{"id":5302,"date":"2014-01-10T09:16:00","date_gmt":"2014-01-10T00:16:00","guid":{"rendered":"http:\/\/www.moonmile.net\/blog\/?p=5302"},"modified":"2014-01-07T17:16:52","modified_gmt":"2014-01-07T08:16:52","slug":"f-f%e3%82%89%e3%81%97%e3%81%8flu%e5%88%86%e8%a7%a3%e3%82%92%e6%9b%b8%e3%81%8d%e7%9b%b4%e3%81%97%e3%81%a6%e3%81%bf%e3%82%8b","status":"publish","type":"post","link":"http:\/\/www.moonmile.net\/blog\/archives\/5302","title":{"rendered":"[F#] F#\u3089\u3057\u304fLU\u5206\u89e3\u3092\u66f8\u304d\u76f4\u3057\u3066\u307f\u308b"},"content":{"rendered":"<p>\nLU\u5206\u89e3\u3092 F# \u3089\u3057\u304f\u66f8\u304d\u76f4\u3057\u3066\u307f\u307e\u3059\u3002<br \/>\n\u305b\u3063\u304b\u304f\u306e F# \u306a\u306e\u306b for \u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u304c\u3082\u3063\u305f\u3044\u306a\u3044\u3057\uff08\uff1f\uff09\u3001\u6570\u5f0f\u306e\u03a3\u304b\u3089\u5916\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3092 sum \u95a2\u6570\u3092\u4f7f\u3063\u3066\u66f8\u304d\u76f4\u3057\u305f\u3044\u306e\u3067\u3059\u304c&#8230; matrix \u306b\u5bfe\u3057\u3066\u306e Seq.sum \u3068\u304b\u306f\u8981\u7d20\u5168\u4f53\u306b\u639b\u3051\u7b97\u3057\u3066\u3057\u307e\u3046\u306e\u3067\u7121\u7406\uff08\u3060\u3068\u601d\u3046\uff09\u306a\u306e\u3067\u3001\n<\/p>\n<p>\nC#er \u306e\u305f\u3081\u306e\u3084\u3055\u3057\u3044\u518d\u5e30\u5165\u9580: \u3044\u3052\u592a\u306e\u30d6\u30ed\u30b0<br \/>\n<a href=\"http:\/\/igeta.cocolog-nifty.com\/blog\/2011\/02\/tailcall.html#more\">http:\/\/igeta.cocolog-nifty.com\/blog\/2011\/02\/tailcall.html#more<\/a>\n<\/p>\n<p>\n\u3092\u53c2\u8003\u306b\u3057\u3066\u3001\u518d\u5e30\u95a2\u6570\u5316\u3057\u3066\u3044\u307e\u3059\u3002\n<\/p>\n<p>\/\/\/ LU\u5206\u89e3<br \/>\nlet LU2 ( A : matrix ) =<br \/>\n    let n = A.NumCols<br \/>\n    let L = Matrix.identity n<br \/>\n    let U = Matrix.zero n n<\/p>\n<p>    \/\/ sum(k=0,n) L(i,k)*U(k,j) \u306e\u8a08\u7b97\u3092\u95a2\u6570\u5316<br \/>\n    \/\/ \u4f59\u8a08\u308f\u304b\u308a\u3065\u3089\u3044\u304b\uff1f<br \/>\n    let sum i j k =<br \/>\n        let rec f i j k acc =<br \/>\n            if k < 0 then 0.0\n            elif k > 0 then f i j (k-1) (acc + L.[i,k]*U.[k,j])<br \/>\n            else L.[i,k]*U.[k,j]<br \/>\n        f i j k 0.0<\/p>\n<p>    for j in 0..n-1 do<br \/>\n        \/\/ U\u3092\u8a08\u7b97<br \/>\n        for i in 0..j do<br \/>\n            U.[i,j] <- A.[i,j] - sum i j (i-1)\n        \/\/ L\u3092\u8a08\u7b97\n        for i in j+1..n-1 do\n            L.[i,j] <- (A.[i,j] - sum i j (j-1))\/U.[j,j]\n    \/\/ \u7d50\u679c\u3092\u8fd4\u3059\n    (L,U)\n[\/code]\n\n\n<p>\nL\u3068U\u3092\u8a08\u7b97\u3059\u308b\u3068\u3053\u308d\u3067\u3001\u03a3L.[i,k]*U.[k.j] \u304c\u540c\u3058\u306a\u306e\u3067\u3001\u62ec\u308a\u3060\u3057\u3066\u307f\u305f\u306e\u3067\u3059\u304c\u3001\u4f59\u8a08\u308f\u304b\u308a\u3065\u3089\u3044\u304b\u3082\u3002\u6700\u5f8c\u306e for \u30eb\u30fc\u30d7\u306b\u9069\u7528\u3059\u308b\u3068\u3088\u3044\u306e\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u307e\u3042\u3001\u3053\u306e\u7a0b\u5ea6\u306e\u7c21\u5358\u306a\u3082\u306e\u306a\u3089\u3070\u518d\u5e30\u3092\u4f7f\u3046\u3068\u304b\u3048\u3063\u3066\u3084\u3084\u3053\u3057\u3044\u3068\u3044\u3046\u611f\u3058\u3067\u3059\u304b\u306d\u3002\n<\/p>\n<p>\n\u306a\u3089\u3070\u3001for \u306e\u4e8c\u91cd\u30eb\u30fc\u30d7\u306e\u4e2d\u3067\u3001sum \u3092\u5b9a\u7fa9\u3057\u3066\u3001\u3061\u3087\u3063\u3068\u7c21\u5358\u306b\u3057\u3066\u307f\u305f\u306e\u304c\u6b21\u306e\u30b3\u30fc\u30c9\u3067\u3059\u3002\n<\/p>\n<p>\/\/\/ LU\u5206\u89e3<br \/>\nlet LU3 ( A : matrix ) =<br \/>\n    let n = A.NumCols<br \/>\n    let L = Matrix.identity n<br \/>\n    let U = Matrix.zero n n<\/p>\n<p>    \/\/ sum(k=0,n) L(i,k)*U(k,j) \u306e\u8a08\u7b97\u3092\u95a2\u6570\u5316<br \/>\n    \/\/ \u666e\u901a\u306bfor\u30eb\u30fc\u30d7\u3067\u5408\u8a08\u3092\u8a08\u7b97\u3059\u308b<\/p>\n<p>    for j in 0..n-1 do<br \/>\n        \/\/ U\u3092\u8a08\u7b97<br \/>\n        for i in 0..n-1 do<br \/>\n            let sum max =<br \/>\n                let mutable s = 0.0<br \/>\n                for k in 0..max do<br \/>\n                    s <- s + L.[i,k]*U.[k,j]\n                s\n\n            if i <= j then\n                \/\/ U\u3092\u8a08\u7b97\n                U.[i,j] <- A.[i,j] - sum (i-1)\n            else \n                \/\/ L\u3092\u8a08\u7b97\n                L.[i,j] <- (A.[i,j] - sum (j-1))\/U.[j,j]\n    \/\/ \u7d50\u679c\u3092\u8fd4\u3059\n    (L,U)\n[\/code]\n\n\n<p>\n\u30eb\u30fc\u30d7\u306e\u4e2d\u3067\u95a2\u6570\u304c\u5b9a\u7fa9\u3067\u304d\u308b\u304b\u3089\u3001\u4fbf\u5229\u3063\u3066\u306e\u304c\u3042\u308a\u307e\u3059\u306d\u3002\u30eb\u30fc\u30d7\u5909\u6570\u306ei,j\u3082\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u306e\u3067\u3001sum \u95a2\u6570\u306e\u5f15\u6570\u304c\u5c11\u306a\u304f\u3066\u6e08\u307f\u307e\u3059\u3002\n<\/p>\n<p>\n\u304a\u6b21\u306f\u3001\u3053\u306eLU\u5206\u89e3\u3092\u4f7f\u3063\u3066\u3001\u4e8c\u6b21\u5143\u30c8\u30e9\u30b9\u3092\u5177\u4f53\u7684\u306b\u89e3\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>LU\u5206\u89e3\u3092 F# \u3089\u3057\u304f\u66f8\u304d\u76f4\u3057\u3066\u307f\u307e\u3059\u3002 \u305b\u3063\u304b\u304f\u306e F# \u306a\u306e\u306b for \u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u304c\u3082\u3063\u305f\u3044\u306a\u3044\u3057\uff08\uff1f\uff09\u3001\u6570\u5f0f\u306e\u03a3\u304b\u3089\u5916\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3092 sum \u95a2\u6570\u3092\u4f7f\u3063\u3066\u66f8\u304d\u76f4\u3057\u305f\u3044\u306e\u3067\u3059\u304c&#8230; matr &hellip; <a href=\"http:\/\/www.moonmile.net\/blog\/archives\/5302\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[59],"tags":[],"class_list":["post-5302","post","type-post","status-publish","format-standard","hentry","category-f"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/posts\/5302","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/comments?post=5302"}],"version-history":[{"count":1,"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/posts\/5302\/revisions"}],"predecessor-version":[{"id":5303,"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/posts\/5302\/revisions\/5303"}],"wp:attachment":[{"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/media?parent=5302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/categories?post=5302"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.moonmile.net\/blog\/wp-json\/wp\/v2\/tags?post=5302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}