{"id":6118,"date":"2026-08-25T17:36:01","date_gmt":"2026-08-25T08:36:01","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=6118"},"modified":"2026-08-25T17:36:01","modified_gmt":"2026-08-25T08:36:01","slug":"5-1_sparse","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/5-1_sparse\/","title":{"rendered":"5.1 \u758e\u884c\u5217\u306e\u683c\u7d0d\u5f62\u5f0f"},"content":{"rendered":"\n<h3>5.1.1 \u758e\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u69cb\u6210<\/h3>\n<p>\u758e\u884c\u5217\u7528\u306e\u683c\u7d0d\u5f62\u5f0f\u306b\u306f\u4f7f\u7528\u76ee\u7684\u306b\u9069\u3057\u305f\u591a\u304f\u306e\u7a2e\u985e\u304c\u3042\u308a, \u7d76\u5bfe\u7684\u306a\u6a19\u6e96\u5f62\u5f0f\u3068\u3044\u3063\u305f\u3082\u306e\u306f\u306a\u3044.<\/p>\n<p>\u305d\u3053\u3067, \u758e\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u758e\u884c\u5217\u306e\u683c\u7d0d\u5f62\u5f0f\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3088\u3046\u306a\u4f5c\u308a\u306b\u306a\u3063\u3066\u3044\u308b\u3082\u306e\u304c\u591a\u3044.<\/p>\n<p>\u5177\u4f53\u7684\u306b\u306f, \u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u3084\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u5f62\u5f0f\u306b\u3088\u308a\u758e\u884c\u5217\u3068\u30d9\u30af\u30c8\u30eb\u306e\u7a4d\u306e\u8a08\u7b97\u3092\u5916\u4ed8\u3051\u306b\u3059\u308b\u3053\u3068\u306b\u3088\u308a, \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5\u304b\u3089\u683c\u7d0d\u5f62\u5f0f\u306b\u4f9d\u5b58\u3059\u308b\u90e8\u5206\u3092\u5207\u308a\u96e2\u3059\u3068\u3044\u3063\u305f\u3082\u306e\u3067\u3042\u308b. \u3053\u308c\u306b\u3088\u308a, \u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u306a\u304f, \u6570\u591a\u304f\u3042\u308b\u683c\u7d0d\u5f62\u5f0f\u304b\u3089\u597d\u307f\u306e\u3082\u306e\u3092\u9078\u629e\u3057\u3066\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p>\u306a\u304a, \u6700\u8fd1\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f, \u683c\u7d0d\u5f62\u5f0f\u306e\u8a73\u7d30\u306f\u96a0\u3057\u3066\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3068\u3057\u3066\u6271\u3046\u3082\u306e\u3082\u3042\u308b. \u3053\u306e\u5834\u5408\u306f\u683c\u7d0d\u30c7\u30fc\u30bf\u306e\u5165\u51fa\u529b\u65b9\u6cd5 (\u30e1\u30bd\u30c3\u30c9) \u3060\u3051\u304c\u516c\u958b\u3055\u308c\u308b.<\/p>\n<p>5.3 \u3067\u8aac\u660e\u3059\u308b\u30af\u30ea\u30ed\u30d5\u90e8\u5206\u7a7a\u9593\u6cd5\u3067\u306f, \u6b21\u306e 2 \u3064\u306e\u64cd\u4f5c\u3092\u5b9a\u7fa9\u3059\u308c\u3070\u3088\u3044\u3088\u3046\u306b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u8a18\u8ff0\u3055\u308c\u3066\u3044\u308b. \u306a\u304a, \u4fc2\u6570\u884c\u5217\u3092 A, \u524d\u51e6\u7406\u884c\u5217\u3092 M, \u30d9\u30af\u30c8\u30eb\u3092 x, y \u3067\u8868\u3059.<\/p>\n<ul>\n<li>Matvec\u6f14\u7b97: \\(Ax\\) \u3092\u6c42\u3081\u308b<\/li>\n<li>Psolve\u6f14\u7b97: \\(x = M^{-1}y\\) (\\(Mx = y\\) \u306e\u89e3 \\(x\\)) \u3092\u6c42\u3081\u308b (\u524d\u51e6\u7406\u306a\u3057\u306e\u5834\u5408\u306b\u306f\u4e0d\u8981)<\/li>\n<\/ul>\n<p>\u4e00\u90e8\u306e\u89e3\u6cd5 (BICG \u6cd5\u3068 QMR \u6cd5) \u3067\u306f\u3055\u3089\u306b\u6b21\u306e 2 \u3064\u304c\u5fc5\u8981\u3067\u3042\u308b. \u8aac\u660e\u306e\u4e2d\u3067\u300c\\(A^T\\) \u306b\u95a2\u3059\u308b\u8a08\u7b97\u300d\u3068\u8868\u8a18\u3055\u308c\u308b\u5834\u5408\u306b\u306f\u3053\u308c\u3089\u3092\u6307\u3059.<\/p>\n<ul>\n<li>MatvecTrans\u6f14\u7b97: \\(A^Tx\\) \u3092\u6c42\u3081\u308b<\/li>\n<li>PsolveTrans\u6f14\u7b97: \\(x = (M^T)^{-1}y\\) (\\(M^Tx = y\\) \u306e\u89e3 \\(x\\)) \u3092\u6c42\u3081\u308b (\u524d\u51e6\u7406\u306a\u3057\u306e\u5834\u5408\u306b\u306f\u4e0d\u8981)<\/li>\n<\/ul>\n<p>XLPack \u306e\u30af\u30ea\u30ed\u30d5\u90e8\u5206\u7a7a\u9593\u6cd5\u3067\u306f 1 \u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5bfe\u3057\u3066 3 \u7a2e\u985e\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u7528\u610f\u3057\u3066\u3044\u308b. \u3059\u306a\u308f\u3061, \u2460 \u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u7248, \u2461 \u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u7248, \u2462 CSR \/ CSC \u7248\u3067\u3042\u308b. \u2462\u306f\u683c\u7d0d\u5f62\u5f0f\u3092 CSR \/ CSC \u5f62\u5f0f (\u4e0b\u8a18\u53c2\u7167) \u306b\u9650\u5b9a\u3059\u308b\u4ee3\u308f\u308a\u306b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5bb9\u6613\u306b\u4f7f\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u305f\u3082\u306e\u3067\u3042\u308b.