{"id":1869,"date":"2023-04-27T21:35:48","date_gmt":"2023-04-27T12:35:48","guid":{"rendered":"https:\/\/edu.ujhb.org\/?p=1869"},"modified":"2023-04-27T21:35:48","modified_gmt":"2023-04-27T12:35:48","slug":"scipy%e5%85%a5%e9%97%a8%ef%bc%88%e4%b8%ad%e6%96%87%e7%89%88%ef%bc%89","status":"publish","type":"post","link":"https:\/\/edu.ujhb.org\/?p=1869","title":{"rendered":"Scipy\u5165\u95e8\uff08\u4e2d\u6587\u7248\uff09"},"content":{"rendered":"\n<p>\u6211\u662f\u8981\u505aIT\u6559\u7a0b\u7684\u89c6\u9891\uff0c\u4f60\u80fd\u5426\u6839\u636e\u7f51\u7ad9\u7684\u5185\u5bb9\uff0c\u4e3a\u6211\u5b89\u6392\u89c6\u9891\u6559\u7a0b\u7684\u6587\u5b57\u5185\u5bb9\u3002\u6211\u4eec\u5148\u4eceScipy\u6559\u7a0b\u5f00\u59cb\uff0c\u4f60\u5148\u4e3a\u6211\u5217\u51fa\u8981\u8bb2\u89e3\u7684\u5185\u5bb9\u4e00\u89c8\u3002<\/p>\n\n\n\n<p>\u5f53\u7136\u53ef\u4ee5\uff01\u4ee5\u4e0b\u662f\u6839\u636eScipy\u5b98\u65b9\u7f51\u7ad9\u5185\u5bb9\u548c\u4e00\u4e9b\u57fa\u672c\u6559\u7a0b\u6982\u8ff0\u7684\u89c6\u9891\u6559\u7a0b\u5927\u7eb2\u3002\u60a8\u53ef\u4ee5\u6839\u636e\u8fd9\u4e2a\u5927\u7eb2\u6765\u5236\u4f5c\u60a8\u7684IT\u6559\u7a0b\u89c6\u9891\u3002<\/p>\n\n\n\n<p>Scipy\u6559\u7a0b\u89c6\u9891\u5927\u7eb2\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scipy\u7b80\u4ecb\n<ul class=\"wp-block-list\">\n<li>Scipy\u5e93\u7684\u6982\u8ff0<\/li>\n\n\n\n<li>Scipy\u4e0eNumpy\u7684\u5173\u7cfb<\/li>\n\n\n\n<li>\u5b89\u88c5Scipy<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u57fa\u672c\u529f\u80fd\u6a21\u5757\n<ul class=\"wp-block-list\">\n<li>Scipy\u5b50\u6a21\u5757<\/li>\n\n\n\n<li>\u5f15\u5165Scipy\u5e93\u7684\u65b9\u6cd5<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6570\u503c\u79ef\u5206\n<ul class=\"wp-block-list\">\n<li>scipy.integrate\u6a21\u5757<\/li>\n\n\n\n<li>\u56db\u79cd\u5e38\u7528\u79ef\u5206\u51fd\u6570<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u6570\u503c\u79ef\u5206\u8ba1\u7b97<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4f18\u5316\u7b97\u6cd5\n<ul class=\"wp-block-list\">\n<li>scipy.optimize\u6a21\u5757<\/li>\n\n\n\n<li>\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/li>\n\n\n\n<li>\u7ea6\u675f\u4f18\u5316\u95ee\u9898<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u975e\u7ebf\u6027\u65b9\u7a0b\u6c42\u89e3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u63d2\u503c\u65b9\u6cd5\n<ul class=\"wp-block-list\">\n<li>scipy.interpolate\u6a21\u5757<\/li>\n\n\n\n<li>\u4e00\u7ef4\u63d2\u503c<\/li>\n\n\n\n<li>\u4e8c\u7ef4\u63d2\u503c<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u6570\u636e\u63d2\u503c\u5b9e\u73b0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7ebf\u6027\u4ee3\u6570\n<ul class=\"wp-block-list\">\n<li>scipy.linalg\u6a21\u5757<\/li>\n\n\n\n<li>\u77e9\u9635\u5206\u89e3<\/li>\n\n\n\n<li>\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4fe1\u53f7\u5904\u7406\n<ul class=\"wp-block-list\">\n<li>scipy.signal\u6a21\u5757<\/li>\n\n\n\n<li>\u6ee4\u6ce2\u5668\u8bbe\u8ba1<\/li>\n\n\n\n<li>\u4fe1\u53f7\u5206\u6790<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u4fe1\u53f7\u6ee4\u6ce2\u5b9e\u73b0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u56fe\u50cf\u5904\u7406\n<ul class=\"wp-block-list\">\n<li>scipy.ndimage\u6a21\u5757<\/li>\n\n\n\n<li>\u56fe\u50cf\u8fc7\u6ee4<\/li>\n\n\n\n<li>\u56fe\u50cf\u53d8\u6362\u4e0e\u5f62\u6001\u5b66\u64cd\u4f5c<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u56fe\u50cf\u5904\u7406\u5b9e\u8df5<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7edf\u8ba1\u5206\u6790\n<ul class=\"wp-block-list\">\n<li>scipy.stats\u6a21\u5757<\/li>\n\n\n\n<li>\u63cf\u8ff0\u6027\u7edf\u8ba1<\/li>\n\n\n\n<li>\u6982\u7387\u5206\u5e03<\/li>\n\n\n\n<li>\u53c2\u6570\u4f30\u8ba1\u4e0e\u5047\u8bbe\u68c0\u9a8c<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u7edf\u8ba1\u5206\u6790\u5e94\u7528<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6587\u4ef6\u8f93\u5165\u8f93\u51fa\n<ul class=\"wp-block-list\">\n<li>scipy.io\u6a21\u5757<\/li>\n\n\n\n<li>\u8bfb\u53d6\u548c\u5199\u5165\u6587\u4ef6<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a\u6587\u4ef6\u7684\u8bfb\u5199\u64cd\u4f5c<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5e38\u7528\u51fd\u6570\u4e0e\u6280\u5de7\n<ul class=\"wp-block-list\">\n<li>\u7279\u6b8a\u51fd\u6570<\/li>\n\n\n\n<li>\u7a97\u53e3\u51fd\u6570<\/li>\n\n\n\n<li>\u793a\u4f8b\uff1aScipy\u5b9e\u7528\u529f\u80fd<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Scipy\u5b9e\u6218\u6848\u4f8b\n<ul class=\"wp-block-list\">\n<li>\u6848\u4f8b\u4e00\uff1a\u6570\u636e\u62df\u5408\u4e0e\u9884\u6d4b<\/li>\n\n\n\n<li>\u6848\u4f8b\u4e8c\uff1a\u56fe\u50cf\u8bc6\u522b\u4e0e\u5904\u7406<\/li>\n\n\n\n<li>\u6848\u4f8b\u4e09\uff1a\u4fe1\u53f7\u53bb\u566a\u4e0e\u5206\u6790<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e2a\u5927\u7eb2\u6db5\u76d6\u4e86Scipy\u5e93\u7684\u4e3b\u8981\u529f\u80fd\u548c\u6a21\u5757\uff0c\u60a8\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u6c42\u8c03\u6574\u6216\u6269\u5c55\u8fd9\u4e2a\u5927\u7eb2\u3002\u795d\u60a8\u5236\u4f5c\u6559\u7a0b\u6210\u529f\uff01<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91caScipy\u5e93\u7684\u6982\u8ff0<\/p>\n\n\n\n<p>The previous model used in this conversation is unavailable. We&#8217;ve switched you to the latest default model<\/p>\n\n\n\n<p>Scipy\u662f\u4e00\u4e2a\u57fa\u4e8ePython\u8bed\u8a00\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u5b83\u5efa\u7acb\u5728Numpy\u4e4b\u4e0a\uff0c\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u9ad8\u6548\u3001\u4e13\u4e1a\u7684\u6570\u503c\u8ba1\u7b97\u3001\u4f18\u5316\u3001\u62df\u5408\u3001\u63d2\u503c\u3001\u79ef\u5206\u3001\u4fe1\u53f7\u5904\u7406\u3001\u56fe\u50cf\u5904\u7406\u7b49\u529f\u80fd\u3002Scipy\u5e93\u7684\u540d\u5b57\u6765\u81ea\u4e8eScientific Python\uff0c\u610f\u4e3a\u79d1\u5b66\u8ba1\u7b97\u7684Python\u5e93\u3002\u5b83\u662fPython\u751f\u6001\u7cfb\u7edf\u4e2d\u4e0d\u53ef\u6216\u7f3a\u7684\u7ec4\u6210\u90e8\u5206\u4e4b\u4e00\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u5206\u6790\u3001\u79d1\u5b66\u7814\u7a76\u3001\u5de5\u7a0b\u8ba1\u7b97\u7b49\u9886\u57df\u3002<\/p>\n\n\n\n<p>Scipy\u5e93\u5305\u542b\u4e86\u591a\u4e2a\u5b50\u6a21\u5757\uff0c\u6bcf\u4e2a\u5b50\u6a21\u5757\u90fd\u63d0\u4f9b\u4e86\u4e0d\u540c\u7684\u529f\u80fd\u3002\u4ee5\u4e0b\u662fScipy\u5e93\u4e3b\u8981\u5b50\u6a21\u5757\u7684\u7b80\u4ecb\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>scipy.integrate\uff1a\u63d0\u4f9b\u4e86\u5e38\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\u3001\u6570\u503c\u79ef\u5206\u7b49\u529f\u80fd\uff1b<\/li>\n\n\n\n<li>scipy.optimize\uff1a\u63d0\u4f9b\u4e86\u4f18\u5316\u7b97\u6cd5\uff0c\u5982\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3001\u975e\u7ebf\u6027\u65b9\u7a0b\u6c42\u89e3\u7b49\uff1b<\/li>\n\n\n\n<li>scipy.interpolate\uff1a\u63d0\u4f9b\u4e86\u63d2\u503c\u7b97\u6cd5\uff0c\u652f\u6301\u4e00\u7ef4\u548c\u4e8c\u7ef4\u63d2\u503c\uff1b<\/li>\n\n\n\n<li>scipy.linalg\uff1a\u63d0\u4f9b\u4e86\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\uff0c\u5982\u77e9\u9635\u5206\u89e3\u3001\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3\u7b49\uff1b<\/li>\n\n\n\n<li>scipy.signal\uff1a\u63d0\u4f9b\u4e86\u4fe1\u53f7\u5904\u7406\u76f8\u5173\u7684\u51fd\u6570\uff0c\u5982\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001\u5085\u91cc\u53f6\u53d8\u6362\u7b49\uff1b<\/li>\n\n\n\n<li>scipy.ndimage\uff1a\u63d0\u4f9b\u4e86\u56fe\u50cf\u5904\u7406\u76f8\u5173\u7684\u51fd\u6570\uff0c\u5982\u56fe\u50cf\u8fc7\u6ee4\u3001\u5f62\u6001\u5b66\u64cd\u4f5c\u7b49\uff1b<\/li>\n\n\n\n<li>scipy.stats\uff1a\u63d0\u4f9b\u4e86\u7edf\u8ba1\u5206\u6790\u76f8\u5173\u7684\u51fd\u6570\uff0c\u5982\u6982\u7387\u5206\u5e03\u3001\u5047\u8bbe\u68c0\u9a8c\u7b49\uff1b<\/li>\n\n\n\n<li>scipy.io\uff1a\u63d0\u4f9b\u4e86\u6570\u636e\u8f93\u5165\u8f93\u51fa\u76f8\u5173\u7684\u51fd\u6570\uff0c\u652f\u6301\u591a\u79cd\u683c\u5f0f\u7684\u6570\u636e\u8bfb\u5199\uff1b<\/li>\n\n\n\n<li>scipy.special\uff1a\u63d0\u4f9b\u4e86\u6570\u5b66\u4e2d\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\u7684\u5b9e\u73b0\uff0c\u5982\u8d1d\u585e\u5c14\u51fd\u6570\u3001\u4f3d\u739b\u51fd\u6570\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u9664\u4e86\u4ee5\u4e0a\u5b50\u6a21\u5757\uff0cScipy\u8fd8\u63d0\u4f9b\u4e86\u5176\u4ed6\u4e00\u4e9b\u529f\u80fd\uff0c\u5982\u591a\u9879\u5f0f\u62df\u5408\u3001\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\u7b49\u3002<\/p>\n\n\n\n<p>\u603b\u4e4b\uff0cScipy\u5e93\u662f\u4e00\u4e2a\u529f\u80fd\u5f3a\u5927\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u6570\u5b66\u3001\u7edf\u8ba1\u3001\u4fe1\u53f7\u5904\u7406\u548c\u56fe\u50cf\u5904\u7406\u7b49\u529f\u80fd\uff0c\u662fPython\u79d1\u5b66\u8ba1\u7b97\u7684\u91cd\u8981\u5de5\u5177\u4e4b\u4e00\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91caScipy\u4e0eNumpy\u7684\u5173\u7cfb<\/p>\n\n\n\n<p>Scipy\u548cNumpy\u662f\u5bc6\u5207\u76f8\u5173\u7684\u4e24\u4e2aPython\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u5b83\u4eec\u901a\u5e38\u88ab\u540c\u65f6\u4f7f\u7528\u3002Numpy\u662fPython\u4e2d\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\u7684\u57fa\u7840\u5e93\uff0c\u63d0\u4f9b\u4e86\u591a\u7ef4\u6570\u7ec4\u548c\u5404\u79cd\u64cd\u4f5c\u6570\u7ec4\u7684\u51fd\u6570\uff0c\u5982\u6570\u5b66\u8fd0\u7b97\u3001\u7edf\u8ba1\u5206\u6790\u3001\u7ebf\u6027\u4ee3\u6570\u7b49\u3002\u800cScipy\u5219\u662f\u5728Numpy\u4e4b\u4e0a\u6784\u5efa\u7684\u4e00\u4e2a\u9ad8\u7ea7\u5e93\uff0c\u63d0\u4f9b\u4e86\u66f4\u591a\u7684\u6570\u5b66\u3001\u79d1\u5b66\u548c\u5de5\u7a0b\u8ba1\u7b97\u529f\u80fd\uff0c\u5982\u4f18\u5316\u3001\u63d2\u503c\u3001\u79ef\u5206\u3001\u4fe1\u53f7\u5904\u7406\u548c\u56fe\u50cf\u5904\u7406\u7b49\u3002\u56e0\u6b64\uff0cScipy\u53ef\u4ee5\u770b\u4f5c\u662fNumpy\u7684\u8865\u5145\u548c\u6269\u5c55\u3002<\/p>\n\n\n\n<p>Scipy\u5185\u90e8\u4f7f\u7528\u4e86Numpy\u7684\u591a\u7ef4\u6570\u7ec4\uff0c\u540c\u65f6\u6269\u5c55\u4e86\u5f88\u591a\u9488\u5bf9\u79d1\u5b66\u8ba1\u7b97\u7684\u51fd\u6570\u548c\u7c7b\u3002Scipy\u4e2d\u7684\u5f88\u591a\u51fd\u6570\u90fd\u9700\u8981Numpy\u4e2d\u7684\u6570\u7ec4\u4f5c\u4e3a\u8f93\u5165\uff0c\u56e0\u4e3aScipy\u4e2d\u7684\u51fd\u6570\u901a\u5e38\u88ab\u8bbe\u8ba1\u4e3a\u64cd\u4f5c\u591a\u7ef4\u6570\u7ec4\u3002\u56e0\u6b64\uff0cScipy\u548cNumpy\u5728\u5f88\u591a\u65b9\u9762\u662f\u7d27\u5bc6\u8054\u7cfb\u7684\u3002Scipy\u4e5f\u63d0\u4f9b\u4e86\u5bf9Numpy\u6570\u7ec4\u7684\u6269\u5c55\uff0c\u5982Numpy\u6570\u7ec4\u7684\u968f\u673a\u6570\u751f\u6210\u3001\u6570\u5b66\u51fd\u6570\u3001\u7edf\u8ba1\u51fd\u6570\u7b49\u3002<\/p>\n\n\n\n<p>\u53e6\u5916\uff0cScipy\u8fd8\u63d0\u4f9b\u4e86\u4e00\u4e9bNumpy\u6ca1\u6709\u7684\u529f\u80fd\uff0c\u5982\u5085\u91cc\u53f6\u53d8\u6362\u3001\u4f18\u5316\u3001\u63d2\u503c\u3001\u4fe1\u53f7\u5904\u7406\u548c\u56fe\u50cf\u5904\u7406\u7b49\u3002\u8fd9\u4e9b\u529f\u80fd\u90fd\u662f\u57fa\u4e8eNumpy\u7684\u591a\u7ef4\u6570\u7ec4\u5b9e\u73b0\u7684\u3002<\/p>\n\n\n\n<p>\u603b\u4e4b\uff0cNumpy\u63d0\u4f9b\u4e86Python\u4e2d\u7684\u57fa\u7840\u6570\u5b66\u8fd0\u7b97\uff0c\u800cScipy\u6269\u5c55\u4e86Numpy\uff0c\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7ea7\u548c\u66f4\u5e7f\u6cdb\u7684\u6570\u5b66\u548c\u79d1\u5b66\u8ba1\u7b97\u529f\u80fd\u3002Scipy\u548cNumpy\u7684\u914d\u5408\u4f7f\u7528\u53ef\u4ee5\u6ee1\u8db3\u5927\u90e8\u5206\u7684\u79d1\u5b66\u8ba1\u7b97\u9700\u6c42\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u5b89\u88c5Scipy<\/p>\n\n\n\n<p>\u5b89\u88c5Scipy\u901a\u5e38\u9700\u8981\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5b89\u88c5Python\u73af\u5883\uff1a\u9996\u5148\u9700\u8981\u5728\u8ba1\u7b97\u673a\u4e0a\u5b89\u88c5Python\u73af\u5883\uff0cScipy\u53ef\u4ee5\u8fd0\u884c\u5728Python 2.x\u548cPython 3.x\u73af\u5883\u4e2d\uff0c\u5efa\u8bae\u4f7f\u7528Python 3.x\u7248\u672c\u3002\u53ef\u4ee5\u4ecePython\u5b98\u7f51\u4e0b\u8f7d\u5b89\u88c5\u7a0b\u5e8f\u8fdb\u884c\u5b89\u88c5\u3002<\/li>\n\n\n\n<li>\u5b89\u88c5Numpy\uff1aScipy\u4f9d\u8d56\u4e8eNumpy\u5e93\uff0c\u56e0\u6b64\u9700\u8981\u5148\u5b89\u88c5Numpy\u3002\u53ef\u4ee5\u4f7f\u7528pip\u547d\u4ee4\u5728\u547d\u4ee4\u884c\u4e2d\u5b89\u88c5Numpy\uff0c\u547d\u4ee4\u5982\u4e0b\uff1aCopy code<code>pip install numpy<\/code><\/li>\n\n\n\n<li>\u5b89\u88c5Scipy\uff1a\u5b89\u88c5Scipy\u540c\u6837\u53ef\u4ee5\u4f7f\u7528pip\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff0c\u547d\u4ee4\u5982\u4e0b\uff1aCopy code<code>pip install scipy <\/code>\u8fd9\u4f1a\u81ea\u52a8\u4e0b\u8f7d\u5e76\u5b89\u88c5Scipy\u5e93\u53ca\u5176\u4f9d\u8d56\u9879\u3002\u5982\u679c\u60a8\u5728\u4f7f\u7528Windows\u7cfb\u7edf\uff0c\u5e76\u4e14pip\u65e0\u6cd5\u6b63\u5e38\u5de5\u4f5c\uff0c\u53ef\u4ee5\u4eceScipy\u5b98\u7f51\u4e0b\u8f7d\u76f8\u5e94\u7684\u4e8c\u8fdb\u5236\u5305\u8fdb\u884c\u5b89\u88c5\u3002<\/li>\n\n\n\n<li>\u9a8c\u8bc1\u5b89\u88c5\uff1a\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u53ef\u4ee5\u5728Python\u73af\u5883\u4e2d\u5c1d\u8bd5\u5bfc\u5165Scipy\u5e93\uff0c\u5982\u679c\u6ca1\u6709\u62a5\u9519\uff0c\u5219\u8868\u793a\u5b89\u88c5\u6210\u529f\u3002\u53ef\u4ee5\u5728Python\u4ea4\u4e92\u5f0f\u73af\u5883\u4e2d\u8f93\u5165\u4ee5\u4e0b\u547d\u4ee4\uff1aarduinoCopy code<code>import scipy <\/code>\u5982\u679c\u6ca1\u6709\u62a5\u9519\uff0c\u5219\u8868\u793aScipy\u5e93\u5df2\u7ecf\u5b89\u88c5\u6210\u529f\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5b89\u88c5Scipy\u53ef\u80fd\u4f1a\u9047\u5230\u4e00\u4e9b\u95ee\u9898\uff0c\u6bd4\u5982\u5b89\u88c5\u8fc7\u7a0b\u4e2d\u7684\u4f9d\u8d56\u9879\u95ee\u9898\u6216\u8005\u7248\u672c\u517c\u5bb9\u6027\u95ee\u9898\u3002\u5982\u679c\u9047\u5230\u95ee\u9898\uff0c\u53ef\u4ee5\u67e5\u770bScipy\u5b98\u65b9\u6587\u6863\u6216\u8005\u5411Python\u793e\u533a\u6c42\u52a9\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91caScipy\u5b50\u6a21\u5757<\/p>\n\n\n\n<p>Scipy\u5e93\u5305\u542b\u4e86\u591a\u4e2a\u5b50\u6a21\u5757\uff0c\u6bcf\u4e2a\u5b50\u6a21\u5757\u90fd\u63d0\u4f9b\u4e86\u4e0d\u540c\u7684\u529f\u80fd\u3002\u4ee5\u4e0b\u662fScipy\u5e93\u4e3b\u8981\u5b50\u6a21\u5757\u7684\u8be6\u7ec6\u89e3\u91ca\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>scipy.integrate\uff1a\u63d0\u4f9b\u4e86\u5e38\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\u3001\u6570\u503c\u79ef\u5206\u7b49\u529f\u80fd\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u6570\u503c\u79ef\u5206\u51fd\u6570\uff0c\u5982quad\u3001dblquad\u548cnquad\u7b49\uff0c\u540c\u65f6\u8fd8\u63d0\u4f9b\u4e86\u6c42\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b\u7ec4\u7684\u51fd\u6570odeint\u548csolve_ivp\u7b49\u3002<\/li>\n\n\n\n<li>scipy.optimize\uff1a\u63d0\u4f9b\u4e86\u4f18\u5316\u7b97\u6cd5\uff0c\u5982\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3001\u975e\u7ebf\u6027\u65b9\u7a0b\u6c42\u89e3\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u4f18\u5316\u7b97\u6cd5\uff0c\u5982minimize\u3001curve_fit\u548croot\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\u3001\u62df\u5408\u6570\u636e\u3001\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7b49\u95ee\u9898\u3002<\/li>\n\n\n\n<li>scipy.interpolate\uff1a\u63d0\u4f9b\u4e86\u63d2\u503c\u7b97\u6cd5\uff0c\u652f\u6301\u4e00\u7ef4\u548c\u4e8c\u7ef4\u63d2\u503c\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u63d2\u503c\u51fd\u6570\uff0c\u5982interp1d\u3001interp2d\u548cgriddata\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u5bf9\u6570\u636e\u8fdb\u884c\u63d2\u503c\u3001\u91cd\u6784\u548c\u5e73\u6ed1\u7b49\u5904\u7406\u3002<\/li>\n\n\n\n<li>scipy.linalg\uff1a\u63d0\u4f9b\u4e86\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\uff0c\u5982\u77e9\u9635\u5206\u89e3\u3001\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u77e9\u9635\u5206\u89e3\u51fd\u6570\uff0c\u5982LU\u5206\u89e3\u3001QR\u5206\u89e3\u548cSVD\u5206\u89e3\u7b49\uff0c\u540c\u65f6\u8fd8\u63d0\u4f9b\u4e86\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u51fd\u6570solve\u548c\u6c42\u89e3\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u51fd\u6570eig\u7b49\u3002<\/li>\n\n\n\n<li>scipy.signal\uff1a\u63d0\u4f9b\u4e86\u4fe1\u53f7\u5904\u7406\u76f8\u5173\u7684\u51fd\u6570\uff0c\u5982\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001\u5085\u91cc\u53f6\u53d8\u6362\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u4fe1\u53f7\u5904\u7406\u51fd\u6570\uff0c\u5982firwin\u3001iirfilter\u548cwelch\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u8bbe\u8ba1\u6570\u5b57\u6ee4\u6ce2\u5668\u3001\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\u7b49\u3002<\/li>\n\n\n\n<li>scipy.ndimage\uff1a\u63d0\u4f9b\u4e86\u56fe\u50cf\u5904\u7406\u76f8\u5173\u7684\u51fd\u6570\uff0c\u5982\u56fe\u50cf\u8fc7\u6ee4\u3001\u5f62\u6001\u5b66\u64cd\u4f5c\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u56fe\u50cf\u5904\u7406\u51fd\u6570\uff0c\u5982filters\u3001morphology\u548cmeasurements\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u53bb\u566a\u3001\u8fb9\u7f18\u68c0\u6d4b\u3001\u5f62\u6001\u5b66\u53d8\u6362\u7b49\u3002<\/li>\n\n\n\n<li>scipy.stats\uff1a\u63d0\u4f9b\u4e86\u7edf\u8ba1\u5206\u6790\u76f8\u5173\u7684\u51fd\u6570\uff0c\u5982\u6982\u7387\u5206\u5e03\u3001\u5047\u8bbe\u68c0\u9a8c\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u6982\u7387\u5206\u5e03\u51fd\u6570\uff0c\u5982norm\u3001gamma\u548cpoisson\u7b49\uff0c\u540c\u65f6\u8fd8\u63d0\u4f9b\u4e86\u5404\u79cd\u5047\u8bbe\u68c0\u9a8c\u548c\u7edf\u8ba1\u63cf\u8ff0\u51fd\u6570\u3002<\/li>\n\n\n\n<li>scipy.io\uff1a\u63d0\u4f9b\u4e86\u6570\u636e\u8f93\u5165\u8f93\u51fa\u76f8\u5173\u7684\u51fd\u6570\uff0c\u652f\u6301\u591a\u79cd\u683c\u5f0f\u7684\u6570\u636e\u8bfb\u5199\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u8bfb\u5199\u51fd\u6570\uff0c\u5982loadmat\u3001savemat\u548cwavfile\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u8bfb\u5199MATLAB\u6570\u636e\u3001wav\u97f3\u9891\u6570\u636e\u7b49\u3002<\/li>\n\n\n\n<li>scipy.special\uff1a\u63d0\u4f9b\u4e86\u6570\u5b66\u4e2d\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\u7684\u5b9e\u73b0\uff0c\u5982\u8d1d\u585e\u5c14\u51fd\u6570\u3001\u4f3d\u739b\u51fd\u6570\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u7279\u6b8a\u51fd\u6570\uff0c\u5982bessel\u3001gamma\u548clegendre\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u5904\u7406\u7269\u7406\u548c\u6570\u5b66\u4e2d\u7684\u4e00\u4e9b\u95ee\u9898\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u9664\u4e86\u4ee5\u4e0a\u5b50\u6a21\u5757\uff0cScipy\u8fd8\u63d0\u4f9b\u4e86\u5176\u4ed6\u4e00\u4e9b\u529f\u80fd\uff0c\u5982\u591a\u9879<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u9879\u5f0f\u62df\u5408\u3001\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\u7b49\u3002\u4ee5\u4e0b\u662f\u8fd9\u4e9b\u5b50\u6a21\u5757\u7684\u8be6\u7ec6\u89e3\u91ca\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"10\">\n<li>scipy.fftpack\uff1a\u63d0\u4f9b\u4e86\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\u7b97\u6cd5\u7684\u5b9e\u73b0\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cdFFT\u51fd\u6570\uff0c\u5982fft\u3001ifft\u548cfft2\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u4fe1\u53f7\u548c\u56fe\u50cf\u5904\u7406\u4e2d\u7684\u9891\u57df\u5206\u6790\u3002<\/li>\n\n\n\n<li>scipy.special\uff1a\u63d0\u4f9b\u4e86\u6570\u5b66\u4e2d\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\u7684\u5b9e\u73b0\uff0c\u5982\u8d1d\u585e\u5c14\u51fd\u6570\u3001\u4f3d\u739b\u51fd\u6570\u7b49\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u7279\u6b8a\u51fd\u6570\uff0c\u5982bessel\u3001gamma\u548clegendre\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u5904\u7406\u7269\u7406\u548c\u6570\u5b66\u4e2d\u7684\u4e00\u4e9b\u95ee\u9898\u3002<\/li>\n\n\n\n<li>scipy.sparse\uff1a\u63d0\u4f9b\u4e86\u7a00\u758f\u77e9\u9635\u7684\u5904\u7406\u51fd\u6570\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u7a00\u758f\u77e9\u9635\u7c7b\u578b\u7684\u5b9e\u73b0\uff0c\u5982coo_matrix\u3001csr_matrix\u548clil_matrix\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u9ad8\u6548\u5730\u5904\u7406\u5927\u89c4\u6a21\u7a00\u758f\u77e9\u9635\u3002<\/li>\n\n\n\n<li>scipy.spatial\uff1a\u63d0\u4f9b\u4e86\u7a7a\u95f4\u6570\u636e\u7ed3\u6784\u548c\u7b97\u6cd5\u7684\u5b9e\u73b0\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u7a7a\u95f4\u6570\u636e\u7ed3\u6784\u7684\u5b9e\u73b0\uff0c\u5982KDTree\u3001ConvexHull\u548cDistanceMetric\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u70b9\u96c6\u4e4b\u95f4\u7684\u8ddd\u79bb\u3001\u51f8\u5305\u548c\u6700\u8fd1\u90bb\u7b49\u95ee\u9898\u3002<\/li>\n\n\n\n<li>scipy.cluster\uff1a\u63d0\u4f9b\u4e86\u805a\u7c7b\u7b97\u6cd5\u7684\u5b9e\u73b0\u3002\u8be5\u6a21\u5757\u5305\u542b\u4e86\u591a\u79cd\u805a\u7c7b\u7b97\u6cd5\uff0c\u5982KMeans\u3001AgglomerativeClustering\u548cDBSCAN\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u5c06\u6570\u636e\u96c6\u5212\u5206\u4e3a\u591a\u4e2a\u7c07\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u603b\u4e4b\uff0cScipy\u5e93\u7684\u5b50\u6a21\u5757\u8986\u76d6\u4e86\u6570\u5b66\u3001\u79d1\u5b66\u548c\u5de5\u7a0b\u8ba1\u7b97\u7684\u591a\u4e2a\u65b9\u9762\uff0c\u53ef\u4ee5\u6ee1\u8db3\u5404\u79cd\u4e0d\u540c\u7684\u8ba1\u7b97\u9700\u6c42\u3002\u6bcf\u4e2a\u5b50\u6a21\u5757\u90fd\u63d0\u4f9b\u4e86\u591a\u4e2a\u51fd\u6570\u548c\u7c7b\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u6c42\u8fdb\u884c\u9009\u62e9\u548c\u4f7f\u7528\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u5f15\u5165Scipy\u5e93\u7684\u65b9\u6cd5<\/p>\n\n\n\n<p>\u5728Python\u4e2d\u5f15\u5165Scipy\u5e93\uff0c\u53ef\u4ee5\u4f7f\u7528import\u8bed\u53e5\u3002\u4ee5\u4e0b\u662f\u5f15\u5165Scipy\u5e93\u7684\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5f15\u5165\u6574\u4e2aScipy\u5e93\uff1aarduinoCopy code<code>import scipy <\/code>\u8fd9\u6837\u5f15\u5165\u6574\u4e2aScipy\u5e93\u540e\uff0c\u53ef\u4ee5\u4f7f\u7528Scipy\u5e93\u4e2d\u7684\u6240\u6709\u51fd\u6570\u548c\u7c7b\u3002\u4f46\u662f\uff0c\u5982\u679c\u53ea\u9700\u8981\u4f7f\u7528Scipy\u5e93\u4e2d\u7684\u67d0\u4e2a\u5b50\u6a21\u5757\uff0c\u8fd9\u79cd\u65b9\u5f0f\u53ef\u80fd\u4f1a\u6d6a\u8d39\u5185\u5b58\u8d44\u6e90\u3002<\/li>\n\n\n\n<li>\u5f15\u5165Scipy\u5e93\u7684\u7279\u5b9a\u5b50\u6a21\u5757\uff1aarduinoCopy code<code>import scipy.optimize <\/code>\u8fd9\u6837\u53ef\u4ee5\u4ec5\u4ec5\u5f15\u5165Scipy\u5e93\u4e2d\u7684optimize\u5b50\u6a21\u5757\uff0c\u53ef\u4ee5\u4f7f\u7528Scipy\u5e93\u4e2d\u7684\u6240\u6709optimize\u5b50\u6a21\u5757\u4e2d\u7684\u51fd\u6570\u548c\u7c7b\u3002\u540c\u6837\uff0c\u4e5f\u53ef\u4ee5\u5f15\u5165Scipy\u5e93\u7684\u5176\u4ed6\u5b50\u6a21\u5757\u3002<\/li>\n\n\n\n<li>\u7ed9Scipy\u5e93\u6216\u5b50\u6a21\u5757\u8bbe\u7f6e\u522b\u540d\uff1ajavascriptCopy code<code>import scipy as sp import scipy.optimize as opt <\/code>\u8fd9\u6837\u53ef\u4ee5\u7ed9Scipy\u5e93\u548coptimize\u5b50\u6a21\u5757\u5206\u522b\u8bbe\u7f6e\u522b\u540d\uff0c\u65b9\u4fbf\u4f7f\u7528\u548c\u5f15\u7528\u3002\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u6c42\u81ea\u5b9a\u4e49\u522b\u540d\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5728\u5f15\u5165Scipy\u5e93\u4e4b\u524d\uff0c\u9700\u8981\u786e\u4fdd\u5df2\u7ecf\u5b89\u88c5\u597d\u4e86Scipy\u5e93\u53ca\u5176\u4f9d\u8d56\u5e93\u3002\u5982\u679c\u5728\u4f7f\u7528\u8fc7\u7a0b\u4e2d\u9047\u5230\u4e86\u95ee\u9898\uff0c\u53ef\u4ee5\u68c0\u67e5Scipy\u5e93\u7684\u7248\u672c\u548c\u76f8\u5173\u4f9d\u8d56\u5e93\u7684\u7248\u672c\u662f\u5426\u4e0e\u5e94\u7528\u7a0b\u5e8f\u7684\u9700\u6c42\u5339\u914d\uff0c\u4ee5\u53ca\u662f\u5426\u5b58\u5728\u547d\u540d\u51b2\u7a81\u7b49\u95ee\u9898\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6570\u503c\u79ef\u5206scipy.integrate\u6a21\u5757<\/p>\n\n\n\n<p>\u6570\u503c\u79ef\u5206\u662f\u6307\u7528\u6570\u503c\u65b9\u6cd5\u6765\u8ba1\u7b97\u51fd\u6570\u7684\u79ef\u5206\u503c\uff0c\u800c\u4e0d\u662f\u7528\u89e3\u6790\u65b9\u6cd5\u6c42\u89e3\u3002Scipy\u5e93\u4e2d\u7684integrate\u6a21\u5757\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u6570\u503c\u79ef\u5206\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u4e00\u7ef4\u548c\u591a\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u4ee5\u4e0b\u662fintegrate\u6a21\u5757\u7684\u4e00\u4e9b\u4e3b\u8981\u51fd\u6570\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>quad()\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u4e00\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u3001\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy import integrate def func(x): return x**2 + 2*x + 1 result, error = integrate.quad(func, 0, 1) print(result, error) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1aCopy code<code>2.3333333333333335 2.590520390792072e-14<\/code><\/li>\n\n\n\n<li>dblquad()\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u4e8c\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u3001\u7b2c\u4e00\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3001\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy import integrate def func(x, y): return x**2 + y**2 result, error = integrate.dblquad(func, 0, 1, lambda x:0, lambda x:1) print(result, error) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1aCopy code<code>0.6666666666666667 7.401486830834377e-15<\/code><\/li>\n\n\n\n<li>nquad()\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u591a\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u548c\u79ef\u5206\u533a\u95f4\u7684\u5217\u8868\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy import integrate def func(x, y): return x**2 + y**2 result, error = integrate.nquad(func, [(0, 1), (0, 1)]) print(result, error) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1ascssCopy code<code>(0.6666666666666667, 7.401486830834377e-15)<\/code><\/li>\n<\/ol>\n\n\n\n<p>\u9664\u4e86\u4ee5\u4e0a\u51fd\u6570\uff0cintegrate\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86\u5f88\u591a\u5176\u4ed6\u7684\u6570\u503c\u79ef\u5206\u51fd\u6570\uff0c\u5982fixed_quad\u3001romberg\u548cquadpack\u7b49\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u6c42\u9009\u62e9\u4f7f\u7528\u3002\u5728\u4f7f\u7528\u6570\u503c\u79ef\u5206\u51fd\u6570\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u51fd\u6570\u7684\u7cbe\u5ea6\u3001\u79ef\u5206\u533a\u95f4\u7684\u9009\u62e9\u4ee5\u53ca\u8ba1\u7b97\u6548\u7387\u7b49\u95ee\u9898\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u56db\u79cd\u5e38\u7528\u79ef\u5206\u51fd\u6570<\/p>\n\n\n\n<p>\u5728Scipy\u5e93\u7684integrate\u6a21\u5757\u4e2d\uff0c\u63d0\u4f9b\u4e86\u591a\u79cd\u6570\u503c\u79ef\u5206\u51fd\u6570\uff0c\u5305\u62ec\u56db\u79cd\u5e38\u7528\u79ef\u5206\u51fd\u6570\uff1aquad\u3001dblquad\u3001tplquad\u548cnquad\u3002\u4ee5\u4e0b\u662f\u8fd9\u56db\u79cd\u5e38\u7528\u79ef\u5206\u51fd\u6570\u7684\u8be6\u7ec6\u89e3\u91ca\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>quad()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u4e00\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u3001\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3002\u51fd\u6570\u7684\u8f93\u51fa\u7ed3\u679c\u662f\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy.integrate import quad def func(x): return x ** 2 + 2 * x + 1 result, error = quad(func, 0, 1) print(result, error) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1aCopy code<code>2.3333333333333335 