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We could conveniently use Matlab's |cov| function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.\r\n\r\n*Task*\r\n\r\nBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data matrix.\r\n\r\nAdd the following field to those already produced by your |zscore| function.\r\n\r\n* |Cov|: a square matrix of covariances \r\n\r\n*Tips*\r\n\r\n* It's not as complicated as it sounds. Write one new line of code.\r\n* Don't just call Matlab's own |cov| function.\r\n* Keep to the structure of the code template with |zscore| as a local function. ","description_html":"\u003cp\u003e\u003cb\u003ePrevious problems in this series\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize\"\u003eStep 1: Centre and Standardize\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eStep 2: Covariance\u003c/b\u003e\u003c/p\u003e\u003cp\u003eFor the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's \u003ctt\u003ecov\u003c/tt\u003e function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTask\u003c/b\u003e\u003c/p\u003e\u003cp\u003eBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data matrix.\u003c/p\u003e\u003cp\u003eAdd the following field to those already produced by your \u003ctt\u003ezscore\u003c/tt\u003e function.\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003eCov\u003c/tt\u003e: a square matrix of covariances\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eTips\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eIt's not as complicated as it sounds. Write one new line of code.\u003c/li\u003e\u003cli\u003eDon't just call Matlab's own \u003ctt\u003ecov\u003c/tt\u003e function.\u003c/li\u003e\u003cli\u003eKeep to the structure of the code template with \u003ctt\u003ezscore\u003c/tt\u003e as a local function.\u003c/li\u003e\u003c/ul\u003e","function_template":"function s = covs(x)\r\n  s = zscore(x); \r\n  ... add your new code here\r\n\r\n\r\nfunction out = zscore(x)\r\n  ... add your code from Step 1 here","test_suite":"%%\r\nm = 100;\r\nn = 10;\r\nrng(2000,'twister')\r\nx = rand(m,n);\r\nk = false(1,n);\r\nk(randi(n,1,3)) = true;\r\nx(:,k) = rand; \r\ntol = 1.0e-12;\r\ns = covs(x);\r\nassert(isstruct(s),'Struct test failed.')\r\nassert(isfield(s,'Z'),'Z field test failed.')\r\nassert(isfield(s,'Mu'),'Mu field test failed.')\r\nassert(isfield(s,'Sigma'),'Sigma field test failed.')\r\nassert(isequal(size(x),size(s.Z)),'Z size test failed.')\r\nassert(isequal(size(x(1,:)),size(s.Mu)),'Mu size test failed.')\r\nassert(isequal(size(x(1,:)),size(s.Sigma)),'Sigma size test failed.')\r\nassert(all(abs(mean(s.Z))\u003ctol),'Mean test failed.')\r\nassert(all(abs(std(s.Z(:,~k))-1)\u003ctol),'STD test failed.')\r\nassert(all(abs(std(s.Z(:,k)))\u003ctol),'STD test for invariant data failed.')\r\nassert(isequal(s.Mu,mean(x,1)),'Mean equality test failed.')\r\nassert(isequal(s.Sigma,std(x,0,1)),'STD equality test failed.')\r\nassert(isfield(s,'Cov'),'Cov field test failed.')\r\nassert(all(all(abs(s.Cov-cov(s.Z))\u003c1e-12)),'Cov equality test failed.')\r\n\r\n%%\r\nstr = fileread('covs.m');\r\nassert(isempty(regexp(str,'=[ ]*cov[ ]*(')),'Don''t call Matlab''s own cov function.')\r\nassert(isempty(regexp(str,'@[\\s\\.'']*c[\\s\\.'']*o[\\s\\.'']*v')),'This could go on a while :-)')\r\nassert(numel(regexp(str,'zscore'))\u003e=2,'Keep to the structure of the original template.')","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":1016,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2013-12-17T15:50:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-14T23:01:22.000Z","updated_at":"2013-12-17T15:51:09.000Z","published_at":"2013-12-16T11:27:12.000Z","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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePrevious problems in this series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: Centre and Standardize\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eStep 2: Covariance\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\u003eFor the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecov\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.\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\u003eTask\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\u003eBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data 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\u003eAdd the following field to those already produced by your\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ezscore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCov\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: a square matrix of covariances\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\u003eTips\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt's not as complicated as it sounds. Write one new line of code.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDon't just call Matlab's own\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecov\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKeep to the structure of the code template with\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ezscore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a local function.