{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":1704,"title":"Triangular matrices in 3D array","description":"Given a 3D numeric array _x_, return an array _y_ of the same size in which all entries to the right of the main diagonal are zero for _y_(:,:,i).\r\n\r\n*Example*\r\n\r\nIf\r\n\r\n  x(:,:,1) = 1 2 3\r\n             4 5 6\r\n             7 8 9\r\n\r\n  x(:,:,2) = 1 4 7\r\n             2 5 8\r\n             3 6 9\r\n\r\n  x(:,:,3) = 1 2 3\r\n             1 2 3\r\n             1 2 3\r\n\r\nthen\r\n\r\n  y(:,:,1) = 1 0 0\r\n             4 5 0\r\n             7 8 9\r\n\r\n  y(:,:,2) = 1 0 0\r\n             2 5 0\r\n             3 6 9\r\n\r\n  y(:,:,3) = 1 0 0\r\n             1 2 0\r\n             1 2 3","description_html":"\u003cp\u003eGiven a 3D numeric array \u003ci\u003ex\u003c/i\u003e, return an array \u003ci\u003ey\u003c/i\u003e of the same size in which all entries to the right of the main diagonal are zero for \u003ci\u003ey\u003c/i\u003e(:,:,i).\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex(:,:,1) = 1 2 3\r\n           4 5 6\r\n           7 8 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex(:,:,2) = 1 4 7\r\n           2 5 8\r\n           3 6 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex(:,:,3) = 1 2 3\r\n           1 2 3\r\n           1 2 3\r\n\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,1) = 1 0 0\r\n           4 5 0\r\n           7 8 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,2) = 1 0 0\r\n           2 5 0\r\n           3 6 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,3) = 1 0 0\r\n           1 2 0\r\n           1 2 3\r\n\u003c/pre\u003e","function_template":"function y = tril3(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx(:,:,1) = [1 2 3;4 5 6;7 8 9];\r\nx(:,:,2) = [1 4 7;2 5 8;3 6 9];\r\nx(:,:,3) = [1 2 3;1 2 3;1 2 3];\r\ny_correct(:,:,1) = [1 0 0;4 5 0;7 8 9];\r\ny_correct(:,:,2) = [1 0 0;2 5 0;3 6 9];\r\ny_correct(:,:,3) = [1 0 0;1 2 0;1 2 3];\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = cumsum(ones(3,3,50));\r\ny_correct = repmat([1 0 0;2 2 0; 3 3 3],[1,1,50]);\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = cumsum(ones(5,5,100),2);\r\ny_correct = repmat(tril(cumsum(ones(5,5),2)),[1,1,100]);\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = rand([1 1 400]);\r\ny_correct = x;\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = reshape(1:40,[2,2,10]);\r\ny_correct(:,:,1) = [1 0;2 4];\r\ny_correct(:,:,2) = [5 0;6 8];\r\ny_correct(:,:,3) = [9 0;10 12];\r\ny_correct(:,:,4) = [13 0;14 16];\r\ny_correct(:,:,5) = [17 0;18 20];\r\ny_correct(:,:,6) = [21 0;22 24];\r\ny_correct(:,:,7) = [25 0;26 28];\r\ny_correct(:,:,8) = [29 0;30 32];\r\ny_correct(:,:,9) = [33 0;34 36];\r\ny_correct(:,:,10) = [37 0;38 40];\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = randi([0 1],[4,4,5]);\r\ny_correct(:,:,1) = tril(x(:,:,1));\r\ny_correct(:,:,2) = tril(x(:,:,2));\r\ny_correct(:,:,3) = tril(x(:,:,3));\r\ny_correct(:,:,4) = tril(x(:,:,4));\r\ny_correct(:,:,5) = tril(x(:,:,5));\r\nassert(isequal(tril3(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":169,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":31,"created_at":"2013-07-09T14:02:30.000Z","updated_at":"2026-03-21T07:18:04.000Z","published_at":"2013-07-09T14:02:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a 3D numeric array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return an array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the same size in which all entries to the right of the main diagonal are zero for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(:,:,i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x(:,:,1) = 1 2 3\\n           4 5 6\\n           7 8 9\\n\\nx(:,:,2) = 1 4 7\\n           2 5 8\\n           3 6 9\\n\\nx(:,:,3) = 1 2 3\\n           1 2 3\\n           1 2 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[y(:,:,1) = 1 0 0\\n           4 5 0\\n           7 8 9\\n\\ny(:,:,2) = 1 0 0\\n           2 5 0\\n           3 6 9\\n\\ny(:,:,3) = 1 0 0\\n           1 2 0\\n           1 2 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1972,"title":"Convert matrix to 3D array of triangular matrices","description":"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.