CODEWITHSUNDEEP
matlabmatrixvectorizationconvolution
Nick X Tsui
Nick X Tsui

Reputation: 2912

doing 1-d convolution in batches/parallel

I am having following code, basically doing 1-d convolution on each row of a 2-D matrix. The convolution kernel is the same. So really the SIMD case.

a = [   1,2,3,4,5;
        6,7,8,9,7; 
        7,6,2,3,4; 
        23, 54, 1, 3 ,7];

f = [1,2,3];


for n = 1:size(a,1)
    conv(a(n,:),f,'same')
end

When the matrix size(and the kernel size) gets larger, the speed really becomes a problem. I am wondering is there any way to this in batch (parallelize this process)?

I did something like this, but the results are different from above code:

a = [   1,2,3,4,5;
        6,7,8,9,7; 
        7,6,2,3,4; 
        23, 54, 1, 3 ,7];

f = [1,2,3];

ff = repmat(f, [size(a,1) 1]);

for n = 1:size(a,1)
    conv(a(n,:),f,'same')
end

convn(a,ff,'same')

conv2(f,2,a,'same')

Please advise. Thanks.

PS: I am currently only seeking solution using convolution, not using fft equivalent.

Upvotes: 3

Views: 467

Answers (1)

fiveclubs
fiveclubs

Reputation: 2431

You'll want to use a 2-dimensional convolution:

conv2(1, f, a, 'same')

or

conv2(a, f, 'same')

In the first method, the first argument is 1 because it's a column-wise convolution, and based on what you said, you only want to do row convolution, which is taken care of using the second argument, f.

From the Matlab docs for conv2:

C = conv2(H1, H2, A) first convolves each column of A with the vector H1 and then convolves each row of the result with the vector H2.

Convolving a scalar 1 along the columns is an identity operation, allowing the f vector to convolve along the original matrix rows, which is the desired result.

For the second method above, this is a direct 2-dimensional convolution of the two input matrices, so if you take care to understand your input dimensions and argument order, this actually performs a faster operation.

Upvotes: 4

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