{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":43627,"title":"Find Euclidean norm of given vector u.","description":"Find Euclidean norm of given vector u.\r\nhttps://en.wikipedia.org/wiki/Euclidean_distance\r\nExample \r\nx=[1 1]\r\nresult=sqrt(1^2+1^2)=1.4142","description_html":"\u003cp\u003eFind Euclidean norm of given vector u.\r\nhttps://en.wikipedia.org/wiki/Euclidean_distance\r\nExample \r\nx=[1 1]\r\nresult=sqrt(1^2+1^2)=1.4142\u003c/p\u003e","function_template":"function y = VecNorm(u)\r\n  y = u;\r\nend","test_suite":"%%\r\nu = 1;\r\ny_correct = 1;\r\nassert(isequal(VecNorm(u),y_correct))\r\n%%\r\nu = [1 1];\r\ny_correct = 1.4142 ;\r\nassert(abs(VecNorm(u)-y_correct)\u003c10^(-4))\r\n%%\r\nu = [5     2     0     5     3     0];\r\ny_correct =  7.9373;\r\nassert(abs(VecNorm(u)-y_correct)\u003c10^(-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T19:13:22.000Z","updated_at":"2026-02-10T18:14:53.000Z","published_at":"2016-10-25T19:13:22.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eFind Euclidean norm of given vector u. https://en.wikipedia.org/wiki/Euclidean_distance Example x=[1 1] result=sqrt(1^2+1^2)=1.4142\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":1520,"title":"Frobenius Norm","description":"Write your own version of Frobenius Norm without using the 'norm' function.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.5px 8px; transform-origin: 237.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite your own version of Frobenius Norm without using the 'norm' function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = myFrobeniusnormal(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('myFrobeniusnormal.m');\r\nassert(isempty(strfind(filetext, 'norm('))\u0026isempty(strfind(filetext, '\"fro\"'))...\r\n    \u0026isempty(strfind(filetext, '''fro''')))\r\n\r\n%% test 1\r\nx = magic(3);\r\ny_correct = norm(x,'fro'); %16.8819\r\nassert(isequal(myFrobeniusnormal(x),y_correct))\r\n%% test 2\r\nx = magic(4)\r\ny_correct = norm(x,'fro'); % 38.6782;\r\nassert(isequal(myFrobeniusnormal(x),y_correct))\r\n%% test 3\r\nx = ones(5)\r\nassert(isequal(myFrobeniusnormal(x),5))\r\n%% test 4\r\nx = zeros(2)\r\nassert(isequal(myFrobeniusnormal(x),0))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":1103,"edited_by":427930,"edited_at":"2022-10-21T12:10:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":99,"test_suite_updated_at":"2022-10-21T10:01:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-25T00:29:14.000Z","updated_at":"2026-02-15T14:18:38.000Z","published_at":"2013-05-25T00:29:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite your own version of Frobenius Norm without using the 'norm' function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43628,"title":"Find cosine between two given vectors u and v.","description":"Find cosine between two given vectors u and v.\r\n\r\nExample \r\n\r\nu = [5     2     0     5     3     0];\r\nv = [3     2     5     1     0     2];\r\n\r\nresult = 0.4611;","description_html":"\u003cp\u003eFind cosine between two given vectors u and v.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eu = [5     2     0     5     3     0];\r\nv = [3     2     5     1     0     2];\u003c/p\u003e\u003cp\u003eresult = 0.4611;\u003c/p\u003e","function_template":"function y = VecCos(u,v)\r\n  y = u;\r\nend","test_suite":"%%\r\nu = [5     2     0     5     3     0];\r\nv = [3     2     5     1     0     2];\r\ny_correct = 0.4611;\r\nassert(abs(VecCos(u,v)-y_correct)\u003c10^(-4))\r\n%%\r\nu = 2:0.05:3;\r\nv = 3:-0.05:2;\r\ny_correct = 0.9711;\r\nassert(abs(VecCos(u,v)-y_correct)\u003c10^(-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T19:33:42.000Z","updated_at":"2026-03-30T13:40:20.000Z","published_at":"2016-10-25T19:33:42.