{"id":2006,"date":"2024-06-02T20:09:37","date_gmt":"2024-06-02T12:09:37","guid":{"rendered":"https:\/\/17aitech.com\/?p=2006"},"modified":"2024-10-08T15:23:39","modified_gmt":"2024-10-08T07:23:39","slug":"%e3%80%90%e8%af%be%e7%a8%8b%e6%80%bb%e7%bb%93%e3%80%91day5%e4%b8%8a%ef%bc%9a%e7%a7%91%e5%ad%a6%e8%ae%a1%e7%ae%97%e7%a5%9e%e5%99%a8numpy%e3%80%81pytorch%e5%92%8c%e6%95%b0%e6%8d%ae%e9%a2%84%e5%a4%84","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=2006","title":{"rendered":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day5\uff08\u4e0a\uff09\uff1a\u79d1\u5b66\u8ba1\u7b97\u795e\u5668Numpy\u3001Pytorch\u548c\u6570\u636e\u9884\u5904\u7406"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 ez-toc-wrap-left-text counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u6587\u7ae0\u76ee\u5f55<\/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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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 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href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%9F%A9%E9%98%B5%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%93%8D%E4%BD%9C%E4%BD%BF%E7%94%A8Numpy\" >\u77e9\u9635\u7684\u57fa\u672c\u64cd\u4f5c(\u4f7f\u7528Numpy)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%9F%A9%E9%98%B5%E7%9A%84%E7%94%9F%E6%88%90%E4%BD%BF%E7%94%A8Numpy\" >\u77e9\u9635\u7684\u751f\u6210(\u4f7f\u7528Numpy)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%9F%A9%E9%98%B5%E7%9A%84%E5%A0%86%E5%8F%A0%E5%92%8C%E6%8B%BC%E6%8E%A5%E4%BD%BF%E7%94%A8Numpy\" >\u77e9\u9635\u7684\u5806\u53e0\u548c\u62fc\u63a5(\u4f7f\u7528Numpy)<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/17aitech.com\/?p=2006\/#npconcatenate%E5%92%8Cnpstack\" >np.concatenate\u548cnp.stack<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/17aitech.com\/?p=2006\/#npstack\" >np.stack<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%A7%91%E5%AD%A6%E8%AE%A1%E7%AE%97%E7%A5%9E%E5%99%A8%E4%B9%8B%E4%BA%8CPytorch%E7%9A%84%E4%BD%BF%E7%94%A8\" >\u79d1\u5b66\u8ba1\u7b97\u795e\u5668\u4e4b\u4e8cPytorch\u7684\u4f7f\u7528<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E5%AE%89%E8%A3%85Pytorch\" >\u5b89\u88c5Pytorch<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%9F%A9%E9%98%B5%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%93%8D%E4%BD%9C%E4%BD%BF%E7%94%A8torch\" >\u77e9\u9635\u7684\u57fa\u672c\u64cd\u4f5c(\u4f7f\u7528torch)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%9F%A9%E9%98%B5%E7%9A%84%E7%94%9F%E6%88%90%E4%BD%BF%E7%94%A8torch\" >\u77e9\u9635\u7684\u751f\u6210(\u4f7f\u7528torch)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E7%9F%A9%E9%98%B5%E7%9A%84%E5%A0%86%E5%8F%A0%E5%92%8C%E6%8B%BC%E6%8E%A5%E4%BD%BF%E7%94%A8torch\" >\u77e9\u9635\u7684\u5806\u53e0\u548c\u62fc\u63a5(\u4f7f\u7528torch)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E6%95%B0%E6%8D%AE%E4%BF%A1%E6%81%AF\" >\u6570\u636e\u4fe1\u606f<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E5%9F%BA%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F\" >\u57fa\u672c\u7edf\u8ba1\u91cf<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E5%9D%87%E5%80%BC%EF%BC%88Mean%EF%BC%89\" >\u5747\u503c\uff08Mean\uff09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E6%A0%87%E5%87%86%E5%B7%AE%EF%BC%88Standard_Deviation%EF%BC%89\" >\u6807\u51c6\u5dee\uff08Standard Deviation\uff09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E6%96%B9%E5%B7%AE%EF%BC%88Variance%EF%BC%89\" >\u65b9\u5dee\uff08Variance\uff09<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86\" >\u6570\u636e\u9884\u5904\u7406<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E5%BD%92%E4%B8%80%E5%8C%96%EF%BC%88Normalization%EF%BC%89_%E7%BA%BF%E6%80%A7%E6%98%A0%E5%B0%84%EF%BC%9A\" >\u5f52\u4e00\u5316\uff08Normalization\uff09\/ \u7ebf\u6027\u6620\u5c04\uff1a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E5%8E%BB%E4%B8%AD%E5%BF%83%E5%8C%96%EF%BC%88Mean_Normalization%EF%BC%89_%E5%8E%BB%E5%9D%87%E5%80%BC_center_data%EF%BC%9A\" >\u53bb\u4e2d\u5fc3\u5316\uff08Mean Normalization\uff09\/ \u53bb\u5747\u503c \/ center data\uff1a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E8%A7%84%E8%8C%83%E5%8C%96%EF%BC%88Standardization%EF%BC%89_%E8%A7%84%E8%8C%83%E5%8C%96%EF%BC%9A\" >\u89c4\u8303\u5316\uff08Standardization\uff09\/ \u89c4\u8303\u5316\uff1a<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E4%BF%A1%E6%81%AF%E8%95%B4%E5%90%AB%E5%9C%A8%E6%95%B0%E6%8D%AE%E7%9A%84%E7%9B%B8%E5%AF%B9%E5%A4%A7%E5%B0%8F\" >\u4fe1\u606f\u8574\u542b\u5728\u6570\u636e\u7684\u76f8\u5bf9\u5927\u5c0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86%E7%9A%84%E5%BA%94%E7%94%A8\" >\u6570\u636e\u9884\u5904\u7406\u7684\u5e94\u7528<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86%E7%9A%84%E5%8E%9F%E5%88%99\" >\u6570\u636e\u9884\u5904\u7406\u7684\u539f\u5219<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/17aitech.com\/?p=2006\/#%E5%86%85%E5%AE%B9%E5%B0%8F%E7%BB%93\" >\u5185\u5bb9\u5c0f\u7ed3<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E6%95%B0%E6%8D%AE%E7%A7%91%E5%AD%A6%E5%9F%BA%E7%A1%80\"><\/span>\u6570\u636e\u79d1\u5b66\u57fa\u7840<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"%E7%A7%91%E5%AD%A6%E8%AE%A1%E7%AE%97%E7%A5%9E%E5%99%A8%E4%B9%8B%E4%B8%80Numpy%E7%9A%84%E4%BD%BF%E7%94%A8\"><\/span>\u79d1\u5b66\u8ba1\u7b97\u795e\u5668\u4e4b\u4e00Numpy\u7684\u4f7f\u7528<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%93%8D%E4%BD%9C%E4%BD%BF%E7%94%A8Numpy\"><\/span>\u77e9\u9635\u7684\u57fa\u672c\u64cd\u4f5c(\u4f7f\u7528Numpy)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-python\">import