{"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":44543,"title":"Normie Function","description":"So, I built a function and gave it a name- _Normie_.\r\n*Find the nth term of Normie function:*\r\n_f(n)= 1*f(n-1)+ 2*f(n-3)+ 3_ , *when n\u003e3* and _0_ , *when n\u003c=3*.","description_html":"\u003cp\u003eSo, I built a function and gave it a name- \u003ci\u003eNormie\u003c/i\u003e. \u003cb\u003eFind the nth term of Normie function:\u003c/b\u003e \u003ci\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e0\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e.\u003c/p\u003e","function_template":"function y = nth_term(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 2;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 3;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 4;\r\ny_correct = 3;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 10;\r\ny_correct = 93;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 11;\r\ny_correct = 162;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 20;\r\ny_correct = 18753;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 35;\r\ny_correct = 51651090;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 142236278205;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 5490159117130629;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 75;\r\ny_correct = 76953534045721408;\r\nassert(isequal(nth_term(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2018-03-28T11:14:13.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-21T19:10:33.000Z","updated_at":"2026-03-16T11:15:12.000Z","published_at":"2018-03-21T19:30:30.000Z","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\u003eSo, I built a function and gave it a name-\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\u003eNormie\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: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\u003eFind the nth term of Normie function:\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\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\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: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\u003ewhen n\u0026gt;3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\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\u003e0\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: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\u003ewhen n\u0026lt;=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\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":44544,"title":"Normie Function (2)","description":"Another _Normie Function_ defined as _f(n)= f(n-1)+f(n-2)+f(n-3)_ , *when n\u003e3* and _1_ , *when n\u003c=3*. *Find the nth term of this function* .","description_html":"\u003cp\u003eAnother \u003ci\u003eNormie Function\u003c/i\u003e defined as 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794174268033812736;\r\nassert(isequal(normie(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2018-03-28T11:02:45.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-22T09:27:39.000Z","updated_at":"2026-03-16T11:16:28.000Z","published_at":"2018-03-22T09:27:39.000Z","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\u003eAnother\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\u003eNormie Function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defined as\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\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\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:t\u003e 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.\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":44830,"title":"Twists in 2D","description":"So far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.\r\n\r\nAn alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2).  The matrix exponential of the Lie algebra matrix is a Lie group matrix.\r\n\r\nGiven a homogeneous transformation, return the corresponding twist as a column vector with the translational elements first.  ","description_html":"\u003cp\u003eSo far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.\u003c/p\u003e\u003cp\u003eAn alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2).  The matrix exponential of the Lie algebra matrix is a Lie group matrix.\u003c/p\u003e\u003cp\u003eGiven a homogeneous transformation, return the corresponding twist as a column vector with the translational elements first.\u003c/p\u003e","function_template":"function tw = user_function(T)\r\n  % Input: T a 3x3 homogeneous transformation matrix\r\n  % Outout: tw a 3x1 twist vector with translational elements first\r\n  tw = ;\r\nend","test_suite":"th = 2*pi*rand;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nT = [R t; 0 0 1];\r\n\r\ntw = user_function(T);\r\n%%\r\nassert(all(size(tw)==[3 1]), 'The twist must be a 3-element column vector');\r\n%%\r\nassert(isreal(tw), 'The twist must be real, not complex');\r\n\r\n%%\r\nTT = expm([0 -tw(3) tw(1); tw(3) 0 tw(2); 0 0 0]);\r\nassert(norm(abs(TT-T)) \u003c 1e-6, 'The twist is not correct')\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2019-01-10T07:12:32.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T06:47:50.000Z","updated_at":"2026-02-15T06:57:38.000Z","published_at":"2019-01-10T07:12:32.000Z","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\u003eSo far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.\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\u003eAn alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2). 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0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 4;\r\ny_correct = 3;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 10;\r\ny_correct = 93;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 11;\r\ny_correct = 162;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 20;\r\ny_correct = 18753;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 35;\r\ny_correct = 51651090;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 142236278205;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 5490159117130629;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 75;\r\ny_correct = 76953534045721408;\r\nassert(isequal(nth_term(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2018-03-28T11:14:13.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-21T19:10:33.000Z","updated_at":"2026-03-16T11:15:12.000Z","published_at":"2018-03-21T19:30:30.000Z","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\u003eSo, I built a function and gave it a name-\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\u003eNormie\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: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\u003eFind the nth term of Normie function:\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\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\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: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\u003ewhen n\u0026gt;3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\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\u003e0\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: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\u003ewhen n\u0026lt;=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\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":44544,"title":"Normie Function (2)","description":"Another _Normie Function_ defined as _f(n)= f(n-1)+f(n-2)+f(n-3)_ , *when n\u003e3* and _1_ , *when n\u003c=3*. *Find the nth term of this function* .","description_html":"\u003cp\u003eAnother \u003ci\u003eNormie Function\u003c/i\u003e defined as \u003ci\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e1\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e. \u003cb\u003eFind the nth term of this function\u003c/b\u003e .\u003c/p\u003e","function_template":"function y = normie(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 23;\r\ny_correct = 289329;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 36;\r\ny_correct = 797691075;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 37;\r\ny_correct = 1467182629;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 40;\r\ny_correct = 9129195487;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 4045078385041;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 794174268033812736;\r\nassert(isequal(normie(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2018-03-28T11:02:45.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-22T09:27:39.000Z","updated_at":"2026-03-16T11:16:28.000Z","published_at":"2018-03-22T09:27:39.000Z","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\u003eAnother\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\u003eNormie Function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defined as\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\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\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:t\u003e 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.\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":44830,"title":"Twists in 2D","description":"So far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.\r\n\r\nAn alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2).  The matrix exponential of the Lie algebra matrix is a Lie group matrix.\r\n\r\nGiven a homogeneous transformation, return the corresponding twist as a column vector with the translational elements first.  ","description_html":"\u003cp\u003eSo far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.\u003c/p\u003e\u003cp\u003eAn alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2).  The matrix exponential of the Lie algebra matrix is a Lie group matrix.\u003c/p\u003e\u003cp\u003eGiven a homogeneous transformation, return the corresponding twist as a column vector with the translational elements first.\u003c/p\u003e","function_template":"function tw = user_function(T)\r\n  % Input: T a 3x3 homogeneous transformation matrix\r\n  % Outout: tw a 3x1 twist vector with translational elements first\r\n  tw = ;\r\nend","test_suite":"th = 2*pi*rand;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nT = [R t; 0 0 1];\r\n\r\ntw = user_function(T);\r\n%%\r\nassert(all(size(tw)==[3 1]), 'The twist must be a 3-element column vector');\r\n%%\r\nassert(isreal(tw), 'The twist must be real, not complex');\r\n\r\n%%\r\nTT = expm([0 -tw(3) tw(1); tw(3) 0 tw(2); 0 0 0]);\r\nassert(norm(abs(TT-T)) \u003c 1e-6, 'The twist is not correct')\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2019-01-10T07:12:32.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T06:47:50.000Z","updated_at":"2026-02-15T06:57:38.000Z","published_at":"2019-01-10T07:12:32.000Z","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\u003eSo far we have represented the pose of an object in the plane using a homogeneous transformation, a 3x3 matrix belonging to the special Euclidean group SE(2), which is also a Lie group.\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\u003eAn alternative, and compact, representation of pose is as a twist, a 3-vector comprising the unique elements of the corresponding 3x3 matrix in the Lie algebra se(2). 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