{"id":201143,"date":"2024-05-10T02:21:20","date_gmt":"2024-05-09T18:21:20","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/201143.html"},"modified":"2024-05-10T02:21:23","modified_gmt":"2024-05-09T18:21:23","slug":"%e4%b8%89%e9%98%b6%e7%9f%a9%e9%98%b5%ef%bc%88%e4%ba%8c%e9%98%b6%e5%bc%a0%e9%87%8f%ef%bc%89%e5%90%84%e7%a7%8d%e4%b9%98%e6%b3%95%e7%9a%84%e8%ae%a1%e7%ae%97%e6%96%b9%e6%b3%95%e6%98%af%e4%bb%80%e4%b9%88","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/201143.html","title":{"rendered":"\u4e09\u9636\u77e9\u9635\uff08\u4e8c\u9636\u5f20\u91cf\uff09\u5404\u79cd\u4e58\u6cd5\u7684\u8ba1\u7b97\u65b9\u6cd5\u662f\u4ec0\u4e48\u6837\u7684"},"content":{"rendered":"

\"\u4e09\u9636\u77e9\u9635\uff08\u4e8c\u9636\u5f20\u91cf\uff09\u5404\u79cd\u4e58\u6cd5\u7684\u8ba1\u7b97\u65b9\u6cd5\u662f\u4ec0\u4e48\u6837\u7684\"<\/p>\n

\u4e09\u9636\u77e9\u9635\uff08\u4e8c\u9636\u5f20\u91cf\uff09\u7684\u5404\u79cd\u4e58\u6cd5\u5305\u62ec\u77e9\u9635\u4e58\u6cd5\u3001\u54c8\u8fbe\u739b\u4e58\u79ef\u3001\u514b\u7f57\u5185\u514b\u79ef<\/strong>\uff0c\u8fd9\u4e9b\u4e58\u6cd5\u65b9\u5f0f\u5728\u6570\u636e\u5904\u7406\u548c\u6570\u5b66\u5efa\u6a21\u4e2d\u5177\u6709\u91cd\u8981\u7684\u4f5c\u7528\u3002\u5176\u4e2d\uff0c\u77e9\u9635\u4e58\u6cd5<\/strong>\u662f\u6700\u5e38\u89c1\u7684\u64cd\u4f5c\uff0c\u5b83\u8981\u6c42\u5de6\u4fa7\u77e9\u9635\u7684\u5217\u6570\u4e0e\u53f3\u4fa7\u77e9\u9635\u7684\u884c\u6570\u76f8\u7b49\uff0c\u7136\u540e\u6839\u636e\u70b9\u79ef\u89c4\u5219\u8ba1\u7b97\u5bf9\u5e94\u4f4d\u7f6e\u7684\u503c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5728\u77e9\u9635\u4e58\u6cd5\u4e2d\uff0c\u7ed3\u679c\u77e9\u9635\u7684\u6bcf\u4e2a\u5143\u7d20\u662f\u7531\u5de6\u4fa7\u77e9\u9635\u7684\u884c\u5411\u91cf\u4e0e\u53f3\u4fa7\u77e9\u9635\u7684\u5217\u5411\u91cf\u8fdb\u884c\u70b9\u79ef\u8fd0\u7b97\u5f97\u5230\u7684\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u77e9\u9635\u4e58\u6cd5<\/p>\n<\/p>\n

\u77e9\u9635\u4e58\u6cd5\u8981\u6c42\u4e24\u4e2a\u77e9\u9635\u6ee1\u8db3\u4e58\u6cd5\u7684\u6761\u4ef6\uff1a\u7b2c\u4e00\u4e2a\u77e9\u9635\u7684\u5217\u6570\u5fc5\u987b\u4e0e\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u884c\u6570\u76f8\u7b49\u3002\u5bf9\u4e8e\u4e24\u4e2a\u4e09\u9636\u77e9\u9635A\u548cB\uff0c\u5176\u77e9\u9635\u4e58\u79ef(C = AB)\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u8fdb\u884c\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n

    \n
  1. \u786e\u5b9a\u7ed3\u679c\u77e9\u9635C\u7684\u5927\u5c0f\u3002\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u76f8\u4e58\u5f97\u5230\u7684\u7ed3\u679c\u4ecd\u7136\u662f\u4e00\u4e2a\u4e09\u9636\u77e9\u9635\u3002<\/li>\n
  2. \u8ba1\u7b97C\u7684\u6bcf\u4e2a\u5143\u7d20(c_{ij})\u3002\u8fd9\u4e2a\u5143\u7d20\u662f\u7531A\u7684\u7b2ci\u884c\u548cB\u7684\u7b2cj\u5217\u6309\u5143\u7d20\u5bf9\u5e94\u76f8\u4e58\u540e\u6c42\u548c\u5f97\u5230\uff0c\u5373\uff1a<\/p>\n

