Problem 43494. Weighted Convolution

Created by Peng Liu

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given two input vectors x = [x_1, x_2, ..., x_K] and y = [y_1, y_2, ..., y_K] of equal length, compute the weighted convolution output z = [z_1, z_2, ..., z_K], where</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[     z_k = sum(nchoosek(k-1,j-1)*x_{k-j+1}*y_j, j = 1..k),  k = 1, 2, ..., K]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example: x = [1, 2, 3]; y = [4, 5, 6]. Then z = [z_1, z_2, z_3] where</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[z_1 = nchoosek(0,0)*1*4 = 4\nz_2 = nchoosek(1,0)*2*4 + nchoosek(1,1)*1*5 = 13\nz_3 = nchoosek(2,0)*3*4 + nchoosek(2,1)*2*5 + nchoosek(2,2)*1*6 = 38]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Hint: This can be seen as the linear convolution weighted by the binomial coefficient. It is straightforward to solve this problem using a for loop. I am wondering if there exists some more elegant way (e.g., vectorization) to do this.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

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30 Solutions
19 Solvers

Last Solution submitted on Jun 16, 2020

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James on 13 Oct 2016

Liked because 1) It's not spam and 2) You use my "better way to do this?" tag for the same reason I do.

Peng Liu on 13 Oct 2016

I also dislike the recent trend of spoiling Cody with trivial problems. Some people, especially those top 4 players on the Triathlon scoreboard, have generated too many trivial problems, in the hope of wining the Triathlon prizes (related to MATLAB central's 15 years celebration). This shameful behavior damaged not just the Triathlon competition, but also our Cody platform.

Jean-Marie Sainthillier on 14 Oct 2016

I understand better now why Cody becomes so boring. Thank you for the explanations.

Aditya Jain on 14 Oct 2016

We have increased the score required to create a problem. So this should not happen anymore.

Peng Liu on 15 Oct 2016

Hi Aditya, Could you take a look at this problem: http://nl.mathworks.com/matlabcentral/cody/problems/43117-2d-indexes? Every time I click the "Solve" button, my internet browser cannot be directed to the right page.

Peng Liu on 15 Oct 2016

I figured out what 's wrong there. The correct link is www.mathworks.com/ ..., not nl.mathworks.com/...

Aditya Jain on 16 Oct 2016

Awesome.

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Problem 43494. Weighted Convolution

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Problem 43494. Weighted Convolution

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