\r\n\r\n* 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)\r\n* You may assume that P\u003c=100\r\n\r\n*Example*\r\n\r\nIf\r\n\r\n  x = 1  7 13\r\n      2  8 14\r\n      3  9 15\r\n      4 10 16\r\n      5 11 17\r\n      6 12 18\r\n\r\nthen\r\n\r\n  y(:,:,1) =  1  2  4\r\n              0  3  5\r\n              0  0  6\r\n\r\n  y(:,:,2) =  7  8 10\r\n              0  9 11\r\n              0  0 12\r\n\r\n  y(:,:,3) = 13 14 16\r\n              0 15 17\r\n              0  0 18\r\n\r\n_NOTE:_ If you are wondering why this seems like a strange task, it is inspired by a genotype-\u003ephenotype mapping I am doing in a genetic algorithm.","description_html":"\u003cp\u003eGiven 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.\u003c/p\u003e\u003cul\u003e\u003cli\u003eIf the size of the input matrix x is MxN, then the size of the output matrix y is PxPxN, where M = sum(1:P)\u003c/li\u003e\u003cli\u003eYou may assume that P\u0026lt;=100\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = 1  7 13\r\n    2  8 14\r\n    3  9 15\r\n    4 10 16\r\n    5 11 17\r\n    6 12 18\r\n\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,1) =  1  2  4\r\n            0  3  5\r\n            0  0  6\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,2) =  7  8 10\r\n            0  9 11\r\n            0  0 12\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,3) = 13 14 16\r\n            0 15 17\r\n            0  0 18\r\n\u003c/pre\u003e\u003cp\u003e\u003ci\u003eNOTE:\u003c/i\u003e If you are wondering why this seems like a strange task, it is inspired by a genotype-\u0026gt;phenotype mapping I am doing in a genetic algorithm.\u003c/p\u003e","function_template":"function y = mat2triu3(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1:100;\r\ny_correct = shiftdim(x,-1);\r\nassert(isequal(mat2triu3(x),y_correct))\r\n\r\n%%\r\nx = reshape(1:15,3,[]);\r\ny_correct(:,:,1) = [1 2;0 3];\r\ny_correct(:,:,2) = [4 5;0 6];\r\ny_correct(:,:,3) = [7 8;0 9];\r\ny_correct(:,:,4) = [10 11;0 12];\r\ny_correct(:,:,5) = [13 14;0 15];\r\nassert(isequal(mat2triu3(x),y_correct))\r\n\r\n%%\r\nx = reshape(1:18,3,[])';\r\ny_correct(:,:,1) = [1 4 10; 0 7 13; 0 0 16];\r\ny_correct(:,:,2) = [2 5 11; 0 8 14; 0 0 17];\r\ny_correct(:,:,3) = [3 6 12; 0 9 15; 0 0 18];\r\nassert(isequal(mat2triu3(x),y_correct))\r\n\r\n%%\r\nx = randi(50,sum(1:100),22);\r\ny = mat2triu3(x);\r\nmask = (y~=0);\r\nxb = reshape(y(mask),[],size(y,3));\r\nassert(isequal(size(y),[100 100 22]))\r\nassert(isequal(x,xb))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":135,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":23,"created_at":"2013-11-07T22:49:47.000Z","updated_at":"2026-03-31T09:10:36.000Z","published_at":"2013-11-07T22:58:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the size of the input matrix x is MxN, then the size of the output matrix y is PxPxN, where M = sum(1:P)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou may assume that P\u0026lt;=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![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]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![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]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e If you are wondering why this seems like a strange task, it is inspired by a genotype-\u0026gt;phenotype mapping I am doing in a genetic algorithm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":1704,"title":"Triangular matrices in 3D array","description":"Given a 3D numeric array _x_, return an array _y_ of the same size in which all entries to the right of the main diagonal are zero for _y_(:,:,i).