{"id":55,"date":"2023-02-16T16:44:10","date_gmt":"2023-02-16T08:44:10","guid":{"rendered":"https:\/\/boostup.cf\/?p=55"},"modified":"2023-02-17T16:00:32","modified_gmt":"2023-02-17T08:00:32","slug":"winograd%e6%80%bb%e7%bb%93","status":"publish","type":"post","link":"https:\/\/189505.xyz\/?p=55","title":{"rendered":"winograd\u603b\u7ed3"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69e05faa5cb23\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69e05faa5cb23\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/189505.xyz\/?p=55\/#%E5%8F%82%E8%80%83%E5%8D%9A%E5%AE%A2\" title=\"\u53c2\u8003\u535a\u5ba2\">\u53c2\u8003\u535a\u5ba2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/189505.xyz\/?p=55\/#2D%E5%BD%A2%E5%BC%8F%E6%8E%A8%E5%AF%BC\" title=\"\n2D\u5f62\u5f0f\u63a8\u5bfc \n\">\n2D\u5f62\u5f0f\u63a8\u5bfc \n<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E5%8D%9A%E5%AE%A2\"><\/span>\u53c2\u8003\u535a\u5ba2<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p><a href=\"https:\/\/www.cnblogs.com\/shine-lee\/p\/10906535.html\">https:\/\/www.cnblogs.com\/shine-lee\/p\/10906535.html<\/a><br \/>\n<a href=\"https:\/\/www.cnblogs.com\/Matrix_Yao\/p\/11640310.html\">https:\/\/www.cnblogs.com\/Matrix_Yao\/p\/11640310.html<\/a><br \/>\n<\/p>\n<p>\\begin{equation}<br \/>\nY = A^{T}[(Gg) \\odot (B^{T}d)]<br \/>\n\\end{equation}<\/p>\n<p>\\begin{equation}<br \/>\n= \\begin{bmatrix}<br \/>\n1 &amp; 1 &amp; 1 &amp; 0\\\\<br \/>\n0 &amp; 1 &amp; -1 &amp; -1<br \/>\n\\end{bmatrix}<br \/>\n[(\\begin{bmatrix}<br \/>\n1  &amp;  0 &amp; 0\\\\<br \/>\n1\/2 &amp; 1\/2 &amp; 1\/2\\\\<br \/>\n1\/2 &amp; -1\/2 &amp; 1\/2\\\\<br \/>\n0 &amp; 0 &amp; 1<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\ng_0 &amp; g_1 &amp; g_2<br \/>\n\\end{bmatrix}^T) \\odot (<br \/>\n\\begin{bmatrix}<br \/>\n1 &amp; 0 &amp; -1 &amp; 0 \\\\<br \/>\n0 &amp; 1 &amp; 1 &amp; 0 \\\\<br \/>\n0 &amp; -1 &amp; 1 &amp; 0 \\\\<br \/>\n0 &amp; 1 &amp; 0 &amp; -1<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\nd_0 &amp; d_1 &amp; d_2 &amp; d_3<br \/>\n\\end{bmatrix}^{T}<br \/>\n)]<br \/>\n\\end{equation}<\/p>\n<p>\\begin{equation}<br \/>\n= \\begin{bmatrix}<br \/>\n1 &amp; 1 &amp; 1 &amp; 0\\\\<br \/>\n0 &amp; 1 &amp; -1 &amp; -1<br \/>\n\\end{bmatrix}<br \/>\n[\\begin{bmatrix}<br \/>\ng_0 \\\\<br \/>\n(g_0 + g_1 + g_2) \/ 2\\\\<br \/>\n(g_0 - g_1 + g_2) \/ 2\\\\<br \/>\ng_2<br \/>\n\\end{bmatrix} \\odot<br \/>\n\\begin{bmatrix}\\<br \/>\nd_0 - d_2\\\\<br \/>\nd_1 + d_2\\\\<br \/>\nd_2 - d_1\\\\<br \/>\nd_1 - d_3<br \/>\n\\end{bmatrix}]<br \/>\n\\end{equation}<\/p>\n<p>\\begin{equation}<br \/>\n\\label{linelast}<br \/>\n= \\begin{bmatrix}<br \/>\n1 &amp; 1 &amp; 1 &amp; 0\\\\<br \/>\n0 &amp; 1 &amp; -1 &amp; -1<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\n(d_0 - d_2)g_0 \\\\<br \/>\n(d_1 + d_2)(g_0 + g_1 + g_2)\/2 \\\\<br \/>\n(d_2 - d_1)(g_0 - g_1 + g_2)\/2 \\\\<br \/>\n(d_1 - d_3)g_2<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<\/p>\n<p>\\begin{equation}<br \/>\n\\label{mfirst}<br \/>\nm_1 = (d_0 - d_2)g_0<br \/>\n\\end{equation}<br \/>\n\\begin{equation}<br \/>\nm_2 = (d_1 + d_2)(g_0 + g_1 + g_2)\/2<br \/>\n\\end{equation}<\/p>\n<p>\\begin{equation}<br \/>\nm_3 = (d_2 - d_1)(g_0 - g_1 + g_2)\/2<br \/>\n\\end{equation}<\/p>\n<p>\\begin{equation}<br \/>\nm_4 = (d_1 - d_3)g_2<br \/>\n\\label{last}<br \/>\n\\end{equation}<\/p>\n<p>substitute \\ref{mfirst} to \\ref{last} into \\ref{linelast}<br \/>\nwe get<br \/>\n\\begin{equation}<br \/>\nY = \\begin{bmatrix}<br \/>\nm_1 + m_2 + m_3 \\\\<br \/>\nm_2 - m_3 - m_4<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<\/p>\n<h1><span class=\"ez-toc-section\" id=\"2D%E5%BD%A2%E5%BC%8F%E6%8E%A8%E5%AF%BC\"><\/span>\n2D\u5f62\u5f0f\u63a8\u5bfc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\\begin{equation}<br \/>\nD = \\begin{bmatrix}<br \/>\nd_{00} &amp; d_{01} &amp; d_{02} &amp; d_{03} \\\\<br \/>\nd_{10} &amp; d_{11} &amp; d_{12} &amp; d_{13} \\\\<br \/>\nd_{20} &amp; d_{21} &amp; d_{22} &amp; d_{23} \\\\<br \/>\nd_{30} &amp; d_{31} &amp; d_{32} &amp; d_{33}<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<br \/>\n\u5377\u79ef\u6838<br \/>\n\\begin{equation}<br \/>\nK = \\begin{bmatrix}<br \/>\nk_{00} &amp; k_{01} &amp; k_{02} \\\\<br \/>\nk_{10} &amp; k_{11} &amp; k_{12} \\\\<br \/>\nk_{20} &amp; k_{21} &amp; k_{22}<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<\/p>\n<p>\u5199\u6210\u77e9\u9635\uff0c\u5c55\u5f00\u662f<\/p>\n<p>\\begin{equation}<br \/>\n\\begin{bmatrix}<br \/>\nd_{00} &amp; d_{01} &amp; d_{02} &amp; d_{10} &amp; d_{11} &amp; d_{12} &amp; d_{20} &amp; d_{21} &amp; d_{22} \\\\<br \/>\nd_{01} &amp; d_{02} &amp; d_{03} &amp; d_{11} &amp; d_{12} &amp; d_{13} &amp; d_{21} &amp; d_{22} &amp; d_{23} \\\\<br \/>\nd_{10} &amp; d_{11} &amp; d_{12} &amp; d_{20} &amp; d_{21} &amp; d_{22} &amp; d_{30} &amp; d_{31} &amp; d_{32} \\\\<br \/>\nd_{11} &amp; d_{12} &amp; d_{13} &amp; d_{21} &amp; d_{22} &amp; d_{23} &amp; d_{31} &amp; d_{32} &amp; d_{33}<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\nk_{00} \\\\ k_{01} \\\\ k_{02} \\\\<br \/>\nk_{10} \\\\ k_{11} \\\\ k_{12} \\\\<br \/>\nk_{20} \\\\ k_{21} \\\\ k_{22}<br \/>\n\\end{bmatrix}=<br \/>\n\\begin{bmatrix}<br \/>\nr_{00} \\\\<br \/>\nr_{01} \\\\<br \/>\nr_{10} \\\\<br \/>\nr_{11} \\\\<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<br \/>\n\u5206\u5757\u77e9\u9635\uff0c\u6210\u5458\u5206\u5f00\u5199:<br \/>\n\\begin{equation}<br \/>\n\\begin{bmatrix}<br \/>\n\\begin{array}{ccc|ccc|ccc}<br \/>\nd_{00} &amp; d_{01} &amp; d_{02} &amp; d_{10} &amp; d_{11} &amp; d_{12} &amp; d_{20} &amp; d_{21} &amp; d_{22} \\\\<br \/>\nd_{01} &amp; d_{02} &amp; d_{03} &amp; d_{11} &amp; d_{12} &amp; d_{13} &amp; d_{21} &amp; d_{22} &amp; d_{23} \\\\ \\hline<br \/>\nd_{10} &amp; d_{11} &amp; d_{12} &amp; d_{20} &amp; d_{21} &amp; d_{22} &amp; d_{30} &amp; d_{31} &amp; d_{32} \\\\<br \/>\nd_{11} &amp; d_{12} &amp; d_{13} &amp; d_{21} &amp; d_{22} &amp; d_{23} &amp; d_{31} &amp; d_{32} &amp; d_{33}<br \/>\n\\end{array}<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\n\\begin{array}{c}<br \/>\nk_{00} \\\\ k_{01} \\\\ k_{02} \\\\ \\hline<br \/>\nk_{10} \\\\ k_{11} \\\\ k_{12} \\\\ \\hline<br \/>\nk_{20} \\\\ k_{21} \\\\ k_{22}<br \/>\n\\end{array}<br \/>\n\\end{bmatrix} =<br \/>\n\\begin{bmatrix}<br \/>\n\\begin{array}{c}<br \/>\nr_{00} \\\\<br \/>\nr_{01} \\\\ \\hline<br \/>\nr_{10} \\\\<br \/>\nr_{11} \\\\<br \/>\n\\end{array}<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<\/p>\n<p>\u76f4\u63a5\u5199\u6210\u5206\u5757\u77e9\u9635<br \/>\n\\begin{equation}<br \/>\n\\begin{bmatrix}<br \/>\nD_{00} &amp; D_{10} &amp; D_{20} \\\\<br \/>\nD_{10} &amp; D_{20} &amp; D_{30}<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\n\\vec{k_0} \\\\<br \/>\n\\vec{k_1} \\\\<br \/>\n\\vec{k_2}<br \/>\n\\end{bmatrix}=<br \/>\n\\begin{bmatrix}<br \/>\n\\vec{r_0} \\\\<br \/>\n\\vec{r_1}<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<\/p>\n<p>\u5bf9\u4e8e\u5b9e\u6218<br \/>\n\\begin{equation}<br \/>\n\\begin{bmatrix}<br \/>\nD_{00} &amp; D_{10} &amp; D_{20} \\\\<br \/>\nD_{10} &amp; D_{20} &amp; D_{30}<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\n\\vec{k_0} \\\\<br \/>\n\\vec{k_1} \\\\<br \/>\n\\vec{k_2}<br \/>\n\\end{bmatrix}=<br \/>\n\\begin{bmatrix}<br \/>\n\\vec{r_0} \\\\<br \/>\n\\vec{r_1}<br \/>\n\\end{bmatrix}=<br \/>\n\\begin{bmatrix}<br \/>\nM_0 + M_1 + M_2 \\\\<br \/>\nM_1 - M_2 - M_3<br \/>\n\\end{bmatrix}<br \/>\n\\end{equation}<\/p>\n<p>\u516c\u5f0f\u4e2d<\/p>\n<p>\\begin{equation}<br \/>\n\\begin{split}<br \/>\nM_0 &amp;= (D_{00} - D_{20})\\vec{k_0} \\\\<br \/>\nM_1 &amp;= (D_{10} + D_{20})\\frac{\\vec{k_0} + \\vec{k_1} + \\vec{k_2}}{2} \\\\<br \/>\nM_2 &amp;= (D_{20} - D_{10})\\frac{\\vec{k_0} - \\vec{k_1} + \\vec{k_2}}{2} \\\\<br \/>\nM_3 &amp;= (D_{10} - D_{30})\\vec{k_2}<br \/>\n\\end{split}<br \/>\n\\end{equation}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u53c2\u8003\u535a\u5ba2 https:\/\/www.cnblogs.com\/shine-lee\/p\/10906535.html  &#8230; <a title=\"winograd\u603b\u7ed3\" class=\"read-more\" href=\"https:\/\/189505.xyz\/?p=55\" aria-label=\"More on winograd\u603b\u7ed3\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/189505.xyz\/index.php?rest_route=\/wp\/v2\/posts\/55"}],"collection":[{"href":"https:\/\/189505.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/189505.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/189505.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/189505.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=55"}],"version-history":[{"count":67,"href":"https:\/\/189505.xyz\/index.php?rest_route=\/wp\/v2\/posts\/55\/revisions"}],"predecessor-version":[{"id":129,"href":"https:\/\/189505.xyz\/index.php?rest_route=\/wp\/v2\/posts\/55\/revisions\/129"}],"wp:attachment":[{"href":"https:\/\/189505.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=55"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/189505.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=55"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/189505.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=55"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}