{"id":4734,"date":"2025-03-31T13:37:38","date_gmt":"2025-03-31T04:37:38","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=4734"},"modified":"2025-05-25T13:52:16","modified_gmt":"2025-05-25T04:52:16","slug":"3-eigen","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/tutorial\/3-eigen\/","title":{"rendered":"3. \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb"},"content":{"rendered":"\n

3.1 \u6982\u8981<\/h3>\n

\u884c\u5217 \\(\\boldsymbol{A}\\) \u306b\u95a2\u3059\u308b\u56fa\u6709\u5024\u554f\u984c\u3068\u306f,
\n\\[
\n\\boldsymbol{A}\\boldsymbol{x} = \\lambda \\boldsymbol{x}, \\boldsymbol{x} \\neq \\boldsymbol{0}
\n\\]\n\u3092\u6e80\u305f\u3059\u30b9\u30ab\u30e9\u30fc \\(\\lambda\\) \u3068\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{x}\\) \u3092\u6c42\u3081\u308b\u3082\u306e\u3067, \\(\\lambda\\) \u3092\u56fa\u6709\u5024, \\(\\boldsymbol{x}\\) \u3092\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3044\u307e\u3059. \\(\\boldsymbol{A}\\) \u304c \\(n \\times n\\) \u884c\u5217\u306e\u5834\u5408\u306b\u306f \\(n\\) \u500b\u306e\u56fa\u6709\u5024\u3068\u305d\u308c\u305e\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6301\u3061\u307e\u3059.<\/p>\n

\u591a\u304f\u306e\u5fdc\u7528\u306b\u304a\u3044\u3066\u73fe\u308c\u308b\u306e\u306f\u5bfe\u79f0\u884c\u5217\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3042\u308b\u305f\u3081, \u4ee5\u4e0b\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059.<\/p>\n

\\(\\boldsymbol{A}\\) \u304c\u5bfe\u79f0\u884c\u5217\u306a\u3089\u3070\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u306f\u5b9f\u6570\u306b\u306a\u308a\u307e\u3059. \u3061\u306a\u307f\u306b, \u4e00\u822c(\u975e\u5bfe\u79f0)\u884c\u5217\u306e\u5834\u5408\u306b\u306f \\(\\boldsymbol{A}\\) \u304c\u5b9f\u884c\u5217\u3067\u3042\u3063\u3066\u3082\u56fa\u6709\u5024\u306f\u4e00\u822c\u7684\u306b\u306f\u8907\u7d20\u6570\u3068\u306a\u308a\u307e\u3059.<\/p>\n

\u56fa\u6709\u5024\u306f\u6b21\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059.
\n\\[
\ndet(\\boldsymbol{A} – \\lambda \\boldsymbol{I}) = 0
\n\\]\n\u3053\u308c\u306f\u7279\u6027\u65b9\u7a0b\u5f0f\u3068\u547c\u3070\u308c, \\(\\lambda\\) \u306b\u95a2\u3059\u308b \\(n\\) \u6b21\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306b\u306a\u308a\u307e\u3059. \u3053\u306e\u4ee3\u6570\u65b9\u7a0b\u5f0f\u3092\u76f4\u63a5\u89e3\u3051\u3070\u56fa\u6709\u5024 \\(\\lambda\\) \u3092\u6c42\u3081\u3089\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059. \u3057\u304b\u3057, \u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u3092\u6c42\u3081\u308b\u8a08\u7b97\u91cf\u304c\u591a\u3044\u3053\u3068\u3068, \u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u8a08\u7b97\u304c\u5927\u5909\u306a\u305f\u3081\u5225\u306e\u89e3\u6cd5\u304c\u4f7f\u308f\u308c\u307e\u3059.<\/p>\n

3.2 \u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5<\/h3>\n

3.2.1 \u7d76\u5bfe\u5024\u6700\u5927 (\u307e\u305f\u306f\u7279\u5b9a) \u306e\u56fa\u6709\u5024 1 \u500b\u3060\u3051\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u5834\u5408<\/h4>\n