    [ c_{ij} = a_{i1}b_{1j} + a_{i2}b_{2j} + a_{i3}b_{3j} ]<\/li>\n<\/p>\n<\/ol>\n

    \u5bf9\u4e8e\u6574\u4e2a\u77e9\u9635\uff0c\u4f60\u9700\u8981\u91cd\u590d\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u8ba1\u7b97\u51fa\u6240\u6709\u4e5d\u4e2a(c_{ij})\u7684\u503c\u3002<\/p>\n<\/p>\n

    \u4e8c\u3001\u54c8\u8fbe\u739b\u4e58\u79ef<\/p>\n<\/p>\n

    \u4e0e\u77e9\u9635\u4e58\u79ef\u4e0d\u540c\uff0c\u54c8\u8fbe\u739b\u4e58\u79ef\uff08Hadamard Product\uff09\u662f\u4e00\u79cd\u5143\u7d20\u4e58\u6cd5\uff0c\u4e24\u4e2a\u77e9\u9635\u5fc5\u987b\u5f62\u72b6\u5b8c\u5168\u76f8\u540c\u3002\u4e09\u9636\u77e9\u9635\u7684\u54c8\u8fbe\u739b\u4e58\u79ef\u5982\u4e0b\uff1a<\/p>\n<\/p>\n

      \n
    1. \u5bf9\u5e94\u5143\u7d20\u76f8\u4e58\u3002\u4e0e\u77e9\u9635\u4e58\u79ef\u4e0d\u540c\u7684\u662f\uff0c\u8fd9\u91cc\u4e0d\u6d89\u53ca\u5143\u7d20\u4e4b\u95f4\u7684\u52a0\u548c\u64cd\u4f5c\u3002<\/li>\n
    2. \u7ed3\u679c\u77e9\u9635\u7684\u5143\u7d20\u5c31\u662f\u4e24\u4e2a\u539f\u77e9\u9635\u76f8\u540c\u4f4d\u7f6e\u5143\u7d20\u7684\u4e58\u79ef\uff0c\u5373\uff1a<\/p>\n

      [ (A \\circ B){ij} = a<\/em>{ij} \\cdot b_{ij} ]<\/li>\n<\/p>\n<\/ol>\n

      \u5bf9\u5e94\u4e8e\u6bcf\u4e2a\u5143\u7d20\uff0c\u90fd\u6267\u884c\u4e0a\u8ff0\u64cd\u4f5c\u3002<\/p>\n<\/p>\n

      \u4e09\u3001\u514b\u7f57\u5185\u514b\u79ef<\/p>\n<\/p>\n

      \u514b\u7f57\u5185\u514b\u79ef\uff08Kronecker Product\uff09\uff0c\u4e5f\u79f0\u76f4\u79ef\uff0c\u662f\u53e6\u4e00\u79cd\u77e9\u9635\u4e58\u6cd5\u3002\u5f53\u6211\u4eec\u5bf9\u4e24\u4e2a\u4e09\u9636\u77e9\u9635A\u548cB\u8ba1\u7b97\u514b\u7f57\u5185\u514b\u79ef\u65f6\uff1a<\/p>\n<\/p>\n

        \n
      1. \u8ba1\u7b97\u7ed3\u679c\u77e9\u9635\u7684\u5927\u5c0f\u3002\u77e9\u9635A\u548c\u77e9\u9635B\u7684\u514b\u7f57\u5185\u514b\u79ef\u5c06\u4ea7\u751f\u4e00\u4e2a(3^2)\u9636\u53739\u9636\u7684\u77e9\u9635\u3002<\/li>\n
      2. \u7ed3\u679c\u77e9\u9635\u7531\u77e9\u9635B\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u4e58\u4ee5\u77e9\u9635A\u7684\u4e00\u4e2a\u590d\u5236\u6784\u6210\u3002\u5373\uff1a<\/p>\n

        [ (A \\otimes B){(i-1)m+p,(j-1)n+q} = a<\/em>{ij} \\cdot b_{pq} ]<\/p>\n

        \u5176\u4e2d\uff0c(m,n)\u662fA\u7684\u884c\u5217\u6570\uff0c(p,q)\u662fB\u7684\u884c\u5217\u6570\u3002<\/li>\n<\/p>\n<\/ol>\n