\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":2049,"title":"Six Steps to PCA - Step 2: Covariance","description":"*Previous problems in this series*\r\n\r\n* \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize Step 1: Centre and Standardize\u003e\r\n\r\n*Step 2: Covariance*\r\n\r\nFor the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's |cov| function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.\r\n\r\n*Task*\r\n\r\nBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data matrix.\r\n\r\nAdd the following field to those already produced by your |zscore| function.\r\n\r\n* |Cov|: a square matrix of covariances \r\n\r\n*Tips*\r\n\r\n* It's not as complicated as it sounds. Write one new line of code.\r\n* Don't just call Matlab's own |cov| function.\r\n* Keep to the structure of the code template with |zscore| as a local function. ","description_html":"\u003cp\u003e\u003cb\u003ePrevious problems in this series\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize\"\u003eStep 1: Centre and Standardize\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eStep 2: Covariance\u003c/b\u003e\u003c/p\u003e\u003cp\u003eFor the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's \u003ctt\u003ecov\u003c/tt\u003e function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTask\u003c/b\u003e\u003c/p\u003e\u003cp\u003eBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data matrix.\u003c/p\u003e\u003cp\u003eAdd the following field to those already produced by your \u003ctt\u003ezscore\u003c/tt\u003e function.\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003eCov\u003c/tt\u003e: a square matrix of covariances\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eTips\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eIt's not as complicated as it sounds. Write one new line of code.\u003c/li\u003e\u003cli\u003eDon't just call Matlab's own \u003ctt\u003ecov\u003c/tt\u003e function.\u003c/li\u003e\u003cli\u003eKeep to the structure of the code template with \u003ctt\u003ezscore\u003c/tt\u003e as a local function.\u003c/li\u003e\u003c/ul\u003e","function_template":"function s = covs(x)\r\n  s = zscore(x); \r\n  ... add your new code here\r\n\r\n\r\nfunction out = zscore(x)\r\n  ... add your code from Step 1 here","test_suite":"%%\r\nm = 100;\r\nn = 10;\r\nrng(2000,'twister')\r\nx = rand(m,n);\r\nk = false(1,n);\r\nk(randi(n,1,3)) = true;\r\nx(:,k) = rand; \r\ntol = 1.0e-12;\r\ns = covs(x);\r\nassert(isstruct(s),'Struct test failed.')\r\nassert(isfield(s,'Z'),'Z field test failed.')\r\nassert(isfield(s,'Mu'),'Mu field test failed.')\r\nassert(isfield(s,'Sigma'),'Sigma field test failed.')\r\nassert(isequal(size(x),size(s.Z)),'Z size test failed.')\r\nassert(isequal(size(x(1,:)),size(s.Mu)),'Mu size test failed.')\r\nassert(isequal(size(x(1,:)),size(s.Sigma)),'Sigma size test failed.')\r\nassert(all(abs(mean(s.Z))\u003ctol),'Mean test failed.')\r\nassert(all(abs(std(s.Z(:,~k))-1)\u003ctol),'STD test failed.')\r\nassert(all(abs(std(s.Z(:,k)))\u003ctol),'STD test for invariant data failed.')\r\nassert(isequal(s.Mu,mean(x,1)),'Mean equality test failed.')\r\nassert(isequal(s.Sigma,std(x,0,1)),'STD equality test failed.')\r\nassert(isfield(s,'Cov'),'Cov field test failed.')\r\nassert(all(all(abs(s.Cov-cov(s.Z))\u003c1e-12)),'Cov equality test failed.')\r\n\r\n%%\r\nstr = fileread('covs.m');\r\nassert(isempty(regexp(str,'=[ ]*cov[ ]*(')),'Don''t call Matlab''s own cov function.')\r\nassert(isempty(regexp(str,'@[\\s\\.'']*c[\\s\\.'']*o[\\s\\.'']*v')),'This could go on a while :-)')\r\nassert(numel(regexp(str,'zscore'))\u003e=2,'Keep to the structure of the original template.')","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":1016,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2013-12-17T15:50:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-14T23:01:22.000Z","updated_at":"2013-12-17T15:51:09.000Z","published_at":"2013-12-16T11:27:12.000Z","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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePrevious problems in this series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: Centre and Standardize\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eStep 2: Covariance\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\u003eFor the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecov\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.\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\u003eTask\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\u003eBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data 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\u003eAdd the following field to those already produced by your\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ezscore\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCov\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: a square matrix of covariances\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\u003eTips\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt's not as complicated as it sounds. 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