{"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":43737,"title":"Alternative Dimensions","description":"Given a multidimensional matrix, transform the matrix so the dimensions are in the order given by variable ord. For example, given the following matrix:\r\n\r\nm has 3 dimensions\r\n\r\n  m(1,:,:) = all 1s\r\n  m(2,:,:) = all 2s\r\n  m(3,:,:) = all 3s\r\n\r\nAfter the transformation to [3 2 1], the matrix should be:\r\n\r\n  m(:,:,1) = all 1s\r\n  m(:,:,2) = all 2s\r\n  m(:,:,3) = all 3s","description_html":"\u003cp\u003eGiven a multidimensional matrix, transform the matrix so the dimensions are in the order given by variable ord. For example, given the following matrix:\u003c/p\u003e\u003cp\u003em has 3 dimensions\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003em(1,:,:) = all 1s\r\nm(2,:,:) = all 2s\r\nm(3,:,:) = all 3s\r\n\u003c/pre\u003e\u003cp\u003eAfter the transformation to [3 2 1], the matrix should be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003em(:,:,1) = all 1s\r\nm(:,:,2) = all 2s\r\nm(:,:,3) = all 3s\r\n\u003c/pre\u003e","function_template":"function y = transform(M,ord)\r\n  y = x;\r\nend","test_suite":"%%\r\nM=ones(3,3,3);\r\nM(2,:,:)=2.*M(2,:,:);\r\nM(3,:,:)=3.*M(3,:,:);\r\nord = [3,2,1];\r\nMC = ones(3,3,3);\r\nMC(:,:,2)=2.*MC(:,:,2);\r\nMC(:,:,3)=3.*MC(:,:,3);\r\nassert(isequal(transform(M,ord),MC))\r\n%%\r\nM=rand(1,2,3,4,5,6);\r\nord = [6 1 5 2 4 3];\r\nassert(isequal(size(transform(M,ord)),ord))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-12-06T23:42:04.000Z","updated_at":"2026-02-19T15:41:13.000Z","published_at":"2016-12-06T23:42:04.000Z","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 multidimensional matrix, transform the matrix so the dimensions are in the order given by variable ord. For example, given the following 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\u003em has 3 dimensions\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[m(1,:,:) = all 1s\\nm(2,:,:) = all 2s\\nm(3,:,:) = all 3s]]\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\u003eAfter the transformation to [3 2 1], the matrix should be:\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[m(:,:,1) = all 1s\\nm(:,:,2) = all 2s\\nm(:,:,3) = all 3s]]\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":2215,"title":"Power supply: 230V to 115V","description":"The problem is simple: we have a wall outlet which supplies 230V and an apparatus that requires 115V.\r\n\r\nSoftware is always cheaper than hardware (well, most of the time), so we solve this with a program, a Matlab function, to be precise.\r\n\r\nWrite a program that converts the supplied input voltage to the required output voltage.\r\n\r\n*If you like this problem, please like it (after solving).*","description_html":"\u003cp\u003eThe problem is simple: we have a wall outlet which supplies 230V and an apparatus that requires 115V.\u003c/p\u003e\u003cp\u003eSoftware is always cheaper than hardware (well, most of the time), so we solve this with a program, a Matlab function, to be precise.\u003c/p\u003e\u003cp\u003eWrite a program that converts the supplied input voltage to the required output voltage.\u003c/p\u003e\u003cp\u003e\u003cb\u003eIf you like this problem, please like it (after solving).\u003c/b\u003e\u003c/p\u003e","function_template":"function V_out = transformer(V_in)\r\n  N_primary = 5432; % Number of windings on primary coil.\r\n  N_secondary = 2716; % Number of windings on secondary coil.