\u9069\u5f53\u306a\u521d\u671f\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol{x^0}\\) \u3068\u3057\u3066, \u6b21\u306e\u53cd\u5fa9\u3092\u884c\u3044\u307e\u3059.
\n\\[
\n\\boldsymbol{x^1} = \\boldsymbol{Ax^0}, \\boldsymbol{x^2} = \\boldsymbol{Ax^1}, \\dots, \\boldsymbol{x^k} = \\boldsymbol{Ax^{k-1}}
\n\\]\n\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{x^k}\\) \u306f\u7d76\u5bfe\u5024\u6700\u5927\u306e\u56fa\u6709\u5024\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306b\u53ce\u675f\u3057\u307e\u3059. \u56fa\u6709\u5024\u306f\u6b21\u5f0f\u3067\u6c42\u3081\u3089\u308c\u307e\u3059.
\n\\[
\n\\lambda = (\\boldsymbol{x^k}, \\boldsymbol{x^k})\/(\\boldsymbol{x^k}, \\boldsymbol{x^{k-1}})
\n\\]\n\u305f\u3060\u3057, \u8a18\u53f7 \\(( , )\\) \u306f\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u8868\u3057\u307e\u3059.<\/p>\n

\u3053\u308c\u306f\u300c\u3079\u304d\u4e57\u6cd5\u300d\u3068\u547c\u3070\u308c, \u53e4\u304f\u304b\u3089\u4f7f\u308f\u308c\u3066\u3044\u308b\u89e3\u6cd5\u3067, \u7c21\u5358\u306a\u8a08\u7b97\u624b\u9806\u3067\u3059\u304c\u73fe\u5728\u3067\u3082\u6709\u52b9\u3067\u3059. \u3053\u306e\u89e3\u6cd5\u3067\u306f\u7d76\u5bfe\u5024\u6700\u5927\u306e\u56fa\u6709\u5024\u304c 1 \u3064\u3067\u3042\u308b (\u91cd\u6839\u3067\u306a\u3044) \u3053\u3068\u304c\u5fc5\u8981\u3067\u3059.<\/p>\n

\\(\\boldsymbol{A^{-1}}\\) \u306e\u56fa\u6709\u5024\u306f \\(\\lambda^{-1}\\) \u3067\u4e0e\u3048\u3089\u308c\u307e\u3059.
\n\\[
\n\\boldsymbol{A^{-1}}\\boldsymbol{x} = \\lambda^{-1}\\boldsymbol{x}, \\space \\boldsymbol{x} \\neq 0
\n\\]\n\u5f93\u3063\u3066, \\(\\boldsymbol{A^{-1}}\\) \u306b\u3079\u304d\u4e57\u6cd5\u3092\u9069\u7528\u3059\u308b\u3068\u7d76\u5bfe\u5024\u6700\u5927\u306e\u56fa\u6709\u5024 \\(\\lambda^{-1}\\), \u3059\u306a\u308f\u3061\u7d76\u5bfe\u5024\u6700\u5c0f\u306e\u56fa\u6709\u5024 \\(\\lambda\\) \u304c\u6c42\u3081\u3089\u307e\u3059. \u3053\u308c\u3092\u9006\u3079\u304d\u4e57\u6cd5\u3068\u3044\u3044\u307e\u3059. \u307e\u305f, \\((\\boldsymbol{A} – \\sigma \\boldsymbol{I})^{-1}\\) \u306b\u9069\u7528\u3059\u308b\u3068 \\(\\sigma\\) \u306b\u6700\u3082\u8fd1\u3044\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059.<\/p>\n

3.2.2 \u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u305f\u3044\u5834\u5408<\/h4>\n

\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u305f\u3044\u5834\u5408\u306e\u73fe\u5728\u306e\u6a19\u6e96\u7684\u306a\u89e3\u6cd5\u306f, \u4ee5\u4e0b\u3067\u8aac\u660e\u3059\u308b\u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u3092\u7d4c\u7531\u3059\u308b\u65b9\u6cd5\u3067\u3059.<\/p>\n