numpy as np\n\n# \u5feb\u901f\u6784\u5efa\u77e9\u9635\nmatrix = np.array([[1, 2, 3], [4, 5, 6]])\n\nprint(&quot;\u77e9\u9635\u6570\u636e\uff1a&quot;, matrix)\n\n# \u67e5\u770b\u77e9\u9635\u7684\u7ef4\u5ea6\u4fe1\u606f\nprint(&quot;\u77e9\u9635\u7ef4\u5ea6\uff1a&quot;, matrix.ndim)\n\n# \u67e5\u770b\u77e9\u9635\u7684\u5f62\u72b6\nprint(&quot;\u77e9\u9635\u5f62\u72b6\uff1a&quot;, matrix.shape)\n\n# \u67e5\u770b\u77e9\u9635\u7684size\nprint(&quot;\u77e9\u9635size\uff1a&quot;, matrix.size)\n\n# \u5bf9\u77e9\u9635\u8fdb\u884creshape\u4e3a\u4e00\u4e2a\u77e9\u9635\nreshaped_matrix = matrix.reshape(3, 2)\nprint(&quot;\u91cd\u5851\u540e\u7684\u77e9\u9635\uff1a\\n&quot;, reshaped_matrix)\n\n# \u4fee\u6539\u77e9\u9635\u4e2d\u7684\u6570\u636e\u5185\u5bb9\nmatrix[0, 1] = 10\nprint(&quot;\u4fee\u6539\u540e\u7684\u77e9\u9635\uff1a\\n&quot;, matrix)\n\n# \u5c06\u77e9\u9635\u7684\u6570\u636e\u7c7b\u578b\u8f6c\u6362\nmatrix = matrix.astype(float)\nprint(&quot;\u8f6c\u6362\u6570\u636e\u7c7b\u578b\u540e\u7684\u77e9\u9635\uff1a\\n&quot;, matrix)\n\n# \u968f\u673a\u751f\u6210\u4e00\u4e2a\u65b0\u7684\u77e9\u9635\nnew_matrix = np.random.rand(2, 3)\nprint(&quot;\u968f\u673a\u751f\u6210\u7684\u65b0\u77e9\u9635\uff1a\\n&quot;, new_matrix)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602093724644.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602093724644.png\" alt=\"\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E7%94%9F%E6%88%90%E4%BD%BF%E7%94%A8Numpy\"><\/span>\u77e9\u9635\u7684\u751f\u6210(\u4f7f\u7528Numpy)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-python\"># \u751f\u6210\u4e00\u4e2a\u5f62\u72b6\u4e3a (3, 4, 5) \u7684\u6570\u7ec4,\u5185\u5bb9\u90fd\u4e3a0\narry_zero = np.zeros((3, 4, 5))\nprint(arry_zero)\n\n# \u751f\u6210\u4e00\u4e2a\u5f62\u72b6\u4e3a (3, 4, 5) \u7684\u6570\u7ec4,\u5185\u5bb9\u90fd\u4e3a1\narray_ones = np.ones((3, 4, 5))\nprint(array_ones)\n\n# \u751f\u6210\u4e00\u4e2a\u5f62\u72b6\u4e3a (3, 4, 5) \u7684\u6570\u7ec4\uff0c\u5185\u5bb9\u4e3a\u968f\u673a\narray_random = np.random.rand(3, 4, 5)\nprint(array_random)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602101612516.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602101612516.png\" alt=\"\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E5%A0%86%E5%8F%A0%E5%92%8C%E6%8B%BC%E6%8E%A5%E4%BD%BF%E7%94%A8Numpy\"><\/span>\u77e9\u9635\u7684\u5806\u53e0\u548c\u62fc\u63a5(\u4f7f\u7528Numpy)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u5728 NumPy \u4e2d\uff0c<code><code>np.concatenate<\/code><code>\u3001<\/code><code>np.stack<\/code><code>\u3001<\/code><code>np.vstack<\/code><code>\u3001<\/code><code>np.hstack<\/code><code> \u548c <\/code><code>np.dstack<\/code><\/code> \u662f\u7528\u4e8e\u6570\u7ec4\u5806\u53e0\u548c\u8fde\u63a5\u7684\u51fd\u6570\uff0c\u5b83\u4eec\u4e4b\u95f4\u6709\u4e00\u4e9b\u533a\u522b\u548c\u8054\u7cfb\uff1a<\/p>\n<ul>\n<li>np.concatenate\uff1a\n<ul>\n<li>np.concatenate \u662f\u4e00\u4e2a\u901a\u7528\u7684\u51fd\u6570\uff0c\u7528\u4e8e\u6cbf\u6307\u5b9a\u8f74\u8fde\u63a5\u6570\u7ec4\u3002<\/li>\n<li>\u53ef\u4ee5\u5728\u6307\u5b9a\u7684\u8f74\uff08axis\uff09\u4e0a\u8fde\u63a5\u4e24\u4e2a\u6216\u591a\u4e2a\u6570\u7ec4\u3002<\/li>\n<li>\u53ef\u4ee5\u63a7\u5236\u8fde\u63a5\u7684\u65b9\u5411\uff0c\u4f8b\u5982\u6cbf\u884c\uff08axis=0\uff09\u6216\u5217\uff08axis=1\uff09\u8fdb\u884c\u8fde\u63a5\u3002<\/li>\n<\/ul>\n<\/li>\n<li>np.stack\uff1a\n<ul>\n<li>np.stack \u662f\u7528\u4e8e\u6cbf\u65b0\u8f74\uff08\u5806\u53e0\u8f74\uff09\u5806\u53e0\u6570\u7ec4\u7684\u51fd\u6570\u3002<\/li>\n<li>\u521b\u5efa\u4e00\u4e2a\u65b0\u8f74\u6765\u5806\u53e0\u6570\u7ec4\uff0c\u6539\u53d8\u6570\u7ec4\u7684\u7ef4\u5ea6\u3002<\/li>\n<li>\u53ef\u4ee5\u901a\u8fc7 axis \u53c2\u6570\u63a7\u5236\u5728\u54ea\u4e2a\u4f4d\u7f6e\u6dfb\u52a0\u65b0\u8f74\u3002<\/li>\n<\/ul>\n<\/li>\n<li>np.vstack\uff1a\n<ul>\n<li>np.vstack \u662f\u7528\u4e8e\u5782\u76f4\uff08\u6cbf\u7740\u884c\u65b9\u5411\uff09\u5806\u53e0\u6570\u7ec4\u7684\u51fd\u6570\u3002<\/li>\n<li>\u5c06\u4e24\u4e2a\u6216\u591a\u4e2a\u6570\u7ec4\u6309\u884c\u5806\u53e0\u5728\u4e00\u8d77\u3002<\/li>\n<\/ul>\n<\/li>\n<li>np.hstack\uff1a\n<ul>\n<li>np.hstack \u662f\u7528\u4e8e\u6c34\u5e73\uff08\u6cbf\u7740\u5217\u65b9\u5411\uff09\u5806\u53e0\u6570\u7ec4\u7684\u51fd\u6570\u3002<\/li>\n<li>\u5c06\u4e24\u4e2a\u6216\u591a\u4e2a\u6570\u7ec4\u6309\u5217\u5806\u53e0\u5728\u4e00\u8d77\u3002<\/li>\n<\/ul>\n<\/li>\n<li>np.dstack\uff1a\n<ul>\n<li>np.dstack \u662f\u7528\u4e8e\u6df1\u5ea6\uff08\u6cbf\u7740\u7b2c\u4e09\u7ef4\uff09\u5806\u53e0\u6570\u7ec4\u7684\u51fd\u6570\u3002<\/li>\n<li>\u5c06\u4e24\u4e2a\u6216\u591a\u4e2a\u6570\u7ec4\u6309\u6df1\u5ea6\u65b9\u5411\u5806\u53e0\u5728\u4e00\u8d77\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"npconcatenate%E5%92%8Cnpstack\"><\/span>np.concatenate\u548cnp.stack<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<pre><code class=\"language-python\">import numpy as np\n\na = np.arange(1, 28).reshape(3, 3, 3)\nb = np.arange(28, 55).reshape(3, 3, 3)\n\n#  np.dstack((a, b))\u4e0e np.concatenate((a, b), axis=2) \u6548\u679c\u4e00\u6837\nprint(&quot;np.dstack((a, b))\uff1a&quot;, np.dstack((a, b)))\nprint(&quot;np.concatenate((a, b), axis=2)\uff1a&quot;, np.concatenate((a, b), axis=2))\n\n#  np.hstack((a, b))\u4e0e np.concatenate((a, b), axis=1) \u6548\u679c\u4e00\u6837\nprint(&quot;np.hstack((a, b))\uff1a&quot;, np.hstack((a, b)))\nprint(&quot;np.concatenate((a, b), axis=1)\uff1a&quot;, np.concatenate((a, b), axis=1))\n\n#  np.vstack((a, b))\u4e0e np.concatenate((a, b), axis=0) \u6548\u679c\u4e00\u6837\nprint(&quot;np.vstack((a, b))\uff1a&quot;, np.vstack((a, b)))\nprint(&quot;np.concatenate((a, b), axis=0)\uff1a&quot;, np.concatenate((a, b), axis=0))\n<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602115805585.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602115805585.png\" alt=\"\" \/><\/a><\/p>\n<blockquote>\n<p>\u5728Numpy\u8fdb\u884c\u6570\u636e\u5904\u7406\u65f6\uff0c\u9700\u8981\u638c\u63e1\u7ef4\u5ea6\u7684\u6982\u5ff5\uff1a<\/p>\n<ul>\n<li>\u6309\u7ef4\u5ea6\u5b9a\u4e49\u6570\u636e<\/li>\n<li>\u6309\u7ef4\u5ea6\u8bfb\u53d6\u6570\u636e<\/li>\n<li>\u6309\u7ef4\u5ea6\u5904\u7406\u6570\u636e<\/li>\n<\/ul>\n<\/blockquote>\n<h5><span class=\"ez-toc-section\" id=\"npstack\"><\/span>np.stack<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<pre><code class=\"language-python\"># \u4e00\u7ef4\u6570\u7ec4\u5806\u53e0\u4e3a\u4e8c\u7ef4\u6570\u7ec4\na1 = np.arange(1, 13)\nprint(&quot;a1\u6570\u7ec4\uff1a&quot;, a1)\n\na2 = np.arange(13, 25)\nprint(&quot;a2\u6570\u7ec4\uff1a&quot;, a2)\n\nstack0 = np.stack((a1, a1, a2, a2))     # \u9ed8\u8ba4\u60c5\u51b5\u4e0b axis=0\nprint(&quot;a1\u548ca2\u9ed8\u8ba4\u60c5\u51b5\u4e0b(axis=0)\u5806\u53e0\uff1a&quot;, stack0)\n\nstack1 = np.stack((a1, a1, a2, a2), axis=1)\nprint(&quot;a1\u548ca2\u5782\u76f4\u65b9\u5411\u4e0b(axis=0)\u5806\u53e0\uff1a&quot;,stack1)\n\nstack_long = np.hstack((a1, a2))\nprint(stack_long)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602094925127.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602094925127.png\" alt=\"\" \/><\/a><\/p>\n<pre><code class=\"language-python\"># \u4e8c\u7ef4\u77e9\u9635\u5806\u53e0\u4e3a\u4e09\u7ef4\n\n# \u521b\u5efa\u4e00\u4e2a3*4\u7684\u77e9\u9635\na1_ = np.arange(1, 13).reshape(3, -1)  # 3_4\nprint(&quot;a1\u77e9\u9635\uff1a&quot;, a1_)\n\n# \u521b\u5efa\u53e6\u5916\u4e00\u4e2a3*4\u7684\u77e9\u9635\na2_ = np.arange(13, 25).reshape(3, -1)  # 3_4\nprint(&quot;a2\u77e9\u9635\uff1a&quot;, a2_)\n\n# a1\u548ca2\u77e9\u9635\u5728\u9ed8\u8ba4axis=0\u65b9\u5411\u4e0a\u7684\u5806\u53e0\na3_0 = np.stack((a1_, a2_))             # default axis=0 (dimension 0)\nprint(&quot;\u5806\u53e0a3_0\u77e9\u9635\u7684\u7ef4\u5ea6\uff1a&quot;, a3_0.ndim) \nprint(&quot;\u5806\u53e0a3_0\u77e9\u9635\u7684\u5143\u7d20\u4e2a\u6570\uff1a&quot;, a3_0.size)  \nprint(&quot;\u5806\u53e0a3_0\u77e9\u9635\u7684\u5f62\u72b6\uff1a&quot;, a3_0.shape)  # 2_3_4\nprint(&quot;\u5806\u53e0a3_0\u77e9\u9635\u7684\u5185\u5bb9\uff1a&quot;, a3_0)\n\n# a1\u548ca2\u77e9\u9635\u5728\u9ed8\u8ba4axis=1\u65b9\u5411\u4e0a\u7684\u5806\u53e0\na3_1 = np.stack((a1, a2), axis=1)\nprint(&quot;\u5806\u53e0a3_1\u77e9\u9635\u7684\u5f62\u72b6\uff1a&quot;, a3_1.shape)  # 3_2_4\nprint(a3_1)\n\n# a1\u548ca2\u77e9\u9635\u5728\u9ed8\u8ba4axis=2\u65b9\u5411\u4e0a\u7684\u5806\u53e0\na3_2 = np.stack((a1, a2), axis=2)  # dimension 2\nprint(&quot;\u5806\u53e0a3_2\u77e9\u9635\u7684\u5f62\u72b6\uff1a&quot;,a3_2.shape)  # 3_4_2\nprint(a3_2)\n<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602095151961.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602095151961.png\" alt=\"\" \/><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E7%A7%91%E5%AD%A6%E8%AE%A1%E7%AE%97%E7%A5%9E%E5%99%A8%E4%B9%8B%E4%BA%8CPytorch%E7%9A%84%E4%BD%BF%E7%94%A8\"><\/span>\u79d1\u5b66\u8ba1\u7b97\u795e\u5668\u4e4b\u4e8cPytorch\u7684\u4f7f\u7528<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>PyTorch\u4e5f\u662f\u4e00\u4e2a\u5e38\u7528\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u76f8\u6bd4Numpy\u53ea\u80fd\u8fd0\u884c\u5728CPU\uff0cPyTorch\u53ef\u4ee5\u8fd0\u884c\u5728GPU\u4e0a\uff0c\u52a0\u5feb\u76f8\u5173\u8ba1\u7b97\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E5%AE%89%E8%A3%85Pytorch\"><\/span>\u5b89\u88c5Pytorch<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u7b2c\u4e00\u6b65\uff1a\u66f4\u6362pypi\u7684\u6e90\uff0c\u63d0\u5347\u5b89\u88c5\u901f\u5ea6\u3002<\/p>\n<pre><code># \u5347\u7ea7pip\npython -m pip install --upgrade pip\n# \u66f4\u6362 pypi \u6e90\u52a0\u901f\u5e93\u7684\u5b89\u88c5\npip config set global.index-url https:\/\/pypi.tuna.tsinghua.edu.cn\/simple<\/code><\/pre>\n<p>\u7b2c\u4e8c\u6b65\uff1a\u8bbf\u95eehttps:\/\/pytorch.org\/ ,\u6839\u636e\u81ea\u5df1\u673a\u5668\u7684\u73af\u5883\u9009\u62e9\u5bf9\u5e94\u7684pytorch\u5b89\u88c5\u547d\u4ee4<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602121815834.