\r\n  V_out = N_secondary*i*V_in/N_primary; % Volt\r\nend","test_suite":"%%\r\nx = 230;\r\ny = transformer(x);\r\ny_correct = 115;\r\nif ~isequal(y,y_correct)\r\ndisp('That is not correct!');\r\ndisp('ÆÆÆÆÆÆÆÆÆÆÆÆÈØ8áÿèqBDüaZF$TWËF®H0ÑÓKÛÆÆÆÈÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÆÆÆÆÉÔ$ÜWçXwí/+«}{}º°{×}pÔ¿*/\u0026v\u0026F§ÉgÁÂÔÔÔÆÆÆÆÆÆÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÆÆÆÔÔpæ¼í¢rîC/ìn[**ª°\"²_!*\\\"_^¬ï7\u0026¼n/V2¼ÿ§ÖHÔÆÆÆÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÆWÐ0õCtîv½»¬°\"¡^¬°³;:²-::÷\";^¬¬³°÷¬(}(}{I¾$ÖE¶MÈÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÛP9{{{ï{}ª°³º°²ª²,:::¨¨¨¸'';::¹¹;²ª*{}|¬}íí\u003ct=åÚBÔÕÆÆÆÆ');\r\ndisp('ÆÆÆÐÿj\u0026£j{/»°°³\"_;;¹;:¸.¸¨¸¸¸¨,¨,''^^°¬¡\"ª¦¦{¿{î46bôBÆÈÑÕÆ');\r\ndisp('ÆÆÆÕKC¿}¦º~²²!^;:¨¸¨¸¨¸··´·.¸¨¸¸¸:;::~~¯°÷÷{(*\u003c}íIàãK¶ÑÑÆ');\r\ndisp('ÆÆÔMýwri¦¯;'':''::¨´.¨  ··  ···`¨¨:;,,¨¨,;²\"°°°\"_°÷{r±¼FÛÆÆ');\r\ndisp('ÆƧTî{¬¬º\":;,¸´¸``.··  · ·····´.´···..`¸¨:;__^¯\"÷{i{zagWÈ');\r\ndisp('ÆÆÖ¼l|²²\"¬²;¸.···   · ·   ······´.¨:_²¨`¸¨:;_ª°¬°¦»}[uaßN');\r\ndisp('ÈÔ©n/÷º\"\"_,¸´····    ·········.´¸¨:::-¹;,::;^°*|{+}}}\u003eJ5F');\r\ndisp('ÆpIc}*«÷²_:¨¸¸`·   ´¸.········.``¸¸¨,;­;;;:;­²\"ª÷¦}»}vI6ë');\r\ndisp('Èdc+¦/}÷\"-:''¨`··  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vÊÔÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆÆÆÆÆÆÆÆÆÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÖ¿  ·;¬÷²¸   ¦ÊÅÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆÆÆÆÆÆÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ·  ·*42/\u0026bî^:¿ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆÆÆÆÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ:´-ÊÊÊÊÊÊÖÔ^  ½ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆËÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ· :ëÊÊÊÊÊʬ  PÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ   ²ÞÊÊÊÊÝ  WÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÉ    {ÊÊÊʲ ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÅ   ¹ÊÊÊÊÊ:ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊg  µÊÊÊÊËÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ8·gÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('Is this problem a hair-raiser?');\r\nend\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\n% On request of Ned Gulley, some extra testcases (for the, hopefully, stable voltage regulator within the input voltage range specified on the box).\r\nassert(isequal(transformer(173),115))\r\nassert(isequal(transformer(225),115))\r\nassert(isequal(transformer(145),115))\r\nassert(isequal(transformer(238),115))\r\nassert(isequal(transformer(163),115))\r\nassert(isequal(transformer(128),115))\r\nassert(isequal(transformer(216),115))\r\nassert(isequal(transformer(164),115))\r\nassert(isequal(transformer(136),115))\r\nassert(isequal(transformer(156),115))\r\nassert(isequal(transformer(166),115))\r\nassert(isequal(transformer(132),115))\r\nassert(isequal(transformer(162),115))\r\nassert(isequal(transformer(227),115))\r\nassert(isequal(transformer(203),115))\r\nassert(isequal(transformer(168),115))\r\nassert(isequal(transformer(174),115))\r\nassert(isequal(transformer(170),115))\r\nassert(isequal(transformer(161),115))\r\nassert(isequal(transformer(226),115))\r\nassert(isequal(transformer(232),115))\r\nassert(isequal(transformer(146),115))\r\nassert(isequal(transformer(151),115))\r\nassert(isequal(transformer(152),115))\r\nassert(isequal(transformer(193),115))\r\nassert(isequal(transformer(201),115))\r\nassert(isequal(transformer(192),115))\r\nassert(isequal(transformer(133),115))\r\nassert(isequal(transformer(137),115))\r\nassert(isequal(transformer(224),115))\r\nassert(isequal(transformer(200),115))\r\nassert(isequal(transformer(221),115))\r\nassert