3.2.2.1 \u4e09\u91cd\u5bfe\u89d2\u5316<\/h5>\n

\u307e\u305a\u884c\u5217\u306e\u56fa\u6709\u5024\u3092\u5909\u3048\u306a\u3044\u3088\u3046\u306b\u3057\u3066\u884c\u5217 \\(\\boldsymbol{A}\\) \u3092\u4e09\u91cd\u5bfe\u89d2\u884c\u5217 (\u5bfe\u89d2\u8981\u7d20\u3068\u305d\u306e\u96a3\u306e\u4e0a\u4e0b\u306e\u8981\u7d20\u3060\u3051\u304c 0 \u3067\u306a\u3044\u884c\u5217) \u306b\u5909\u63db\u3057\u307e\u3059. \u3053\u306e\u3088\u3046\u306a\u5909\u63db\u3068\u3057\u3066\u306f\u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u5909\u63db\u304c\u3088\u304f\u4f7f\u308f\u308c\u307e\u3059.<\/p>\n

\\(n\\) \u30d9\u30af\u30c8\u30eb \\(u\\) \u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306a \\(n \\times n\\) \u884c\u5217 \\(\\boldsymbol{H}\\) \u3092\u5b9a\u7fa9\u3057\u307e\u3059.
\n\\[
\n\\boldsymbol{H} = \\boldsymbol{I} – 2\\boldsymbol{uu^T} \/ (\\boldsymbol{u^Tu})
\n\\]\n\u305d\u3046\u3059\u308b\u3068, \\(\\boldsymbol{H}\\) \u306f\u6b21\u5f0f\u3092\u307f\u305f\u3057\u307e\u3059. \u3059\u306a\u308f\u3061, \\(\\boldsymbol{H}\\) \u306f\u76f4\u4ea4\u884c\u5217\u306b\u306a\u308a\u307e\u3059.
\n\\[
\n\\boldsymbol{H^{-1}} = \\boldsymbol{H^T} = \\boldsymbol{H}
\n\\]\n\\(\\boldsymbol{H}\\) \u3092\u4f7f\u3063\u305f\u884c\u5217 \\(\\boldsymbol{A}\\) \u306b\u5bfe\u3059\u308b\u6b21\u306e\u3088\u3046\u306a\u5909\u63db\u3092\u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u5909\u63db\u3068\u3044\u3044\u307e\u3059.
\n\\[
\n\\boldsymbol{H^{-1}AH} = \\boldsymbol{HAH}
\n\\]\n\\(\\boldsymbol{P^{-1}AP}\\) \u306e\u5f62\u306e\u5909\u63db\u306f\u76f8\u4f3c\u5909\u63db\u3068\u547c\u3070\u308c, \u5909\u63db\u306b\u3088\u3063\u3066 \\(\\boldsymbol{A}\\) \u306e\u56fa\u6709\u5024\u306f\u5909\u308f\u308a\u307e\u305b\u3093. \u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u5909\u63db\u3067\u306f \\(\\boldsymbol{H}\\) \u306e\u9006\u884c\u5217\u3092\u6c42\u3081\u305a\u306b\u76f8\u4f3c\u5909\u63db\u3092\u8a08\u7b97\u3067\u304d\u308b\u7279\u9577\u304c\u3042\u308a\u307e\u3059.<\/p>\n

\u6b21\u306b, \u884c\u5217 \\(\\boldsymbol{A}\\) \u306e\u7b2c 1 \u5217\u306e\u8981\u7d20\u3092 \\(a_{11}, a_{21}, \\dots, a_{n1}\\) \u3068\u66f8\u304d, \u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{u}\\) \u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059.
\n\\[
\n\\boldsymbol{u} =
\n\\begin{pmatrix}
\n0 \\\\
\na_{21} + s \\\\
\na_{31} \\\\
\na_{41} \\\\
\n\\vdots \\\\
\na_{n1} \\\\
\n\\end{pmatrix}
\n\\]\n\u3053\u3053\u3067, \\(s^2 = \\sum_{i=2}^{n}a_{i1}^2\\). \u305f\u3060\u3057, \\(s\\) \u306f \\(a_{21}\\) \u3068\u540c\u7b26\u53f7\u3068\u3057\u307e\u3059.<\/p>\n