<\/p>\n<h3>5.1.2 \u758e\u884c\u5217\u306e\u683c\u7d0d\u5f62\u5f0f<\/h3>\n<p>\u758e\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u4efb\u610f\u306e\u758e\u884c\u5217\u683c\u7d0d\u5f62\u5f0f\u3092\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u4f5c\u3089\u308c\u3066\u3044\u308b\u3068\u306f\u3044\u3048, \u3067\u304d\u308b\u3060\u3051\u30e1\u30b8\u30e3\u30fc\u306a\u5f62\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u304a\u3044\u305f\u65b9\u304c\u3088\u3044.<\/p>\n<p>\u3053\u3053\u3067\u306f\u6c4e\u7528\u7684\u306b\u4f7f\u3048\u308b\u6b21\u306e\u4ee3\u8868\u7684\u306a 3 \u7a2e\u985e\u306b\u3064\u3044\u3066\u8aac\u660e\u3059\u308b.<\/p>\n<p>(1) \u5727\u7e2e\u884c\u683c\u7d0d (Compressed Sparse Row (CSR)) \u5f62\u5f0f<br \/>\n(2) \u5727\u7e2e\u5217\u683c\u7d0d (Compressed Sparse Column (CSC)) \u5f62\u5f0f<br \/>\n(3) \u5ea7\u6a19 (Coordinate (COO)) \u5f62\u5f0f<\/p>\n<p>\u3053\u308c\u3089\u306f XLPack \u3067\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b\u5f62\u5f0f\u3067\u3042\u308b. (1) \u3068 (2) \u306f\u4e3b\u306b\u8a08\u7b97\u306b\u4f7f\u308f\u308c, (3) \u306f\u4e3b\u306b\u5165\u51fa\u529b\u306b\u4f7f\u308f\u308c\u308b.<\/p>\n<h4>5.1.2.1 \u4f8b\u984c\u758e\u884c\u5217<\/h4>\n<p>\u4ee5\u4e0b, \u683c\u7d0d\u5f62\u5f0f\u306e\u8aac\u660e\u3067\u4f7f\u7528\u3059\u308b\u4f8b\u984c\u3068\u3057\u3066\u6b21\u306e 6 x 6 \u884c\u5217\u3092\u8003\u3048\u308b.<\/p>\n<table>\n<tbody style=\"border:solid 2px;\">\n<tr>\n<td style=\"width: 30px; background-color:lightpink;\">10<\/td>\n<td style=\"width: 30px;\">0<\/td>\n<td style=\"width: 30px;\">0<\/td>\n<td style=\"width: 30px;\">0<\/td>\n<td style=\"width: 30px; background-color:lightpink;\">-2<\/td>\n<td style=\"width: 30px;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">4<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink;\">-1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>5.1.2.2 \u5727\u7e2e\u884c\u683c\u7d0d (Compressed Sparse Row (CSR)) \u5f62\u5f0f<\/h4>\n<p>CRS (Compressed Row Storage) \u5f62\u5f0f\u3068\u3088\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308b. \u758e\u884c\u5217\u306e\u69cb\u9020\u306b\u3064\u3044\u3066\u4f55\u3082\u4eee\u5b9a\u3057\u306a\u3044\u4e00\u822c\u7684\u306a\u5f62\u5f0f\u3067\u3042\u308a\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u308b. \u7279\u5b9a\u306e\u69cb\u9020\u3084\u8a08\u7b97\u306b\u7279\u5316\u3057\u305f\u3088\u3046\u306a\u5f62\u5f0f\u306b\u6bd4\u3079\u308b\u3068\u52b9\u7387\u306f\u843d\u3061\u308b\u3082\u306e\u306e\u6c4e\u7528\u6027\u3092\u7279\u9577\u3068\u3059\u308b.<\/p>\n<p>1 \u672c\u306e\u6d6e\u52d5\u5c0f\u6570\u914d\u5217 val \u3068 2 \u672c\u306e\u6574\u6570\u914d\u5217 rowptr \u304a\u3088\u3073 colind \u306b\u975e\u30bc\u30ed\u8981\u7d20\u3060\u3051\u3092\u683c\u7d0d\u3059\u308b. val \u306b\u306f\u975e\u30bc\u30ed\u8981\u7d20\u306e\u5024\u3092\u884c\u65b9\u5411\u9806\u306b\u683c\u7d0d\u3059\u308b. rowptr \u306f\u5404\u884c\u306e\u5148\u982d\u8981\u7d20\u306e val \u914d\u5217\u4e2d\u306e\u4f4d\u7f6e\u3092\u8868\u3059. colind \u306f\u5bfe\u5fdc\u3059\u308b val \u306e\u8981\u7d20\u306e\u5217\u756a\u53f7\u3067\u3042\u308b. rowptr \u306e\u6700\u5f8c\u306b\u306f val \u914d\u5217\u306e\u6700\u5f8c + 1 \u3092\u5165\u308c\u3066\u304a\u304f.