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eFind cosine between two given vectors u and v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = [5 2 0 5 3 0]; v = [3 2 5 1 0 2];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult = 0.4611;\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":2769,"title":"Find out magnitude of vector","description":"Find out magnitude of vector. \r\n\r\nSay x=[1 2 3], then answer must sqrt(1^2+2^2+3^2)\r\n\r\nPlease don't use sum function. \r\nIf you like this proble, please like it.. (Request)","description_html":"\u003cp\u003eFind out magnitude of vector.\u003c/p\u003e\u003cp\u003eSay x=[1 2 3], then answer must sqrt(1^2+2^2+3^2)\u003c/p\u003e\u003cp\u003ePlease don't use sum function. \r\nIf you like this proble, please like it.. (Request)\u003c/p\u003e","function_template":"function y = vector_mag(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3];\r\ny_correct = 3.7417;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = [-1 5 -6];\r\ny_correct = 7.8740;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = [3 4 5];\r\ny_correct = 7.0711;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = [5 5 -5];\r\ny_correct = 8.6603;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%% \r\nisempty(regexp(evalc('type vector_mag'),'sum'))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":268,"test_suite_updated_at":"2014-12-10T09:57:33.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-12-10T08:59:36.000Z","updated_at":"2026-02-18T10:31:27.000Z","published_at":"2014-12-10T08:59:36.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eFind out magnitude of vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSay x=[1 2 3], then answer must sqrt(1^2+2^2+3^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease don't use sum function. If you like this proble, please like it.. (Request)\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":389,"title":"Column norms of a matrix","description":"Given a matrix M, return a vector y such that for each k\r\n\r\n    y(k)=norm(M(:,k))\r\n\r\n(y(k) is the Euclidean norm of the k-th column of M)\r\n\r\nEDIT: changed the test case so that proper handling of complex values is required.","description_html":"\u003cp\u003eGiven a matrix M, return a vector y such that for each k\u003c/p\u003e\u003cpre\u003e    y(k)=norm(M(:,k))\u003c/pre\u003e\u003cp\u003e(y(k) is the Euclidean norm of the k-th column of M)\u003c/p\u003e\u003cp\u003eEDIT: changed the test case so that proper handling of complex values is required.\u003c/p\u003e","function_template":"function y = your_fcn_name(M)\r\n  y = M;\r\nend","test_suite":"%%\r\nM = [1 2 3; 4 5 6; 7 8 9+2i];\r\nfor k=1:size(M,2)\r\n  y_correct(k)=norm(M(:,k));\r\nend\r\nassert(isequal(your_fcn_name(M),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":1,"created_by":1258,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":569,"test_suite_updated_at":"2012-02-24T14:50:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-23T09:33:39.000Z","updated_at":"2026-03-29T18:47:57.000Z","published_at":"2012-02-24T14:50:55.000Z","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 matrix M, return a vector y such that for each k\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(k)=norm(M(:,k))]]\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\u003e(y(k) is the Euclidean norm of the k-th column of M)\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\u003eEDIT: changed the test case so that proper handling of complex values is required.