\u3053\u306e\u3088\u3046\u306b \\(\\boldsymbol{u}\\) \u3092\u3068\u308b\u3068, \u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u5909\u63db\u5f8c\u306e \\(\\boldsymbol{A}\\) \u306e\u7b2c 1 \u5217\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059.
\n\\[
\n\\begin{pmatrix}
\na_{11} \\\\
\n-s \\\\
\n0 \\\\
\n\\vdots \\\\
\n0 \\\\
\n\\end{pmatrix}
\n\\]\n\u3059\u306a\u308f\u3061, \\(\\boldsymbol{A}\\) \u306e\u7b2c 1 \u5217\u306f\u7b2c 3 \u884c\u4ee5\u964d\u306e\u6210\u5206\u304c 0 \u306b\u306a\u308a\u307e\u3059. \u5bfe\u79f0\u6027\u306f\u4fdd\u305f\u308c\u3066\u3044\u308b\u306e\u3067\u7b2c 1 \u884c\u306e\u7b2c 3 \u5217\u4ee5\u964d\u306e\u6210\u5206\u3082 0 \u306b\u306a\u308a\u307e\u3059.<\/p>\n

\u3053\u308c\u3092, \u4ee5\u4e0b\u7b2c 2 \u5217, \u7b2c 3 \u5217, …, \u7b2c n – 2 \u5217\u3068 n – 2 \u56de\u7e70\u308a\u8fd4\u3057\u5909\u63db\u3092\u9069\u7528\u3059\u308b\u3068, \u56fa\u6709\u5024\u3092\u5909\u3048\u305a\u306b \\(\\boldsymbol{A}\\) \u3092\u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n

3.2.2.2 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97<\/h5>\n

\u6b21\u306b, \u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u306e\u56fa\u6709\u5024\u3092\u53cd\u5fa9\u6cd5(QR \u6cd5)\u306b\u3088\u308a\u6c42\u3081\u307e\u3059.<\/p>\n

\u884c\u5217 \\(\\boldsymbol{A}\\) \u306e QR \u5206\u89e3\u306f\u6b21\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059.
\n\\[
\n\\boldsymbol{A} = \\boldsymbol{QR}
\n\\]\n\u305f\u3060\u3057, \\(\\boldsymbol{Q}\\) \u306f\u76f4\u4ea4\u884c\u5217, \\(\\boldsymbol{R}\\) \u306f\u4e0a\u4e09\u89d2\u884c\u5217\u3068\u3057\u307e\u3059.<\/p>\n

\\(\\boldsymbol{A}\\) \u3092 QR \u5206\u89e3\u5f8c\u306b\u9806\u5e8f\u3092\u9006\u306b\u3057\u3066\u4e57\u305a\u308b\u3068
\n\\[
\n\\boldsymbol{RQ} = \\boldsymbol{Q^{-1}AQ} = \\boldsymbol{Q^TAQ}
\n\\]\n\u3068\u306a\u308a, \u56fa\u6709\u5024\u304c\u5909\u308f\u3089\u306a\u3044\u76f8\u4f3c\u5909\u63db\u306e\u5f62\u306b\u306a\u3063\u3066\u3044\u307e\u3059.<\/p>\n

\u3053\u306e\u5909\u63db\u3092\u7e70\u308a\u8fd4\u3057\u3066\u3044\u304f\u3068, \u5909\u63db\u7d50\u679c\u306f\u5bfe\u89d2\u884c\u5217\u306b\u53ce\u675f\u3057\u3066\u3086\u304d, \u5bfe\u89d2\u6210\u5206\u3068\u3057\u3066\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n

\u4e09\u91cd\u5bfe\u89d2\u5316\u305b\u305a\u306b\u6700\u521d\u304b\u3089 QR \u5206\u89e3\u3092\u9069\u7528\u3059\u308c\u3070\u3088\u3044\u3088\u3046\u306b\u601d\u308f\u308c\u307e\u3059\u304c, \u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u306e\u5834\u5408\u306b\u306f\u53ce\u675f\u3082\u901f\u304f\u52b9\u7387\u306e\u3088\u3044\u8a08\u7b97\u624b\u9806\u304c\u8003\u3048\u3089\u308c\u3066\u304a\u308a, \u4e09\u91cd\u5bfe\u89d2\u5316\u306e\u5206\u3068\u3042\u308f\u305b\u3066\u3082\u8a08\u7b97\u91cf\u304c\u5c11\u306a\u304f\u3066\u3059\u307f\u307e\u3059.<\/p>\n