(isequal(transformer(160),115))\r\nassert(isequal(transformer(230),115))\r\nassert(isequal(transformer(176),115))\r\nassert(isequal(transformer(210),115))\r\nassert(isequal(transformer(159),115))\r\nassert(isequal(transformer(177),115))\r\nassert(isequal(transformer(126),115))\r\nassert(isequal(transformer(197),115))\r\nassert(isequal(transformer(141),115))\r\nassert(isequal(transformer(222),115))\r\nassert(isequal(transformer(189),115))\r\nassert(isequal(transformer(223),115))\r\nassert(isequal(transformer(140),115))\r\nassert(isequal(transformer(231),115))\r\nassert(isequal(transformer(236),115))\r\nassert(isequal(transformer(180),115))\r\nassert(isequal(transformer(191),115))\r\nassert(isequal(transformer(149),115))\r\nassert(isequal(transformer(172),115))\r\nassert(isequal(transformer(196),115))\r\nassert(isequal(transformer(135),115))\r\nassert(isequal(transformer(209),115))\r\nassert(isequal(transformer(144),115))\r\nassert(isequal(transformer(233),115))\r\nassert(isequal(transformer(215),115))\r\nassert(isequal(transformer(204),115))\r\nassert(isequal(transformer(187),115))\r\nassert(isequal(transformer(202),115))\r\nassert(isequal(transformer(217),115))\r\nassert(isequal(transformer(171),115))\r\nassert(isequal(transformer(153),115))\r\nassert(isequal(transformer(139),115))\r\nassert(isequal(transformer(148),115))\r\nassert(isequal(transformer(169),115))\r\nassert(isequal(transformer(130),115))\r\nassert(isequal(transformer(219),115))\r\nassert(isequal(transformer(206),115))\r\nassert(isequal(transformer(127),115))\r\nassert(isequal(transformer(129),115))\r\nassert(isequal(transformer(218),115))\r\nassert(isequal(transformer(220),115))\r\nassert(isequal(transformer(213),115))\r\nassert(isequal(transformer(207),115))\r\nassert(isequal(transformer(188),115))\r\nassert(isequal(transformer(179),115))\r\nassert(isequal(transformer(185),115))\r\nassert(isequal(transformer(131),115))\r\nassert(isequal(transformer(157),115))\r\nassert(isequal(transformer(143),115))\r\nassert(isequal(transformer(147),115))\r\nassert(isequal(transformer(138),115))\r\nassert(isequal(transformer(214),115))\r\nassert(isequal(transformer(178),115))\r\nassert(isequal(transformer(182),115))\r\nassert(isequal(transformer(195),115))\r\nassert(isequal(transformer(237),115))\r\nassert(isequal(transformer(155),115))\r\nassert(isequal(transformer(158),115))\r\nassert(isequal(transformer(199),115))\r\nassert(isequal(transformer(211),115))\r\nassert(isequal(transformer(228),115))\r\nassert(isequal(transformer(175),115))\r\nassert(isequal(transformer(150),115))\r\nassert(isequal(transformer(194),115))\r\nassert(isequal(transformer(134),115))\r\nassert(isequal(transformer(229),115))\r\nassert(isequal(transformer(181),115))\r\nassert(isequal(transformer(190),115))\r\nassert(isequal(transformer(165),115))\r\nassert(isequal(transformer(235),115))\r\nassert(isequal(transformer(239),115))\r\nassert(isequal(transformer(212),115))\r\nassert(isequal(transformer(208),115))\r\nassert(isequal(transformer(142),115))\r\nassert(isequal(transformer(198),115))\r\nassert(isequal(transformer(184),115))\r\nassert(isequal(transformer(240),115))\r\nassert(isequal(transformer(205),115))\r\nassert(isequal(transformer(234),115))\r\nassert(isequal(transformer(186),115))\r\nassert(isequal(transformer(183),115))\r\nassert(isequal(transformer(167),115))\r\nassert(isequal(transformer(154),115))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":108,"test_suite_updated_at":"2014-02-26T08:04:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-24T15:36:09.000Z","updated_at":"2026-02-18T14:03:38.000Z","published_at":"2014-02-24T15:36:09.000Z","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\u003eThe problem is simple: we have a wall outlet which supplies 230V and an apparatus that requires 115V.