<\/p>\n<p>\u884c\u756a\u53f7\u3068\u5217\u756a\u53f7\u306e\u632f\u308a\u65b9\u306b\u306f 2 \u7a2e\u985e\u3042\u308b\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b, \u3059\u306a\u308f\u3061, FORTRAN \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5834\u5408\u306b\u306f 1 \u304b\u3089, C \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5834\u5408\u306b\u306f 0 \u304b\u3089\u59cb\u307e\u308b.<\/p>\n<p>\u4e0a\u306e\u4f8b\u984c\u884c\u5217\u3092 CSR \u5f62\u5f0f\u3067\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p>(FORTRAN \u5f62\u5f0f)<\/p>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"width: 80px\">i<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">1<\/td>\n<td style=\"width: 30px\">2<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">3<\/td>\n<td style=\"width: 30px\">4<\/td>\n<td style=\"width: 30px\">5<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">6<\/td>\n<td style=\"width: 30px\">7<\/td>\n<td style=\"width: 30px\">8<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">9<\/td>\n<td style=\"width: 30px\">10<\/td>\n<td style=\"width: 30px\">11<\/td>\n<td style=\"width: 30px\">12<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">13<\/td>\n<td style=\"width: 30px\">14<\/td>\n<td style=\"width: 30px\">15<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">16<\/td>\n<td style=\"width: 30px\">17<\/td>\n<td style=\"width: 30px\">18<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td>val(i)<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">10<\/td>\n<td style=\"background-color:lightpink;\">-2<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">3<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">3<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">8<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">4<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink; border-right:solid 2px;\">-1<\/td>\n<\/tr>\n<tr style=\"border:solid;\">\n<td>colind(i)<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>2<\/td>\n<td>6<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>4<\/td>\n<td>6<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>5<\/td>\n<td style=\"border-right:solid 2px;\">6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr style=\"border:solid;\">\n<td style=\"border-left:solid 2px; width: 80px\">rowptr(i)<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">1<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">3<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">6<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">9<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">13<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">16<\/td>\n<td style=\"border-left:solid 2px; width: 30px\">19<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(C \u5f62\u5f0f)<\/p>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"width: 80px\">i<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">0<\/td>\n<td style=\"width: 30px\">1<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">2<\/td>\n<td style=\"width: 30px\">3<\/td>\n<td style=\"width: 30px\">4<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">5<\/td>\n<td style=\"width: 30px\">6<\/td>\n<td style=\"width: 30px\">7<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">8<\/td>\n<td style=\"width: 30px\">9<\/td>\n<td style=\"width: 30px\">10<\/td>\n<td style=\"width: 30px\">11<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">12<\/td>\n<td style=\"width: 30px\">13<\/td>\n<td style=\"width: 30px\">14<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">15<\/td>\n<td style=\"width: 30px\">16<\/td>\n<td style=\"width: 30px\">17<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td>val[i]<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">10<\/td>\n<td style=\"background-color:lightpink;\">-2<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">3<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">3<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">8<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">4<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink; border-right:solid 