3.3 XLPack \u3092\u4f7f\u3063\u305f\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u304d\u65b9<\/h3>\n

VBA \u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Dsyev<\/strong> \u3042\u308b\u3044\u306f\u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u95a2\u6570 WDsyev<\/strong> \u3092\u4f7f\u3046\u3053\u3068\u306b\u3088\u308a, \u5bfe\u79f0\u884c\u5217\u306e\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u3068\u5bfe\u5fdc\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb, \u3042\u308b\u3044\u306f, \u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u3060\u3051\u3092\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n

\u3053\u308c\u3089\u306f, \u7dda\u5f62\u8a08\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea LAPACK \u306e\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 DSYEV \u3092\u4f7f\u7528\u3057\u3066\u304a\u308a, \u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u5909\u63db\u306b\u3088\u308a\u4e09\u91cd\u5bfe\u89d2\u5316\u3057, QR \u6cd5\u306b\u3088\u308a\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u307e\u3059.<\/p>\n

\u4f8b\u984c<\/h5>\n

\u6b21\u306e\u5bfe\u79f0\u884c\u5217\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u308b.
\n\\[
\n\\boldsymbol{A} =
\n\\begin{pmatrix}
\n10 & -3 & 5 \\\\
\n-3 & 2 & -1 \\\\
\n5 & -1 & 5 \\\\
\n\\end{pmatrix}
\n\\]\n

3.3.1 \u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9<\/h4>\n

\u307e\u305a, \u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u306e\u9069\u5f53\u306a\u5834\u6240\u306b\u5bfe\u79f0\u884c\u5217 \\(A\\) \u306e\u30c7\u30fc\u30bf\u3092\u5165\u529b\u3057\u307e\u3059 (\u30aa\u30ec\u30f3\u30b8\u8272\u306e\u30bb\u30eb). \u305d\u3057\u3066, \u89e3\u3092\u5165\u308c\u308b\u5834\u6240\u3068\u3057\u3066(\u89e3\u306e\u9818\u57df + 1\u884c\u306e\u30bb\u30eb)\u3092\u9078\u629e\u3057\u3066\u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u95a2\u6570 WDsyev<\/strong> \u3092\u5165\u529b\u3057\u307e\u3059 (\u7dd1\u8272\u306e\u30bb\u30eb).<\/p>\n

WDsyev<\/strong> \u306e\u5fc5\u8981\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u306f, Jobz, Uplo, N, A \u3067\u3059. Jobz = “V” \u306a\u3089\u3070\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081, Jobz = “N” \u306a\u3089\u3070\u56fa\u6709\u5024\u306e\u307f\u6c42\u3081\u307e\u3059. Uplo = “U” \u306a\u3089\u3070 A \u306e\u4e0a\u4e09\u89d2\u90e8\u5206\u3092\u53c2\u7167\u3057, Uplo = “L” \u306a\u3089\u3070 A \u306e\u4e0b\u4e09\u89d2\u90e8\u5206\u3092\u53c2\u7167\u3057\u307e\u3059. N \u306f\u8981\u7d20\u6570 (\u3053\u306e\u4f8b\u3067\u306f 3), A \u306f\u5bfe\u79f0\u884c\u5217 \\(\\boldsymbol{A}\\) \u306e\u30bb\u30eb\u7bc4\u56f2\u3067\u3059.<\/p>\n

\u3053\u3053\u3067\u306f\u5bfe\u79f0\u884c\u5217 \\(\\boldsymbol{A}\\) \u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u306e\u5024\u3092\u5165\u529b\u3057\u3066\u3044\u307e\u3059\u304c, WDsyev<\/strong> \u306f\u6307\u5b9a\u3055\u308c\u305f\u4e0a\u307e\u305f\u306f\u4e0b\u4e09\u89d2\u90e8\u5206\u3068\u5bfe\u89d2\u8981\u7d20\u3057\u304b\u4f7f\u308f\u306a\u3044\u306e\u3067, \u6b8b\u308a\u306e\u4e09\u89d2\u90e8\u5206\u306f\u5165\u529b\u3057\u306a\u304f\u3066\u3082\u69cb\u3044\u307e\u305b\u3093.<\/p>\n