\r\n\r\n*Example*\r\n\r\nIf\r\n\r\n  x(:,:,1) = 1 2 3\r\n             4 5 6\r\n             7 8 9\r\n\r\n  x(:,:,2) = 1 4 7\r\n             2 5 8\r\n             3 6 9\r\n\r\n  x(:,:,3) = 1 2 3\r\n             1 2 3\r\n             1 2 3\r\n\r\nthen\r\n\r\n  y(:,:,1) = 1 0 0\r\n             4 5 0\r\n             7 8 9\r\n\r\n  y(:,:,2) = 1 0 0\r\n             2 5 0\r\n             3 6 9\r\n\r\n  y(:,:,3) = 1 0 0\r\n             1 2 0\r\n             1 2 3","description_html":"\u003cp\u003eGiven a 3D numeric array \u003ci\u003ex\u003c/i\u003e, return an array \u003ci\u003ey\u003c/i\u003e of the same size in which all entries to the right of the main diagonal are zero for \u003ci\u003ey\u003c/i\u003e(:,:,i).\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex(:,:,1) = 1 2 3\r\n           4 5 6\r\n           7 8 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex(:,:,2) = 1 4 7\r\n           2 5 8\r\n           3 6 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ex(:,:,3) = 1 2 3\r\n           1 2 3\r\n           1 2 3\r\n\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,1) = 1 0 0\r\n           4 5 0\r\n           7 8 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,2) = 1 0 0\r\n           2 5 0\r\n           3 6 9\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,3) = 1 0 0\r\n           1 2 0\r\n           1 2 3\r\n\u003c/pre\u003e","function_template":"function y = tril3(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx(:,:,1) = [1 2 3;4 5 6;7 8 9];\r\nx(:,:,2) = [1 4 7;2 5 8;3 6 9];\r\nx(:,:,3) = [1 2 3;1 2 3;1 2 3];\r\ny_correct(:,:,1) = [1 0 0;4 5 0;7 8 9];\r\ny_correct(:,:,2) = [1 0 0;2 5 0;3 6 9];\r\ny_correct(:,:,3) = [1 0 0;1 2 0;1 2 3];\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = cumsum(ones(3,3,50));\r\ny_correct = repmat([1 0 0;2 2 0; 3 3 3],[1,1,50]);\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = cumsum(ones(5,5,100),2);\r\ny_correct = repmat(tril(cumsum(ones(5,5),2)),[1,1,100]);\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = rand([1 1 400]);\r\ny_correct = x;\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = reshape(1:40,[2,2,10]);\r\ny_correct(:,:,1) = [1 0;2 4];\r\ny_correct(:,:,2) = [5 0;6 8];\r\ny_correct(:,:,3) = [9 0;10 12];\r\ny_correct(:,:,4) = [13 0;14 16];\r\ny_correct(:,:,5) = [17 0;18 20];\r\ny_correct(:,:,6) = [21 0;22 24];\r\ny_correct(:,:,7) = [25 0;26 28];\r\ny_correct(:,:,8) = [29 0;30 32];\r\ny_correct(:,:,9) = [33 0;34 36];\r\ny_correct(:,:,10) = [37 0;38 40];\r\nassert(isequal(tril3(x),y_correct))\r\n\r\n%%\r\nx = randi([0 1],[4,4,5]);\r\ny_correct(:,:,1) = tril(x(:,:,1));\r\ny_correct(:,:,2) = tril(x(:,:,2));\r\ny_correct(:,:,3) = tril(x(:,:,3));\r\ny_correct(:,:,4) = tril(x(:,:,4));\r\ny_correct(:,:,5) = tril(x(:,:,5));\r\nassert(isequal(tril3(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":169,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":31,"created_at":"2013-07-09T14:02:30.000Z","updated_at":"2026-03-21T07:18:04.000Z","published_at":"2013-07-09T14:02:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a 3D numeric array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return an array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the same size in which all entries to the right of the main diagonal are zero for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(:,:,i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x(:,:,1) = 