2px;\">-1<\/td>\n<\/tr>\n<tr style=\"border:solid;\">\n<td>colind[i]<\/td>\n<td style=\"border-left:solid 2px;\">0<\/td>\n<td>4<\/td>\n<td style=\"border-left:solid 2px;\">0<\/td>\n<td>1<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td style=\"border-left:solid 2px;\">0<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>4<\/td>\n<td style=\"border-right:solid 2px;\">5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr style=\"border:solid;\">\n<td style=\"border-left:solid 2px; width: 80px\">rowptr[i]<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">0<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">2<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">5<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">8<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">12<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">15<\/td>\n<td style=\"border-left:solid 2px; width: 30px\">18<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306b\u306f, \u5bfe\u89d2\u8981\u7d20\u3068\u305d\u306e\u5de6\u5074\u306e\u307f, \u3042\u308b\u3044\u306f, \u5bfe\u89d2\u8981\u7d20\u3068\u305d\u306e\u53f3\u5074\u306e\u307f\u3092\u683c\u7d0d\u3057\u3066\u4f7f\u7528\u30e1\u30e2\u30ea\u30fc\u3092\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u308b. XLPack \u3067\u306f\u3053\u308c\u3092\u72ec\u81ea\u306b SSR \u5f62\u5f0f\u3068\u8868\u793a\u3057\u3066\u3044\u308b.<\/p>\n<p>\u4e0a\u306e\u4f8b\u3067\u306f\u5404\u884c\u306e\u4e2d\u3067\u5217\u756a\u53f7\u306e\u6607\u9806\u306b\u4e26\u3093\u3067\u3044\u308b\u304c, \u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u3063\u3066\u306f\u884c\u5185\u306e\u4e26\u3073\u9806\u306f\u4efb\u610f\u3067\u3088\u3044\u3053\u3068\u304c\u3042\u308b. XLPack \u3067\u306f\u57fa\u672c\u7684\u306b\u306f\u6607\u9806\u306b\u4e26\u3093\u3067\u3044\u308b\u3053\u3068\u3092\u4eee\u5b9a\u3057\u3066\u8a08\u7b97\u52b9\u7387\u3092\u4e0a\u3052\u308b\u3088\u3046\u306a\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n<p>CSR \u5f62\u5f0f\u306f\u5b9f\u306f\u8106\u5f31\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u3067, rowptr \u304a\u3088\u3073 colind \u306f\u6574\u6570\u5024\u3067\u306f\u3042\u308b\u304c val \u3092\u6307\u3059\u30dd\u30a4\u30f3\u30bf\u30fc\u307f\u305f\u3044\u306a\u3082\u306e\u3067\u3042\u308b\u304b\u3089, \u8aa4\u3063\u305f\u5024\u3092\u8a2d\u5b9a\u3059\u308b\u3068\u7c21\u5358\u306b\u30e1\u30e2\u30ea\u30fc\u30a2\u30af\u30bb\u30b9\u30a8\u30e9\u30fc\u3092\u5f15\u304d\u8d77\u3053\u3057\u3066\u3057\u307e\u3046\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b.<\/p>\n<h4>5.1.2.3 \u5727\u7e2e\u5217\u683c\u7d0d (Compressed Sparse Column (CSC)) \u5f62\u5f0f<\/h4>\n<p>CCS (Compressed Column Storage) \u5f62\u5f0f\u3068\u3088\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308b. CSR \u5f62\u5f0f\u3068\u306f\u8ee2\u7f6e\u306e\u95a2\u4fc2\u306b\u3042\u308b. \u3059\u306a\u308f\u3061, CSR \u5f62\u5f0f\u3067\u683c\u7d0d\u3057\u305f\u884c\u5217 A \u3092 CSC \u5f62\u5f0f\u3068\u307f\u306a\u3057\u3066\u8aad\u307f\u3060\u3059\u3068\u8ee2\u7f6e\u884c\u5217 A<sup>T<\/sup> \u306b\u306a\u308b.<\/p>\n<p>1 \u672c\u306e\u6d6e\u52d5\u5c0f\u6570\u914d\u5217 val \u3068 2 \u672c\u306e\u6574\u6570\u914d\u5217 colptr \u304a\u3088\u3073 rowind \u306b\u975e\u30bc\u30ed\u8981\u7d20\u3060\u3051\u3092\u683c\u7d0d\u3059\u308b. val \u306b\u306f\u975e\u30bc\u30ed\u8981\u7d20\u306e\u5024\u3092\u5217\u65b9\u5411\u9806\u306b\u683c\u7d0d\u3059\u308b. colptr \u306f\u5404\u5217\u306e\u5148\u982d\u8981\u7d20\u306e val \u914d\u5217\u4e2d\u306e\u4f4d\u7f6e\u3092\u8868\u3059. rowind \u306f\u5bfe\u5fdc\u3059\u308b val \u306e\u8981\u7d20\u306e\u884c\u756a\u53f7\u3067\u3042\u308b. colptr \u306e\u6700\u5f8c\u306b\u306f val \u914d\u5217\u306e\u6700\u5f8c + 1 \u3092\u5165\u308c\u3066\u304a\u304f.