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602121815834.png\" alt=\"\" \/><\/a><\/p>\n<p>\u7b2c\u4e09\u6b65\uff1a\u542f\u52a8\u547d\u4ee4\u884c\uff0c\u8fd0\u884c\u5bf9\u5e94\u7684\u5b89\u88c5\u547d\u4ee4<\/p>\n<blockquote>\n<p>\u6ce8\u610f\uff1a\u5982\u679c\u4f7f\u7528\u7684\u662fjupyter\uff0c\u5efa\u8bae\u901a\u8fc7\u5f00\u59cb\u83dc\u5355\u542f\u52a8anaconda prompt\u7684\u65b9\u5f0f\u8fd0\u884c\u547d\u4ee4\u884c<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/c9cfce6df27f35195697ce1f8c049b6.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/c9cfce6df27f35195697ce1f8c049b6.png\" alt=\"\" \/><\/a><\/p>\n<pre><code># \u5982\u679c\u64cd\u4f5c\u7cfb\u7edf=window\u3001\u663e\u5361\u6709\u82f1\u4f1f\u8fbe\u663e\u5361\u3001\u663e\u5b58&gt;4G\uff0c\u5219\u53ef\u4ee5\u8fd0\u884c\u5982\u4e0b\u547d\u4ee4\uff1a\npip3 install torch torchvision torchaudio --index-url https:\/\/download.pytorch.org\/whl\/cu121<\/code><\/pre>\n<pre><code># \u5982\u679c\u64cd\u4f5c\u7cfb\u7edf=window\u3001\u65e0\u82f1\u4f1f\u8fbe\u663e\u5361\u3001\u663e\u5b58\u4e0d\u591f\u53ea\u80fd\u4f7f\u7528CPU\uff0c\u5219\u53ef\u4ee5\u8fd0\u884c\u5982\u4e0b\u5b89\u88c5\u547d\u4ee4\uff1a\npip3 install torch torchvision torchaudio<\/code><\/pre>\n<pre><code># \u5982\u679c\u64cd\u4f5c\u7cfb\u7edf=Mac\uff0c\u5219\u53ef\u4ee5\u8fd0\u884c\u5982\u4e0b\u5b89\u88c5\u547d\u4ee4\uff1a\npip3 install torch torchvision torchaudio<\/code><\/pre>\n<pre><code># \u5982\u679c\u64cd\u4f5c\u7cfb\u7edf=Linux\uff0c\u5219\u53ef\u4ee5\u8fd0\u884c\u5982\u4e0b\u5b89\u88c5\u547d\u4ee4\uff1a\npip3 install torch torchvision torchaudio\n<\/code><\/pre>\n<p>\u663e\u793a\u5982\u4e0b\u63d0\u793a\u5373\u6210\u529f\u5b89\u88c5<br \/>\n<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602133221763.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602133221763.png\" alt=\"\" \/><\/a><\/p>\n<blockquote>\n<p>\u5982\u679c\u6ca1\u6709GPU\u73af\u5883\u6216\u8005\u5b89\u88c5pytorch\u4e00\u76f4\u4e0d\u6210\u529f\u7684\u8bdd\uff0c\u4e5f\u53ef\u4ee5\u8003\u8651\u79df\u7528\u4e91\u7aefGPU\u670d\u52a1\u5668\u3002\u5177\u4f53\u65b9\u6cd5\u8bf7\u89c1\u2192<a href=\"https:\/\/17aitech.com\/?p=2018\">\u300aAutoDL\u5e73\u53f0\u7684\u4f7f\u7528\u6307\u5357\u300b<\/a><\/p>\n<\/blockquote>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%93%8D%E4%BD%9C%E4%BD%BF%E7%94%A8torch\"><\/span>\u77e9\u9635\u7684\u57fa\u672c\u64cd\u4f5c(\u4f7f\u7528torch)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-python\">import torch\n\n# \u5feb\u901f\u6784\u5efa\u77e9\u9635\nmatrix = torch.tensor([[1, 2, 3], [4, 5, 6]])\n\nprint(&quot;\u77e9\u9635\u6570\u636e\uff1a&quot;, matrix)\n\n# \u67e5\u770b\u77e9\u9635\u7684\u7ef4\u5ea6\u4fe1\u606f\nprint(&quot;\u77e9\u9635\u7ef4\u5ea6\uff1a&quot;, matrix.dim())\n\n# \u67e5\u770b\u77e9\u9635\u7684\u5f62\u72b6\nprint(&quot;\u77e9\u9635\u5f62\u72b6\uff1a&quot;, matrix.size())\n\n# \u67e5\u770b\u77e9\u9635\u7684size\nprint(&quot;\u77e9\u9635size\uff1a&quot;, matrix.numel())\n\n# \u5bf9\u77e9\u9635\u8fdb\u884creshape\u4e3a\u4e00\u4e2a\u77e9\u9635\nreshaped_matrix = matrix.view(3, 2)\nprint(&quot;\u91cd\u5851\u540e\u7684\u77e9\u9635\uff1a\\n&quot;, reshaped_matrix)\n\n# \u4fee\u6539\u77e9\u9635\u4e2d\u7684\u6570\u636e\u5185\u5bb9\nmatrix[0, 1] = 10\nprint(&quot;\u4fee\u6539\u540e\u7684\u77e9\u9635\uff1a\\n&quot;, matrix)\n\n# \u5c06\u77e9\u9635\u7684\u6570\u636e\u7c7b\u578b\u8f6c\u6362\nmatrix = matrix.type(torch.float)\nprint(&quot;\u8f6c\u6362\u6570\u636e\u7c7b\u578b\u540e\u7684\u77e9\u9635\uff1a\\n&quot;, matrix)\n\n# \u968f\u673a\u751f\u6210\u4e00\u4e2a\u65b0\u7684\u77e9\u9635\nnew_matrix = torch.rand(2, 3)\nprint(&quot;\u968f\u673a\u751f\u6210\u7684\u65b0\u77e9\u9635\uff1a\\n&quot;, new_matrix)<\/code><\/pre>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E7%94%9F%E6%88%90%E4%BD%BF%E7%94%A8torch\"><\/span>\u77e9\u9635\u7684\u751f\u6210(\u4f7f\u7528torch)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-py\">import torch\n\n# \u751f\u6210\u4e00\u4e2a\u5f62\u72b6\u4e3a (3, 4, 5) \u7684\u6570\u7ec4,\u5185\u5bb9\u90fd\u4e3a0\ntensor_zeros = torch.zeros((3, 4, 5))\nprint(tensor_zeros)\n\n# \u751f\u6210\u4e00\u4e2a\u5f62\u72b6\u4e3a (3, 4, 5) \u7684\u6570\u7ec4,\u5185\u5bb9\u90fd\u4e3a1\ntensor_ones = torch.ones((3, 4, 5))\nprint(tensor_ones)\n\n# \u751f\u6210\u4e00\u4e2a\u5f62\u72b6\u4e3a (3, 4, 5) \u7684\u6570\u7ec4\uff0c\u5185\u5bb9\u4e3a\u968f\u673a\ntensor_random = torch.rand(3, 4, 5)\nprint(tensor_random)\n<\/code><\/pre>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E5%A0%86%E5%8F%A0%E5%92%8C%E6%8B%BC%E6%8E%A5%E4%BD%BF%E7%94%A8torch\"><\/span>\u77e9\u9635\u7684\u5806\u53e0\u548c\u62fc\u63a5(\u4f7f\u7528torch)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-python\">import torch\n\na = torch.arange(1, 28).reshape(3, 3, 3)\nb = torch.arange(28, 