\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":42755,"title":"Angle bisectors","description":"Given 2 direction vectors, calculate the *_two_ (2) normalized angle bisectors* (which are perpendicular between them).\r\n\r\nInput vectors can be 2-D or 3-D.\r\n\r\nThe two output vectors must have a norm equal to 1 (unit vectors).\r\n\r\nYou may find some help here:\r\n\u003chttps://proofwiki.org/wiki/Angle_Bisector_Vector\u003e","description_html":"\u003cp\u003eGiven 2 direction vectors, calculate the \u003cb\u003e\u003ci\u003etwo\u003c/i\u003e (2) normalized angle bisectors\u003c/b\u003e (which are perpendicular between them).\u003c/p\u003e\u003cp\u003eInput vectors can be 2-D or 3-D.\u003c/p\u003e\u003cp\u003eThe two output vectors must have a norm equal to 1 (unit vectors).\u003c/p\u003e\u003cp\u003eYou may find some help here: \u003ca href = \"https://proofwiki.org/wiki/Angle_Bisector_Vector\"\u003ehttps://proofwiki.org/wiki/Angle_Bisector_Vector\u003c/a\u003e\u003c/p\u003e","function_template":"function [b1,b2] = bisectors(v1,v2)\r\n  b1 = cross(v1,v2);\r\n  b2 = cross(v1,-v2);\r\nend","test_suite":"%%\r\nv1 = [1 0];\r\nv2 = [0 1];\r\n[b1,b2] = bisectors(v1,v2);\r\n\r\nb1ok = [1 1]/sqrt(2);\r\nb2ok = [-1 1]/sqrt(2);\r\n\r\n% Tests performed\r\nt1 = (abs(norm(b1)-1)\u003c1e-6); % Unit b1\r\nt2 = (abs(norm(b2)-1)\u003c1e-6); % Unit b2\r\nt3 = (abs(b1*b2') \u003c 1e-12); % b1 and b2 are perpendicular\r\nt4 = (abs(sum((b1-b1ok)))\u003c1e-12);  % b1 is equal to [1/sqrt(2) 1/sqrt(2)]\r\nt5 = (abs(sum((b1+b1ok)))\u003c1e-12); % or its opposite\r\nt6 = (abs(sum((b2-b2ok)))\u003c1e-12); % b2 is equal to [1/sqrt(2) -1/sqrt(2)]\r\nt7 = (abs(sum((b2+b2ok)))\u003c1e-12); % or its opposite\r\ntest = (t1 \u0026\u0026 t2 \u0026\u0026 t3 \u0026\u0026 xor(t4,t5) \u0026\u0026 xor(t6,t7));\r\n\r\n%%\r\nv1 = [4 0 3];\r\nv2 = [-2 2 1];\r\n[b1,b2] = bisectors(v1,v2);\r\n\r\nb1ok=[0.2 1 1.4]/sqrt(3);\r\nb2ok=[2.2 -1 0.4]/sqrt(6);\r\n  \r\n% Tests performed\r\nt1 = (abs(norm(b1)-1)\u003c1e-6); % Unit b1\r\nt2 = (abs(norm(b2)-1)\u003c1e-6); % Unit b2\r\nt3 = (abs(b1*b2') \u003c 1e-12); % b1 and b2 are perpendicular\r\nt4 = (abs(sum((b1-b1ok)))\u003c1e-12);  % b1 is equal to [1/sqrt(2) 1/sqrt(2)]\r\nt5 = (abs(sum((b1+b1ok)))\u003c1e-12); % or its opposite\r\nt6 = (abs(sum((b2-b2ok)))\u003c1e-12); % b2 is equal to [1/sqrt(2) -1/sqrt(2)]\r\nt7 = (abs(sum((b2+b2ok)))\u003c1e-12); % or its opposite\r\nassert(t1 \u0026\u0026 t2 \u0026\u0026 t3 \u0026\u0026 xor(t4,t5) \u0026\u0026 xor(t6,t7));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":12767,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2016-04-27T12:55:46.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2016-02-25T17:55:08.000Z","updated_at":"2026-02-27T10:16:23.000Z","published_at":"2016-02-25T17:57:35.000Z","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 2 direction vectors, calculate the\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e (2) normalized angle bisectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which are perpendicular between them).\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\u003eInput vectors can be 2-D or 3-D.\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\u003eThe two output vectors must have a norm equal to 1 (unit vectors).\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\u003eYou may find some help here:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://proofwiki.org/wiki/Angle_Bisector_Vector\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://proofwiki.org/wiki/Angle_Bisector_Vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\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":43627,"title":"Find Euclidean norm of given vector u.","description":"Find Euclidean norm of given vector u.