<\/p>\n<p>\u884c\u756a\u53f7\u3068\u5217\u756a\u53f7\u306e\u632f\u308a\u65b9\u304c 2 \u7a2e\u985e\u3042\u308b\u306e\u306f CSR \u5f62\u5f0f\u3068\u540c\u69d8\u3067\u3042\u308b, \u3059\u306a\u308f\u3061, FORTRAN \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5834\u5408\u306b\u306f 1 \u304b\u3089, C \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5834\u5408\u306b\u306f 0 \u304b\u3089\u59cb\u307e\u308b.<\/p>\n<p>\u4e0a\u306e\u4f8b\u984c\u884c\u5217\u3092 CSC \u5f62\u5f0f\u3067\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p>(FORTRAN \u5f62\u5f0f)<\/p>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"width: 80px\">i<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">1<\/td>\n<td style=\"width: 30px\">2<\/td>\n<td style=\"width: 30px\">3<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">4<\/td>\n<td style=\"width: 30px\">5<\/td>\n<td style=\"width: 30px\">6<\/td>\n<td style=\"width: 30px\">7<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">8<\/td>\n<td style=\"width: 30px\">9<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">10<\/td>\n<td style=\"width: 30px\">11<\/td>\n<td style=\"width: 30px\">12<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">13<\/td>\n<td style=\"width: 30px\">14<\/td>\n<td style=\"width: 30px\">15<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">16<\/td>\n<td style=\"width: 30px\">17<\/td>\n<td style=\"width: 30px\">18<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td>val(i)<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">10<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">9<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">4<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">8<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">7<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">-2<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">3<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<td style=\"background-color:lightpink;\">-1<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td>rowind(i)<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td style=\"border-left:solid 2px;\">3<\/td>\n<td>4<\/td>\n<td style=\"border-left:solid 2px;\">3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>4<\/td>\n<td>6<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-left:solid 2px; width: 80px\">colptr(i)<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">1<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">4<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">8<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">10<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">13<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">16<\/td>\n<td style=\"border-left:solid 2px; width: 30px\">19<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(C \u5f62\u5f0f)<\/p>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"width: 80px\">i<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">0<\/td>\n<td style=\"width: 30px\">1<\/td>\n<td style=\"width: 30px\">2<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">3<\/td>\n<td style=\"width: 30px\">4<\/td>\n<td style=\"width: 30px\">5<\/td>\n<td style=\"width: 30px\">6<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">7<\/td>\n<td style=\"width: 30px\">8<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">9<\/td>\n<td style=\"width: 30px\">10<\/td>\n<td style=\"width: 30px\">11<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">12<\/td>\n<td style=\"width: 30px\">13<\/td>\n<td style=\"width: 30px\">14<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">15<\/td>\n<td style=\"width: 30px\">16<\/td>\n<td style=\"width: 30px\">17<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td>val[i]<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">10<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">9<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">4<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">8<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">7<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">-2<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink; border-left:solid 