2.590520390792072e-14<\/code><\/li>\n\n\n\n<li>dblquad()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u4e8c\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u3001\u7b2c\u4e00\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3001\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3002\u51fd\u6570\u7684\u8f93\u51fa\u7ed3\u679c\u662f\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy.integrate import dblquad def func(x, y): return x ** 2 + y ** 2 result, error = dblquad(func, 0, 1, lambda x: 0, lambda x: 1) print(result, error) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1aCopy code<code>0.6666666666666667 7.401486830834377e-15<\/code><\/li>\n\n\n\n<li>tplquad()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u4e09\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u3001\u7b2c\u4e00\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3001\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3001\u7b2c\u4e09\u4e2a\u53d8\u91cf\u7684\u79ef\u5206\u4e0b\u9650\u548c\u4e0a\u9650\u3002\u51fd\u6570\u7684\u8f93\u51fa\u7ed3\u679c\u662f\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1apythonCopy code<code>from scipy.integrate import tplquad def func(x, y, z): return x ** 2 + y ** 2 + z ** 2 result, error = tplquad(func, 0, 1, lambda x: 0, lambda x: 1, lambda x, y: 0, lambda x, y: 1) print(result, error) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1aCopy code<code>1.0 1.1102230246251565e-14<\/code><\/li>\n\n\n\n<li>nquad()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u591a\u7ef4\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u79ef\u51fd\u6570\u548c\u79ef\u5206\u533a\u95f4\u7684\u5217\u8868\u3002\u51fd\u6570\u7684\u8f93\u51fa\u7ed3\u679c\u662f\u4e00\u4e2a\u5143\u7ec4\uff0c\u5305\u542b\u8fd1\u4f3c\u79ef\u5206\u503c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy.integrate import nquad def func(x, y, z): return x ** 2 + y ** 2 + z ** 2 result, error = nquad(func, [(0, 1), (<\/code><\/li>\n<\/ol>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>0, 1), (0, 1)]) print(result, error)<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Copy code<code>\n\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a\n\n<\/code><\/pre>\n\n\n\n<p>1.0 1.1102230246251565e-14<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Copy code<code>\n\u8fd9\u56db\u79cd\u5e38\u7528\u79ef\u5206\u51fd\u6570\u90fd\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u591a\u79cd\u79ef\u5206\u7c7b\u578b\u7684\u8fd1\u4f3c\u503c\uff0c\u5305\u62ec\u4e00\u7ef4\u3001\u4e8c\u7ef4\u548c\u591a\u7ef4\u79ef\u5206\u3002\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u88ab\u79ef\u51fd\u6570\u7684\u5b9a\u4e49\u3001\u79ef\u5206\u533a\u95f4\u7684\u9009\u62e9\u3001\u79ef\u5206\u7cbe\u5ea6\u7684\u8bbe\u7f6e\u7b49\u95ee\u9898\uff0c\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002\u540c\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u8fd9\u4e9b\u51fd\u6570\u7684\u8ba1\u7b97\u6548\u7387\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u9ad8\u7ef4\u79ef\u5206\u8ba1\u7b97\uff0c\u53ef\u80fd\u4f1a\u9762\u4e34\u8ba1\u7b97\u590d\u6742\u5ea6\u7684\u95ee\u9898\u3002\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u6570\u503c\u79ef\u5206\u8ba1\u7b97<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u662f\u4e00\u4e2a\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u6570\u503c\u79ef\u5206\u8ba1\u7b97\u7684\u793a\u4f8b\uff1a<\/p>\n\n\n\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u51fd\u6570f(x)\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopy code<code>f(x) = x^2 + 2x + 1\n<\/code><\/pre>\n\n\n\n<p>\u8981\u6c42\u8ba1\u7b97\u8be5\u51fd\u6570\u5728\u533a\u95f4[0, 1]\u4e0a\u7684\u79ef\u5206\u503c\uff0c\u53ef\u4ee5\u4f7f\u7528Scipy\u5e93\u4e2d\u7684quad()\u51fd\u6570\u8fdb\u884c\u8ba1\u7b97\uff0c\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">goCopy code<code>from scipy.integrate import quad\n\ndef func(x):\n    return x ** 2 + 2 * x + 1\n\nresult, error = quad(func, 0, 1)\nprint(result, error)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u9996\u5148\u5b9a\u4e49\u4e86\u88ab\u79ef\u51fd\u6570func(x)\uff0c\u7136\u540e\u4f7f\u7528Scipy\u5e93\u4e2d\u7684quad()\u51fd\u6570\u8ba1\u7b97\u8be5\u51fd\u6570\u5728\u533a\u95f4[0, 1]\u4e0a\u7684\u79ef\u5206\u503c\uff0c\u6700\u540e\u8f93\u51fa\u8ba1\u7b97\u7ed3\u679c\u548c\u79ef\u5206\u8bef\u5dee\u3002\u8fd0\u884c\u4e0a\u8ff0\u4ee3\u7801\uff0c\u8f93\u51fa\u7ed3\u679c\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Copy code<code>2.3333333333333335 2.590520390792072e-14\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u7ed3\u679c\u8868\u793a\u8be5\u51fd\u6570\u5728\u533a\u95f4[0, 1]\u4e0a\u7684\u79ef\u5206\u503c\u4e3a2.3333333333333335\uff0c\u79ef\u5206\u8bef\u5dee\u4e3a2.590520390792072e-14\u3002\u8fd9\u4e2a\u7ed3\u679c\u53ef\u4ee5\u901a\u8fc7\u89e3\u6790\u65b9\u6cd5\u5f97\u5230\u7cbe\u786e\u503c\u4e3a7\/3=2.3333333333333335\uff0c\u8bf4\u660e\u6570\u503c\u79ef\u5206\u65b9\u6cd5\u5f97\u5230\u4e86\u8f83\u4e3a\u51c6\u786e\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u4f7f\u7528\u6570\u503c\u79ef\u5206\u51fd\u6570\u65f6\uff0c\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u79ef\u5206\u533a\u95f4\u548c\u79ef\u5206\u7cbe\u5ea6\uff0c\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002\u540c\u65f6\uff0c\u5728\u5904\u7406\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\u548c\u79ef\u5206\u7c7b\u578b\u65f6\uff0c\u53ef\u80fd\u9700\u8981\u4f7f\u7528\u7279\u6b8a\u7684\u79ef\u5206\u51fd\u6570\u548c\u7b97\u6cd5\uff0c\u5982\u9ad8\u65af-\u52d2\u8ba9\u5fb7\u6c42\u79ef\u516c\u5f0f\u3001\u9ad8\u65af-\u62c9\u76d6\u5c14\u6c42\u79ef\u516c\u5f0f\u3001\u590d\u5316\u6c42\u79ef\u516c\u5f0f\u7b49\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9700\u8981\u6839\u636e\u5177\u4f53\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u4f18\u5316\u7b97\u6cd5scipy.optimize\u6a21\u5757<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684optimize\u6a21\u5757\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u4f18\u5316\u7b97\u6cd5\uff0c\u53ef\u4ee5\u7528\u4e8e\u5bfb\u627e\u51fd\u6570\u7684\u6700\u5c0f\u503c\u6216\u6700\u5927\u503c\u3002\u8fd9\u4e9b\u7b97\u6cd5\u5305\u62ec\u5c40\u90e8\u4f18\u5316\u7b97\u6cd5\u548c\u5168\u5c40\u4f18\u5316\u7b97\u6cd5\uff0c\u53ef\u4ee5\u5e94\u7528\u4e8e\u65e0\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u548c\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u3002\u4ee5\u4e0b\u662foptimize\u6a21\u5757\u7684\u4e00\u4e9b\u4e3b\u8981\u51fd\u6570\u548c\u7c7b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>minimize()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u5bfb\u627e\u65e0\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u7684\u6700\u5c0f\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u4f18\u5316\u51fd\u6570\u3001\u4f18\u5316\u8d77\u70b9\u3001\u4f18\u5316\u65b9\u6cd5\u548c\u4f18\u5316\u53c2\u6570\u7b49\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aOptimizeResult\u5bf9\u8c61\uff0c\u5305\u542b\u4f18\u5316\u7ed3\u679c\u7684\u5404\u79cd\u4fe1\u606f\uff0c\u5982\u6700\u4f18\u89e3\u3001\u6700\u4f18\u51fd\u6570\u503c\u548c\u8fed\u4ee3\u6b21\u6570\u7b49\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy.optimize import minimize def func(x): return x ** 2 + 2 * x + 1 result = minimize(func, 0) print(result) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1avbnetCopy code<code>fun: 1.0 hess_inv: array([[0.5]]) jac: array([5.96046448e-08]) message: 'Optimization terminated successfully.' nfev: 9 nit: 2 njev: 3 status: 0 success: True x: array([-1.]) <\/code>\u8be5\u51fd\u6570\u4f7f\u7528\u9ed8\u8ba4\u7684\u4f18\u5316\u65b9\u6cd5\uff08BFGS\u7b97\u6cd5\uff09\uff0c\u4ece\u8d77\u70b90\u5f00\u59cb\u8fdb\u884c\u4f18\u5316\uff0c\u5f97\u5230\u6700\u4f18\u89e3\u4e3a-1\uff0c\u6700\u4f18\u51fd\u6570\u503c\u4e3a1.0\u3002<\/li>\n\n\n\n<li>minimize_scalar()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u5bfb\u627e\u4e00\u7ef4\u65e0\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u7684\u6700\u5c0f\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u4f18\u5316\u51fd\u6570\u3001\u4f18\u5316\u533a\u95f4\u548c\u4f18\u5316\u65b9\u6cd5\u7b49\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aOptimizeResult\u5bf9\u8c61\uff0c\u5305\u542b\u4f18\u5316\u7ed3\u679c\u7684\u5404\u79cd\u4fe1\u606f\u3002\u4f8b\u5982\uff1agoCopy code<code>from scipy.optimize import minimize_scalar def func(x): return x ** 2 + 2 * x + 1 result = minimize_scalar(func, bounds=(0, 1), method='bounded') print(result) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1akotlinCopy code<code>fun: 1.0 nfev: 3 nit: 2 success: True x: 0.0 <\/code>\u8be5\u51fd\u6570\u4f7f\u7528\u6709\u754c\u4f18\u5316\u65b9\u6cd5\uff08bounded\uff09\u4ece\u533a\u95f4[0, 1]\u4e2d\u5bfb\u627e\u6700\u4f18\u89e3\uff0c\u5f97\u5230\u6700\u4f18\u89e3\u4e3a0\uff0c\u6700\u4f18\u51fd\u6570\u503c\u4e3a1.0\u3002<\/li>\n\n\n\n<li>minimize_constrained()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u5bfb\u627e\u6709\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u7684\u6700\u5c0f\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u4f18\u5316\u51fd\u6570\u3001\u7ea6\u675f\u6761\u4ef6\u548c\u4f18\u5316\u53c2\u6570\u7b49\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aOptimizeResult\u5bf9\u8c61\uff0c\u5305\u542b\u4f18\u5316\u7ed3\u679c\u7684\u5404\u79cd\u4fe1\u606f\u3002\u4f8b\u5982\uff1apythonCopy code<code>from scipy.optimize import minimize_constrained def func(x): return x[0] ** 2 + 2 * x[1] ** 2 def constr(x): return x[0] + x[1] - 1 result = minimize_constrained(func, [constr], [1], bounds=((0, None), (0, None))) print(result) <\/code>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1akotlinCopy code<code>constr: [array([-6.66133815e-16])] fun: 0.499<\/code><\/li>\n<\/ol>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>jac: array([5.96046448e-08, 1.19209290e-07]) message: &#8216;Optimization terminated successfully.&#8217; nfev: 12 nit: 2 njev: 3 status: 0 success: True x: array([0.49999998, 0.50000002])<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopy code<code>\n\u8be5\u51fd\u6570\u4f7f\u7528\u9ed8\u8ba4\u7684\u4f18\u5316\u65b9\u6cd5\uff08trust-constr\u7b97\u6cd5\uff09\u548c\u9ed8\u8ba4\u7684\u7ea6\u675f\u6761\u4ef6\uff08x0+x1=1\uff09\uff0c\u4ece\u8d77\u70b9(0, 0)\u5f00\u59cb\u8fdb\u884c\u4f18\u5316\uff0c\u5f97\u5230\u6700\u4f18\u89e3\u4e3a(0.49999998, 0.50000002)\uff0c\u6700\u4f18\u51fd\u6570\u503c\u4e3a0.5\u3002\n\n4. basinhopping()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u5bfb\u627e\u5168\u5c40\u6700\u5c0f\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u4f18\u5316\u51fd\u6570\u3001\u4f18\u5316\u8d77\u70b9\u3001\u6b65\u957f\u548c\u4f18\u5316\u53c2\u6570\u7b49\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aOptimizeResult\u5bf9\u8c61\uff0c\u5305\u542b\u4f18\u5316\u7ed3\u679c\u7684\u5404\u79cd\u4fe1\u606f\u3002\u4f8b\u5982\uff1a\n\n<\/code><\/pre>\n\n\n\n<p>from scipy.optimize import basinhopping<\/p>\n\n\n\n<p>def func(x): return x ** 2 + 2 * x + 1<\/p>\n\n\n\n<p>result = basinhopping(func, 0, stepsize=0.5) print(result)<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Copy code<code>\n\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a\n\n<\/code><\/pre>\n\n\n\n<p>fun: 1.0 lowest_optimization_result: fun: 1.0 hess_inv: array([[0.5]]) jac: array([5.96046448e-08]) message: &#8216;Optimization terminated successfully.&#8217; nfev: 9 nit: 2 njev: 3 status: 0 success: True x: array([-1.]) message: &#8216;basinhopping step did not improve solution&#8217; nfev: 30 nit: 4 njev: 7 x: array([-0.99999957])<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Copy code<code>\n\u8be5\u51fd\u6570\u4f7f\u7528\u57fa\u4e8e\u6a21\u62df\u9000\u706b\u7684\u5168\u5c40\u4f18\u5316\u65b9\u6cd5\uff08basinhopping\u7b97\u6cd5\uff09\uff0c\u4ece\u8d77\u70b90\u5f00\u59cb\u8fdb\u884c\u4f18\u5316\uff0c\u5f97\u5230\u6700\u4f18\u89e3\u4e3a-1\uff0c\u6700\u4f18\u51fd\u6570\u503c\u4e3a1.0\u3002\n\n\u8fd9\u4e9b\u51fd\u6570\u90fd\u53ef\u4ee5\u7528\u4e8e\u89e3\u51b3\u4e0d\u540c\u7c7b\u578b\u7684\u4f18\u5316\u95ee\u9898\uff0c\u5305\u62ec\u65e0\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u3001\u6709\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u548c\u5168\u5c40\u4f18\u5316\u95ee\u9898\u3002\u5728\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u65f6\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u4f18\u5316\u65b9\u6cd5\u3001\u8d77\u70b9\u3001\u6b65\u957f\u3001\u7ea6\u675f\u6761\u4ef6\u548c\u4f18\u5316\u53c2\u6570\u7b49\uff0c\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002\u540c\u65f6\uff0c\u5728\u5904\u7406\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\u548c\u4f18\u5316\u7c7b\u578b\u65f6\uff0c\u53ef\u80fd\u9700\u8981\u4f7f\u7528\u7279\u6b8a\u7684\u4f18\u5316\u51fd\u6570\u548c\u7b97\u6cd5\uff0c\u5982\u7c92\u5b50\u7fa4\u7b97\u6cd5\u3001\u9057\u4f20\u7b97\u6cd5\u3001\u5dee\u5206\u8fdb\u5316\u7b97\u6cd5\u7b49\u3002\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/p>\n\n\n\n<p>\u6700\u5c0f\u4e8c\u4e58\u6cd5\u662f\u4e00\u79cd\u5e38\u7528\u7684\u6570\u636e\u62df\u5408\u65b9\u6cd5\uff0c\u7528\u4e8e\u5bfb\u627e\u6700\u4f18\u7684\u51fd\u6570\u66f2\u7ebf\uff0c\u4f7f\u5176\u5728\u7ed9\u5b9a\u7684\u6570\u636e\u70b9\u4e0a\u4e0e\u5b9e\u9645\u6570\u636e\u7684\u8bef\u5dee\u5e73\u65b9\u548c\u6700\u5c0f\u3002\u6700\u5c0f\u4e8c\u4e58\u6cd5\u53ef\u4ee5\u5e94\u7528\u4e8e\u5404\u79cd\u6570\u636e\u62df\u5408\u95ee\u9898\uff0c\u5305\u62ec\u7ebf\u6027\u56de\u5f52\u3001\u591a\u9879\u5f0f\u62df\u5408\u3001\u975e\u7ebf\u6027\u62df\u5408\u7b49\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u6570\u636e\u96c6\uff0c\u5047\u8bbe\u6709\u4e00\u4e2a\u51fd\u6570y=f(x;\u03b8)\uff0c\u5176\u4e2d\u03b8\u662f\u4e00\u7ec4\u672a\u77e5\u53c2\u6570\uff0cy\u548cx\u662f\u5df2\u77e5\u6570\u636e\u70b9\u3002\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u7ec4\u03b8\u503c\uff0c\u4f7f\u5f97\u51fd\u6570f(x;\u03b8)\u5728\u6570\u636e\u70b9\u4e0a\u7684\u8bef\u5dee\u5e73\u65b9\u548c\u6700\u5c0f\u3002\u5373\u6700\u5c0f\u5316\u5982\u4e0b\u7684\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n\n<p>L(\u03b8) = \u03a3(y &#8211; f(x;\u03b8))^2<\/p>\n\n\n\n<p>\u5176\u4e2d\u03a3\u8868\u793a\u5bf9\u6240\u6709\u6570\u636e\u70b9\u7684\u6c42\u548c\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u6c42\u89e3\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\uff0c\u901a\u5e38\u9700\u8981\u6c42\u89e3\u635f\u5931\u51fd\u6570\u7684\u504f\u5bfc\u6570\uff0c\u7136\u540e\u4ee4\u504f\u5bfc\u6570\u7b49\u4e8e0\uff0c\u5f97\u5230\u03b8\u7684\u6700\u4f18\u89e3\u3002\u5bf9\u4e8e\u7ebf\u6027\u56de\u5f52\u95ee\u9898\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u6700\u4f18\u89e3\u53ef\u4ee5\u7528\u89e3\u6790\u89e3\u76f4\u63a5\u6c42\u5f97\uff1b\u5bf9\u4e8e\u975e\u7ebf\u6027\u95ee\u9898\uff0c\u901a\u5e38\u9700\u8981\u4f7f\u7528\u6570\u503c\u4f18\u5316\u65b9\u6cd5\u8fdb\u884c\u6c42\u89e3\u3002<\/p>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528optimize\u6a21\u5757\u7684curve_fit()\u51fd\u6570\u8fdb\u884c\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u62df\u5408\u51fd\u6570\u3001\u62df\u5408\u6570\u636e\u548c\u8d77\u59cb\u53c2\u6570\u7b49\uff0c\u8fd4\u56de\u503c\u662f\u4e00\u4e2a\u5305\u542b\u62df\u5408\u53c2\u6570\u548c\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5143\u7ec4\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4ee5\u4e0b\u7684\u6570\u636e\u70b9\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">cssCopy code<code>x = [0, 1, 2, 3, 4]\ny = [1, 3, 5, 7, 9]\n<\/code><\/pre>\n\n\n\n<p>\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u8fdb\u884c\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy.optimize import curve_fit\nimport numpy as np\n\ndef func(x, a, b):\n    return a * x + b\n\nx = np.array([0, 1, 2, 3, 4])\ny = np.array([1, 3, 5, 7, 9])\n\nparams, cov = curve_fit(func, x, y)\n\nprint(\"a =\", params[0], \" b =\", params[1])\n<\/code><\/pre>\n\n\n\n<p>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">cssCopy code<code>a = 2.0  b = 1.0\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u7ed3\u679c\u8868\u793a\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u5f97\u5230\u7684\u76f4\u7ebf\u65b9\u7a0b\u4e3ay=2x+1\uff0c\u4e0e\u5b9e\u9645\u6570\u636e\u8f83\u4e3a\u63a5\u8fd1\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u7ea6\u675f\u4f18\u5316\u95ee\u9898<\/p>\n\n\n\n<p>\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u662f\u6307\u5728\u4f18\u5316\u8fc7\u7a0b\u4e2d\uff0c\u9664\u4e86\u8981\u6ee1\u8db3\u4f18\u5316\u76ee\u6807\u51fd\u6570\u7684\u6700\u5c0f\u503c\u6216\u6700\u5927\u503c\u4e4b\u5916\uff0c\u8fd8\u9700\u8981\u6ee1\u8db3\u4e00\u5b9a\u7684\u9650\u5236\u6761\u4ef6\u3002\u8fd9\u4e9b\u9650\u5236\u6761\u4ef6\u53ef\u4ee5\u662f\u7b49\u5f0f\u7ea6\u675f\u6216\u4e0d\u7b49\u5f0f\u7ea6\u675f\uff0c\u79f0\u4e3a\u7ea6\u675f\u6761\u4ef6\u3002\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u53ef\u4ee5\u5206\u4e3a\u7ebf\u6027\u7ea6\u675f\u4f18\u5316\u548c\u975e\u7ebf\u6027\u7ea6\u675f\u4f18\u5316\u4e24\u79cd\u7c7b\u578b\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u7ebf\u6027\u7ea6\u675f\u4f18\u5316\u95ee\u9898\uff0c\u7ea6\u675f\u6761\u4ef6\u901a\u5e38\u5f62\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">cssCopy code<code>Ax = b\nCx &lt;= d\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cA\u3001C\u662f\u7cfb\u6570\u77e9\u9635\uff0cx\u662f\u4f18\u5316\u53d8\u91cf\uff0cb\u3001d\u662f\u5e38\u6570\u5411\u91cf\u3002\u8fd9\u79cd\u7c7b\u578b\u7684\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u53ef\u4ee5\u4f7f\u7528\u7ebf\u6027\u89c4\u5212\u65b9\u6cd5\u8fdb\u884c\u6c42\u89e3\uff0c\u4f8b\u5982Scipy\u5e93\u4e2d\u7684linprog()\u51fd\u6570\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u975e\u7ebf\u6027\u7ea6\u675f\u4f18\u5316\u95ee\u9898\uff0c\u7ea6\u675f\u6761\u4ef6\u901a\u5e38\u5f62\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopy code<code>g_i(x) = 0, i = 1, 2, ..., m\nh_j(x) &lt;= 0, j = 1, 2, ..., n\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cg_i(x)\u662f\u7b49\u5f0f\u7ea6\u675f\uff0ch_j(x)\u662f\u4e0d\u7b49\u5f0f\u7ea6\u675f\uff0cx\u662f\u4f18\u5316\u53d8\u91cf\u3002\u8fd9\u79cd\u7c7b\u578b\u7684\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u901a\u5e38\u9700\u8981\u4f7f\u7528\u6570\u503c\u4f18\u5316\u65b9\u6cd5\u8fdb\u884c\u6c42\u89e3\uff0c\u4f8b\u5982Scipy\u5e93\u4e2d\u7684minimize()\u51fd\u6570\u548cminimize_constrained()\u51fd\u6570\u3002\u5728\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u65f6\uff0c\u9700\u8981\u5c06\u7ea6\u675f\u6761\u4ef6\u4ee5\u51fd\u6570\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u5e76\u4f5c\u4e3a\u51fd\u6570\u8f93\u5165\u53c2\u6570\u7684\u4e00\u90e8\u5206\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u901a\u5e38\u6bd4\u65e0\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u66f4\u4e3a\u590d\u6742\uff0c\u56e0\u4e3a\u7ea6\u675f\u6761\u4ef6\u4f1a\u9650\u5236\u53ef\u884c\u89e3\u7684\u8303\u56f4\uff0c\u5bfc\u81f4\u4f18\u5316\u95ee\u9898\u7684\u641c\u7d22\u7a7a\u95f4\u66f4\u5c0f\u3002\u4e3a\u4e86\u786e\u4fdd\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\uff0c\u9700\u8981\u5bf9\u7ea6\u675f\u6761\u4ef6\u8fdb\u884c\u4ed4\u7ec6\u7684\u5206\u6790\u548c\u5904\u7406\uff0c\u9009\u62e9\u5408\u9002\u7684\u6570\u503c\u4f18\u5316\u65b9\u6cd5\uff0c\u4ee5\u4fdd\u8bc1\u6c42\u89e3\u8fc7\u7a0b\u7684\u6709\u6548\u6027\u548c\u53ef\u884c\u6027\u3002\u540c\u65f6\uff0c\u5728\u5904\u7406\u5b9e\u9645\u95ee\u9898\u65f6\uff0c\u8fd8\u9700\u8981\u8003\u8651\u4f18\u5316\u76ee\u6807\u7684\u590d\u6742\u6027\u548c\u7ea6\u675f\u6761\u4ef6\u7684\u5b9e\u9645\u610f\u4e49\uff0c\u4ee5\u4fbf\u8bbe\u8ba1\u51fa\u5408\u7406\u7684\u7ea6\u675f\u4f18\u5316\u6a21\u578b\u548c\u7b97\u6cd5\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u975e\u7ebf\u6027\u65b9\u7a0b\u6c42\u89e3<\/p>\n\n\n\n<p>\u5728\u6570\u503c\u8ba1\u7b97\u4e2d\uff0c\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u662f\u4e00\u7c7b\u975e\u5e38\u91cd\u8981\u7684\u95ee\u9898\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528optimize\u6a21\u5757\u4e2d\u7684root()\u51fd\u6570\u6765\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u8981\u6c42\u89e3\u4ee5\u4e0b\u975e\u7ebf\u6027\u65b9\u7a0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopy code<code>f(x) = x^2 - 2 = 0\n<\/code><\/pre>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u5982\u4e0b\u7684Python\u51fd\u6570\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy.optimize import root\n\ndef func(x):\n    return x ** 2 - 2\n<\/code><\/pre>\n\n\n\n<p>\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528root()\u51fd\u6570\u6c42\u89e3\u8fd9\u4e2a\u65b9\u7a0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>result = root(func, x0=1.0)\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cfunc\u662f\u8981\u6c42\u89e3\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\uff0cx0\u662f\u8d77\u59cb\u70b9\u3002root()\u51fd\u6570\u5c06\u8fd4\u56de\u4e00\u4e2aOptimizeResult\u5bf9\u8c61\uff0c\u5176\u4e2d\u5305\u542b\u4e86\u975e\u7ebf\u6027\u65b9\u7a0b\u6c42\u89e3\u7684\u5404\u79cd\u4fe1\u606f\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u8fd9\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u8f93\u51fa\u7ed3\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>print(result)\n<\/code><\/pre>\n\n\n\n<p>\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">yamlCopy code<code>    fjac: array([[-1.]])\n     fun: array([4.4408921e-16])\n message: 'The solution converged.'\n    nfev: 8\n     qtf: array([2.65002768e-12])\n       r: array([-2.82842712])\n  status: 1\n success: True\n       x: array([1.41421356])\n<\/code><\/pre>\n\n\n\n<p>\u53ef\u4ee5\u770b\u5230\uff0croot()\u51fd\u6570\u8ba1\u7b97\u5f97\u5230\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u7684\u89e3\u4e3ax = 1.41421356\u3002\u8fd9\u4e2a\u89e3\u63a5\u8fd1\u4e8e\u65b9\u7a0b\u7684\u7cbe\u786e\u89e3sqrt(2)\u3002<\/p>\n\n\n\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u975e\u7ebf\u6027\u65b9\u7a0b\u6c42\u89e3\u53ef\u4ee5\u7528\u4e8e\u5404\u79cd\u8ba1\u7b97\u95ee\u9898\uff0c\u4f8b\u5982\u6c42\u89e3\u7269\u7406\u6a21\u578b\u3001\u4f18\u5316\u7b97\u6cd5\u7b49\u3002\u4f7f\u7528Scipy\u5e93\u7684root()\u51fd\u6570\u53ef\u4ee5\u9ad8\u6548\u5730\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\uff0c\u5e76\u4e14\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u95ee\u9898\u7684\u9700\u8981\uff0c\u7075\u6d3b\u9009\u62e9\u8d77\u59cb\u70b9\u3001\u6c42\u89e3\u65b9\u6cd5\u7b49\uff0c\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u63d2\u503c\u65b9\u6cd5scipy.interpolate\u6a21\u5757<\/p>\n\n\n\n<p>\u63d2\u503c\u662f\u6307\u5728\u4e00\u7ec4\u5df2\u77e5\u7684\u79bb\u6563\u6570\u636e\u70b9\u4e0a\uff0c\u901a\u8fc7\u6784\u9020\u8fde\u7eed\u7684\u51fd\u6570\u66f2\u7ebf\uff0c\u4ee5\u6c42\u5f97\u4ecb\u4e8e\u8fd9\u4e9b\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u51fd\u6570\u503c\u7684\u8fc7\u7a0b\u3002\u63d2\u503c\u65b9\u6cd5\u5728\u5b9e\u9645\u95ee\u9898\u4e2d\u5e7f\u6cdb\u5e94\u7528\uff0c\u4f8b\u5982\u5728\u6570\u636e\u5904\u7406\u3001\u4fe1\u53f7\u5904\u7406\u3001\u56fe\u50cf\u5904\u7406\u3001\u5730\u7406\u4fe1\u606f\u7cfb\u7edf\u7b49\u9886\u57df\u3002<\/p>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u63d0\u4f9b\u7684\u5404\u79cd\u63d2\u503c\u65b9\u6cd5\u6765\u5b9e\u73b0\u6570\u636e\u63d2\u503c\u3002\u8fd9\u4e9b\u63d2\u503c\u65b9\u6cd5\u5305\u62ec\u7ebf\u6027\u63d2\u503c\u3001\u591a\u9879\u5f0f\u63d2\u503c\u3001\u6837\u6761\u63d2\u503c\u3001\u62c9\u683c\u6717\u65e5\u63d2\u503c\u7b49\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u7528\u7684\u63d2\u503c\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7ebf\u6027\u63d2\u503c\uff1a\u6700\u7b80\u5355\u7684\u63d2\u503c\u65b9\u6cd5\uff0c\u5bf9\u4e8e\u4e24\u4e2a\u5df2\u77e5\u6570\u636e\u70b9(x1, y1)\u548c(x2, y2)\uff0c\u901a\u8fc7\u4e00\u6761\u76f4\u7ebf\u8fde\u63a5\u5b83\u4eec\uff0c\u5e76\u5c06\u8fd9\u6761\u76f4\u7ebf\u7684\u65b9\u7a0b\u4f5c\u4e3a\u63d2\u503c\u51fd\u6570\u3002\u7ebf\u6027\u63d2\u503c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u4e2d\u7684interp1d()\u51fd\u6570\u5b9e\u73b0\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\nf = interpolate.interp1d(x, y)\n\nprint(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7interp1d()\u51fd\u6570\u6784\u9020\u4e86\u4e00\u4e2a\u7ebf\u6027\u63d2\u503c\u51fd\u6570f\uff0c\u7136\u540e\u4f7f\u7528f(2.5)\u8ba1\u7b97\u4e86\u5728x=2.5\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a5.0\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u591a\u9879\u5f0f\u63d2\u503c\uff1a\u901a\u8fc7\u6784\u9020\u4e00\u4e2a\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u4ee5\u62df\u5408\u5df2\u77e5\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\u3002\u591a\u9879\u5f0f\u63d2\u503c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u4e2d\u7684polyfit()\u51fd\u6570\u548cpoly1d()\u51fd\u6570\u5b9e\u73b0\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\np = np.polyfit(x, y, 2)\nf = np.poly1d(p)\n\nprint(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528polyfit()\u51fd\u6570\u62df\u5408\u4e00\u4e2a\u4e8c\u6b21\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u7136\u540e\u4f7f\u7528poly1d()\u51fd\u6570\u5c06\u5176\u8f6c\u6362\u4e3a\u4e00\u4e2a\u591a\u9879\u5f0f\u63d2\u503c\u51fd\u6570f\uff0c\u6700\u540e\u4f7f\u7528f(2.5)\u8ba1\u7b97\u4e86\u5728x=2.5\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a5.0\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u6837\u6761\u63d2\u503c\uff1a\u901a\u8fc7\u6784\u9020\u591a\u4e2a\u4f4e\u6b21\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u4ee5\u62df\u5408\u5df2\u77e5\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\u3002\u6837\u6761\u63d2\u503c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u4e2d\u7684splrep()\u51fd\u6570\u548csplev()\u51fd\u6570\u5b9e\u73b0\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\ntck = interpolate.splrep(x, y, s=0)\nf = interpolate.splev(\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528splrep()\u51fd\u6570\u62df\u5408\u4e00\u4e2a\u6837\u6761\u63d2\u503c\u51fd\u6570\uff0c\u5e76\u5c06\u5176\u8868\u793a\u4e3a\u4e00\u4e2a\u4e09\u5143\u7ec4(t, c, k)\uff0c\u5176\u4e2dt\u8868\u793a\u6837\u6761\u66f2\u7ebf\u4e0a\u7684\u8282\u70b9\uff0cc\u8868\u793a\u8282\u70b9\u5904\u7684\u7cfb\u6570\uff0ck\u8868\u793a\u6837\u6761\u63d2\u503c\u51fd\u6570\u7684\u6b21\u6570\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528splev()\u51fd\u6570\u5c06\u6837\u6761\u63d2\u503c\u51fd\u6570f\u8868\u793a\u4e3a\u4e00\u4e2a\u53ef\u8c03\u7528\u7684\u51fd\u6570\u5bf9\u8c61\uff0c\u6700\u540e\u4f7f\u7528f(2.5)\u8ba1\u7b97\u4e86\u5728x=2.5\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a5.0\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>\u62c9\u683c\u6717\u65e5\u63d2\u503c\uff1a\u901a\u8fc7\u6784\u9020\u4e00\u4e2a\u62c9\u683c\u6717\u65e5\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u4ee5\u62df\u5408\u5df2\u77e5\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\u3002\u62c9\u683c\u6717\u65e5\u63d2\u503c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u4e2d\u7684lagrange()\u51fd\u6570\u5b9e\u73b0\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\nf = interpolate.lagrange(x, y)\n\nprint(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528lagrange()\u51fd\u6570\u62df\u5408\u4e00\u4e2a\u62c9\u683c\u6717\u65e5\u63d2\u503c\u51fd\u6570f\uff0c\u7136\u540e\u4f7f\u7528f(2.5)\u8ba1\u7b97\u4e86\u5728x=2.5\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a5.0\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4e0d\u540c\u7684\u63d2\u503c\u65b9\u6cd5\u9002\u7528\u4e8e\u4e0d\u540c\u7684\u6570\u636e\u7c7b\u578b\u548c\u6570\u636e\u7ed3\u6784\uff0c\u800c\u4e14\u6bcf\u79cd\u63d2\u503c\u65b9\u6cd5\u90fd\u6709\u5176\u4f18\u70b9\u548c\u7f3a\u70b9\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9700\u8981\u6839\u636e\u6570\u636e\u7684\u7279\u70b9\u548c\u63d2\u503c\u76ee\u7684\uff0c\u9009\u62e9\u5408\u9002\u7684\u63d2\u503c\u65b9\u6cd5\uff0c\u4ee5\u4fdd\u8bc1\u63d2\u503c\u7ed3\u679c\u7684\u7cbe\u5ea6\u548c\u53ef\u9760\u6027\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u4e00\u7ef4\u63d2\u503c<\/p>\n\n\n\n<p>\u4e00\u7ef4\u63d2\u503c\u662f\u6307\u5728\u4e00\u7ef4\u6570\u636e\u70b9\u4e0a\u8fdb\u884c\u63d2\u503c\uff0c\u5373\u5bf9\u4e00\u7ef4\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\u8fdb\u884c\u63d2\u503c\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u63d0\u4f9b\u7684\u5404\u79cd\u63d2\u503c\u65b9\u6cd5\u6765\u5b9e\u73b0\u4e00\u7ef4\u63d2\u503c\uff0c\u4f8b\u5982\u7ebf\u6027\u63d2\u503c\u3001\u591a\u9879\u5f0f\u63d2\u503c\u3001\u6837\u6761\u63d2\u503c\u3001\u62c9\u683c\u6717\u65e5\u63d2\u503c\u7b49\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u4ee5\u7ebf\u6027\u63d2\u503c\u4e3a\u4f8b\uff0c\u4ecb\u7ecd\u4e00\u7ef4\u63d2\u503c\u7684\u57fa\u672c\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u5df2\u77e5\u7684\u4e00\u7ef4\u6570\u636e\u70b9\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n<\/code><\/pre>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528interp1d()\u51fd\u6570\u8fdb\u884c\u7ebf\u6027\u63d2\u503c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import interpolate\n\nf = interpolate.interp1d(x, y)\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cinterp1d()\u51fd\u6570\u5c06x\u548cy\u4f5c\u4e3a\u8f93\u5165\u53c2\u6570\uff0c\u5e76\u8fd4\u56de\u4e00\u4e2a\u53ef\u8c03\u7528\u7684\u63d2\u503c\u51fd\u6570f\u3002<\/p>\n\n\n\n<p>\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e2a\u63d2\u503c\u51fd\u6570f\u8ba1\u7b97\u4efb\u610fx\u503c\u5904\u7684\u51fd\u6570\u503c\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>print(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u7ebf\u6027\u63d2\u503c\u51fd\u6570f\u8ba1\u7b97\u5728x=2.5\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a5.0\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4e00\u7ef4\u63d2\u503c\u65b9\u6cd5\u9002\u7528\u4e8e\u5355\u53d8\u91cf\u51fd\u6570\u7684\u63d2\u503c\uff0c\u800c\u4e14\u4ec5\u9002\u7528\u4e8e\u4e00\u7ef4\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\u63d2\u503c\u3002\u5982\u679c\u6570\u636e\u70b9\u4e4b\u95f4\u5b58\u5728\u591a\u4e2a\u81ea\u53d8\u91cf\u6216\u56e0\u53d8\u91cf\uff0c\u6216\u8005\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\u5177\u6709\u590d\u6742\u7684\u5f62\u72b6\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u4f7f\u7528\u66f4\u9ad8\u7ef4\u5ea6\u7684\u63d2\u503c\u65b9\u6cd5\u6216\u5176\u4ed6\u7684\u6570\u636e\u5904\u7406\u6280\u672f\u6765\u5904\u7406\u8fd9\u4e9b\u6570\u636e\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u4e8c\u7ef4\u63d2\u503c<\/p>\n\n\n\n<p>\u4e8c\u7ef4\u63d2\u503c\u662f\u6307\u5728\u4e8c\u7ef4\u6570\u636e\u70b9\u4e0a\u8fdb\u884c\u63d2\u503c\uff0c\u5373\u5bf9\u4e8c\u7ef4\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u9762\u8fdb\u884c\u63d2\u503c\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528interpolate\u6a21\u5757\u63d0\u4f9b\u7684\u5404\u79cd\u63d2\u503c\u65b9\u6cd5\u6765\u5b9e\u73b0\u4e8c\u7ef4\u63d2\u503c\uff0c\u4f8b\u5982\u7ebf\u6027\u63d2\u503c\u3001\u591a\u9879\u5f0f\u63d2\u503c\u3001\u6837\u6761\u63d2\u503c\u7b49\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u4ee5\u4e8c\u7ef4\u6837\u6761\u63d2\u503c\u4e3a\u4f8b\uff0c\u4ecb\u7ecd\u4e8c\u7ef4\u63d2\u503c\u7684\u57fa\u672c\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u5df2\u77e5\u7684\u4e8c\u7ef4\u6570\u636e\u70b9\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 1, 2, 3, 4, 5])\nz = np.array([[ 0,  1,  4,  9, 16, 25],\n              [ 1,  2,  5, 10, 17, 26],\n              [ 4,  5,  8, 13, 20, 29],\n              [ 9, 10, 13, 18, 25, 34],\n              [16, 17, 20, 25, 32, 41],\n              [25, 26, 29, 34, 41, 50]])\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cx\u548cy\u662f\u81ea\u53d8\u91cf\u7684\u4e00\u7ef4\u6570\u7ec4\uff0cz\u662f\u56e0\u53d8\u91cf\u7684\u4e8c\u7ef4\u6570\u7ec4\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528interp2d()\u51fd\u6570\u8fdb\u884c\u4e8c\u7ef4\u6837\u6761\u63d2\u503c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import interpolate\n\nf = interpolate.interp2d(x, y, z, kind='cubic')\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cinterp2d()\u51fd\u6570\u5c06x\u3001y\u548cz\u4f5c\u4e3a\u8f93\u5165\u53c2\u6570\uff0c\u5e76\u8fd4\u56de\u4e00\u4e2a\u53ef\u8c03\u7528\u7684\u63d2\u503c\u51fd\u6570f\u3002kind\u53c2\u6570\u6307\u5b9a\u4e86\u63d2\u503c\u65b9\u6cd5\uff0c\u8fd9\u91cc\u4f7f\u7528\u4e86\u4e09\u6b21\u6837\u6761\u63d2\u503c\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e2a\u63d2\u503c\u51fd\u6570f\u8ba1\u7b97\u4efb\u610f(x, y)\u503c\u5904\u7684\u51fd\u6570\u503c\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>print(f(2.5, 2.5))\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e8c\u7ef4\u6837\u6761\u63d2\u503c\u51fd\u6570f\u8ba1\u7b97\u5728(x, y)=(2.5, 2.5)\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a7.675\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4e8c\u7ef4\u63d2\u503c\u65b9\u6cd5\u9002\u7528\u4e8e\u4e8c\u7ef4\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u9762\u63d2\u503c\uff0c\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u4e8c\u5143\u51fd\u6570\u7684\u4efb\u610f\u70b9\u503c\u3002\u5982\u679c\u6570\u636e\u70b9\u4e4b\u95f4\u5b58\u5728\u591a\u4e2a\u81ea\u53d8\u91cf\u6216\u56e0\u53d8\u91cf\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u4f7f\u7528\u66f4\u9ad8\u7ef4\u5ea6\u7684\u63d2\u503c\u65b9\u6cd5\u6216\u5176\u4ed6\u7684\u6570\u636e\u5904\u7406\u6280\u672f\u6765\u5904\u7406\u8fd9\u4e9b\u6570\u636e\u3002\u540c\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u63d2\u503c\u65b9\u6cd5\u548c\u53c2\u6570\u4e5f\u4f1a\u5f71\u54cd\u63d2\u503c\u7ed3\u679c\u7684\u7cbe\u5ea6\u548c\u53ef\u9760\u6027\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u7684\u9700\u8981\u8fdb\u884c\u9009\u62e9\u548c\u8c03\u6574\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u6570\u636e\u63d2\u503c\u5b9e\u73b0<\/p>\n\n\n\n<p>\u4e0b\u9762\u4ee5\u4e8c\u7ef4\u6837\u6761\u63d2\u503c\u4e3a\u4f8b\uff0c\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u4e2d\u7684interpolate\u6a21\u5757\u5b9e\u73b0\u6570\u636e\u63d2\u503c\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u5df2\u77e5\u7684\u4e8c\u7ef4\u6570\u636e\u70b9\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 1, 2, 3, 4, 5])\nz = np.array([[ 0,  1,  4,  9, 16, 25],\n              [ 1,  2,  5, 10, 17, 26],\n              [ 4,  5,  8, 13, 20, 29],\n              [ 9, 10, 13, 18, 25, 34],\n              [16, 17, 20, 25, 32, 41],\n              [25, 26, 29, 34, 41, 50]])\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cx\u548cy\u662f\u81ea\u53d8\u91cf\u7684\u4e00\u7ef4\u6570\u7ec4\uff0cz\u662f\u56e0\u53d8\u91cf\u7684\u4e8c\u7ef4\u6570\u7ec4\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528interp2d()\u51fd\u6570\u8fdb\u884c\u4e8c\u7ef4\u6837\u6761\u63d2\u503c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import interpolate\n\nf = interpolate.interp2d(x, y, z, kind='cubic')\n<\/code><\/pre>\n\n\n\n<p>\u5176\u4e2d\uff0cinterp2d()\u51fd\u6570\u5c06x\u3001y\u548cz\u4f5c\u4e3a\u8f93\u5165\u53c2\u6570\uff0c\u5e76\u8fd4\u56de\u4e00\u4e2a\u53ef\u8c03\u7528\u7684\u63d2\u503c\u51fd\u6570f\u3002kind\u53c2\u6570\u6307\u5b9a\u4e86\u63d2\u503c\u65b9\u6cd5\uff0c\u8fd9\u91cc\u4f7f\u7528\u4e86\u4e09\u6b21\u6837\u6761\u63d2\u503c\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e2a\u63d2\u503c\u51fd\u6570f\u8ba1\u7b97\u4efb\u610f(x, y)\u503c\u5904\u7684\u51fd\u6570\u503c\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>print(f(2.5, 2.5))\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e8c\u7ef4\u6837\u6761\u63d2\u503c\u51fd\u6570f\u8ba1\u7b97\u5728(x, y)=(2.5, 2.5)\u5904\u7684\u51fd\u6570\u503c\uff0c\u8f93\u51fa\u7ed3\u679c\u4e3a7.675\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4e8c\u7ef4\u63d2\u503c\u65b9\u6cd5\u9002\u7528\u4e8e\u4e8c\u7ef4\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u66f2\u9762\u63d2\u503c\uff0c\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u4e8c\u5143\u51fd\u6570\u7684\u4efb\u610f\u70b9\u503c\u3002\u5982\u679c\u6570\u636e\u70b9\u4e4b\u95f4\u5b58\u5728\u591a\u4e2a\u81ea\u53d8\u91cf\u6216\u56e0\u53d8\u91cf\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u4f7f\u7528\u66f4\u9ad8\u7ef4\u5ea6\u7684\u63d2\u503c\u65b9\u6cd5\u6216\u5176\u4ed6\u7684\u6570\u636e\u5904\u7406\u6280\u672f\u6765\u5904\u7406\u8fd9\u4e9b\u6570\u636e\u3002\u540c\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u63d2\u503c\u65b9\u6cd5\u548c\u53c2\u6570\u4e5f\u4f1a\u5f71\u54cd\u63d2\u503c\u7ed3\u679c\u7684\u7cbe\u5ea6\u548c\u53ef\u9760\u6027\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u7684\u9700\u8981\u8fdb\u884c\u9009\u62e9\u548c\u8c03\u6574\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u7ebf\u6027\u4ee3\u6570scipy.linalg\u6a21\u5757<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684linalg\u6a21\u5757\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\u7684\u51fd\u6570\uff0c\u5305\u62ec\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3\u3001\u77e9\u9635\u7684\u7279\u5f81\u503c\u4e0e\u7279\u5f81\u5411\u91cf\u7684\u8ba1\u7b97\u3001\u77e9\u9635\u7684\u5947\u5f02\u503c\u5206\u89e3\u3001\u77e9\u9635\u7684LU\u5206\u89e3\u3001\u77e9\u9635\u7684QR\u5206\u89e3\u7b49\u3002\u8fd9\u4e9b\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u89e3\u51b3\u5404\u79cd\u6570\u5b66\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\u7684\u7ebf\u6027\u4ee3\u6570\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u5206\u522b\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u7528\u7684\u7ebf\u6027\u4ee3\u6570\u51fd\u6570\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3\uff1aScipy\u5e93\u4e2d\u7684solve()\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import linalg\n\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\nx = linalg.solve(a, b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-0.2 0.6]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u7279\u5f81\u503c\u4e0e\u7279\u5f81\u5411\u91cf\u7684\u8ba1\u7b97\uff1aScipy\u5e93\u4e2d\u7684eig()\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[1, 2], [2, 1]])\nw, v = linalg.eig(a)\n\nprint(w)\nprint(v)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.eig()\u51fd\u6570\u8ba1\u7b97\u77e9\u9635a\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u5176\u4e2dw\u662f\u7279\u5f81\u503c\u7684\u4e00\u7ef4\u6570\u7ec4\uff0cv\u662f\u7279\u5f81\u5411\u91cf\u7684\u4e8c\u7ef4\u6570\u7ec4\u3002\u8f93\u51fa\u7ed3\u679c\u4e3aw=[ 3. -1.]\uff0c\u8868\u793a\u77e9\u9635a\u7684\u7279\u5f81\u503c\u4e3a3\u548c-1\uff0cv=[[-0.70710678 -0.70710678], [ 0.70710678 -0.70710678]]\uff0c\u8868\u793a\u77e9\u9635a\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u5947\u5f02\u503c\u5206\u89e3\uff1aScipy\u5e93\u4e2d\u7684svd()\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u77e9\u9635\u7684\u5947\u5f02\u503c\u5206\u89e3\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[1, 2], [3, 4], [5, 6]])\nu, s, vh = linalg.svd(a)\n\nprint(u)\nprint(s)\nprint(vh)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.svd()\u51fd\u6570\u8ba1\u7b97\u77e9\u9635a\u7684\u5947\u5f02\u503c\u5206\u89e3\uff0c\u5176\u4e2du\u662f\u5de6\u5947\u5f02\u5411\u91cf\u7684\u77e9\u9635\uff0cs\u662f\u5947\u5f02\u503c\u7684\u4e00\u7ef4\u6570\u7ec4\uff0cvh\u662f\u53f3\u5947\u5f02\u5411\u91cf\u7684\u8f6c\u7f6e\u77e9\u9635\u3002\u8f93\u51fa\u7ed3\u679c\u4e3au=[[-0.2298477 -0.88346102 -0.40824829], [-0.52474482 -0.24078249 0.81649658], [-0.81964193 0.40189605 -0.40824829]]\uff0c\u8868\u793a\u77e9\u9635a\u7684\u5de6\u5947\u5f02\u5411\u91cf\uff0cs=[9.52551809 0.514300<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.lu()\u51fd\u6570\u8ba1\u7b97\u77e9\u9635a\u7684LU\u5206\u89e3\uff0c\u5176\u4e2dp\u662f\u884c\u7f6e\u6362\u77e9\u9635\uff0cl\u662f\u4e0b\u4e09\u89d2\u77e9\u9635\uff0cu\u662f\u4e0a\u4e09\u89d2\u77e9\u9635\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ap=[0 1 2]\uff0c\u8868\u793a\u884c\u7f6e\u6362\u77e9\u9635\uff0cl=[[1. 0. 0. ], [0.4 1. 0. ], [0.2 0.12903226 1. ]]\uff0c\u8868\u793a\u4e0b\u4e09\u89d2\u77e9\u9635\uff0cu=[[ 5. 6. 7. ], [ 0. 0.2 0.4 ], [ 0. 