\r\nhttps://en.wikipedia.org/wiki/Euclidean_distance\r\nExample \r\nx=[1 1]\r\nresult=sqrt(1^2+1^2)=1.4142","description_html":"\u003cp\u003eFind Euclidean norm of given vector u.\r\nhttps://en.wikipedia.org/wiki/Euclidean_distance\r\nExample \r\nx=[1 1]\r\nresult=sqrt(1^2+1^2)=1.4142\u003c/p\u003e","function_template":"function y = VecNorm(u)\r\n  y = u;\r\nend","test_suite":"%%\r\nu = 1;\r\ny_correct = 1;\r\nassert(isequal(VecNorm(u),y_correct))\r\n%%\r\nu = [1 1];\r\ny_correct = 1.4142 ;\r\nassert(abs(VecNorm(u)-y_correct)\u003c10^(-4))\r\n%%\r\nu = [5     2     0     5     3     0];\r\ny_correct =  7.9373;\r\nassert(abs(VecNorm(u)-y_correct)\u003c10^(-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T19:13:22.000Z","updated_at":"2026-02-10T18:14:53.000Z","published_at":"2016-10-25T19:13:22.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eFind Euclidean norm of given vector u. https://en.wikipedia.org/wiki/Euclidean_distance Example x=[1 1] result=sqrt(1^2+1^2)=1.4142\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":1520,"title":"Frobenius Norm","description":"Write your own version of Frobenius Norm without using the 'norm' function.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.5px 8px; transform-origin: 237.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite your own version of Frobenius Norm without using the 'norm' function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = myFrobeniusnormal(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('myFrobeniusnormal.m');\r\nassert(isempty(strfind(filetext, 'norm('))\u0026isempty(strfind(filetext, '\"fro\"'))...\r\n    \u0026isempty(strfind(filetext, '''fro''')))\r\n\r\n%% test 1\r\nx = magic(3);\r\ny_correct = norm(x,'fro'); %16.8819\r\nassert(isequal(myFrobeniusnormal(x),y_correct))\r\n%% test 2\r\nx = magic(4)\r\ny_correct = norm(x,'fro'); % 38.6782;\r\nassert(isequal(myFrobeniusnormal(x),y_correct))\r\n%% test 3\r\nx = ones(5)\r\nassert(isequal(myFrobeniusnormal(x),5))\r\n%% test 4\r\nx = zeros(2)\r\nassert(isequal(myFrobeniusnormal(x),0))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":1103,"edited_by":427930,"edited_at":"2022-10-21T12:10:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":99,"test_suite_updated_at":"2022-10-21T10:01:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-25T00:29:14.000Z","updated_at":"2026-02-15T14:18:38.000Z","published_at":"2013-05-25T00:29:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite your own version of Frobenius Norm without using the 'norm' function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43628,"title":"Find cosine between two given vectors u and v.","description":"Find cosine between two given vectors u and v.\r\n\r\nExample \r\n\r\nu = [5     2     0     5     3     0];\r\nv = [3     2     5     1     0     2];\r\n\r\nresult = 0.4611;","description_html":"\u003cp\u003eFind cosine between two given vectors u and v.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eu = [5     2     0     5     3     0];\r\nv = [3     2     5     1     0     2];\u003c/p\u003e\u003cp\u003eresult = 0.4611;\u003c/p\u003e","function_template":"function y = VecCos(u,v)\r\n  y = u;\r\nend","test_suite":"%%\r\nu = [5     2     0     5     3     0];\r\nv = [3     2     5     1     0     2];\r\ny_correct = 0.4611;\r\nassert(abs(VecCos(u,v)-y_correct)\u003c10^(-4))\r\n%%\r\nu = 2:0.05:3;\r\nv = 3:-0.05:2;\r\ny_correct = 0.9711;\r\nassert(abs(VecCos(u,v)-y_correct)\u003c10^(-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T19:33:42.000Z","updated_at":"2026-03-30T13:40:20.000Z","published_at":"2016-10-25T19:33:42.