55).reshape(3, 3, 3)\n\n#  torch.cat((a, b), dim=2) \u4e0e torch.stack((a, b), dim=2) \u6548\u679c\u4e00\u6837\nprint(&quot;torch.stack((a, b), dim=2)\uff1a&quot;, torch.stack((a, b), dim=2))\nprint(&quot;torch.cat((a, b), dim=2)\uff1a&quot;, torch.cat((a, b), dim=2))\n\n#  torch.cat((a, b), dim=1) \u4e0e torch.stack((a, b), dim=1) \u6548\u679c\u4e00\u6837\nprint(&quot;torch.stack((a, b), dim=1)\uff1a&quot;, torch.stack((a, b), dim=1))\nprint(&quot;torch.cat((a, b), dim=1)\uff1a&quot;, torch.cat((a, b), dim=1))\n\n#  torch.cat((a, b), dim=0) \u4e0e torch.stack((a, b), dim=0) \u6548\u679c\u4e00\u6837\nprint(&quot;torch.stack((a, b), dim=0)\uff1a&quot;, torch.stack((a, b), dim=0))\nprint(&quot;torch.cat((a, b), dim=0)\uff1a&quot;, torch.cat((a, b), dim=0))\n<\/code><\/pre>\n<p>\u901a\u8fc7\u4ee5\u4e0a\u5bf9\u6bd4\u53ef\u4ee5\u53d1\u73b0<\/p>\n<ul>\n<li>\n<p>numpy\u548ctorch\u7684\u4f7f\u7528\u65b9\u6cd5\u57fa\u672c\u4e00\u81f4\uff0cnumpy\u652f\u6301\u7684\u8ba1\u7b97\u65b9\u6cd5torch\u4e5f\u652f\u6301\u3002<\/p>\n<\/li>\n<li>\n<p>\u4e24\u8005\u90fd\u63d0\u4f9b\u4e86\u7c7b\u4f3c\u7684\u6570\u7ec4\/(torch\u91cc\u53eb\u5f20\u91cf)\u64cd\u4f5c\uff0c\u5982\u7d22\u5f15\u3001\u5207\u7247\u3001\u5e7f\u64ad\u3001\u6570\u5b66\u8fd0\u7b97\u7b49\u3002<\/p>\n<\/li>\n<li>\n<p>numpy\u4e5f\u53ef\u4ee5\u4e0etorch\u8fdb\u884c\u4e92\u8f6c\uff0c\u4f8b\u5982\uff1a<\/p>\n<pre><code class=\"language-python\">import numpy as np\nimport torch\n\n# \u521b\u5efa\u4e00\u4e2a NumPy \u6570\u7ec4\nnumpy_array = np.array([[1, 2, 3], [4, 5, 6]])\n\n# \u5c06 NumPy \u6570\u7ec4\u8f6c\u6362\u4e3a PyTorch \u5f20\u91cf\ntorch_tensor = torch.from_numpy(numpy_array)\n\n# \u521b\u5efa\u4e00\u4e2a PyTorch \u5f20\u91cf\ntorch_tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])\n\n# \u5c06 PyTorch \u5f20\u91cf\u8f6c\u6362\u4e3a NumPy \u6570\u7ec4\nnumpy_array = torch_tensor.numpy()\n\nprint(\"NumPy \u6570\u7ec4\uff1a\\n\", numpy_array)\nprint(\"PyTorch \u5f20\u91cf\uff1a\\n\", torch_tensor)<\/code><\/pre>\n<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"%E6%95%B0%E6%8D%AE%E4%BF%A1%E6%81%AF\"><\/span>\u6570\u636e\u4fe1\u606f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E5%9F%BA%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F\"><\/span>\u57fa\u672c\u7edf\u8ba1\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h5><span class=\"ez-toc-section\" id=\"%E5%9D%87%E5%80%BC%EF%BC%88Mean%EF%BC%89\"><\/span><strong>\u5747\u503c\uff08Mean\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u5747\u503c\u662f\u4e00\u7ec4\u6570\u636e\u4e2d\u6240\u6709\u6570\u636e\u503c\u7684\u603b\u548c\u9664\u4ee5\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u4e00\u7ec4\u6570\u636e\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u5747\u503c <code class=\"katex-inline\">\\mu = \\frac{\\sum_{i=1}^{n} x_i}{n}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">x_i<\/code> \u662f\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<h5><span class=\"ez-toc-section\" id=\"%E6%A0%87%E5%87%86%E5%B7%AE%EF%BC%88Standard_Deviation%EF%BC%89\"><\/span><strong>\u6807\u51c6\u5dee\uff08Standard Deviation\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839\uff0c\u7528\u4e8e\u8861\u91cf\u6570\u636e\u503c\u7684\u79bb\u6563\u7a0b\u5ea6\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u6570\u636e\u7684\u79bb\u6563\u7a0b\u5ea6\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u6807\u51c6\u5dee <code class=\"katex-inline\">\\sigma = \\sqrt{\\frac{\\sum_{i=1}^{n} (x_i - \\mu)^2}{n}}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">x_i<\/code> \u662f\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">\\mu<\/code> \u662f\u5747\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<h5><span class=\"ez-toc-section\" id=\"%E6%96%B9%E5%B7%AE%EF%BC%88Variance%EF%BC%89\"><\/span><strong>\u65b9\u5dee\uff08Variance\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u65b9\u5dee\u662f\u6bcf\u4e2a\u6570\u636e\u503c\u4e0e\u5747\u503c\u4e4b\u5dee\u7684\u5e73\u65b9\u7684\u5e73\u5747\u503c\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u6570\u636e\u4e0e\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u7a0b\u5ea6\u3002\uff08\u5982\u679c\u6bd4\u8f83\u79bb\u6563\u7684\u8bdd\uff0c\u65b9\u5dee\u8d8a\u5927\uff1b\u5982\u679c\u6bd4\u8f83\u96c6\u4e2d\u7684\u8bdd\uff0c\u65b9\u5dee\u8d8a\u5c0f\uff09<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u65b9\u5dee <code class=\"katex-inline\">\\sigma^2 = \\frac{\\sum_{i=1}^{n} (x_i - \\mu)^2}{n}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">x_i<\/code> \u662f\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">\\mu<\/code> \u662f\u5747\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<pre><code class=\"language-python\">import numpy as np\n\n# \u793a\u4f8b\u6570\u636e\u96c6\ndata = np.array([1, 2, 3, 4, 5])\n\n# \u8ba1\u7b97\u5747\u503c\nmean = np.mean(data)\n# \u8ba1\u7b97\u6807\u51c6\u5dee\nstd = np.std(data)\n# \u8ba1\u7b97\u65b9\u5dee\nvariance = np.var(data)\n\nprint(&quot;\u5747\u503c:&quot;, mean)\nprint(&quot;\u6807\u51c6\u5dee:&quot;, std)\nprint(&quot;\u65b9\u5dee:&quot;, variance)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716965434335.