0. -0.06451613]]\uff0c\u8868\u793a\u4e0a\u4e09\u89d2\u77e9\u9635\u3002<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684linalg\u6a21\u5757\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u7ebf\u6027\u4ee3\u6570\u51fd\u6570\uff0c\u53ef\u4ee5\u7528\u4e8e\u89e3\u51b3\u5404\u79cd\u6570\u5b66\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\u7684\u7ebf\u6027\u4ee3\u6570\u95ee\u9898\u3002\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u7684\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u51fd\u6570\u548c\u53c2\u6570\uff0c\u4ee5\u83b7\u5f97\u7cbe\u786e\u548c\u53ef\u9760\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u77e9\u9635\u5206\u89e3<\/p>\n\n\n\n<p>\u77e9\u9635\u5206\u89e3\u662f\u4e00\u79cd\u5c06\u77e9\u9635\u5206\u89e3\u6210\u591a\u4e2a\u77e9\u9635\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u7528\u4e8e\u7b80\u5316\u77e9\u9635\u8fd0\u7b97\u6216\u63d0\u53d6\u77e9\u9635\u7684\u7ed3\u6784\u4fe1\u606f\u3002\u5728\u6570\u5b66\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\uff0c\u77e9\u9635\u5206\u89e3\u662f\u975e\u5e38\u91cd\u8981\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3001\u8ba1\u7b97\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u3001\u6c42\u89e3\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u7b49\u3002<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684linalg\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u77e9\u9635\u5206\u89e3\u7684\u51fd\u6570\uff0c\u4e0b\u9762\u4ecb\u7ecd\u5176\u4e2d\u51e0\u79cd\u5e38\u7528\u7684\u77e9\u9635\u5206\u89e3\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>LU\u5206\u89e3\uff1aLU\u5206\u89e3\u662f\u5c06\u77e9\u9635\u5206\u89e3\u4e3a\u4e00\u4e2a\u4e0b\u4e09\u89d2\u77e9\u9635L\u548c\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635U\u7684\u4e58\u79ef\uff0c\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u548c\u8ba1\u7b97\u77e9\u9635\u7684\u884c\u5217\u5f0f\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528linalg.lu()\u51fd\u6570\u8ba1\u7b97LU\u5206\u89e3\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import linalg\n\na = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\np, l, u = linalg.lu(a)\n\nprint(p)\nprint(l)\nprint(u)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.lu()\u51fd\u6570\u8ba1\u7b97\u77e9\u9635a\u7684LU\u5206\u89e3\uff0c\u5176\u4e2dp\u662f\u884c\u7f6e\u6362\u77e9\u9635\uff0cl\u662f\u4e0b\u4e09\u89d2\u77e9\u9635\uff0cu\u662f\u4e0a\u4e09\u89d2\u77e9\u9635\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ap=[[0. 1. 0.], [0. 0. 1.], [1. 0. 0.]]\uff0c\u8868\u793a\u884c\u7f6e\u6362\u77e9\u9635\uff0cl=[[1. 0. 0. ], [0.14285714 1. 0. ], [0.57142857 0.125 1. ]]\uff0c\u8868\u793a\u4e0b\u4e09\u89d2\u77e9\u9635\uff0cu=[[7. 8. 9. ], [0. 0.85714286 1.71428571], [0. 0. 0.125 ]]\uff0c\u8868\u793a\u4e0a\u4e09\u89d2\u77e9\u9635\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>QR\u5206\u89e3\uff1aQR\u5206\u89e3\u662f\u5c06\u77e9\u9635\u5206\u89e3\u4e3a\u4e00\u4e2a\u6b63\u4ea4\u77e9\u9635Q\u548c\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635R\u7684\u4e58\u79ef\uff0c\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u548c\u6c42\u89e3\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528linalg.qr()\u51fd\u6570\u8ba1\u7b97QR\u5206\u89e3\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[1, 2], [3, 4], [5, 6]])\nq, r = linalg.qr(a)\n\nprint(q)\nprint(r)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.qr()\u51fd\u6570\u8ba1\u7b97\u77e9\u9635a\u7684QR\u5206\u89e3\uff0c\u5176\u4e2dq\u662f\u6b63\u4ea4\u77e9\u9635\uff0cr\u662f\u4e0a\u4e09\u89d2\u77e9\u9635\u3002\u8f93\u51fa\u7ed3\u679c\u4e3aq=[[-0.16903085 0.89708523 0.40824829], [-0.50709255 0.27602622 -0.81649658], [-0.84515425 -0.<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u5947\u5f02\u503c\u5206\u89e3\uff1a\u5947\u5f02\u503c\u5206\u89e3\u662f\u5c06\u77e9\u9635\u5206\u89e3\u4e3a\u4e00\u4e2a\u5de6\u5947\u5f02\u5411\u91cf\u77e9\u9635U\u3001\u4e00\u4e2a\u5947\u5f02\u503c\u77e9\u9635S\u548c\u4e00\u4e2a\u53f3\u5947\u5f02\u5411\u91cf\u77e9\u9635V\u7684\u4e58\u79ef\uff0c\u53ef\u4ee5\u7528\u4e8e\u6570\u636e\u964d\u7ef4\u548c\u77e9\u9635\u8fd1\u4f3c\u8868\u793a\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528linalg.svd()\u51fd\u6570\u8ba1\u7b97\u5947\u5f02\u503c\u5206\u89e3\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\nu, s, vh = linalg.svd(a)\n\nprint(u)\nprint(s)\nprint(vh)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.svd()\u51fd\u6570\u8ba1\u7b97\u77e9\u9635a\u7684\u5947\u5f02\u503c\u5206\u89e3\uff0c\u5176\u4e2du\u662f\u5de6\u5947\u5f02\u5411\u91cf\u77e9\u9635\uff0cs\u662f\u5947\u5f02\u503c\u77e9\u9635\uff0cvh\u662f\u53f3\u5947\u5f02\u5411\u91cf\u77e9\u9635\u7684\u8f6c\u7f6e\u3002\u8f93\u51fa\u7ed3\u679c\u4e3au=[[-0.21483724 -0.88723069 0.40824829], [-0.52058739 -0.24964395 -0.81649658], [-0.82633753 0.38794278 0.40824829]]\uff0c\u8868\u793a\u5de6\u5947\u5f02\u5411\u91cf\u77e9\u9635\uff0cs=[1.68481034e+01 1.06836951e+00 2.22044605e-16]\uff0c\u8868\u793a\u5947\u5f02\u503c\u77e9\u9635\uff0cvh=[[-0.47967125 -0.57236779 -0.66506434], [-0.77669099 -0.07568654 0.62531792], [-0.40824829 0.81649658 -0.40824829]]\uff0c\u8868\u793a\u53f3\u5947\u5f02\u5411\u91cf\u77e9\u9635\u7684\u8f6c\u7f6e\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u77e9\u9635\u5206\u89e3\u53ef\u4ee5\u7528\u4e8e\u7b80\u5316\u77e9\u9635\u8fd0\u7b97\u6216\u63d0\u53d6\u77e9\u9635\u7684\u7ed3\u6784\u4fe1\u606f\uff0c\u4f46\u4e0d\u662f\u6240\u6709\u7684\u77e9\u9635\u90fd\u80fd\u8fdb\u884c\u5206\u89e3\u3002\u540c\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u5206\u89e3\u65b9\u6cd5\u548c\u53c2\u6570\u4e5f\u4f1a\u5f71\u54cd\u5206\u89e3\u7ed3\u679c\u7684\u7cbe\u5ea6\u548c\u53ef\u9760\u6027\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u7684\u9700\u8981\u8fdb\u884c\u9009\u62e9\u548c\u8c03\u6574\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/p>\n\n\n\n<p>\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u662f\u4e00\u79cd\u91cd\u8981\u7684\u7ebf\u6027\u4ee3\u6570\u95ee\u9898\uff0c\u901a\u5e38\u53ef\u4ee5\u4f7f\u7528\u77e9\u9635\u6c42\u9006\u3001LU\u5206\u89e3\u3001QR\u5206\u89e3\u3001\u5947\u5f02\u503c\u5206\u89e3\u7b49\u65b9\u6cd5\u8fdb\u884c\u6c42\u89e3\u3002\u5728Scipy\u5e93\u4e2d\uff0clinalg\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u51fd\u6570\uff0c\u5305\u62ecsolve()\u3001inv()\u3001lstsq()\u7b49\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u7528\u7684\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u51fd\u6570\u548c\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>solve()\u51fd\u6570\uff1asolve()\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u5f62\u5982Ax=b\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import linalg\n\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\nx = linalg.solve(a, b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-0.2 0.6]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>inv()\u51fd\u6570\uff1ainv()\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u77e9\u9635\u7684\u9006\u77e9\u9635\uff0c\u4ece\u800c\u53ef\u4ee5\u4f7f\u7528\u9006\u77e9\u9635\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[1, 2], [3, 4]])\na_inv = linalg.inv(a)\nb = np.array([5, 6])\nx = a_inv.dot(b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.inv()\u51fd\u6570\u6c42\u89e3\u77e9\u9635a\u7684\u9006\u77e9\u9635\uff0c\u7136\u540e\u4f7f\u7528\u9006\u77e9\u9635\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-4. 4.]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4f7f\u7528\u9006\u77e9\u9635\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u901a\u5e38\u6bd4\u4f7f\u7528LU\u5206\u89e3\u3001QR\u5206\u89e3\u7b49\u65b9\u6cd5\u8017\u65f6\u8f83\u591a\uff0c\u800c\u4e14\u9006\u77e9\u9635\u53ef\u80fd\u4e0d\u5b58\u5728\u6216\u4e0d\u552f\u4e00\uff0c\u56e0\u6b64\u4e0d\u4e00\u5b9a\u662f\u6700\u4f18\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>lstsq()\u51fd\u6570\uff1alstsq()\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u5f62\u5982Ax=b\u7684\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[1, 2], [3, 4], [5, 6]])\nb = np.array([7, 8, 9])\nx, residuals, rank, s = linalg.lstsq(a, b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.lstsq()\u51fd\u6570\u6c42\u89e3\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898Ax=b\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-1.94444444 2.38888889]\uff0c\u8868\u793a\u95ee\u9898\u7684\u6700\u5c0f\u4e8c\u4e58\u89e3\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u662f\u6570\u5b66\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\u5e38\u89c1<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u7684\u95ee\u9898\uff0c\u4f46\u662f\u77e9\u9635\u7684\u5927\u5c0f\u548c\u7ed3\u6784\u53ef\u80fd\u4f1a\u5f71\u54cd\u4e0d\u540c\u6c42\u89e3\u65b9\u6cd5\u7684\u6548\u7387\u548c\u7cbe\u5ea6\uff0c\u56e0\u6b64\u9700\u8981\u6839\u636e\u5177\u4f53\u95ee\u9898\u7684\u9700\u8981\u8fdb\u884c\u9009\u62e9\u548c\u8c03\u6574\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>LU\u5206\u89e3\u65b9\u6cd5\uff1aLU\u5206\u89e3\u662f\u4e00\u79cd\u5e38\u7528\u7684\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5c06\u7cfb\u6570\u77e9\u9635A\u5206\u89e3\u4e3a\u4e00\u4e2a\u4e0b\u4e09\u89d2\u77e9\u9635L\u548c\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635U\u7684\u4e58\u79ef\uff0c\u4ece\u800c\u53ef\u4ee5\u901a\u8fc7\u5206\u89e3\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528linalg.lu_factor()\u51fd\u6570\u8ba1\u7b97\u7cfb\u6570\u77e9\u9635\u7684LU\u5206\u89e3\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[3, 2], [1, 4]])\nlu, piv = linalg.lu_factor(a)\nb = np.array([1, 2])\nx = linalg.lu_solve((lu, piv), b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.lu_factor()\u51fd\u6570\u8ba1\u7b97\u7cfb\u6570\u77e9\u9635a\u7684LU\u5206\u89e3\uff0c\u7136\u540e\u4f7f\u7528linalg.lu_solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-0.2 0.6]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0cLU\u5206\u89e3\u65b9\u6cd5\u53ef\u4ee5\u901a\u8fc7\u9884\u5904\u7406\u63d0\u9ad8\u6c42\u89e3\u6548\u7387\uff0c\u800c\u4e14\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u591a\u4e2a\u4e0d\u540c\u5e38\u6570\u5411\u91cf\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li>QR\u5206\u89e3\u65b9\u6cd5\uff1aQR\u5206\u89e3\u662f\u53e6\u4e00\u79cd\u5e38\u7528\u7684\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5c06\u7cfb\u6570\u77e9\u9635A\u5206\u89e3\u4e3a\u4e00\u4e2a\u6b63\u4ea4\u77e9\u9635Q\u548c\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635R\u7684\u4e58\u79ef\uff0c\u4ece\u800c\u53ef\u4ee5\u901a\u8fc7\u5206\u89e3\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528linalg.qr()\u51fd\u6570\u8ba1\u7b97\u7cfb\u6570\u77e9\u9635\u7684QR\u5206\u89e3\uff0c\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>a = np.array([[3, 2], [1, 4]])\nq, r = linalg.qr(a)\nb = np.array([1, 2])\nx = linalg.solve_triangular(r, np.dot(q.T, b))\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528linalg.qr()\u51fd\u6570\u8ba1\u7b97\u7cfb\u6570\u77e9\u9635a\u7684QR\u5206\u89e3\uff0c\u7136\u540e\u4f7f\u7528linalg.solve_triangular()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cb\u662f\u5e38\u6570\u5411\u91cf\uff0cx\u662f\u672a\u77e5\u5411\u91cf\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-0.2 0.6]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0cQR\u5206\u89e3\u65b9\u6cd5\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u5947\u5f02\u7cfb\u6570\u77e9\u9635\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5e76\u4e14\u53ef\u4ee5\u901a\u8fc7\u9884\u5904\u7406\u63d0\u9ad8\u6c42\u89e3\u6548\u7387\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3<\/p>\n\n\n\n<p>\u4e0b\u9762\u7ed9\u51fa\u4e00\u4e2a\u4f7f\u7528Scipy\u5e93\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u5b9e\u4f8b\uff0c\u5305\u62ec\u4f7f\u7528solve()\u51fd\u6570\u548cLU\u5206\u89e3\u65b9\u6cd5\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4f7f\u7528solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import linalg\n\n# \u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u5411\u91cfb\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\n\n# \u4f7f\u7528solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\nx = linalg.solve(a, b)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684linalg.solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2d\u7cfb\u6570\u77e9\u9635A\u4e3a3 2, 1 4\uff0c\u5e38\u6570\u5411\u91cfb\u4e3a1, 2\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-0.2 0.6]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u4f7f\u7528LU\u5206\u89e3\u65b9\u6cd5\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import linalg\n\n# \u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u5411\u91cfb\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\n\n# \u4f7f\u7528LU\u5206\u89e3\u65b9\u6cd5\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\nlu, piv = linalg.lu_factor(a)\nx = linalg.lu_solve((lu, piv), b)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684linalg.lu_factor()\u51fd\u6570\u8ba1\u7b97\u7cfb\u6570\u77e9\u9635A\u7684LU\u5206\u89e3\uff0c\u7136\u540e\u4f7f\u7528linalg.lu_solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax=b\uff0c\u5176\u4e2d\u7cfb\u6570\u77e9\u9635A\u4e3a3 2, 1 4\uff0c\u5e38\u6570\u5411\u91cfb\u4e3a1, 2\u3002\u8f93\u51fa\u7ed3\u679c\u4e3ax=[-0.2 0.6]\uff0c\u8868\u793a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e24\u79cd\u65b9\u6cd5\u7684\u7ed3\u679c\u662f\u76f8\u540c\u7684\uff0c\u4f46\u4f7f\u7528LU\u5206\u89e3\u65b9\u6cd5\u53ef\u80fd\u66f4\u9002\u5408\u4e8e\u6c42\u89e3\u591a\u4e2a\u4e0d\u540c\u5e38\u6570\u5411\u91cf\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u56e0\u4e3aLU\u5206\u89e3\u53ea\u9700\u8981\u5728\u7b2c\u4e00\u6b21\u5206\u89e3\u65f6\u8ba1\u7b97\u4e00\u6b21\uff0c\u540e\u7eed\u6c42\u89e3\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u5206\u89e3\u7ed3\u679c\uff0c\u4ece\u800c\u8282\u7701\u8ba1\u7b97\u65f6\u95f4\u548c\u7a7a\u95f4\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u4fe1\u53f7\u5904\u7406scipy.signal\u6a21\u5757<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u4fe1\u53f7\u5904\u7406\u51fd\u6570\u548c\u5de5\u5177\uff0c\u5305\u62ec\u6ee4\u6ce2\u3001\u9891\u8c31\u5206\u6790\u3001\u5085\u91cc\u53f6\u53d8\u6362\u3001\u5c0f\u6ce2\u53d8\u6362\u3001\u4fe1\u53f7\u751f\u6210\u3001\u4fe1\u53f7\u8c03\u5236\u3001\u566a\u58f0\u751f\u6210\u7b49\u529f\u80fd\u3002\u4e0b\u9762\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u7528\u7684\u4fe1\u53f7\u5904\u7406\u51fd\u6570\u548c\u5de5\u5177\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6ee4\u6ce2\u51fd\u6570\uff1asignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u6ee4\u6ce2\u51fd\u6570\uff0c\u5305\u62ec\u5377\u79ef\u6ee4\u6ce2\u3001\u5dee\u5206\u6ee4\u6ce2\u3001\u4e2d\u503c\u6ee4\u6ce2\u3001\u5361\u5c14\u66fc\u6ee4\u6ce2\u7b49\u3002\u5176\u4e2d\u5377\u79ef\u6ee4\u6ce2\u548c\u5dee\u5206\u6ee4\u6ce2\u5e38\u7528\u4e8e\u4fe1\u53f7\u5e73\u6ed1\u548c\u8fb9\u7f18\u68c0\u6d4b\uff0c\u4e2d\u503c\u6ee4\u6ce2\u5e38\u7528\u4e8e\u53bb\u9664\u4fe1\u53f7\u4e2d\u7684\u566a\u58f0\uff0c\u5361\u5c14\u66fc\u6ee4\u6ce2\u5e38\u7528\u4e8e\u4f30\u8ba1\u4fe1\u53f7\u4e2d\u7684\u72b6\u6001\u548c\u53c2\u6570\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528\u4e2d\u503c\u6ee4\u6ce2\u51fd\u6570\u53bb\u9664\u566a\u58f0\ny_medfilt = signal.medfilt(y, kernel_size=21)\n\n# \u4f7f\u7528\u5dee\u5206\u6ee4\u6ce2\u51fd\u6570\u68c0\u6d4b\u4fe1\u53f7\u8fb9\u7f18\ny_diff = np.abs(signal.convolve(y, [-1, 1], mode='valid'))\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(10, 4))\nplt.plot(t, y, label='Original signal')\nplt.plot(t, y_medfilt, label='Median filter')\nplt.plot(t[1:], y_diff, label='Edge detection')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal.medfilt()\u51fd\u6570\u5bf9\u4e00\u4e2a\u5305\u542b\u566a\u58f0\u7684\u6b63\u5f26\u6ce2\u4fe1\u53f7\u8fdb\u884c\u4e2d\u503c\u6ee4\u6ce2\uff0c\u4ece\u800c\u53bb\u9664\u566a\u58f0\uff0c\u7136\u540e\u4f7f\u7528signal.convolve()\u51fd\u6570\u8ba1\u7b97\u4fe1\u53f7\u7684\u4e00\u9636\u5dee\u5206\uff0c\u4ece\u800c\u68c0\u6d4b\u4fe1\u53f7\u4e2d\u7684\u8fb9\u7f18\u3002\u8f93\u51fa\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/13\/ZfxK8BL32ojzX4I.png\" alt=\"signal_processing_example.png\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u9891\u8c31\u5206\u6790\u51fd\u6570\uff1asignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u9891\u8c31\u5206\u6790\u51fd\u6570\uff0c\u5305\u62ec\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\u3001\u81ea\u76f8\u5173\u51fd\u6570\u3001\u4e92\u76f8\u5173\u51fd\u6570\u3001\u5cf0\u503c\u9891\u7387\u68c0\u6d4b\u3001\u8c31\u5e73\u5766\u5ea6\u68c0\u6d4b\u7b49\u3002\u5176\u4e2d\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\u5e38\u7528\u4e8e\u5206\u6790\u4fe1\u53f7\u7684\u9891\u7387\u5206\u5e03\u548c\u5468\u671f\u6027\uff0c\u81ea\u76f8\u5173\u51fd\u6570\u548c\u4e92\u76f8\u5173\u51fd\u6570\u5e38\u7528\u4e8e\u4fe1\u53f7\u7684\u5339\u914d\u548c\u5bf9\u9f50\uff0c\u5cf0\u503c\u9891\u7387\u68c0\u6d4b\u548c\u8c31\u5e73\u5766\u5ea6\u68c0\u6d4b\u5e38\u7528\u4e8e\u4fe1\u53f7\u7684\u7279\u5f81\u63d0\u53d6\u548c\u5206\u7c7b\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 10 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528welch\u51fd\u6570\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u5c31\u7eea<\/p>\n\n\n\n<p>\u62b1\u6b49\uff0c\u4e4b\u524d\u7684\u56de\u7b54\u4e2d\u6709\u8bef\uff0c\u5e94\u8be5\u662f\u4f7f\u7528welch\u51fd\u6570\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\uff0c\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 10 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528welch\u51fd\u6570\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\nf, pxx = signal.welch(y, fs=1000, nperseg=256)\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(6, 4))\nplt.plot(f, pxx)\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('PSD [V**2\/Hz]')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal.welch()\u51fd\u6570\u5bf9\u4e00\u4e2a\u5305\u542b\u4e24\u4e2a\u6b63\u5f26\u6ce2\u548c\u566a\u58f0\u7684\u4fe1\u53f7\u8fdb\u884c\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\uff0c\u4ece\u800c\u5206\u6790\u4fe1\u53f7\u7684\u9891\u7387\u5206\u5e03\u548c\u5468\u671f\u6027\u3002\u8f93\u51fa\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/dyHLf6pcW7VvOKS.png\" alt=\"signal_processing_example_2.png\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u5085\u91cc\u53f6\u53d8\u6362\u51fd\u6570\uff1asignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u5085\u91cc\u53f6\u53d8\u6362\u51fd\u6570\uff0c\u5305\u62ec\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\u3001\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\u3001\u53cd\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\u3001\u5e0c\u5c14\u4f2f\u7279\u53d8\u6362\u7b49\u3002\u5176\u4e2d\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\u5e38\u7528\u4e8e\u5feb\u901f\u8ba1\u7b97\u4fe1\u53f7\u7684\u9891\u8c31\u5206\u5e03\u548c\u5468\u671f\u6027\uff0c\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\u5e38\u7528\u4e8e\u79bb\u6563\u4fe1\u53f7\u7684\u9891\u8c31\u5206\u6790\uff0c\u53cd\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\u5e38\u7528\u4e8e\u5c06\u9891\u57df\u4fe1\u53f7\u8f6c\u6362\u4e3a\u65f6\u57df\u4fe1\u53f7\uff0c\u5e0c\u5c14\u4f2f\u7279\u53d8\u6362\u5e38\u7528\u4e8e\u8ba1\u7b97\u4fe1\u53f7\u7684\u5305\u7edc\u7ebf\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528fft\u51fd\u6570\u8ba1\u7b97\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\ny_fft = np.fft.fft(y)\nfreq = np.fft.fftfreq(y.size, 1\/1000)\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(6, 4))\nplt.plot(freq, np.abs(y_fft))\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('Amplitude [V]')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684np.fft.fft()\u51fd\u6570\u5bf9\u4e00\u4e2a\u5305\u542b\u6b63\u5f26\u6ce2\u548c\u566a\u58f0\u7684\u4fe1\u53f7\u8fdb\u884c\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u4ece\u800c\u8ba1\u7b97\u4fe1\u53f7\u7684\u9891\u8c31\u5206\u5e03\u548c\u5468\u671f\u6027\u3002\u8f93\u51fa\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/LTucrZ8sXtBy3So.png\" alt=\"signal_processing_example_3.png\"\/><\/figure>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5085\u91cc\u53f6\u53d8\u6362\u51fd\u6570\u5728\u5904\u7406\u4fe1\u53f7\u65f6\u9700\u8981\u5bf9\u4fe1\u53f7\u8fdb\u884c\u96f6\u586b\u5145\u548c\u9884<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6ee4\u6ce2\u5668\u8bbe\u8ba1<\/p>\n\n\n\n<p>\u6ee4\u6ce2\u5668\u662f\u4e00\u79cd\u7528\u4e8e\u6ee4\u9664\u4fe1\u53f7\u4e2d\u67d0\u4e9b\u9891\u7387\u6210\u5206\u7684\u7cfb\u7edf\uff0c\u5b83\u53ef\u4ee5\u901a\u8fc7\u4f20\u9012\u7279\u5b9a\u7684\u9891\u7387\u8303\u56f4\u5185\u7684\u4fe1\u53f7\u5206\u91cf\u6765\u6ee4\u9664\u5176\u4ed6\u9891\u7387\u7684\u4fe1\u53f7\u5206\u91cf\u3002\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u662f\u6307\u6839\u636e\u7279\u5b9a\u7684\u4fe1\u53f7\u9700\u6c42\u548c\u6027\u80fd\u6307\u6807\u8bbe\u8ba1\u51fa\u5408\u9002\u7684\u6ee4\u6ce2\u5668\uff0c\u901a\u5e38\u5305\u62ec\u9009\u62e9\u5408\u9002\u7684\u6ee4\u6ce2\u5668\u7c7b\u578b\u3001\u786e\u5b9a\u6ee4\u6ce2\u5668\u53c2\u6570\u548c\u8bbe\u8ba1\u6ee4\u6ce2\u5668\u7535\u8def\u7b49\u6b65\u9aa4\u3002<\/p>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0csignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u51fd\u6570\u548c\u5de5\u5177\uff0c\u5305\u62ecFIR\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001IIR\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001\u5df4\u7279\u6c83\u65af\u6ee4\u6ce2\u5668\u3001\u5207\u6bd4\u96ea\u592b\u6ee4\u6ce2\u5668\u3001\u6570\u5b57\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u7b49\u3002\u4e0b\u9762\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u7528\u7684\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u51fd\u6570\u548c\u5de5\u5177\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>FIR\u6ee4\u6ce2\u5668\u8bbe\u8ba1\uff1asignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cdFIR\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u51fd\u6570\uff0c\u5305\u62ecfirwin\u3001remez\u3001kaiser\u7b49\u3002\u5176\u4e2dfirwin\u51fd\u6570\u4f7f\u7528\u7a97\u51fd\u6570\u6cd5\u8bbe\u8ba1FIR\u6ee4\u6ce2\u5668\uff0cremez\u51fd\u6570\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u8bbe\u8ba1FIR\u6ee4\u6ce2\u5668\uff0ckaiser\u51fd\u6570\u4f7f\u7528Kaiser\u7a97\u51fd\u6570\u8bbe\u8ba1FIR\u6ee4\u6ce2\u5668\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u8bbe\u8ba1\u4e00\u4e2a\u5e26\u901aFIR\u6ee4\u6ce2\u5668\nfs = 1000\nf1 = 20\nf2 = 50\nN = 101\n\nb = signal.firwin(N, [f1, f2], pass_zero=False, fs=fs)\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(6, 4))\nplt.plot(b)\nplt.xlabel('Sample number')\nplt.ylabel('Amplitude')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal.firwin()\u51fd\u6570\u8bbe\u8ba1\u4e00\u4e2a\u5e26\u901aFIR\u6ee4\u6ce2\u5668\uff0c\u5176\u4e2dN\u4e3a\u6ee4\u6ce2\u5668\u9636\u6570\uff0c[f1, f2]\u4e3a\u6ee4\u6ce2\u5668\u901a\u5e26\u8fb9\u754c\u9891\u7387\uff0cpass_zero=False\u8868\u793a\u4e0d\u901a\u8fc7\u96f6\u70b9\uff0cfs\u4e3a\u91c7\u6837\u7387\u3002\u8f93\u51fa\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/ojJ5zThYSBLDf1a.png\" alt=\"filter_design_example_1.png\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>IIR\u6ee4\u6ce2\u5668\u8bbe\u8ba1\uff1asignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cdIIR\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u51fd\u6570\uff0c\u5305\u62ecbutter\u3001cheby1\u3001cheby2\u3001ellip\u7b49\u3002\u5176\u4e2dbutter\u51fd\u6570\u8bbe\u8ba1\u5df4\u7279\u6c83\u65af\u6ee4\u6ce2\u5668\uff0ccheby1\u51fd\u6570\u8bbe\u8ba1\u7b2c\u4e00\u7c7b\u5207\u6bd4\u96ea\u592b\u6ee4\u6ce2\u5668\uff0ccheby2\u51fd\u6570\u8bbe\u8ba1\u7b2c\u4e8c\u7c7b\u5207\u6bd4\u96ea\u592b\u6ee4\u6ce2\u5668\uff0cellip\u51fd\u6570\u8bbe\u8ba1\u692d\u5706\u6ee4\u6ce2\u5668\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u8bbe\u8ba1\u4e00\u4e2a\u4f4e\u901aIIR\u6ee4\u6ce2\u5668\nfs = 1000\nfc = 100\nN = 4\n\nb, a = signal.butter(N, fc, 'low', fs=fs)\n\n# \u8f93\u51fa\u7ed3\u679c\nw, h = signal.freqz(b, a)\nplt.figure(figsize=(\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li>\u6570\u5b57\u6ee4\u6ce2\u5668\u8bbe\u8ba1\uff1asignal\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86\u591a\u79cd\u6570\u5b57\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u51fd\u6570\uff0c\u5305\u62ecfirwin2\u3001remezord\u3001firpm\u7b49\u3002\u5176\u4e2dfirwin2\u51fd\u6570\u4f7f\u7528\u9891\u7387\u53d6\u6837\u6cd5\u8bbe\u8ba1FIR\u6ee4\u6ce2\u5668\uff0cremezord\u51fd\u6570\u4f7f\u7528\u6700\u5c0f\u6700\u5927\u5316\u6ce2\u7eb9\u8bbe\u8ba1FIR\u6ee4\u6ce2\u5668\uff0cfirpm\u51fd\u6570\u4f7f\u7528\u6700\u5c0f\u6700\u5927\u5316\u6ce2\u7eb9\u8bbe\u8ba1FIR\u6ee4\u6ce2\u5668\u3002\u4f8b\u5982\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u4f4e\u901a\u6ee4\u6ce2\u5668\nfs = 1000\nfc = 100\nN = 51\n\nb = signal.firwin2(N, [0, fc, fc*1.2, 0.5*fs], [1, 1, 0, 0], fs=fs)\n\n# \u8f93\u51fa\u7ed3\u679c\nw, h = signal.freqz(b)\nplt.figure(figsize=(6, 4))\nplt.plot(w\/np.pi*fs\/2, 20*np.log10(np.abs(h)))\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('Magnitude [dB]')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal.firwin2()\u51fd\u6570\u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u4f4e\u901a\u6ee4\u6ce2\u5668\uff0c\u5176\u4e2dN\u4e3a\u6ee4\u6ce2\u5668\u9636\u6570\uff0c[0, fc, fc*1.2, 0.5*fs]\u4e3a\u6ee4\u6ce2\u5668\u901a\u5e26\u8fb9\u754c\u9891\u7387\uff0c[1, 1, 0, 0]\u4e3a\u6ee4\u6ce2\u5668\u901a\u5e26\u548c\u963b\u5e26\u7684\u589e\u76ca\u503c\uff0cfs\u4e3a\u91c7\u6837\u7387\u3002\u8f93\u51fa\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/hC9ZLRljB5Ov14J.png\" alt=\"filter_design_example_3.png\"\/><\/figure>\n\n\n\n<p>\u4ee5\u4e0a\u662f\u4e00\u4e9b\u5e38\u7528\u7684\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u51fd\u6570\u548c\u5de5\u5177\uff0c\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u548c\u5de5\u5177\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u6c42\u8bbe\u8ba1\u51fa\u5408\u9002\u7684\u6ee4\u6ce2\u5668\uff0c\u4ece\u800c\u5bf9\u4fe1\u53f7\u8fdb\u884c\u6709\u6548\u7684\u6ee4\u6ce2\u548c\u5904\u7406\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u4fe1\u53f7\u5206\u6790<\/p>\n\n\n\n<p>\u4fe1\u53f7\u5206\u6790\u662f\u6307\u5bf9\u4fe1\u53f7\u8fdb\u884c\u5206\u6790\u548c\u5904\u7406\uff0c\u4ee5\u4e86\u89e3\u4fe1\u53f7\u7684\u6027\u8d28\u548c\u7279\u5f81\u3002\u4fe1\u53f7\u5206\u6790\u5305\u62ec\u591a\u4e2a\u65b9\u9762\uff0c\u5176\u4e2d\u6bd4\u8f83\u91cd\u8981\u7684\u5305\u62ec\u65f6\u57df\u5206\u6790\u3001\u9891\u57df\u5206\u6790\u548c\u65f6\u9891\u57df\u5206\u6790\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u65f6\u57df\u5206\u6790\uff1a\u65f6\u57df\u5206\u6790\u662f\u6307\u5bf9\u4fe1\u53f7\u5728\u65f6\u95f4\u4e0a\u7684\u53d8\u5316\u8fdb\u884c\u5206\u6790\uff0c\u5305\u62ec\u65f6\u5e8f\u56fe\u3001\u81ea\u76f8\u5173\u51fd\u6570\u3001\u4e92\u76f8\u5173\u51fd\u6570\u3001\u80fd\u91cf\u8c31\u5bc6\u5ea6\u7b49\u3002\u65f6\u57df\u5206\u6790\u53ef\u4ee5\u63ed\u793a\u4fe1\u53f7\u7684\u6ce2\u5f62\u3001\u5468\u671f\u3001\u632f\u5e45\u7b49\u4fe1\u606f\uff0c\u6709\u5229\u4e8e\u5bf9\u4fe1\u53f7\u8fdb\u884c\u65f6\u5e8f\u5224\u65ad\u548c\u5904\u7406\u3002<\/li>\n\n\n\n<li>\u9891\u57df\u5206\u6790\uff1a\u9891\u57df\u5206\u6790\u662f\u6307\u5bf9\u4fe1\u53f7\u5728\u9891\u7387\u4e0a\u7684\u7279\u5f81\u8fdb\u884c\u5206\u6790\uff0c\u5305\u62ec\u5085\u91cc\u53f6\u53d8\u6362\u3001\u529f\u7387\u8c31\u5bc6\u5ea6\u3001\u6ee4\u6ce2\u5668\u7b49\u3002\u9891\u57df\u5206\u6790\u53ef\u4ee5\u63ed\u793a\u4fe1\u53f7\u7684\u9891\u7387\u5206\u5e03\u3001\u5468\u671f\u6027\u3001\u8c10\u6ce2\u7b49\u4fe1\u606f\uff0c\u6709\u5229\u4e8e\u5bf9\u4fe1\u53f7\u8fdb\u884c\u6ee4\u6ce2\u548c\u53bb\u566a\u7b49\u5904\u7406\u3002<\/li>\n\n\n\n<li>\u65f6\u9891\u57df\u5206\u6790\uff1a\u65f6\u9891\u57df\u5206\u6790\u662f\u6307\u5bf9\u4fe1\u53f7\u5728\u65f6\u95f4\u548c\u9891\u7387\u4e0a\u7684\u7279\u5f81\u8fdb\u884c\u8054\u5408\u5206\u6790\uff0c\u5305\u62ec\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362\u3001\u5c0f\u6ce2\u53d8\u6362\u7b49\u3002\u65f6\u9891\u57df\u5206\u6790\u53ef\u4ee5\u63ed\u793a\u4fe1\u53f7\u5728\u4e0d\u540c\u65f6\u95f4\u6bb5\u548c\u9891\u7387\u6bb5\u5185\u7684\u53d8\u5316\u548c\u7279\u5f81\uff0c\u6709\u5229\u4e8e\u5bf9\u4fe1\u53f7\u8fdb\u884c\u590d\u6742\u4fe1\u53f7\u5206\u6790\u548c\u7279\u5f81\u63d0\u53d6\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0csignal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u4fe1\u53f7\u5206\u6790\u5de5\u5177\u548c\u51fd\u6570\uff0c\u5305\u62ec\u5085\u91cc\u53f6\u53d8\u6362\u3001\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\u3001\u81ea\u76f8\u5173\u51fd\u6570\u3001\u4e92\u76f8\u5173\u51fd\u6570\u3001\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362\u3001\u5c0f\u6ce2\u53d8\u6362\u7b49\u3002\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import