{"id":16765,"date":"2022-10-22T02:53:54","date_gmt":"2022-10-21T21:23:54","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-function-for-matrix\/"},"modified":"2022-10-22T02:53:54","modified_gmt":"2022-10-21T21:23:54","slug":"solved-function-for-matrix","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-function-for-matrix\/","title":{"rendered":"[Solved] function for matrix"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-26564970\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"26564970\" data-parentid=\"26564606\" data-score=\"2\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>I&#8217;ve tried this, looking at wikipedia.<br \/>\n<a rel=\"nofollow noopener\" target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Invertible_matrix#Blockwise_inversion\">http:\/\/en.wikipedia.org\/wiki\/Invertible_matrix#Blockwise_inversion<\/a><\/p>\n<pre><code>getInverse &lt;- function(mat) {\n\n  if(nrow(mat) == 1)\n  {\n    return (matrix( 1.0\/ mat[1,1] ))\n  }\n\n  idx &lt;- nrow(mat) \/ 2\n  A &lt;- mat[1:idx, 1:idx, drop=F]\n  B &lt;- mat[1:idx, -1:-idx, drop=F]\n  C &lt;- mat[-1:-idx, 1:idx, drop=F]\n  D &lt;- mat[-1:-idx, -1:-idx, drop=F]\n\n  invA &lt;- getInverse(A)\n  temp &lt;- getInverse(D - C %*% invA %*% B)\n  element11 &lt;- invA + invA %*% B %*% temp %*% C %*% invA\n  element12 &lt;- -invA %*% B %*% temp\n  element21 &lt;- -temp %*% C %*% invA\n  element22 &lt;- temp\n\n  result &lt;- cbind(rbind(element11, element21), rbind(element12, element22))\n}\n\nset.seed(1)\nmat &lt;- matrix(rnorm(9), nrow=3)\nprint(\"Function test:\")\nprint(getInverse(mat))\nprint(\"Using Solve:\")\nsolve(mat)\n<\/code><\/pre>\n<p>Update for the question in the comments:<br \/>\nI&#8217;ve chosen these names to match the 4 different elements, or blocks, on the wiki page block matrix inversion formula. I see the result as a matrix of matrices, thus element11 was chosen for row 1, column 1 and element21 for row 2, element 1. I didn&#8217;t really &#8216;work out&#8217; anything I just stored some intermediate calculations into variables. Finally, the result is built by combining the blocks.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">4<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved function for matrix <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] I&#8217;ve tried this, looking at wikipedia. http:\/\/en.wikipedia.org\/wiki\/Invertible_matrix#Blockwise_inversion getInverse &lt;- function(mat) { if(nrow(mat) == 1) { return (matrix( 1.0\/ mat[1,1] )) } idx &lt;- nrow(mat) \/ 2 A &lt;- mat[1:idx, 1:idx, drop=F] B &lt;- mat[1:idx, -1:-idx, drop=F] C &lt;- mat[-1:-idx, 1:idx, drop=F] D &lt;- mat[-1:-idx, -1:-idx, drop=F] invA &lt;- getInverse(A) temp &lt;- getInverse(D &#8211; C &#8230; <a title=\"[Solved] function for matrix\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-function-for-matrix\/\" aria-label=\"More on [Solved] function for matrix\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[321],"class_list":["post-16765","post","type-post","status-publish","format-standard","hentry","category-solved","tag-r"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] function for matrix - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-function-for-matrix\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] function for matrix - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] I&#8217;ve tried this, looking at wikipedia. http:\/\/en.wikipedia.org\/wiki\/Invertible_matrix#Blockwise_inversion getInverse &lt;- function(mat) { if(nrow(mat) == 1) { return (matrix( 1.0\/ mat[1,1] )) } idx &lt;- nrow(mat) \/ 2 A &lt;- mat[1:idx, 1:idx, drop=F] B &lt;- mat[1:idx, -1:-idx, drop=F] C &lt;- mat[-1:-idx, 1:idx, drop=F] D &lt;- mat[-1:-idx, -1:-idx, drop=F] invA &lt;- getInverse(A) temp &lt;- getInverse(D - C ... 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