\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\u003eSoftware is always cheaper than hardware (well, most of the time), so we solve this with a program, a Matlab function, to be precise.\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\u003eWrite a program that converts the supplied input voltage to the required output voltage.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf you like this problem, please like it (after solving).\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":46669,"title":"Rotation matrix of a sequence of 3D points","description":"Given a sequence of rotation matrices Rotation_Matrix [3x3xN], and a sequence of 3D points [3x1xN], compute the [3xN] sequence in the rotated coordinates.","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 21px; text-align: left; transform-origin: 384px 21px; 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: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a sequence of rotation matrices Rotation_Matrix [3x3xN], and a sequence of 3D points [3x1xN], compute the [3xN] sequence in the rotated coordinates.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Rotated_Vector = RotTimesVec(Rotation_Matrix,Vector)\r\n% Rotation_Matrix is [3x3xN]\r\n% Vector is [3x1xN]","test_suite":"%%\r\nRotation_Matrix(:,:,1) = [0.9129    0.8099    0.0542;\r\n                          0.4817    0.1868    0.6090;\r\n                          0.8518    0.2472    0.7772];\r\nRotation_Matrix(:,:,2) = [0.5111    0.5009    0.6256;\r\n                          0.0278    0.3320    0.5751;\r\n                          0.9904    0.1739    0.7510];\r\n\r\nVector(:,:,1) = [0.1535    0.3568    0.1440];\r\nVector(:,:,2) = [0.8506    0.3379    0.2752];\r\ny_correct = [0.4346    0.7166;\r\n             0.2266    0.5861;\r\n             0.3375    0.9332];\r\n\r\nassert(all(abs(RotTimesVec(Rotation_Matrix,Vector)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":416038,"edited_by":223089,"edited_at":"2023-01-28T07:17:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2023-01-28T07:17:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-04T11:09:18.000Z","updated_at":"2023-01-28T07:17:43.000Z","published_at":"2020-10-04T12:28:06.000Z","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\u003eGiven a sequence of rotation matrices Rotation_Matrix [3x3xN], and a sequence of 3D points [3x1xN], compute the [3xN] sequence in the rotated coordinates.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":43737,"title":"Alternative Dimensions","description":"Given a multidimensional matrix, transform the matrix so the dimensions are in the order given by variable ord. For example, given the following matrix:\r\n\r\nm has 3 dimensions\r\n\r\n  m(1,:,:) = all 1s\r\n  m(2,:,:) = all 2s\r\n  m(3,:,:) = all 3s\r\n\r\nAfter the transformation to [3 2 1], the matrix should be:\r\n\r\n  m(:,:,1) = all 1s\r\n  m(:,:,2) = all 2s\r\n  m(:,:,3) = all 3s","description_html":"\u003cp\u003eGiven a multidimensional matrix, transform the matrix so the dimensions are in the order given by variable ord. 