1 2 3\\n           4 5 6\\n           7 8 9\\n\\nx(:,:,2) = 1 4 7\\n           2 5 8\\n           3 6 9\\n\\nx(:,:,3) = 1 2 3\\n           1 2 3\\n           1 2 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[y(:,:,1) = 1 0 0\\n           4 5 0\\n           7 8 9\\n\\ny(:,:,2) = 1 0 0\\n           2 5 0\\n           3 6 9\\n\\ny(:,:,3) = 1 0 0\\n           1 2 0\\n           1 2 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1972,"title":"Convert matrix to 3D array of triangular matrices","description":"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.\r\n\r\n* 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)\r\n* You may assume that P\u003c=100\r\n\r\n*Example*\r\n\r\nIf\r\n\r\n  x = 1  7 13\r\n      2  8 14\r\n      3  9 15\r\n      4 10 16\r\n      5 11 17\r\n      6 12 18\r\n\r\nthen\r\n\r\n  y(:,:,1) =  1  2  4\r\n              0  3  5\r\n              0  0  6\r\n\r\n  y(:,:,2) =  7  8 10\r\n              0  9 11\r\n              0  0 12\r\n\r\n  y(:,:,3) = 13 14 16\r\n              0 15 17\r\n              0  0 18\r\n\r\n_NOTE:_ If you are wondering why this seems like a strange task, it is inspired by a genotype-\u003ephenotype mapping I am doing in a genetic algorithm.","description_html":"\u003cp\u003eGiven 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.\u003c/p\u003e\u003cul\u003e\u003cli\u003eIf the size of the input matrix x is MxN, then the size of the output matrix y is PxPxN, where M = sum(1:P)\u003c/li\u003e\u003cli\u003eYou may assume that P\u0026lt;=100\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = 1  7 13\r\n    2  8 14\r\n    3  9 15\r\n    4 10 16\r\n    5 11 17\r\n    6 12 18\r\n\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,1) =  1  2  4\r\n            0  3  5\r\n            0  0  6\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,2) =  7  8 10\r\n            0  9 11\r\n            0  0 12\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ey(:,:,3) = 13 14 16\r\n            0 15 17\r\n            0  0 18\r\n\u003c/pre\u003e\u003cp\u003e\u003ci\u003eNOTE:\u003c/i\u003e If you are wondering why this seems like a strange task, it is inspired by a genotype-\u0026gt;phenotype mapping I am doing in a genetic algorithm.\u003c/p\u003e","function_template":"function y = mat2triu3(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1:100;\r\ny_correct = shiftdim(x,-1);\r\nassert(isequal(mat2triu3(x),y_correct))\r\n\r\n%%\r\nx = reshape(1:15,3,[]);\r\ny_correct(:,:,1) = [1 2;0 3];\r\ny_correct(:,:,2) = [4 5;0 6];\r\ny_correct(:,:,3) = [7 8;0 9];\r\ny_correct(:,:,4) = [10 11;0 12];\r\ny_correct(:,:,5) = [13 14;0 15];\r\nassert(isequal(mat2triu3(x),y_correct))\r\n\r\n%%\r\nx = reshape(1:18,3,[])';\r\ny_correct(:,:,1) = [1 4 10; 0 7 13; 0 0 16];\r\ny_correct(:,:,2) = [2 5 11; 0 8 14; 0 0 17];\r\ny_correct(:,:,3) = [3 6 12; 0 9 15; 0 0 18];\r\nassert(isequal(mat2triu3(x),y_correct))\r\n\r\n%%\r\nx = randi(50,sum(1:100),22);\r\ny = mat2triu3(x);\r\nmask = (y~=0);\r\nxb = reshape(y(mask),[],size(y,3));\r\nassert(isequal(size(y),[100 100 22]))\r\nassert(isequal(x,xb))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":135,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":23,"created_at":"2013-11-07T22:49:47.000Z","updated_at":"2026-03-31T09:10:36.000Z","published_at":"2013-11-07T22:58:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the size of the input matrix x is MxN, then the size of the output matrix y is PxPxN, where M = sum(1:P)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou may assume that P\u0026lt;=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![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]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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