{"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":42501,"title":"Toeplitize a matrix","description":"Similar to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/3094-hankelize-a-matrix Problem 3094. Hankelize a matrix\u003e, now consider Toeplitization of a matrix.\r\n\r\nGiven an input matrix A, convert it to a Toeplitz matrix B by replacing the diagonal of A with the mean of the respective diagonal. For example, \r\n\r\nInput \r\n \r\n   A = [6     3     2     7\r\n\r\n        3     5     1     2\r\n\r\n        3     7    10     2]\r\n\r\nOutput:\r\n\r\n   B = [7     2     2     7 \r\n\r\n        5     7     2     2\r\n\r\n        3     5     7     2]\r\n","description_html":"\u003cp\u003eSimilar to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/3094-hankelize-a-matrix\"\u003eProblem 3094. Hankelize a matrix\u003c/a\u003e, now consider Toeplitization of a matrix.\u003c/p\u003e\u003cp\u003eGiven an input matrix A, convert it to a Toeplitz matrix B by replacing the diagonal of A with the mean of the respective diagonal. For example,\u003c/p\u003e\u003cp\u003eInput\u003c/p\u003e\u003cpre\u003e   A = [6     3     2     7\u003c/pre\u003e\u003cpre\u003e        3     5     1     2\u003c/pre\u003e\u003cpre\u003e        3     7    10     2]\u003c/pre\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cpre\u003e   B = [7     2     2     7 \u003c/pre\u003e\u003cpre\u003e        5     7     2     2\u003c/pre\u003e\u003cpre\u003e        3     5     7     2]\u003c/pre\u003e","function_template":"function B = toeplitize(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nA = 100;\r\nB = 100;\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [9,4;2,3;2,0];\r\nB = [6,4;1,6;2,1];\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [7,10,9;5,1,0];\r\nB = [4,5,9;5,4,5];\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [6 3 2 7;3 5 1 2;3 7 10 2];\r\nB = [7,2,2,7;5,7,2,2;3,5,7,2];\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [3,-1,-10,1,4,2;8,4,0,4,2,0;2,0,-1,10,-3,6];\r\nB = [2,3,-3,3,2,2;4,2,3,-3,3,2;2,4,2,3,-3,3];\r\nassert(isequal(toeplitize(A),B))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":149,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":23,"created_at":"2015-08-10T05:48:40.000Z","updated_at":"2026-03-29T07:17:50.000Z","published_at":"2015-08-10T05:49:54.000Z","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\u003eSimilar to\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=\\\"http://www.mathworks.com/matlabcentral/cody/problems/3094-hankelize-a-matrix\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3094. Hankelize a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, now consider Toeplitization of a matrix.\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\u003eGiven an input matrix A, convert it to a Toeplitz matrix B by replacing the diagonal of A with the mean of the respective diagonal. For example,\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\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[   A = [6     3     2     7\\n\\n        3     5     1     2\\n\\n        3     7    10     2]]]\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\u003eOutput:\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[   B = [7     2     2     7 \\n\\n        5     7     2     2\\n\\n        3     5     7     2]]]\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":3094,"title":"Hankelize a matrix","description":"Similar to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42501-toeplitize-a-matrix Problem 42501. Toeplitize a matrix\u003e, let's consider Hankelization of a matrix.\r\n\r\nGiven an input matrix A, convert it to a Hankel matrix B by replacing each skew-diagonal of A with its mean. For example, \r\n\r\nInput \r\n \r\n   A = [3     7    10     2\r\n\r\n        3     5     1     2\r\n\r\n        6     3     2     7]\r\n\r\nOutput:\r\n\r\n   B = [3     5     7     2 \r\n\r\n        5     7     2     2\r\n\r\n        7     2     2     7]\r\n\r\n\r\n","description_html":"\u003cp\u003eSimilar to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42501-toeplitize-a-matrix\"\u003eProblem 42501. Toeplitize a matrix\u003c/a\u003e, let's consider Hankelization of a matrix.