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eFind cosine between two given vectors u and v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = [5 2 0 5 3 0]; v = [3 2 5 1 0 2];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult = 0.4611;\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":2769,"title":"Find out magnitude of vector","description":"Find out magnitude of vector. \r\n\r\nSay x=[1 2 3], then answer must sqrt(1^2+2^2+3^2)\r\n\r\nPlease don't use sum function. \r\nIf you like this proble, please like it.. (Request)","description_html":"\u003cp\u003eFind out magnitude of vector.\u003c/p\u003e\u003cp\u003eSay x=[1 2 3], then answer must sqrt(1^2+2^2+3^2)\u003c/p\u003e\u003cp\u003ePlease don't use sum function. \r\nIf you like this proble, please like it.. (Request)\u003c/p\u003e","function_template":"function y = vector_mag(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3];\r\ny_correct = 3.7417;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = [-1 5 -6];\r\ny_correct = 7.8740;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = [3 4 5];\r\ny_correct = 7.0711;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = [5 5 -5];\r\ny_correct = 8.6603;\r\nassert(abs(vector_mag(x)-y_correct)\u003c0.0001)\r\n%% \r\nisempty(regexp(evalc('type vector_mag'),'sum'))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":268,"test_suite_updated_at":"2014-12-10T09:57:33.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-12-10T08:59:36.000Z","updated_at":"2026-02-18T10:31:27.000Z","published_at":"2014-12-10T08:59:36.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eFind out magnitude of vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSay x=[1 2 3], then answer must sqrt(1^2+2^2+3^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease don't use sum function. If you like this proble, please like it.. (Request)\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":389,"title":"Column norms of a matrix","description":"Given a matrix M, return a vector y such that for each k\r\n\r\n    y(k)=norm(M(:,k))\r\n\r\n(y(k) is the Euclidean norm of the k-th column of M)\r\n\r\nEDIT: changed the test case so that proper handling of complex values is required.","description_html":"\u003cp\u003eGiven a matrix M, return a vector y such that for each k\u003c/p\u003e\u003cpre\u003e    y(k)=norm(M(:,k))\u003c/pre\u003e\u003cp\u003e(y(k) is the Euclidean norm of the k-th column of M)\u003c/p\u003e\u003cp\u003eEDIT: changed the test case so that proper handling of complex values is required.\u003c/p\u003e","function_template":"function y = your_fcn_name(M)\r\n  y = M;\r\nend","test_suite":"%%\r\nM = [1 2 3; 4 5 6; 7 8 9+2i];\r\nfor k=1:size(M,2)\r\n  y_correct(k)=norm(M(:,k));\r\nend\r\nassert(isequal(your_fcn_name(M),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":1,"created_by":1258,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":569,"test_suite_updated_at":"2012-02-24T14:50:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-23T09:33:39.000Z","updated_at":"2026-03-29T18:47:57.000Z","published_at":"2012-02-24T14:50:55.000Z","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 matrix M, return a vector y such that for each k\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(k)=norm(M(:,k))]]\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\u003e(y(k) is the Euclidean norm of the k-th column of M)\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\u003eEDIT: changed the test case so that proper handling of complex values is required.