        \u4ee5\u4e0a\u5c31\u662f\u4e09\u79cd\u5e38\u89c1\u7684\u4e09\u9636\u77e9\u9635\uff08\u6216\u8005\u8bf4\u662f\u4e8c\u9636\u5f20\u91cf\uff09\u7684\u4e58\u6cd5\u8fd0\u7b97\u65b9\u6cd5\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6839\u636e\u4e0d\u540c\u7684\u9700\u6c42\uff0c\u6211\u4eec\u4f1a\u9009\u62e9\u4e0d\u540c\u7c7b\u578b\u7684\u77e9\u9635\u4e58\u6cd5\u6765\u5904\u7406\u6570\u636e\u3002<\/p>\n<\/p>\n

        \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

        1. \u4e09\u9636\u77e9\u9635\u6709\u54ea\u4e9b\u4e58\u6cd5\u8fd0\u7b97\u65b9\u6cd5\uff1f<\/strong><\/p>\n

        \u4e09\u9636\u77e9\u9635\uff08\u4e8c\u9636\u5f20\u91cf\uff09\u7684\u4e58\u6cd5\u8ba1\u7b97\u65b9\u6cd5\u6709\u591a\u79cd\u3002\u5e38\u89c1\u7684\u6709\u9010\u5143\u7d20\u76f8\u4e58\u3001\u70b9\u79ef\u3001\u5f20\u91cf\u53c9\u79ef\u7b49\u3002<\/p>\n

        2. \u5982\u4f55\u8fdb\u884c\u9010\u5143\u7d20\u76f8\u4e58\u8fd0\u7b97\uff1f<\/strong><\/p>\n

        \u9010\u5143\u7d20\u76f8\u4e58\u662f\u6307\u5c06\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u7684\u5bf9\u5e94\u5143\u7d20\u4e00\u4e00\u76f8\u4e58\u751f\u6210\u65b0\u7684\u77e9\u9635\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u5206\u522b\u662fA\u3001B\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u9010\u5143\u7d20\u76f8\u4e58\u7ed3\u679c\u77e9\u9635C\u7684\u5143\u7d20c[i][j]=a[i][j] * b[i][j]\u3002<\/p>\n

        3. \u70b9\u79ef\u548c\u5f20\u91cf\u53c9\u79ef\u7684\u533a\u522b\u662f\u4ec0\u4e48\uff1f<\/strong><\/p>\n

        \u70b9\u79ef\u662f\u6307\u5c06\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u7684\u5bf9\u5e94\u5143\u7d20\u76f8\u4e58\u540e\u6c42\u548c\u5f97\u5230\u4e00\u4e2a\u6807\u91cf\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u5206\u522b\u662fA\u3001B\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u70b9\u79ef\u662f\u5c06A\u548cB\u7684\u5bf9\u5e94\u5143\u7d20\u76f8\u4e58\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u4e09\u9636\u77e9\u9635D\uff0c\u7136\u540e\u5bf9D\u4e2d\u7684\u6240\u6709\u5143\u7d20\u6c42\u548c\u5f97\u5230\u4e00\u4e2a\u6807\u91cf\u3002<\/p>\n

        \u5f20\u91cf\u53c9\u79ef\u662f\u6307\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u7684\u5f20\u91cf\u79ef\uff0c\u7ed3\u679c\u662f\u4e00\u4e2a\u56db\u9636\u77e9\u9635\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e24\u4e2a\u4e09\u9636\u77e9\u9635\u5206\u522b\u662fA\u3001B\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u5f20\u91cf\u53c9\u79ef\u662f\u4e00\u4e2a\u56db\u9636\u77e9\u9635E\uff0c\u5176\u4e2dE\u7684\u5143\u7d20\u7531A\u548cB\u7684\u5bf9\u5e94\u5143\u7d20\u4e4b\u95f4\u7684\u4e58\u79ef\u7ec4\u6210\u3002\u5f20\u91cf\u53c9\u79ef\u53ef\u4ee5\u7528\u6765\u8868\u793a\u591a\u7ef4\u6570\u636e\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e38\u7528\u4e8e\u7269\u7406\u5b66\u548c\u5de5\u7a0b\u5b66\u4e2d\u7684\u6a21\u62df\u548c\u5206\u6790\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u4e09\u9636\u77e9\u9635\uff08\u4e8c\u9636\u5f20\u91cf\uff09\u7684\u5404\u79cd\u4e58\u6cd5\u5305\u62ec\u77e9\u9635\u4e58\u6cd5\u3001\u54c8\u8fbe\u739b\u4e58\u79ef\u3001\u514b\u7f57\u5185\u514b\u79ef\uff0c\u8fd9\u4e9b\u4e58\u6cd5\u65b9\u5f0f\u5728\u6570\u636e\u5904\u7406\u548c\u6570\u5b66\u5efa\u6a21\u4e2d\u5177\u6709\u91cd\u8981 […]","protected":false},"author":3,"featured_media":201145,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/201143"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=201143"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/201143\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/201145"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=201143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=201143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=201143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}