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For example, given the following 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\u003em has 3 dimensions\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[m(1,:,:) = all 1s\\nm(2,:,:) = all 2s\\nm(3,:,:) = all 3s]]\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\u003eAfter the transformation to [3 2 1], the matrix should be:\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[m(:,:,1) = all 1s\\nm(:,:,2) = all 2s\\nm(:,:,3) = all 3s]]\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":2215,"title":"Power supply: 230V to 115V","description":"The problem is simple: we have a wall outlet which supplies 230V and an apparatus that requires 115V.\r\n\r\nSoftware is always cheaper than hardware (well, most of the time), so we solve this with a program, a Matlab function, to be precise.\r\n\r\nWrite a program that converts the supplied input voltage to the required output voltage.\r\n\r\n*If you like this problem, please like it (after solving).*","description_html":"\u003cp\u003eThe problem is simple: we have a wall outlet which supplies 230V and an apparatus that requires 115V.\u003c/p\u003e\u003cp\u003eSoftware is always cheaper than hardware (well, most of the time), so we solve this with a program, a Matlab function, to be precise.\u003c/p\u003e\u003cp\u003eWrite a program that converts the supplied input voltage to the required output voltage.\u003c/p\u003e\u003cp\u003e\u003cb\u003eIf you like this problem, please like it (after solving).\u003c/b\u003e\u003c/p\u003e","function_template":"function V_out = transformer(V_in)\r\n  N_primary = 5432; % Number of windings on primary coil.\r\n  N_secondary = 2716; % Number of windings on secondary coil.\r\n  V_out = N_secondary*i*V_in/N_primary; % Volt\r\nend","test_suite":"%%\r\nx = 230;\r\ny = transformer(x);\r\ny_correct = 115;\r\nif ~isequal(y,y_correct)\r\ndisp('That is not correct!');\r\ndisp('ÆÆÆÆÆÆÆÆÆÆÆÆÈØ8áÿèqBDüaZF$TWËF®H0ÑÓKÛÆÆÆÈÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÆÆÆÆÉÔ$ÜWçXwí/+«}{}º°{×}pÔ¿*/\u0026v\u0026F§ÉgÁÂÔÔÔÆÆÆÆÆÆÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÆÆÆÔÔpæ¼í¢rîC/ìn[**ª°\"²_!*\\\"_^¬ï7\u0026¼n/V2¼ÿ§ÖHÔÆÆÆÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÆWÐ0õCtîv½»¬°\"¡^¬°³;:²-::÷\";^¬¬³°÷¬(}(}{I¾$ÖE¶MÈÆÆÆÆÆÆ');\r\ndisp('ÆÆÆÛP9{{{ï{}ª°³º°²ª²,:::¨¨¨¸'';::¹¹;²ª*{}|¬}íí\u003ct=åÚBÔÕÆÆÆÆ');\r\ndisp('ÆÆÆÐÿj\u0026£j{/»°°³\"_;;¹;:¸.¸¨¸¸¸¨,¨,''^^°¬¡\"ª¦¦{¿{î46bôBÆÈÑÕÆ');\r\ndisp('ÆÆÆÕKC¿}¦º~²²!^;:¨¸¨¸¨¸··´·.¸¨¸¸¸:;::~~¯°÷÷{(*\u003c}íIàãK¶ÑÑÆ');\r\ndisp('ÆÆÔMýwri¦¯;'':''::¨´.¨  ··  ···`¨¨:;,,¨¨,;²\"°°°\"_°÷{r±¼FÛÆÆ');\r\ndisp('ÆƧTî{¬¬º\":;,¸´¸``.··  · ·····´.´···..`¸¨:;__^¯\"÷{i{zagWÈ');\r\ndisp('ÆÆÖ¼l|²²\"¬²;¸.···   · ·   ······´.¨:_²¨`¸¨:;_ª°¬°¦»}[uaßN');\r\ndisp('ÈÔ©n/÷º\"\"_,¸´····    ·········.´¸¨:::-¹;,::;^°*|{+}}}\u003eJ5F');\r\ndisp('ÆpIc}*«÷²_:¨¸¸`·   ´¸.········.``¸¸¨,;­;;;:;­²\"ª÷¦}»}vI6ë');\r\ndisp('Èdc+¦/}÷\"-:''¨`··  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vÊÔÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆÆÆÆÆÆÆÆÆÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÖ¿  ·;¬÷²¸   ¦ÊÅÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆÆÆÆÆÆÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ·  ·*42/\u0026bî^:¿ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆÆÆÆÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ:´-ÊÊÊÊÊÊÖÔ^  ½ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÆÆËÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ· :ëÊÊÊÊÊʬ  PÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ   ²ÞÊÊÊÊÝ  WÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÉ    {ÊÊÊʲ ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÅ   ¹ÊÊÊÊÊ:ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊg  µÊÊÊÊËÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ8·gÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ');\r\ndisp('Is this problem a hair-raiser?');\r\nend\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\n% On request of Ned Gulley, some extra testcases (for the, hopefully, stable voltage regulator within the input voltage range specified on the box).