
also takes 380*380*1*(384-380+1)*(384-380+1)*(8-1+1) = 28880000 multiplications
So why are the two computing time so different?
And is there some ways to implement the convn(T,b,'valid') much faster?
Bruno Luong on 24 Dec 2020
No not FLOPS. As you said the FLOPS are more or less indentical.

Bjorn Gustavsson on 21 Dec 2020
No, n-dimensional fourier-transforms, multiplication of the Fourier-transforms of 5-5-8 a with T will be a fair bit faster than the multiplication of the 380-by-380-by-1 b with T.
HTH

Roshan Hingnekar on 22 Dec 2020
Edited: Walter Roberson on 22 Dec 2020
T and 'a' are 3 dimensional where as 'b' is 2 dimensional, convolution of 3-dimensional with 2-dimensional will be slower than a 3-dimensional with a 3-dimensional.
refer to the below links for further insight on randn and convn functions.
Shen Zhao on 24 Dec 2020
I read the corredponding webpages, could you explain more on why the same dimensional convolution will be faster?

Bruno Luong on 22 Dec 2020
I would suggest to do specific conv with MEX programing.
Not sure the chance to beat MATLAB though.
Shen Zhao on 24 Dec 2020
We once tried to write some C++ code to compete with matlab convn especially for 'valid' convolution, we found it really hard to beat Matalb convn. The matlab convn is really well-optimized.

R2020b

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