Problem 1972. Convert matrix to 3D array of triangular matrices

Created by Matthew Eicholtz

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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 a 2D numeric array x in which each column represents the vectorized form of an upper triangular matrix, return a 3D array y containing the concatenated triangular matrices.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>If the size of the input matrix x is MxN, then the size of the output matrix y is PxPxN, where M = sum(1:P)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>You may assume that P&lt;=100</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[x = 1  7 13\n    2  8 14\n    3  9 15\n    4 10 16\n    5 11 17\n    6 12 18]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>then</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[y(:,:,1) =  1  2  4\n            0  3  5\n            0  0  6\n\ny(:,:,2) =  7  8 10\n            0  9 11\n            0  0 12\n\ny(:,:,3) = 13 14 16\n            0 15 17\n            0  0 18]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> If you are wondering why this seems like a strange task, it is inspired by a genotype-&gt;phenotype mapping I am doing in a genetic algorithm.</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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Last Solution submitted on Feb 03, 2023

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Solution 10350236

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1 Comment

Peter on 3 Feb 2023 at 1:47

Tricky if you don't see the output pattern!

Solution 4613965

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2 Comments

Lincoln Poon on 18 Jan 2021

I keep failing the 'assert(isequal(x,xb))' part of the last test.
Can someone please give me some ideas on how to fix it?

Daigo on 5 Jan 2022

Lincoln> I also had the same issue but figured out the cause. In my case, I was computing P by "P = uint8((-1+sqrt(8*M+1))/2);" but this causes a problem for a large M. After I modified it to "P = round((-1+sqrt(8*M+1))/2);", the error has been solved.

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Problem 1972. Convert matrix to 3D array of triangular matrices

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Problem 1972. Convert matrix to 3D array of triangular matrices

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