2px;\">3<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<td style=\"background-color:lightpink;\">-1<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td>rowind[i]<\/td>\n<td style=\"border-left:solid 2px;\">0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>3<\/td>\n<td style=\"border-left:solid 2px;\">2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td style=\"border-left:solid 2px;\">0<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<td style=\"border-left:solid 2px;\">1<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-left:solid 2px; width: 80px\">colptr[i]<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">0<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">3<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">7<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">9<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">12<\/td>\n<td style=\"border-left:solid 2px; background-color:wheat; width: 30px\">15<\/td>\n<td style=\"border-left:solid 2px; width: 30px\">18<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306b\u306f, \u5bfe\u89d2\u8981\u7d20\u3068\u305d\u306e\u5de6\u5074\u306e\u307f, \u3042\u308b\u3044\u306f, \u5bfe\u89d2\u8981\u7d20\u3068\u305d\u306e\u53f3\u5074\u306e\u307f\u3092\u683c\u7d0d\u3057\u3066\u4f7f\u7528\u30e1\u30e2\u30ea\u30fc\u3092\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u308b. XLPack \u3067\u306f\u3053\u308c\u3092\u72ec\u81ea\u306b SSC \u5f62\u5f0f\u3068\u8868\u793a\u3057\u3066\u3044\u308b.<\/p>\n<p>\u4e0a\u306e\u4f8b\u3067\u306f\u5404\u5217\u306e\u4e2d\u3067\u884c\u756a\u53f7\u306e\u6607\u9806\u306b\u4e26\u3093\u3067\u3044\u308b\u304c, \u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u3063\u3066\u306f\u5217\u5185\u306e\u4e26\u3073\u9806\u306f\u4efb\u610f\u3067\u3088\u3044\u3053\u3068\u304c\u3042\u308b. XLPack \u3067\u306f\u57fa\u672c\u7684\u306b\u306f\u6607\u9806\u306b\u4e26\u3093\u3067\u3044\u308b\u3053\u3068\u3092\u4eee\u5b9a\u3057\u3066\u8a08\u7b97\u52b9\u7387\u3092\u4e0a\u3052\u308b\u3088\u3046\u306a\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n<p>CSC \u5f62\u5f0f\u306f CSR \u5f62\u5f0f\u3068\u540c\u69d8\u306b colptr \u304a\u3088\u3073 rowind \u306b\u8aa4\u3063\u305f\u5024\u3092\u8a2d\u5b9a\u3059\u308b\u3068\u7c21\u5358\u306b\u30e1\u30e2\u30ea\u30fc\u30a2\u30af\u30bb\u30b9\u30a8\u30e9\u30fc\u3092\u5f15\u304d\u8d77\u3053\u3057\u3066\u3057\u307e\u3046\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b.<\/p>\n<h4>5.1.2.4 \u5ea7\u6a19 (Coordinate (COO)) \u5f62\u5f0f<\/h4>\n<p>1 \u672c\u306e\u6d6e\u52d5\u5c0f\u6570\u914d\u5217 val \u3068 2 \u672c\u306e\u6574\u6570\u914d\u5217 rowind \u304a\u3088\u3073 colind \u306b\u975e\u30bc\u30ed\u8981\u7d20\u3060\u3051\u3092\u683c\u7d0d\u3059\u308b. val \u306b\u306f\u975e\u30bc\u30ed\u8981\u7d20\u306e\u5024\u3092\u683c\u7d0d\u3059\u308b. rowind, colind \u306b\u306f\u5bfe\u5fdc\u3059\u308b\u884c\u756a\u53f7, \u5217\u756a\u53f7\u3092\u5165\u308c\u308b.<\/p>\n<p>\u884c\u756a\u53f7\u3068\u5217\u756a\u53f7\u306e\u632f\u308a\u65b9\u306b\u306f 2 \u7a2e\u985e\u3042\u308b\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b, \u3059\u306a\u308f\u3061, FORTRAN \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5834\u5408\u306b\u306f 1 \u304b\u3089, C \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5834\u5408\u306b\u306f 0 \u304b\u3089\u59cb\u307e\u308b.