\u003c/p\u003e\u003cp\u003eGiven an input matrix A, convert it to a Hankel matrix B by replacing each skew-diagonal of A with its mean. For example,\u003c/p\u003e\u003cp\u003eInput\u003c/p\u003e\u003cpre\u003e   A = [3     7    10     2\u003c/pre\u003e\u003cpre\u003e        3     5     1     2\u003c/pre\u003e\u003cpre\u003e        6     3     2     7]\u003c/pre\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cpre\u003e   B = [3     5     7     2 \u003c/pre\u003e\u003cpre\u003e        5     7     2     2\u003c/pre\u003e\u003cpre\u003e        7     2     2     7]\u003c/pre\u003e","function_template":"function B = hankelize(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nA = 100;\r\nB = 100;\r\nassert(isequal(hankelize(A),B));\r\n\r\n%%\r\nA = [2,0\r\n     2,3\r\n     9,4];\r\nB = [2,1\r\n     1,6\r\n     6,4];\r\nassert(isequal(hankelize(A),B));\r\n\r\n%%\r\nA = [5  1   0\r\n     7  10  9];\r\nB = [5   4   5\r\n     4   5   9];\r\nassert(isequal(hankelize(A),B));\r\n\r\n%%\r\nA = [3 7 10 2\r\n     3 5  1 2\r\n     6 3  2 7];\r\nB = [3 5 7 2\r\n     5 7 2 2\r\n     7 2 2 7];\r\nassert(isequal(hankelize(A),B));\r\n\r\n\r\n%%\r\nA = [2  0  -1 10 -3  6\r\n     8  4   0  4  2  0\r\n     3 -1 -10  1  4  2];\r\nB = [2 4  2  3 -3 3\r\n     4 2  3 -3  3 2\r\n     2 3 -3  3  2 2];\r\nassert(isequal(hankelize(A),B));","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":158,"test_suite_updated_at":"2015-10-31T18:03:02.000Z","rescore_all_solutions":false,"group_id":23,"created_at":"2015-03-19T14:42:36.000Z","updated_at":"2026-02-27T20:57:57.000Z","published_at":"2015-08-09T21:41:21.000Z","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\u003eSimilar to\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=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42501-toeplitize-a-matrix\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42501. Toeplitize a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, let's consider Hankelization of a matrix.\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\u003eGiven an input matrix A, convert it to a Hankel matrix B by replacing each skew-diagonal of A with its mean. For example,\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\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[   A = [3     7    10     2\\n\\n        3     5     1     2\\n\\n        6     3     2     7]]]\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\u003eOutput:\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[   B = [3     5     7     2 \\n\\n        5     7     2     2\\n\\n        7     2     2     7]]]\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":42501,"title":"Toeplitize a matrix","description":"Similar to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/3094-hankelize-a-matrix Problem 3094. Hankelize a matrix\u003e, now consider Toeplitization of a matrix.\r\n\r\nGiven an input matrix A, convert it to a Toeplitz matrix B by replacing the diagonal of A with the mean of the respective diagonal. For example, \r\n\r\nInput \r\n \r\n   A = [6     3     2     7\r\n\r\n        3     5     1     2\r\n\r\n        3     7    10     2]\r\n\r\nOutput:\r\n\r\n   B = [7     2     2     7 \r\n\r\n        5     7     2     2\r\n\r\n        3     5     7     2]\r\n","description_html":"\u003cp\u003eSimilar to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/3094-hankelize-a-matrix\"\u003eProblem 3094. Hankelize a matrix\u003c/a\u003e, now consider Toeplitization of a matrix.\u003c/p\u003e\u003cp\u003eGiven an input matrix A, convert it to a Toeplitz matrix B by replacing the diagonal of A with the mean of the respective diagonal. For example,\u003c/p\u003e\u003cp\u003eInput\u003c/p\u003e\u003cpre\u003e   A = [6     3     2     7\u003c/pre\u003e\u003cpre\u003e        3     5     1     2\u003c/pre\u003e\u003cpre\u003e        3     7    10     2]\u003c/pre\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cpre\u003e   B = [7     2     2     7 \u003c/pre\u003e\u003cpre\u003e        5     7     2     2\u003c/pre\u003e\u003cpre\u003e        3     5     7     2]\u003c/pre\u003e","function_template":"function B = toeplitize(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nA = 100;\r\nB = 100;\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [9,4;2,3;2,0];\r\nB = [6,4;1,6;2,1];\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [7,10,9;5,1,0];\r\nB = [4,5,9;5,4,5];\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [6 3 2 7;3 5 1 2;3 7 10 2];\r\nB = [7,2,2,7;5,7,2,2;3,5,7,2];\r\nassert(isequal(toeplitize(A),B))\r\n\r\n%%\r\nA = [3,-1,-10,1,4,2;8,4,0,4,2,0;2,0,-1,10,-3,6];\r\nB = [2,3,-3,3,2,2;4,2,3,-3,3,2;2,4,2,3,-3,3];\r\nassert(isequal(toeplitize(A),B))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":149,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":23,"created_at":"2015-08-10T05:48:40.000Z","updated_at":"2026-03-29T07:17:50.000Z","published_at":"2015-08-10T05:49:54.000Z","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\u003eSimilar to\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=\\\"http://www.mathworks.com/matlabcentral/cody/problems/3094-hankelize-a-matrix\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3094. Hankelize a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, now consider Toeplitization of a matrix.