\"\"<\/p>\n

\u5165\u529b\u304c\u7d42\u4e86\u3057\u305f\u3089 Ctrl + Shift + Enter \u3092\u62bc\u3057\u307e\u3059.<\/p>\n

\"\"<\/p>\n

\u3053\u308c\u3067, 3 \u3064\u306e\u56fa\u6709\u5024 \\(\\lambda\\) \u3068\u305d\u308c\u305e\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{x}\\) (\u7e26\u30d9\u30af\u30c8\u30eb) \u304c\u6c42\u3081\u3089\u308c\u307e\u3057\u305f. \u56fa\u6709\u5024\u306e\u4e0b\u306b\u8868\u793a\u3055\u308c\u3066\u3044\u308b 0 \u306f\u30ea\u30bf\u30fc\u30f3\u30b3\u30fc\u30c9(\u6b63\u5e38\u7d42\u4e86\u3092\u793a\u3059)\u3067\u3059.<\/p>\n

3.3.2 VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9<\/h4>\n

\u4e0a\u3068\u540c\u3058\u4f8b\u984c\u3092 VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u308a\u89e3\u304d\u307e\u3059. Dsyev<\/strong> \u3092\u4f7f\u3063\u305f\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u3092\u793a\u3057\u307e\u3059.<\/p>\n

\n
Sub Start()\r\n    Const NMax = 10\r\n    Dim N As Long, A(NMax, NMax) As Double, W(NMax) As Double\r\n    Dim Info As Long, I As Long, J As Long\r\n    '--- Input data\r\n    N = 3\r\n    For I = 0 To N - 1\r\n        For J = 0 To N - 1\r\n            A(I, J) = Cells(5 + I, 1 + J)\r\n        Next\r\n    Next\r\n    '--- Compute eigenvalues and eigenvectors\r\n    Call Dsyev(\"V\", \"L\", N, A(), W(), Info)\r\n    '--- Output result\r\n    For I = 0 To N - 1\r\n        For J = 0 To N - 1\r\n            Cells(5 + I, 5 + J) = A(I, J)\r\n        Next\r\n        Cells(5 + I, 4) = W(I)\r\n    Next\r\n    Cells(8, 4) = Info\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
\u6240\u5b9a\u306e\u4f4d\u7f6e(\u4e0b\u306e\u30aa\u30ec\u30f3\u30b8\u8272\u306e\u30bb\u30eb)\u306b\u5bfe\u79f0\u884c\u5217 \\(\\boldsymbol{A}\\) \u306e\u5024\u3092\u5165\u529b\u3057, \u30de\u30af\u30ed Start \u3068\u3057\u3066\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3068\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059. \u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u3068\u304d\u3068\u7570\u306a\u308a, \u884c\u5217 \\(\\boldsymbol{A}\\) \u306e\u5024\u3092\u5165\u529b\u3057\u305f\u3060\u3051\u3067\u306f\u7d50\u679c\u304c\u5f97\u3089\u308c\u305a, VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3057\u3066\u3084\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059.<\/p>\n
\u306a\u304a, \u3053\u3053\u3067\u306f\u914d\u5217 A() \u306b\u5168\u8981\u7d20\u3092\u8aad\u307f\u8fbc\u3080\u3088\u3046\u306b\u3057\u3066\u3044\u307e\u3059\u304c, Dsyev<\/strong> \u306f\u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u6307\u5b9a\u3055\u308c\u305f\u4e0a\u307e\u305f\u306f\u4e0b\u4e09\u89d2\u90e8\u5206\u3068\u5bfe\u89d2\u8981\u7d20\u3057\u304b\u4f7f\u3044\u307e\u305b\u3093.<\/p>\n
\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"
\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5\u3068XLPack\u3092\u4f7f\u3063\u305f\u89e3\u304d\u65b9<\/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,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[10],"tags":[],"class_list":["post-4734","post","type-post","status-publish","format-standard","hentry","category-tutorial"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/4734","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/comments?post=4734"}],"version-history":[{"count":5,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/4734\/revisions"}],"predecessor-version":[{"id":5069,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/4734\/revisions\/5069"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=4734"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=4734"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=4734"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}