<\/p>\n<p>\u4e0a\u306e\u4f8b\u984c\u884c\u5217\u3092 COO \u5f62\u5f0f\u3067\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p>(FORTRAN \u5f62\u5f0f)<\/p>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px; width: 80px\">i<\/td>\n<td style=\"width: 30px\">1<\/td>\n<td style=\"width: 30px\">2<\/td>\n<td style=\"width: 30px\">3<\/td>\n<td style=\"width: 30px\">4<\/td>\n<td style=\"width: 30px\">5<\/td>\n<td style=\"width: 30px\">6<\/td>\n<td style=\"width: 30px\">7<\/td>\n<td style=\"width: 30px\">8<\/td>\n<td style=\"width: 30px\">9<\/td>\n<td style=\"width: 30px\">10<\/td>\n<td style=\"width: 30px\">11<\/td>\n<td style=\"width: 30px\">12<\/td>\n<td style=\"width: 30px\">13<\/td>\n<td style=\"width: 30px\">14<\/td>\n<td style=\"width: 30px\">15<\/td>\n<td style=\"width: 30px\">16<\/td>\n<td style=\"width: 30px\">17<\/td>\n<td style=\"width: 30px\">18<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px;\">val(i)<\/td>\n<td style=\"background-color:lightpink;\">10<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">4<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">-2<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<td style=\"background-color:lightpink;\">-1<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px;\">rowind(i)<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<td>4<\/td>\n<td>6<\/td>\n<td>2<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px;\">colind(i)<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(C \u5f62\u5f0f)<\/p>\n<table>\n<tbody>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px; width: 80px\">i<\/td>\n<td style=\"width: 30px\">0<\/td>\n<td style=\"width: 30px\">1<\/td>\n<td style=\"width: 30px\">2<\/td>\n<td style=\"width: 30px\">3<\/td>\n<td style=\"width: 30px\">4<\/td>\n<td style=\"width: 30px\">5<\/td>\n<td style=\"width: 30px\">6<\/td>\n<td style=\"width: 30px\">7<\/td>\n<td style=\"width: 30px\">8<\/td>\n<td style=\"width: 30px\">9<\/td>\n<td style=\"width: 30px\">10<\/td>\n<td style=\"width: 30px\">11<\/td>\n<td style=\"width: 30px\">12<\/td>\n<td style=\"width: 30px\">13<\/td>\n<td style=\"width: 30px\">14<\/td>\n<td style=\"width: 30px\">15<\/td>\n<td style=\"width: 30px\">16<\/td>\n<td style=\"width: 30px\">17<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px;\">val[i]<\/td>\n<td style=\"background-color:lightpink;\">10<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">4<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">8<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">7<\/td>\n<td style=\"background-color:lightpink;\">9<\/td>\n<td style=\"background-color:lightpink;\">-2<\/td>\n<td style=\"background-color:lightpink;\">5<\/td>\n<td style=\"background-color:lightpink;\">2<\/td>\n<td style=\"background-color:lightpink;\">3<\/td>\n<td style=\"background-color:lightpink;\">13<\/td>\n<td style=\"background-color:lightpink;\">-1<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px;\">rowind[i]<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>0<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr style=\"border:solid 2px;\">\n<td style=\"border-right:solid 2px;\">colind[i]<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e0a\u306e\u4f8b\u3067\u306f\u5217\u756a\u53f7, \u884c\u756a\u53f7\u306e\u6607\u9806\u306b\u4e26\u3093\u3067\u3044\u308b\u304c, \u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u3063\u3066\u4e26\u3073\u9806\u306f\u4efb\u610f\u3067\u3088\u3044\u3053\u3068\u304c\u3042\u308b.<\/p>\n<p>COO \u5f62\u5f0f\u306f\u5165\u51fa\u529b\u306b\u5411\u3044\u305f\u5f62\u5f0f\u3067\u3042\u308a, \u305d\u306e\u307e\u307e\u8a08\u7b97\u306b\u4f7f\u3046\u3068\u8a08\u7b97\u52b9\u7387\u304c\u60aa\u3044. \u305d\u306e\u305f\u3081, COO \u5f62\u5f0f\u3092\u5165\u529b\u7528\u306b\u4f7f\u3044, \u8a08\u7b97\u6642\u306b\u306f CSR \u306a\u3069\u4ed6\u306e\u5f62\u5f0f\u306b\u5909\u63db\u3057\u3066\u4f7f\u3046\u3053\u3068\u304c\u591a\u3044.<\/p>\n<h4>5.1.2.5 \u57fa\u672c\u6f14\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u5909\u63db\u30d7\u30ed\u30b0\u30e9\u30e0<\/h4>\n<p>\u305d\u308c\u305e\u308c\u306e\u758e\u884c\u5217\u683c\u7d0d\u5f62\u5f0f\u306b\u5bfe\u3057\u3066\u306f, \u57fa\u672c\u7684\u306a\u6f14\u7b97\u3092\u884c\u3046\u57fa\u672c\u6f14\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u591a\u3044. \u6a19\u6e96\u7684\u306a\u57fa\u672c\u6f14\u7b97\u30bb\u30c3\u30c8\u3082\u3044\u304f\u3064\u304b\u63d0\u6848\u3055\u308c\u3066\u3044\u304c\u6c7a\u5b9a\u7248\u306f\u306a\u3044\u3088\u3046\u3067\u3042\u308b.