{"id":10329,"date":"2024-03-14T11:54:52","date_gmt":"2024-03-14T11:54:52","guid":{"rendered":"https:\/\/www.silicloud.com\/blog\/how-to-use-the-jacobi-method-to-find-eigenvalues-in-c-language\/"},"modified":"2025-08-03T22:09:49","modified_gmt":"2025-08-03T22:09:49","slug":"how-to-use-the-jacobi-method-to-find-eigenvalues-in-c-language","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/blog\/how-to-use-the-jacobi-method-to-find-eigenvalues-in-c-language\/","title":{"rendered":"Jacobi Method Eigenvalues in C: Code Example"},"content":{"rendered":"<p>The Jacobi method is a technique used to solve for the eigenvalues and eigenvectors of a symmetric matrix. In C language, one can implement the Jacobi method by writing a function to compute the eigenvalues.<\/p>\n<p>The following example is a C language code:<\/p>\n<pre class=\"post-pre\"><code><span class=\"hljs-meta\">#<span class=\"hljs-keyword\">include<\/span> <span class=\"hljs-string\">&lt;stdio.h&gt;<\/span><\/span>\r\n<span class=\"hljs-meta\">#<span class=\"hljs-keyword\">include<\/span> <span class=\"hljs-string\">&lt;math.h&gt;<\/span><\/span>\r\n\r\n<span class=\"hljs-meta\">#<span class=\"hljs-keyword\">define<\/span> N 3 <span class=\"hljs-comment\">\/\/ \u77e9\u9635\u7ef4\u5ea6<\/span><\/span>\r\n\r\n<span class=\"hljs-type\">void<\/span> <span class=\"hljs-title function_\">jacobi<\/span><span class=\"hljs-params\">(<span class=\"hljs-type\">double<\/span> A[N][N], <span class=\"hljs-type\">double<\/span> V[N][N], <span class=\"hljs-type\">double<\/span> eigenvalues[N])<\/span> {\r\n    <span class=\"hljs-type\">int<\/span> i, j, p, q;\r\n    <span class=\"hljs-type\">double<\/span> phi, t, c, s;\r\n\r\n    <span class=\"hljs-comment\">\/\/ \u521d\u59cb\u5316V\u4e3a\u5355\u4f4d\u77e9\u9635<\/span>\r\n    <span class=\"hljs-keyword\">for<\/span>(i = <span class=\"hljs-number\">0<\/span>; i &lt; N; i++) {\r\n        <span class=\"hljs-keyword\">for<\/span>(j = <span class=\"hljs-number\">0<\/span>; j &lt; N; j++) {\r\n            V[i][j] = (i == j) ? <span class=\"hljs-number\">1.0<\/span> : <span class=\"hljs-number\">0.0<\/span>;\r\n        }\r\n    }\r\n\r\n    <span class=\"hljs-comment\">\/\/ \u8fed\u4ee3\u6c42\u89e3<\/span>\r\n    <span class=\"hljs-keyword\">for<\/span>(<span class=\"hljs-type\">int<\/span> k = <span class=\"hljs-number\">0<\/span>; k &lt; <span class=\"hljs-number\">100<\/span>; k++) { <span class=\"hljs-comment\">\/\/ \u5047\u8bbe\u6700\u591a\u8fed\u4ee3100\u6b21<\/span>\r\n        <span class=\"hljs-type\">double<\/span> max_offdiag = <span class=\"hljs-number\">0.0<\/span>;\r\n        <span class=\"hljs-keyword\">for<\/span>(i = <span class=\"hljs-number\">0<\/span>; i &lt; N<span class=\"hljs-number\">-1<\/span>; i++) {\r\n            <span class=\"hljs-keyword\">for<\/span>(j = i+<span class=\"hljs-number\">1<\/span>; j &lt; N; j++) {\r\n                <span class=\"hljs-keyword\">if<\/span>(<span class=\"hljs-built_in\">fabs<\/span>(A[i][j]) &gt; max_offdiag) {\r\n                    max_offdiag = <span class=\"hljs-built_in\">fabs<\/span>(A[i][j]);\r\n                    p = i;\r\n                    q = j;\r\n                }\r\n            }\r\n        }\r\n\r\n        <span class=\"hljs-keyword\">if<\/span>(max_offdiag &lt; <span class=\"hljs-number\">1e-6<\/span>) {\r\n            <span class=\"hljs-keyword\">break<\/span>; <span class=\"hljs-comment\">\/\/ \u6536\u655b\u6761\u4ef6<\/span>\r\n        }\r\n\r\n        phi = <span class=\"hljs-number\">0.5<\/span> * <span class=\"hljs-built_in\">atan2<\/span>(<span class=\"hljs-number\">2<\/span> * A[p][q], A[q][q] - A[p][p]);\r\n        c = <span class=\"hljs-built_in\">cos<\/span>(phi);\r\n        s = <span class=\"hljs-built_in\">sin<\/span>(phi);\r\n        \r\n        <span class=\"hljs-comment\">\/\/ \u66f4\u65b0A<\/span>\r\n        t = A[p][q];\r\n        