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716965434335.png\" alt=\"file\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86\"><\/span>\u6570\u636e\u9884\u5904\u7406<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h5><span class=\"ez-toc-section\" id=\"%E5%BD%92%E4%B8%80%E5%8C%96%EF%BC%88Normalization%EF%BC%89_%E7%BA%BF%E6%80%A7%E6%98%A0%E5%B0%84%EF%BC%9A\"><\/span>\u5f52\u4e00\u5316\uff08Normalization\uff09\/ \u7ebf\u6027\u6620\u5c04\uff1a<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u5904\u7406\u65b9\u5f0f\uff1a\u5c06\u6570\u636e\u7f29\u653e\u5230\u4e00\u4e2a\u7279\u5b9a\u7684\u8303\u56f4\uff0c\u901a\u5e38\u662f[0, 1]\u6216[-1, 1]\u3002<\/li>\n<li>\u4f7f\u7528\u573a\u666f\uff1a\u5728\u4f7f\u7528\u57fa\u4e8e\u8ddd\u79bb\u7684\u7b97\u6cd5\uff08\u5982KNN\u3001SVM\uff09\u65f6\uff0c\u9700\u8981\u5bf9\u7279\u5f81\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u4ee5\u907f\u514d\u67d0\u4e9b\u7279\u5f81\u5bf9\u8ddd\u79bb\u8ba1\u7b97\u7684\u5f71\u54cd\u8fc7\u5927\u3002\u4f8b\u5982\uff0c\u5728\u4eba\u8138\u8bc6\u522b\u4e2d\uff0c\u5bf9\u56fe\u50cf\u7279\u5f81\u8fdb\u884c\u5f52\u4e00\u5316\u53ef\u4ee5\u786e\u4fdd\u4e0d\u540c\u7279\u5f81\u4e4b\u95f4\u7684\u6743\u91cd\u76f8\u5bf9\u5e73\u8861\uff0c\u63d0\u9ad8\u8bc6\u522b\u51c6\u786e\u6027\u3002<\/li>\n<\/ul>\n<blockquote>\n<p>\u5907\u6ce8\uff1a\u8fd9\u91cc\u7684\u5f52\u4e00\u5316\u5bb9\u6613\u4e0e\u4e0a\u7bc7\u8bfe\u7a0b<a href=\"https:\/\/17aitech.com\/?p=1945\">\u76ae\u5c14\u900a\u7cfb\u6570\uff1a\u534f\u65b9\u5dee\u7684\u5f52\u4e00\u5316<\/a>\u641e\u6df7\uff0c\u4ed4\u7ec6\u67e5\u770b\u76ae\u5c14\u900a\u7cfb\u6570\u662f\u5c06\u4e24\u5217\u6570\u636e\u53d8\u5316\u8d8b\u52bf\u5f52\u4e00\u5316\u5230[-1,1]\u4e4b\u95f4\uff1b\u6b64\u5904\u7684\u5f52\u4e00\u5316\u662f\u5c06\u4e00\u7ec4\u6570\u636e\u5f52\u4e00\u5316\u5230[-1,1]\u4e4b\u95f4\u3002<\/p>\n<\/blockquote>\n<pre><code class=\"language-python\">import numpy as np\n\n# \u521b\u5efa\u793a\u4f8b\u6570\u636e\ndata = np.array([1, 2, 3, 4, 5])\n\n# \u6570\u636e\u5f52\u4e00\u5316\nnormalized_data = (data - np.min(data)) \/ (np.max(data) - np.min(data))\n\nprint(&quot;\u5f52\u4e00\u5316\u540e\u7684\u6570\u636e\uff1a&quot;, normalized_data)\n<\/code><\/pre>\n<h5><span class=\"ez-toc-section\" id=\"%E5%8E%BB%E4%B8%AD%E5%BF%83%E5%8C%96%EF%BC%88Mean_Normalization%EF%BC%89_%E5%8E%BB%E5%9D%87%E5%80%BC_center_data%EF%BC%9A\"><\/span>\u53bb\u4e2d\u5fc3\u5316\uff08Mean Normalization\uff09\/ \u53bb\u5747\u503c \/ center data\uff1a<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u5904\u7406\u65b9\u5f0f\uff1a\u8ba1\u7b97\u6570\u636e\u96c6\u7684\u5747\u503c\uff0c\u901a\u8fc7\u51cf\u53bb\u5747\u503c\u6765\u5b9e\u73b0\uff0c\u4e3b\u8981\u7528\u4e8e\u89c2\u5bdf\u6570\u636e\u4e2d\u54ea\u4e9b\u6570\u636e&quot;\u505a\u4e86\u8d21\u732e(\u6b63\u6570)&quot;\uff0c\u54ea\u4e9b\u6570\u636e&quot;\u62d6\u540e\u817f&quot;(\u8d1f\u6570)\u3002<\/li>\n<li>\u4f7f\u7528\u573a\u666f\uff1a\u5728\u5904\u7406\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u65f6\uff0c\u53bb\u4e2d\u5fc3\u5316\u53ef\u4ee5\u6d88\u9664\u6570\u636e\u7684\u8d8b\u52bf\u548c\u5b63\u8282\u6027\u53d8\u5316\uff0c\u4f7f\u6a21\u578b\u66f4\u5bb9\u6613\u6355\u6349\u6570\u636e\u7684\u5468\u671f\u6027\u3002\u4f8b\u5982\uff0c\u5728\u80a1\u7968\u5e02\u573a\u5206\u6790\u4e2d\uff0c\u53bb\u4e2d\u5fc3\u5316\u53ef\u4ee5\u5e2e\u52a9\u8bc6\u522b\u80a1\u7968\u4ef7\u683c\u7684\u77ed\u671f\u6ce2\u52a8\u3002<\/li>\n<\/ul>\n<pre><code class=\"language-python\">import numpy as np\n\n# \u521b\u5efa\u793a\u4f8b\u6570\u636e\ndata = np.array([1, 2, 3, 4, 5])\n\n# \u8ba1\u7b97\u6570\u636e\u7684\u5e73\u5747\u503c\nmean = np.mean(data)\n\n# \u53bb\u4e2d\u5fc3\u5316\nzero_centered_data = data - mean\n\nprint(&quot;\u53bb\u4e2d\u5fc3\u5316\u540e\u7684\u6570\u636e\uff1a&quot;, zero_centered_data)<\/code><\/pre>\n<h5><span class=\"ez-toc-section\" id=\"%E8%A7%84%E8%8C%83%E5%8C%96%EF%BC%88Standardization%EF%BC%89_%E8%A7%84%E8%8C%83%E5%8C%96%EF%BC%9A\"><\/span>\u89c4\u8303\u5316\uff08Standardization\uff09\/ \u89c4\u8303\u5316\uff1a<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u5904\u7406\u65b9\u5f0f\uff1a\u5c06\u6570\u636e\u8f6c\u6362\u4e3a\u5747\u503c\u4e3a0\uff0c\u6807\u51c6\u5dee\u4e3a1\u7684\u5206\u5e03\uff0c\u4e3b\u8981\u7528\u4e8e\u4e00\u773c\u770b\u51fa\u54ea\u4e9b\u6570\u636e\u662f\u566a\u58f0(\u4e5f\u53eb\u79bb\u7fa4\u70b9)<\/li>\n<li>\u4f7f\u7528\u573a\u666f\uff1a\u5728\u4f7f\u7528\u9700\u8981\u6807\u51c6\u6b63\u6001\u5206\u5e03\u6570\u636e\u7684\u6a21\u578b\uff08\u5982\u7ebf\u6027\u56de\u5f52\u3001\u903b\u8f91\u56de\u5f52\uff09\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u89c4\u8303\u5316\u3002\u4f8b\u5982\uff0c\u5728\u6587\u672c\u5206\u7c7b\u4e2d\uff0c\u5bf9\u6587\u672c\u7279\u5f81\u8fdb\u884c\u89c4\u8303\u5316\u53ef\u4ee5\u63d0\u9ad8\u5206\u7c7b\u5668\u7684\u51c6\u786e\u6027\u548c\u7a33\u5b9a\u6027\u3002<\/li>\n<\/ul>\n<pre><code class=\"language-python\">import numpy as np\n\n# \u521b\u5efa\u793a\u4f8b\u6570\u636e\ndata = np.array([1, 2, 3, 4, 