\r\nassert(isequal(transformer(173),115))\r\nassert(isequal(transformer(225),115))\r\nassert(isequal(transformer(145),115))\r\nassert(isequal(transformer(238),115))\r\nassert(isequal(transformer(163),115))\r\nassert(isequal(transformer(128),115))\r\nassert(isequal(transformer(216),115))\r\nassert(isequal(transformer(164),115))\r\nassert(isequal(transformer(136),115))\r\nassert(isequal(transformer(156),115))\r\nassert(isequal(transformer(166),115))\r\nassert(isequal(transformer(132),115))\r\nassert(isequal(transformer(162),115))\r\nassert(isequal(transformer(227),115))\r\nassert(isequal(transformer(203),115))\r\nassert(isequal(transformer(168),115))\r\nassert(isequal(transformer(174),115))\r\nassert(isequal(transformer(170),115))\r\nassert(isequal(transformer(161),115))\r\nassert(isequal(transformer(226),115))\r\nassert(isequal(transformer(232),115))\r\nassert(isequal(transformer(146),115))\r\nassert(isequal(transformer(151),115))\r\nassert(isequal(transformer(152),115))\r\nassert(isequal(transformer(193),115))\r\nassert(isequal(transformer(201),115))\r\nassert(isequal(transformer(192),115))\r\nassert(isequal(transformer(133),115))\r\nassert(isequal(transformer(137),115))\r\nassert(isequal(transformer(224),115))\r\nassert(isequal(transformer(200),115))\r\nassert(isequal(transformer(221),115))\r\nassert(isequal(transformer(160),115))\r\nassert(isequal(transformer(230),115))\r\nassert(isequal(transformer(176),115))\r\nassert(isequal(transformer(210),115))\r\nassert(isequal(transformer(159),115))\r\nassert(isequal(transformer(177),115))\r\nassert(isequal(transformer(126),115))\r\nassert(isequal(transformer(197),115))\r\nassert(isequal(transformer(141),115))\r\nassert(isequal(transformer(222),115))\r\nassert(isequal(transformer(189),115))\r\nassert(isequal(transformer(223),115))\r\nassert(isequal(transformer(140),115))\r\nassert(isequal(transformer(231),115))\r\nassert(isequal(transformer(236),115))\r\nassert(isequal(transformer(180),115))\r\nassert(isequal(transformer(191),115))\r\nassert(isequal(transformer(149),115))\r\nassert(isequal(transformer(172),115))\r\nassert(isequal(transformer(196),115))\r\nassert(isequal(transformer(135),115))\r\nassert(isequal(transformer(209),115))\r\nassert(isequal(transformer(144),115))\r\nassert(isequal(transformer(233),115))\r\nassert(isequal(transformer(215),115))\r\nassert(isequal(transformer(204),115))\r\nassert(isequal(transformer(187),115))\r\nassert(isequal(transformer(202),115))\r\nassert(isequal(transformer(217),115))\r\nassert(isequal(transformer(171),115))\r\nassert(isequal(transformer(153),115))\r\nassert(isequal(transformer(139),115))\r\nassert(isequal(transformer(148),115))\r\nassert(isequal(transformer(169),115))\r\nassert(isequal(transformer(130),115))\r\nassert(isequal(transformer(219),115))\r\nassert(isequal(transformer(206),115))\r\nassert(isequal(transformer(127),115))\r\nassert(isequal(transformer(129),115))\r\nassert(isequal(transformer(218),115))\r\nassert(isequal(transformer(220),115))\r\nassert(isequal(transformer(213),115))\r\nassert(isequal(transformer(207),115))\r\nassert(isequal(transformer(188),115))\r\nassert(isequal(transformer(179),115))\r\nassert(isequal(transformer(185),115))\r\nassert(isequal(transformer(131),115))\r\nassert(isequal(transformer(157),115))\r\nassert(isequal(transformer(143),115))\r\nassert(isequal(transformer(147),115))\r\nassert(isequal(transformer(138