A[p][q] = <span class=\"hljs-number\">0.0<\/span>;\r\n        <span class=\"hljs-keyword\">for<\/span>(i = <span class=\"hljs-number\">0<\/span>; i &lt; N; i++) {\r\n            <span class=\"hljs-keyword\">if<\/span>(i != p &amp;&amp; i != q) {\r\n                <span class=\"hljs-type\">double<\/span> api = A[p][i];\r\n                <span class=\"hljs-type\">double<\/span> aqi = A[q][i];\r\n                A[p][i] = api * c - aqi * s;\r\n                A[i][p] = A[p][i];\r\n                A[q][i] = aqi * c + api * s;\r\n                A[i][q] = A[q][i];\r\n            }\r\n        }\r\n        A[q][q] = A[q][q] * c * c + A[p][p] * s * s - <span class=\"hljs-number\">2<\/span> * A[p][q] * c * s;\r\n\r\n        <span class=\"hljs-comment\">\/\/ \u66f4\u65b0V<\/span>\r\n        <span class=\"hljs-keyword\">for<\/span>(i = <span class=\"hljs-number\">0<\/span>; i &lt; N; i++) {\r\n            <span class=\"hljs-type\">double<\/span> vip = V[i][p];\r\n            <span class=\"hljs-type\">double<\/span> viq = V[i][q];\r\n            V[i][p] = vip * c - viq * s;\r\n            V[i][q] = viq * c + vip * s;\r\n        }\r\n    }\r\n\r\n    <span class=\"hljs-comment\">\/\/ \u83b7\u53d6\u7279\u5f81\u503c<\/span>\r\n    <span class=\"hljs-keyword\">for<\/span>(i = <span class=\"hljs-number\">0<\/span>; i &lt; N; i++) {\r\n        eigenvalues[i] = A[i][i];\r\n    }\r\n}\r\n\r\n<span class=\"hljs-type\">int<\/span> <span class=\"hljs-title function_\">main<\/span><span class=\"hljs-params\">()<\/span> {\r\n    <span class=\"hljs-type\">double<\/span> A[N][N] = {{<span class=\"hljs-number\">2.0<\/span>, <span class=\"hljs-number\">-1.0<\/span>, <span class=\"hljs-number\">0.0<\/span>}, {<span class=\"hljs-number\">-1.0<\/span>, <span class=\"hljs-number\">2.0<\/span>, <span class=\"hljs-number\">-1.0<\/span>}, {<span class=\"hljs-number\">0.0<\/span>, <span class=\"hljs-number\">-1.0<\/span>, <span class=\"hljs-number\">2.0<\/span>}};\r\n    <span class=\"hljs-type\">double<\/span> V[N][N];\r\n    <span class=\"hljs-type\">double<\/span> eigenvalues[N];\r\n\r\n    jacobi(A, V, eigenvalues);\r\n\r\n    <span class=\"hljs-built_in\">printf<\/span>(<span class=\"hljs-string\">\"Eigenvalues:\\n\"<\/span>);\r\n    <span class=\"hljs-keyword\">for<\/span>(<span class=\"hljs-type\">int<\/span> i = <span class=\"hljs-number\">0<\/span>; i &lt; N; i++) {\r\n        <span class=\"hljs-built_in\">printf<\/span>(<span class=\"hljs-string\">\"%.6f\\n\"<\/span>, eigenvalues[i]);\r\n    }\r\n\r\n    <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-number\">0<\/span>;\r\n}\r\n<\/code><\/pre>\n<p>The code first defines a function called jacobi for the Jacobi method, then in the main function, it defines a symmetric matrix A and calls the jacobi function to solve for eigenvalues, and outputs the result.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Jacobi method is a technique used to solve for the eigenvalues and eigenvectors of a symmetric matrix. In C language, one can implement the Jacobi method by writing a function to compute the eigenvalues. The following example is a C language code: #include &lt;stdio.h&gt; #include &lt;math.h&gt; #define N 3 \/\/ \u77e9\u9635\u7ef4\u5ea6 void jacobi(double A[N][N], [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","footnotes":""},"categories":[1],"tags":[381,12867,12866,79,12868],"class_list":["post-10329","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-c-programming","tag-eigenvalues","tag-jacobi-method","tag-linear-algebra","tag-numerical-methods"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.5 (Yoast SEO v21.5) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jacobi Method Eigenvalues in C: Code Example - Blog - Silicon Cloud<\/title>\n<meta name=\"description\" content=\"Implement Jacobi method for eigenvalues in C. 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