5])\n\n# \u8ba1\u7b97\u6570\u636e\u7684\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\nmean = np.mean(data)\nstd = np.std(data)\n\n# \u89c4\u8303\u5316\nstandardized_data = (data - mean) \/ std\n\nprint(&quot;\u89c4\u8303\u5316\u540e\u7684\u6570\u636e\uff1a&quot;, standardized_data)\n<\/code><\/pre>\n<h4><span class=\"ez-toc-section\" id=\"%E4%BF%A1%E6%81%AF%E8%95%B4%E5%90%AB%E5%9C%A8%E6%95%B0%E6%8D%AE%E7%9A%84%E7%9B%B8%E5%AF%B9%E5%A4%A7%E5%B0%8F\"><\/span>\u4fe1\u606f\u8574\u542b\u5728\u6570\u636e\u7684\u76f8\u5bf9\u5927\u5c0f<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u4fe1\u606f\u5f80\u5f80\u8574\u542b\u5728\u6570\u636e\u7684\u76f8\u5bf9\u5927\u5c0f\u4e2d\u3002<\/strong><\/p>\n<p>\u4e3a\u4e86\u4fbf\u4e8e\u7406\u89e3\u8fd9\u53e5\u8bdd\uff0c\u6211\u4eec\u901a\u8fc7\u4ee5\u4e0b\u4ee3\u7801\u6765\u76f4\u89c2\u4e86\u89e3\u3002<\/p>\n<pre><code class=\"language-python\">from matplotlib import pyplot as plt\nimport numpy as np\n\n# \u751f\u6210\u968f\u673a\u5206\u6570\u6570\u636e\nscores = np.random.randint(low=0, high=101, size=(50,))\n\n# \u4e2d\u5fc3\u5316\/\u53bb\u5747\u503c\/center data\ncentered_scores = scores - scores.mean()\n\n# \u5f52\u4e00\u5316\uff08\u628a\u6240\u6709\u7684\u6570\u636e\u7ebf\u6027\u6620\u5c04\u5230[0, 1]\uff09\nnormalized_scores = (scores - scores.min()) \/ (scores.max() - scores.min())\n\n# \u6807\u51c6\u5316\/\u89c4\u8303\u5316\u51cf\u5747\u503c\uff0c\u9664\u4ee5\u6807\u51c6\u5dee\nstandardized_scores = (scores - scores.mean()) \/ scores.std()\n\n# \u521b\u5efa\u56db\u4e2a\u5b50\u56fe\u5e76\u7ed8\u5236\u6570\u636e\nfig, axs = plt.subplots(2, 2, figsize=(12, 8))\n\naxs[0, 0].plot(scores)\naxs[0, 0].set_title(&#039;Original Scores&#039;)\n\naxs[0, 1].plot(centered_scores)\naxs[0, 1].set_title(&#039;Centered Scores&#039;)\n\naxs[1, 0].plot(normalized_scores)\naxs[1, 0].set_title(&#039;Normalized Scores&#039;)\n\naxs[1, 1].plot(standardized_scores)\naxs[1, 1].set_title(&#039;Standardized Scores&#039;)\n\nplt.tight_layout()\nplt.show()\n<\/code><\/pre>\n<p>\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602184413296.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/06\/image-20240602184413296.png\" alt=\"\" \/><\/a><\/p>\n<p>\u901a\u8fc7\u4ee5\u4e0a\u7684\u5bf9\u6bd4\u53ef\u4ee5\u770b\u5230\uff0c\u4e2d\u5fc3\u5316Scores\u3001\u5f52\u4e00\u5316Scores\u3001\u6807\u51c6\u5316Scores\u7684\u6570\u636e\u867d\u7136\u88ab\u4fee\u6539\u4e86\uff0c\u4e0e\u539f\u59cbScores\u4e0d\u4e00\u6837\uff0c\u4f46\u662f\u6570\u636e\u4e2d\u6240\u8868\u8fbe\u7684\u4fe1\u606f(\u66f2\u7ebf)\u4ecd\u7136\u6ca1\u6709\u4e22\u5931\uff0c\u8fd9\u5373\u662f\u4fe1\u606f\u8574\u542b\u5728\u6570\u636e\u7684\u76f8\u5bf9\u5927\u5c0f\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86%E7%9A%84%E5%BA%94%E7%94%A8\"><\/span>\u6570\u636e\u9884\u5904\u7406\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u5f53\u4e2d\uff0c\u6211\u4eec\u5f80\u5f80\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u5904\u7406\uff0c\u4ee5\u63d0\u5347\u6570\u636e\u8d28\u91cf\uff0c\u4f7f\u5f97\u4e0d\u540c\u7279\u5f81\u5177\u6709\u76f8\u4f3c\u7684\u5c3a\u5ea6\uff0c\u6709\u52a9\u4e8e\u6a21\u578b\u7684\u6536\u655b\u548c\u6027\u80fd\u63d0\u5347\u3002\u4ee5\u4e0b\u4ecd\u7136\u4f7f\u7528\u9e22\u5c3e\u82b1\u7684\u793a\u4f8b\uff0c\u6765\u5b9e\u9645\u9a8c\u8bc1\u4e0b\u6570\u636e\u9884\u5904\u7406\u662f\u5426\u4f1a\u5bf9\u51c6\u786e\u7387\u6709\u5f71\u54cd\u3002<\/p>\n<h5><span class=\"ez-toc-section\" id=\"%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86%E7%9A%84%E5%8E%9F%E5%88%99\"><\/span>\u6570\u636e\u9884\u5904\u7406\u7684\u539f\u5219<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ol>\n<li>\n<p>\u7279\u5f81\u548c\u6807\u7b7e\u90fd\u9700\u8981\u9884\u5904\u7406\u3002<\/p>\n<ul>\n<li>\u4e00\u822c\u6765\u8bf4\uff0c\u53ea\u9700\u8981\u9884\u5904\u7406\u7279\u5f81\u5373\u53ef<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u9700\u8981\u505a<strong>\u4e00\u6a21\u4e00\u6837<\/strong>\u7684\u9884\u5904\u7406\u3002<\/p>\n<\/li>\n<li>\n<p>\u9884\u5904\u7406\u9700\u8981\u7684\u53c2\u6570\uff0c\u4ece\u8bad\u7ec3\u96c6\u4e2d\u63d0\u53d6<\/p>\n<blockquote>\n<p>\u4f8b\u5982\uff1a\u51cf\u5747\u503c\u65f6\uff0c\u5747\u503c\u4ece\u8bad\u7ec3\u96c6\u4e2d\u83b7\u5f97\u3002\u539f\u56e0\u662f\uff1a\u8bad\u7ec3\u96c6\u4ee3\u8868\u5ba2\u89c2\u4e16\u754c\u3002<\/p>\n<\/blockquote>\n<\/li>\n<\/ol>\n<pre><code class=\"language-python\">from sklearn.datasets import load_iris\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.tree import DecisionTreeClassifier\nfrom sklearn.tree import plot_tree\nimport matplotlib.pyplot as plt\n\n# \u52a0\u8f7d\u5f00\u6e90\u5e93\u4e2d\u7684iris\u6570\u636e\u96c6\nX,y = load_iris(return_X_y=True)\n\n# \u5207\u5206\u6570\u636e\u96c6\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, \n                                                    shuffle=True, \n                                                    random_state=0) \n\n# \u539f\u59cb\u6570\u636e\u9884\u6d4b\nfrom sklearn.tree import DecisionTreeClassifier\n\n# 1, \u6784\u5efa\u6a21\u578b\ndtc0 = DecisionTreeClassifier(criterion=&#039;gini&#039;)\n\n# 