\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":42755,"title":"Angle bisectors","description":"Given 2 direction vectors, calculate the *_two_ (2) normalized angle bisectors* (which are perpendicular between them).\r\n\r\nInput vectors can be 2-D or 3-D.\r\n\r\nThe two output vectors must have a norm equal to 1 (unit vectors).\r\n\r\nYou may find some help here:\r\n\u003chttps://proofwiki.org/wiki/Angle_Bisector_Vector\u003e","description_html":"\u003cp\u003eGiven 2 direction vectors, calculate the \u003cb\u003e\u003ci\u003etwo\u003c/i\u003e (2) normalized angle bisectors\u003c/b\u003e (which are perpendicular between them).\u003c/p\u003e\u003cp\u003eInput vectors can be 2-D or 3-D.\u003c/p\u003e\u003cp\u003eThe two output vectors must have a norm equal to 1 (unit vectors).\u003c/p\u003e\u003cp\u003eYou may find some help here: \u003ca href = \"https://proofwiki.org/wiki/Angle_Bisector_Vector\"\u003ehttps://proofwiki.org/wiki/Angle_Bisector_Vector\u003c/a\u003e\u003c/p\u003e","function_template":"function [b1,b2] = bisectors(v1,v2)\r\n  b1 = cross(v1,v2);\r\n  b2 = cross(v1,-v2);\r\nend","test_suite":"%%\r\nv1 = [1 0];\r\nv2 = [0 1];\r\n[b1,b2] = bisectors(v1,v2);\r\n\r\nb1ok = [1 1]/sqrt(2);\r\nb2ok = [-1 1]/sqrt(2);\r\n\r\n% Tests performed\r\nt1 = (abs(norm(b1)-1)\u003c1e-6); % Unit b1\r\nt2 = (abs(norm(b2)-1)\u003c1e-6); % Unit b2\r\nt3 = (abs(b1*b2') \u003c 1e-12); % b1 and b2 are perpendicular\r\nt4 = (abs(sum((b1-b1ok)))\u003c1e-12);  % b1 is equal to [1/sqrt(2) 1/sqrt(2)]\r\nt5 = (abs(sum((b1+b1ok)))\u003c1e-12); % or its opposite\r\nt6 = (abs(sum((b2-b2ok)))\u003c1e-12); % b2 is equal to [1/sqrt(2) -1/sqrt(2)]\r\nt7 = (abs(sum((b2+b2ok)))\u003c1e-12); % or its opposite\r\ntest = (t1 \u0026\u0026 t2 \u0026\u0026 t3 \u0026\u0026 xor(t4,t5) \u0026\u0026 xor(t6,t7));\r\n\r\n%%\r\nv1 = [4 0 3];\r\nv2 = [-2 2 1];\r\n[b1,b2] = bisectors(v1,v2);\r\n\r\nb1ok=[0.2 1 1.4]/sqrt(3);\r\nb2ok=[2.2 -1 0.4]/sqrt(6);\r\n  \r\n% Tests performed\r\nt1 = (abs(norm(b1)-1)\u003c1e-6); % Unit b1\r\nt2 = (abs(norm(b2)-1)\u003c1e-6); % Unit b2\r\nt3 = (abs(b1*b2') \u003c 1e-12); % b1 and b2 are perpendicular\r\nt4 = (abs(sum((b1-b1ok)))\u003c1e-12);  % b1 is equal to [1/sqrt(2) 1/sqrt(2)]\r\nt5 = (abs(sum((b1+b1ok)))\u003c1e-12); % or its opposite\r\nt6 = (abs(sum((b2-b2ok)))\u003c1e-12); % b2 is equal to [1/sqrt(2) -1/sqrt(2)]\r\nt7 = (abs(sum((b2+b2ok)))\u003c1e-12); % or its opposite\r\nassert(t1 \u0026\u0026 t2 \u0026\u0026 t3 \u0026\u0026 xor(t4,t5) \u0026\u0026 xor(t6,t7));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":12767,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2016-04-27T12:55:46.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2016-02-25T17:55:08.000Z","updated_at":"2026-02-27T10:16:23.000Z","published_at":"2016-02-25T17:57:35.000Z","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 2 direction vectors, calculate the\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e (2) normalized angle bisectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which are perpendicular between them).\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\u003eInput vectors can be 2-D or 3-D.\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\u003eThe two output vectors must have a norm equal to 1 (unit vectors).\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\u003eYou may find some help here:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink 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