\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\u003eGiven an input matrix A, convert it to a Toeplitz matrix B by replacing the diagonal of A with the mean of the respective diagonal. For example,\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\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[   A = [6     3     2     7\\n\\n        3     5     1     2\\n\\n        3     7    10     2]]]\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\u003eOutput:\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[   B = [7     2     2     7 \\n\\n        5     7     2     2\\n\\n        3     5     7     2]]]\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":3094,"title":"Hankelize a matrix","description":"Similar to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42501-toeplitize-a-matrix Problem 42501. Toeplitize a matrix\u003e, let's consider Hankelization of a matrix.\r\n\r\nGiven an input matrix A, convert it to a Hankel matrix B by replacing each skew-diagonal of A with its mean. For example, \r\n\r\nInput \r\n \r\n   A = [3     7    10     2\r\n\r\n        3     5     1     2\r\n\r\n        6     3     2     7]\r\n\r\nOutput:\r\n\r\n   B = [3     5     7     2 \r\n\r\n        5     7     2     2\r\n\r\n        7     2     2     7]\r\n\r\n\r\n","description_html":"\u003cp\u003eSimilar to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42501-toeplitize-a-matrix\"\u003eProblem 42501. Toeplitize a matrix\u003c/a\u003e, let's consider Hankelization of a matrix.\u003c/p\u003e\u003cp\u003eGiven an input matrix A, convert it to a Hankel matrix B by replacing each skew-diagonal of A with its mean. For example,\u003c/p\u003e\u003cp\u003eInput\u003c/p\u003e\u003cpre\u003e   A = [3     7    10     2\u003c/pre\u003e\u003cpre\u003e        3     5     1     2\u003c/pre\u003e\u003cpre\u003e        6     3     2     7]\u003c/pre\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cpre\u003e   B = [3     5     7     2 \u003c/pre\u003e\u003cpre\u003e        5     7     2     2\u003c/pre\u003e\u003cpre\u003e        7     2     2     7]\u003c/pre\u003e","function_template":"function B = hankelize(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nA = 100;\r\nB = 100;\r\nassert(isequal(hankelize(A),B));\r\n\r\n%%\r\nA = [2,0\r\n     2,3\r\n     9,4];\r\nB = [2,1\r\n     1,6\r\n     6,4];\r\nassert(isequal(hankelize(A),B));\r\n\r\n%%\r\nA = [5  1   0\r\n     7  10  9];\r\nB = [5   4   5\r\n     4   5   9];\r\nassert(isequal(hankelize(A),B));\r\n\r\n%%\r\nA = [3 7 10 2\r\n     3 5  1 2\r\n     6 3  2 7];\r\nB = [3 5 7 2\r\n     5 7 2 2\r\n     7 2 2 7];\r\nassert(isequal(hankelize(A),B));\r\n\r\n\r\n%%\r\nA = [2  0  -1 10 -3  6\r\n     8  4   0  4  2  0\r\n     3 -1 -10  1  4  2];\r\nB = [2 4  2  3 -3 3\r\n     4 2  3 -3  3 2\r\n     2 3 -3  3  2 2];\r\nassert(isequal(hankelize(A),B));","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":158,"test_suite_updated_at":"2015-10-31T18:03:02.000Z","rescore_all_solutions":false,"group_id":23,"created_at":"2015-03-19T14:42:36.000Z","updated_at":"2026-02-27T20:57:57.000Z","published_at":"2015-08-09T21:41:21.000Z","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\u003eSimilar to\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=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42501-toeplitize-a-matrix\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42501. Toeplitize a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, let's consider Hankelization of a matrix.\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\u003eGiven an input matrix A, convert it to a Hankel matrix B by replacing each skew-diagonal of A with its mean. For example,\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\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[   A = [3     7    10     2\\n\\n        3     5     1     2\\n\\n        6     3     2     7]]]\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\u003eOutput:\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[   B = [3     5     7     2 \\n\\n        5     7     2     2\\n\\n        7     2     2     7]]]\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\"}]}"}],"term":"tag:\"toeplitz 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