2, \u8bad\u7ec3\u6a21\u578b\ndtc0.fit(X=X_train, y=y_train)\n\n# 3, \u8bc4\u4f30\u6a21\u578b\n\nacc = (dtc0.predict(X=X_test) == y_test).mean()\nacc<\/code><\/pre>\n<pre><code class=\"language-python\"># \u9884\u5904\u7406\u65b9\u5f0f\u4e00\uff1a\u51cf\u5747\u503c(\u4e2d\u5fc3\u5316)\nX_train1 = X_train - _mean\nX_test1 = X_test - _mean\n\n# \u4f7f\u7528\u539f\u59cb\u6570\u636e\nfrom sklearn.tree import DecisionTreeClassifier\n\n# 1, \u6784\u5efa\u6a21\u578b\ndtc1 = DecisionTreeClassifier(criterion=&#039;gini&#039;)\n\n# 2, \u8bad\u7ec3\u6a21\u578b\ndtc1.fit(X=X_train1, y=y_train)\n\n# 3, \u8bc4\u4f30\u6a21\u578b\n\nacc = (dtc1.predict(X=X_test1) == y_test).mean()\nacc<\/code><\/pre>\n<pre><code class=\"language-python\"># \u9884\u5904\u7406\u65b9\u5f0f\u4e8c\uff1a\u5f52\u4e00\u5316\nX_train2 = (X_train - _min) \/ (_max - _min)\nX_test2 =(X_test - _min) \/ (_max - _min)\n\n# \u4f7f\u7528\u539f\u59cb\u6570\u636e\nfrom sklearn.tree import DecisionTreeClassifier\n\n# 1, \u6784\u5efa\u6a21\u578b\ndtc2 = DecisionTreeClassifier(criterion=&#039;gini&#039;)\n\n# 2, \u8bad\u7ec3\u6a21\u578b\ndtc2.fit(X=X_train2, y=y_train)\n\n# 3, \u8bc4\u4f30\u6a21\u578b\n\nacc = (dtc2.predict(X=X_test2) == y_test).mean()\nacc<\/code><\/pre>\n<pre><code class=\"language-python\"># \u9884\u5904\u7406\u65b9\u5f0f\u4e09\uff1a\u89c4\u8303\u5316\nX_train3 = (X_train - _mean) \/ (_std + 1e-9)\nX_test3 =(X_test - _mean) \/ (_std + 1e-9)\n\n# \u4f7f\u7528\u539f\u59cb\u6570\u636e\nfrom sklearn.tree import DecisionTreeClassifier\n\n# 1, \u6784\u5efa\u6a21\u578b\ndtc3 = DecisionTreeClassifier(criterion=&#039;gini&#039;)\n\n# 2, \u8bad\u7ec3\u6a21\u578b\ndtc3.fit(X=X_train3, y=y_train)\n\n# 3, \u8bc4\u4f30\u6a21\u578b\n\nacc = (dtc3.predict(X=X_test3) == y_test).mean()\nacc<\/code><\/pre>\n<p>\u4f9d\u6b21\u6267\u884c\u4ee5\u4e0a\u4ee3\u7801\uff0c\u53ef\u4ee5\u770b\u5230\u539f\u59cb\u6570\u636e\u3001\u5f52\u4e00\u5316\u6570\u636e\u3001\u53bb\u4e2d\u5fc3\u5316\u6570\u636e\u3001\u89c4\u8303\u5316\u6570\u636e\u5728\u8bad\u7ec3\u4e4b\u540e\uff0c\u9884\u6d4b\u7ed3\u679c\u90fd\u4e3a1.0\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%86%85%E5%AE%B9%E5%B0%8F%E7%BB%93\"><\/span>\u5185\u5bb9\u5c0f\u7ed3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u5728\u6570\u636e\u79d1\u5b66\u8ba1\u7b97\u65f6\uff0c\u6709\u4e24\u5927\u5de5\u5177\u53ef\u4ee5\u4f7f\u7528\uff1aNumpy\u548cPytorch<\/li>\n<li>Numpy\u4f7f\u7528\u7684\u662fCPU\u8fdb\u884c\u8ba1\u7b97\uff0c\u66f4\u9002\u5408\u4f20\u7edf\u7684\u6570\u503c\u8ba1\u7b97\u4efb\u52a1\uff1bPyTorch \u53ef\u4ee5\u4f7f\u7528GPU\u8ba1\u7b97\uff0c\u66f4\u9002\u5408\u6df1\u5ea6\u5b66\u4e60\u4efb\u52a1\u3002<\/li>\n<li>\u4fe1\u606f\u8574\u542b\u5728\u6570\u636e\u7684\u76f8\u5bf9\u5927\u5c0f\u4e2d\uff0c\u5373\u662f\u5bf9\u6570\u636e\u505a\u4e86\u4fee\u6539\u4f46\u6ca1\u6709\u6539\u53d8\u76f8\u5bf9\u5927\u5c0f\uff0c\u90a3\u4e48\u4fe1\u606f\u4ecd\u7136\u5b58\u5728\u3002<\/li>\n<li>\u5728\u673a\u5668\u5b66\u4e60\u5f53\u4e2d\uff0c\u6211\u4eec\u5f80\u5f80\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u5904\u7406\uff0c\u4ee5\u63d0\u5347\u6570\u636e\u8d28\u91cf\uff0c\u4f7f\u5f97\u4e0d\u540c\u7279\u5f81\u5177\u6709\u76f8\u4f3c\u7684\u5c3a\u5ea6\uff0c\u6709\u52a9\u4e8e\u6a21\u578b\u7684\u6536\u655b\u548c\u6027\u80fd\u63d0\u5347\u3002<\/li>\n<li>\u6570\u636e\u9884\u5904\u7406\u7684\u65b9\u5f0f\u4e00\u822c\u6709\u5f52\u4e00\u5316\u3001\u53bb\u4e2d\u5fc3\u5316\u3001\u89c4\u8303\u5316\u3002\n<ul>\n<li>\u5f52\u4e00\u5316\uff1a\u5c06\u6570\u636e\u7f29\u653e\u5230\u4e00\u4e2a\u7279\u5b9a\u7684\u8303\u56f4\uff0c\u901a\u5e38\u662f[0, 1]\u6216[-1, 1]<\/li>\n<li>\u53bb\u4e2d\u5fc3\u5316\uff1a\u8ba1\u7b97\u6570\u636e\u96c6\u7684\u5747\u503c\uff0c\u901a\u8fc7\u51cf\u53bb\u5747\u503c\u6765\u5b9e\u73b0\uff0c\u4e3b\u8981\u7528\u4e8e\u89c2\u5bdf\u6570\u636e\u4e2d\u54ea\u4e9b\u6570\u636e&quot;\u505a\u4e86\u8d21\u732e(\u6b63\u6570)&quot;\uff0c\u54ea\u4e9b\u6570\u636e&quot;\u62d6\u540e\u817f&quot;(\u8d1f\u6570)\u3002<\/li>\n<li>\u89c4\u8303\u5316\uff1a\u5c06\u6570\u636e\u8f6c\u6362\u4e3a\u5747\u503c\u4e3a0\uff0c\u6807\u51c6\u5dee\u4e3a1\u7684\u5206\u5e03\uff0c\u4e3b\u8981\u7528\u4e8e\u4e00\u773c\u770b\u51fa\u54ea\u4e9b\u6570\u636e\u662f\u566a\u58f0(\u4e5f\u53eb\u79bb\u7fa4\u70b9)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p align=\"center\">\u6b22\u8fce\u5173\u6ce8\u516c\u4f17\u53f7\u4ee5\u83b7\u5f97\u6700\u65b0\u7684\u6587\u7ae0\u548c\u65b0\u95fb<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/09\/\u626b\u7801_\u641c\u7d22\u8054\u5408\u4f20\u64ad\u6837\u5f0f-\u767d\u8272\u7248.bmp\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/09\/\u626b\u7801_\u641c\u7d22\u8054\u5408\u4f20\u64ad\u6837\u5f0f-\u767d\u8272\u7248.bmp\" alt=\"\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u636e\u79d1\u5b66\u57fa\u7840 \u79d1\u5b66\u8ba1\u7b97\u795e\u5668\u4e4b\u4e00Numpy [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2016,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"aside","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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