<\/p>\n<p>XLPack \u3067\u306f, CSR \u5f62\u5f0f\u306e\u884c\u5217\u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306a\u57fa\u672c\u6f14\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u308b.<\/p>\n<pre> \r\n  <strong>CsrDusmv<\/strong>  y <- &alpha;Ax + &beta;y \u307e\u305f\u306f y <- &alpha;A<sup>T<\/sup>x + &beta;y\r\n  <strong>CsrDussv<\/strong>  Ax = b \u307e\u305f\u306f A<sup>T<\/sup>x = b \u306e\u89e3 (\u4e09\u89d2\u884c\u5217)\r\n  <strong>CsrDusmm<\/strong>  C <- &alpha;AB + &beta;C \u307e\u305f\u306f C <- &alpha;A<sup>T<\/sup>B + &beta;C\r\n  <strong>CsrDussm<\/strong>  AX = B \u307e\u305f\u306f A<sup>T<\/sup>X = B \u306e\u89e3 (\u4e09\u89d2\u884c\u5217)\r\n  <strong>SsrDusmv<\/strong>  y <- &alpha;Ax + &beta;y (\u5bfe\u79f0\u884c\u5217)\r\n  <strong>CsrTrans<\/strong>  \u884c\u5217\u306e\u8ee2\u7f6e\r\n  <strong>CsxDiag<\/strong>  \u884c\u5217\u306e\u5bfe\u89d2\u8981\u7d20\r\n  <strong>CsxDiagInd<\/strong>  \u884c\u5217\u306e\u5bfe\u89d2\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\r\n  <strong>CsxSort<\/strong>  \u884c\u5217\u306e\u8981\u7d20\u306e\u30bd\u30fc\u30c8\r\n\r\n<\/pre>\n<p>&nbsp;<br \/>\n\u307e\u305f, \u6b21\u306e\u5909\u63db\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u308b.<\/p>\n<pre> \r\n  <strong>CooCsr<\/strong>    COO -> CSR\r\n  <strong>CsrCoo<\/strong>    CSR -> COO\r\n  <strong>SsrCsr<\/strong>    SSR (CSR \u5bfe\u79f0\u884c\u5217\u5f62\u5f0f) -> CSR (\u5bfe\u79f0\u306a\u30d5\u30eb\u884c\u5217)\r\n  <strong>CsrSsr<\/strong>    CSR (\u5bfe\u79f0\u306a\u30d5\u30eb\u884c\u5217) -> SSR (CSR \u5bfe\u79f0\u884c\u5217\u5f62\u5f0f)\r\n  <strong>CsrDense<\/strong>  CSR -> \u5bc6\u884c\u5217\r\n  <strong>DenseCsr<\/strong>  \u5bc6\u884c\u5217 -> CSR\r\n\r\n<\/pre>\n<p>&nbsp;<br \/>\n\u540c\u69d8\u306e\u57fa\u672c\u6f14\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u5909\u63db\u30d7\u30ed\u30b0\u30e9\u30e0\u304c CSC \u5f62\u5f0f\u306b\u3082\u7528\u610f\u3055\u308c\u3066\u3044\u308b. \u307e\u305f, \u8907\u7d20\u6570\u578b\u306e\u540c\u69d8\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3082\u7528\u610f\u3055\u308c\u3066\u3044\u308b.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>5.1.1 \u758e\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u69cb\u6210 \u758e\u884c\u5217\u7528\u306e\u683c\u7d0d\u5f62\u5f0f\u306b\u306f\u4f7f\u7528\u76ee\u7684\u306b\u9069\u3057\u305f\u591a\u304f\u306e\u7a2e\u985e\u304c\u3042\u308a, \u7d76\u5bfe\u7684\u306a\u6a19\u6e96\u5f62\u5f0f\u3068\u3044\u3063\u305f\u3082\u306e\u306f\u306a\u3044. \u305d\u3053\u3067, \u758e\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u758e\u884c\u5217\u306e\u683c\u7d0d\u5f62\u5f0f\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3088\u3046\u306a [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-6118","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"5.1.1 \u758e\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u69cb\u6210 \u758e\u884c\u5217\u7528\u306e\u683c\u7d0d\u5f62\u5f0f\u306b\u306f\u4f7f\u7528\u76ee\u7684\u306b\u9069\u3057\u305f\u591a\u304f\u306e\u7a2e\u985e\u304c\u3042\u308a, \u7d76\u5bfe\" \/>\n\t<meta name=\"robots\" content=\"max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n\t<meta name=\"author\" content=\"Administrator\"\/>\n\t<meta name=\"google-site-verification\" content=\"5PEQMQVhF0wv5i-xMYW9a3HzuBwixzVduoR2arr5UDM\" \/>\n\t<meta name=\"msvalidate.01\" content=\"EEB9704E04960338720AEA89E77E749F\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/www.ktech.biz\/jp\/num\/5-1_sparse\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.1.1\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-1_sparse\\\/#article\",\"name\":\"5.1 \\u758e\\u884c\\u5217\\u306e\\u683c\\u7d0d\\u5f62\\u5f0f | K 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