),115))\r\nassert(isequal(transformer(214),115))\r\nassert(isequal(transformer(178),115))\r\nassert(isequal(transformer(182),115))\r\nassert(isequal(transformer(195),115))\r\nassert(isequal(transformer(237),115))\r\nassert(isequal(transformer(155),115))\r\nassert(isequal(transformer(158),115))\r\nassert(isequal(transformer(199),115))\r\nassert(isequal(transformer(211),115))\r\nassert(isequal(transformer(228),115))\r\nassert(isequal(transformer(175),115))\r\nassert(isequal(transformer(150),115))\r\nassert(isequal(transformer(194),115))\r\nassert(isequal(transformer(134),115))\r\nassert(isequal(transformer(229),115))\r\nassert(isequal(transformer(181),115))\r\nassert(isequal(transformer(190),115))\r\nassert(isequal(transformer(165),115))\r\nassert(isequal(transformer(235),115))\r\nassert(isequal(transformer(239),115))\r\nassert(isequal(transformer(212),115))\r\nassert(isequal(transformer(208),115))\r\nassert(isequal(transformer(142),115))\r\nassert(isequal(transformer(198),115))\r\nassert(isequal(transformer(184),115))\r\nassert(isequal(transformer(240),115))\r\nassert(isequal(transformer(205),115))\r\nassert(isequal(transformer(234),115))\r\nassert(isequal(transformer(186),115))\r\nassert(isequal(transformer(183),115))\r\nassert(isequal(transformer(167),115))\r\nassert(isequal(transformer(154),115))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":108,"test_suite_updated_at":"2014-02-26T08:04:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-24T15:36:09.000Z","updated_at":"2026-02-18T14:03:38.000Z","published_at":"2014-02-24T15:36:09.000Z","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\u003eThe problem is simple: we have a wall outlet which supplies 230V and an apparatus that requires 115V.\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\u003eSoftware is always cheaper than hardware (well, most of the time), so we solve this with a program, a Matlab function, to be precise.\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\u003eWrite a program that converts the supplied input voltage to the required output voltage.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf you like this problem, please like it (after solving).\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":46669,"title":"Rotation matrix of a sequence of 3D points","description":"Given a sequence of rotation matrices Rotation_Matrix [3x3xN], and a sequence of 3D points [3x1xN], compute the [3xN] sequence in the rotated coordinates.","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 21px; text-align: left; transform-origin: 384px 21px; 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: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a sequence of rotation matrices Rotation_Matrix [3x3xN], and a sequence of 3D points [3x1xN], compute the [3xN] sequence in the rotated coordinates.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Rotated_Vector = RotTimesVec(Rotation_Matrix,Vector)\r\n% Rotation_Matrix is [3x3xN]\r\n% Vector is [3x1xN]","test_suite":"%%\r\nRotation_Matrix(:,:,1) = [0.9129    0.8099    0.0542;\r\n                          0.4817    0.1868    0.6090;\r\n                          0.8518    0.2472    0.7772];\r\nRotation_Matrix(:,:,2) = [0.5111    0.5009    0.6256;\r\n                          0.0278    0.3320    0.5751;\r\n                          0.9904    0.1739    0.7510];\r\n\r\nVector(:,:,1) = [0.1535    0.3568    0.1440];\r\nVector(:,:,2) = [0.8506    0.3379    0.2752];\r\ny_correct = [0.4346    0.7166;\r\n             0.2266    0.5861;\r\n             0.3375    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