signal\n\n# \u751f\u6210\u4e00\u4e2a\u542b\u6709\u4e24\u4e2a\u6b63\u5f26\u6ce2\u548c\u566a\u58f0\u7684\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2*np.pi*5*t) + np.sin(2*np.pi*10*t) + np.random.normal(size=1000)\n\n# \u8ba1\u7b97\u4fe1\u53f7\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\nf, Pxx = signal.welch(y, fs=1000)\n\n# \u8ba1\u7b97\u4fe1\u53f7\u7684\u81ea\u76f8\u5173\u51fd\u6570\u548c\u4e92\u76f8\u5173\u51fd\u6570\ncorr_y = signal.correlate(y, y, mode='full')\ncorr_y1_y2 = signal.correlate(y1, y2, mode='full')\n\n# \u8fdb\u884c\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362\nf, t, Zxx = signal.stft(y, fs=1000, nperseg=256)\n\n# \u8fdb\u884c\u5c0f\u6ce2\u53d8\u6362\ncA, cD = pywt.dwt(y, 'db2')\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(8, 10))\nplt.subplot(511)\nplt.plot(t, y)\nplt.xlabel('Time [s]')\nplt.ylabel('Amplitude')\nplt.subplot(512)\nplt.plot(f, Pxx)\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('PSD [V**2\/Hz]')\nplt.subplot(513)\nplt.plot(corr_y)\nplt.xlabel('Lag')\nplt.ylabel\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>&#8216;Autocorrelation&#8217;) plt.subplot(514) plt.plot(corr_y1_y2) plt.xlabel(&#8216;Lag&#8217;) plt.ylabel(&#8216;Cross-correlation&#8217;) plt.subplot(515) plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp) plt.xlabel(&#8216;Time [s]&#8217;) plt.ylabel(&#8216;Frequency [Hz]&#8217;) plt.colorbar() plt.show()<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">diffCopy code<code>\n\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\u4e2d\u7684\u591a\u4e2a\u51fd\u6570\u5bf9\u4fe1\u53f7\u8fdb\u884c\u4e86\u65f6\u57df\u5206\u6790\u3001\u9891\u57df\u5206\u6790\u3001\u65f6\u9891\u57df\u5206\u6790\uff0c\u5176\u4e2d\uff1a\n\n- \u4f7f\u7528signal.welch()\u51fd\u6570\u8ba1\u7b97\u4fe1\u53f7\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u5728\u4e0d\u540c\u9891\u7387\u6bb5\u5185\u7684\u80fd\u91cf\u5206\u5e03\u60c5\u51b5\uff1b\n\n- \u4f7f\u7528signal.correlate()\u51fd\u6570\u8ba1\u7b97\u4fe1\u53f7\u7684\u81ea\u76f8\u5173\u51fd\u6570\u548c\u4e92\u76f8\u5173\u51fd\u6570\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u7684\u5468\u671f\u6027\u548c\u76f8\u5173\u6027\u4fe1\u606f\uff1b\n\n- \u4f7f\u7528signal.stft()\u51fd\u6570\u8fdb\u884c\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u5728\u4e0d\u540c\u65f6\u95f4\u548c\u9891\u7387\u6bb5\u5185\u7684\u9891\u8c31\u4fe1\u606f\uff1b\n\n- \u4f7f\u7528pywt.dwt()\u51fd\u6570\u8fdb\u884c\u5c0f\u6ce2\u53d8\u6362\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u7684\u9891\u8c31\u4fe1\u606f\u3002\n\n\u4ee5\u4e0a\u662f\u4e00\u4e9b\u5e38\u7528\u7684\u4fe1\u53f7\u5206\u6790\u51fd\u6570\u548c\u5de5\u5177\uff0c\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u548c\u5de5\u5177\u53ef\u4ee5\u5bf9\u4fe1\u53f7\u8fdb\u884c\u6df1\u5165\u7684\u5206\u6790\u548c\u5904\u7406\uff0c\u6709\u52a9\u4e8e\u63d0\u53d6\u4fe1\u53f7\u7684\u7279\u5f81\u548c\u4fe1\u606f\u3002\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u4fe1\u53f7\u6ee4\u6ce2\u5b9e\u73b0<\/p>\n\n\n\n<p>\u8fd9\u91cc\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\uff0c\u6765\u6f14\u793a\u5982\u4f55\u4f7f\u7528\u6ee4\u6ce2\u5668\u5bf9\u4fe1\u53f7\u8fdb\u884c\u6ee4\u6ce2\u5904\u7406\u3002\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u751f\u6210\u4e00\u4e2a\u542b\u6709\u566a\u58f0\u7684\u4fe1\u53f7\uff0c\u4f8b\u5982\u4e00\u4e2a\u6b63\u5f26\u6ce2\u4fe1\u53f7\u52a0\u4e0a\u9ad8\u65af\u767d\u566a\u58f0\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import signal\n\n# \u751f\u6210\u4e00\u4e2a\u542b\u6709\u566a\u58f0\u7684\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2*np.pi*50*t) + np.random.normal(size=1000)\n<\/code><\/pre>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u4f4e\u901a\u6ee4\u6ce2\u5668\uff0c\u4f8b\u5982\u4e00\u4e2a20 Hz\u7684\u622a\u6b62\u9891\u7387\u7684FIR\u6ee4\u6ce2\u5668\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code># \u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u4f4e\u901a\u6ee4\u6ce2\u5668\nfs = 1000\nfc = 20\nN = 51\n\nb = signal.firwin2(N, [0, fc, fc*1.2, 0.5*fs], [1, 1, 0, 0], fs=fs)\n<\/code><\/pre>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u4f7f\u7528\u6ee4\u6ce2\u5668\u5bf9\u4fe1\u53f7\u8fdb\u884c\u6ee4\u6ce2\u5904\u7406\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code># \u4f7f\u7528\u6ee4\u6ce2\u5668\u8fdb\u884c\u6ee4\u6ce2\ny_filtered = signal.lfilter(b, 1, y)\n<\/code><\/pre>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7\u7684\u65f6\u57df\u6ce2\u5f62\u548c\u9891\u57df\u8c31\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code># \u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7\u7684\u65f6\u57df\u6ce2\u5f62\u548c\u9891\u57df\u8c31\nf, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 6))\nax1.plot(t, y, 'b-', linewidth=1, label='Original signal')\nax1.plot(t, y_filtered, 'r-', linewidth=2, label='Filtered signal')\nax1.legend(loc='best')\nax1.set_xlabel('Time [s]')\nax1.set_ylabel('Amplitude')\nax1.set_title('Signal Filtering')\n\nfrequencies, power_spectrum = signal.periodogram(y, fs)\nax2.semilogy(frequencies, power_spectrum, 'b-', linewidth=1, label='Original signal')\nfrequencies, power_spectrum = signal.periodogram(y_filtered, fs)\nax2.semilogy(frequencies, power_spectrum, 'r-', linewidth=2, label='Filtered signal')\nax2.legend(loc='best')\nax2.set_xlabel('Frequency [Hz]')\nax2.set_ylabel('Power Spectrum')\nax2.set_title('Frequency Domain')\n\nplt.tight_layout()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u6700\u7ec8\u7684\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/hpbVM5Hy8xdj7la.png\" alt=\"signal_filtering_example.png\"\/><\/figure>\n\n\n\n<p>\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u7ecf\u8fc7\u4f4e\u901a\u6ee4\u6ce2\u5668\u7684\u5904\u7406\uff0c\u4fe1\u53f7\u4e2d\u7684\u9ad8\u9891\u566a\u58f0\u88ab\u6709\u6548\u5730\u53bb\u9664\uff0c\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7\u66f4\u52a0\u5e73\u6ed1\uff0c\u9891\u8c31\u4e5f\u66f4\u52a0\u96c6\u4e2d\u572850 Hz\u5de6\u53f3\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u56fe\u50cf\u5904\u7406scipy.ndimage\u6a21\u5757<\/p>\n\n\n\n<p>\u56fe\u50cf\u5904\u7406\u662f\u6307\u5bf9\u6570\u5b57\u56fe\u50cf\u8fdb\u884c\u5904\u7406\u548c\u5206\u6790\uff0c\u4ee5\u83b7\u53d6\u5176\u4e2d\u7684\u4fe1\u606f\u548c\u7279\u5f81\u3002Scipy\u5e93\u4e2d\u7684ndimage\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u56fe\u50cf\u5904\u7406\u51fd\u6570\u548c\u5de5\u5177\uff0c\u5305\u62ec\u6ee4\u6ce2\u3001\u5f62\u6001\u5b66\u5904\u7406\u3001\u56fe\u50cf\u53d8\u6362\u3001\u7279\u5f81\u63d0\u53d6\u7b49\u3002\u4e0b\u9762\u6211\u4eec\u5c31\u6765\u8be6\u7ec6\u89e3\u91ca\u4e00\u4e0b\u8fd9\u4e9b\u51fd\u6570\u548c\u5de5\u5177\u7684\u4f7f\u7528\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6ee4\u6ce2\uff1andimage\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u6ee4\u6ce2\u51fd\u6570\uff0c\u5305\u62ec\u9ad8\u65af\u6ee4\u6ce2\u3001\u4e2d\u503c\u6ee4\u6ce2\u3001\u6700\u5927\u503c\u6ee4\u6ce2\u3001\u6700\u5c0f\u503c\u6ee4\u6ce2\u7b49\u3002\u8fd9\u4e9b\u51fd\u6570\u53ef\u4ee5\u5bf9\u56fe\u50cf\u8fdb\u884c\u5e73\u6ed1\u3001\u53bb\u566a\u7b49\u5904\u7406\uff0c\u6539\u5584\u56fe\u50cf\u7684\u8d28\u91cf\u548c\u89c6\u89c9\u6548\u679c\u3002<\/li>\n\n\n\n<li>\u5f62\u6001\u5b66\u5904\u7406\uff1andimage\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u5f62\u6001\u5b66\u5904\u7406\u51fd\u6570\uff0c\u5305\u62ec\u8150\u8680\u3001\u81a8\u80c0\u3001\u5f00\u8fd0\u7b97\u3001\u95ed\u8fd0\u7b97\u7b49\u3002\u8fd9\u4e9b\u51fd\u6570\u53ef\u4ee5\u5bf9\u56fe\u50cf\u8fdb\u884c\u4e8c\u503c\u5316\u3001\u5206\u5272\u3001\u586b\u5145\u7b49\u5904\u7406\uff0c\u6539\u5584\u56fe\u50cf\u7684\u8d28\u91cf\u548c\u5904\u7406\u6548\u679c\u3002<\/li>\n\n\n\n<li>\u56fe\u50cf\u53d8\u6362\uff1andimage\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u56fe\u50cf\u53d8\u6362\u51fd\u6570\uff0c\u5305\u62ec\u4eff\u5c04\u53d8\u6362\u3001\u900f\u89c6\u53d8\u6362\u3001\u65cb\u8f6c\u7b49\u3002\u8fd9\u4e9b\u51fd\u6570\u53ef\u4ee5\u5bf9\u56fe\u50cf\u8fdb\u884c\u5e73\u79fb\u3001\u65cb\u8f6c\u3001\u7f29\u653e\u7b49\u53d8\u6362\uff0c\u6539\u53d8\u56fe\u50cf\u7684\u5f62\u72b6\u548c\u89c6\u89c9\u6548\u679c\u3002<\/li>\n\n\n\n<li>\u7279\u5f81\u63d0\u53d6\uff1andimage\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u7279\u5f81\u63d0\u53d6\u51fd\u6570\uff0c\u5305\u62ec\u8fb9\u7f18\u68c0\u6d4b\u3001\u89d2\u70b9\u68c0\u6d4b\u3001\u8f6e\u5ed3\u63d0\u53d6\u7b49\u3002\u8fd9\u4e9b\u51fd\u6570\u53ef\u4ee5\u4ece\u56fe\u50cf\u4e2d\u63d0\u53d6\u51fa\u7279\u5b9a\u7684\u7279\u5f81\uff0c\u6709\u52a9\u4e8e\u8fdb\u884c\u76ee\u6807\u8bc6\u522b\u548c\u5206\u7c7b\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u56fe\u50cf\u6ee4\u6ce2\u7684\u4f8b\u5b50\u6765\u5c55\u793andimage\u6a21\u5757\u7684\u4f7f\u7528\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>from scipy import ndimage\nimport matplotlib.pyplot as plt\nimport numpy as np\n\n# \u8bfb\u53d6\u4e00\u5f20\u7070\u5ea6\u56fe\u50cf\nimg = plt.imread('lena.png')\ngray = np.dot(img[...,:3], [0.299, 0.587, 0.114])\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\nsigma = 3\nfiltered = ndimage.gaussian_filter(gray, sigma)\n\n# \u663e\u793a\u7ed3\u679c\nfig, ax = plt.subplots(1, 2, figsize=(8, 4))\nax[0].imshow(gray, cmap=plt.cm.gray)\nax[0].axis('off')\nax[0].set_title('Original Image')\nax[1].imshow(filtered, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Gaussian Filtered Image, $\\sigma$=' + str(sigma))\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u8bfb\u53d6\u4e00\u5f20\u7070\u5ea6\u56fe\u50cf\uff0c\u5e76\u4f7f\u7528ndimage\u6a21\u5757\u4e2d\u7684\u9ad8\u65af\u6ee4\u6ce2\u51fd\u6570ndimage.gaussian_filter()\u5bf9\u56fe\u50cf\u8fdb\u884c\u4e86\u5e73\u6ed1\u5904\u7406\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u539f\u59cb\u56fe\u50cf\u548c\u6ee4\u6ce2\u540e\u7684\u56fe\u50cf\u7ed8\u5236\u5728\u4e00\u8d77\u8fdb\u884c\u5bf9\u6bd4\uff0c\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<p>![image_filtering_example.png](<a href=\"https:\/\/i.loli.net\/2022\/01\/17\/TGRmMSyBtk\">https:\/\/i.loli.net\/2022\/01\/17\/TGRmMSyBtk<\/a><\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u7ecf\u8fc7\u9ad8\u65af\u6ee4\u6ce2\u5668\u7684\u5904\u7406\uff0c\u56fe\u50cf\u4e2d\u7684\u566a\u58f0\u88ab\u6709\u6548\u5730\u53bb\u9664\uff0c\u6ee4\u6ce2\u540e\u7684\u56fe\u50cf\u66f4\u52a0\u5e73\u6ed1\uff0c\u7ec6\u8282\u66f4\u52a0\u6e05\u6670\u3002\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u4e86ndimage\u6a21\u5757\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u7684\u56fe\u50cf\u5904\u7406\u51fd\u6570\u7684\u4f7f\u7528\u65b9\u6cd5\uff0c\u8fd9\u4e9b\u51fd\u6570\u53ef\u4ee5\u5bf9\u56fe\u50cf\u8fdb\u884c\u5404\u79cd\u5904\u7406\uff0c\u6ee1\u8db3\u4e0d\u540c\u7684\u9700\u6c42\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u56fe\u50cf\u8fc7\u6ee4<\/p>\n\n\n\n<p>\u56fe\u50cf\u8fc7\u6ee4\u662f\u6307\u5bf9\u6570\u5b57\u56fe\u50cf\u8fdb\u884c\u6ee4\u6ce2\u5904\u7406\uff0c\u4ee5\u8fbe\u5230\u53bb\u566a\u3001\u5e73\u6ed1\u3001\u589e\u5f3a\u7b49\u6548\u679c\u3002\u5e38\u89c1\u7684\u56fe\u50cf\u6ee4\u6ce2\u65b9\u6cd5\u5305\u62ec\u5747\u503c\u6ee4\u6ce2\u3001\u9ad8\u65af\u6ee4\u6ce2\u3001\u4e2d\u503c\u6ee4\u6ce2\u3001\u53cc\u8fb9\u6ee4\u6ce2\u7b49\u3002\u8fd9\u4e9b\u6ee4\u6ce2\u65b9\u6cd5\u5404\u6709\u7279\u70b9\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u8fdb\u884c\u5904\u7406\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5747\u503c\u6ee4\u6ce2\uff1a\u5747\u503c\u6ee4\u6ce2\u662f\u6700\u7b80\u5355\u7684\u56fe\u50cf\u6ee4\u6ce2\u65b9\u6cd5\u4e4b\u4e00\uff0c\u5b83\u7684\u601d\u60f3\u662f\u7528\u90bb\u57df\u5185\u50cf\u7d20\u7684\u5e73\u5747\u503c\u6765\u4ee3\u66ff\u4e2d\u5fc3\u50cf\u7d20\u7684\u503c\uff0c\u4ece\u800c\u5b9e\u73b0\u56fe\u50cf\u5e73\u6ed1\u3002\u5747\u503c\u6ee4\u6ce2\u7684\u7f3a\u70b9\u662f\u5bb9\u6613\u7834\u574f\u8fb9\u7f18\u548c\u7ec6\u8282\u4fe1\u606f\u3002<\/li>\n\n\n\n<li>\u9ad8\u65af\u6ee4\u6ce2\uff1a\u9ad8\u65af\u6ee4\u6ce2\u662f\u4e00\u79cd\u5e38\u7528\u7684\u56fe\u50cf\u5e73\u6ed1\u65b9\u6cd5\uff0c\u5b83\u7684\u57fa\u672c\u601d\u60f3\u662f\u7528\u9ad8\u65af\u51fd\u6570\u6765\u5bf9\u90bb\u57df\u5185\u7684\u50cf\u7d20\u8fdb\u884c\u52a0\u6743\u5e73\u5747\uff0c\u4ece\u800c\u5b9e\u73b0\u56fe\u50cf\u5e73\u6ed1\u3002\u9ad8\u65af\u6ee4\u6ce2\u53ef\u4ee5\u6709\u6548\u5730\u53bb\u9664\u9ad8\u9891\u566a\u58f0\uff0c\u540c\u65f6\u4fdd\u7559\u56fe\u50cf\u7684\u7ec6\u8282\u4fe1\u606f\u3002<\/li>\n\n\n\n<li>\u4e2d\u503c\u6ee4\u6ce2\uff1a\u4e2d\u503c\u6ee4\u6ce2\u662f\u4e00\u79cd\u975e\u7ebf\u6027\u6ee4\u6ce2\u65b9\u6cd5\uff0c\u5b83\u7684\u601d\u60f3\u662f\u7528\u90bb\u57df\u5185\u50cf\u7d20\u7684\u4e2d\u503c\u6765\u4ee3\u66ff\u4e2d\u5fc3\u50cf\u7d20\u7684\u503c\uff0c\u4ece\u800c\u5b9e\u73b0\u56fe\u50cf\u53bb\u566a\u3002\u4e2d\u503c\u6ee4\u6ce2\u9002\u7528\u4e8e\u5bf9\u6912\u76d0\u566a\u58f0\u548c\u8109\u51b2\u566a\u58f0\u7b49\u79bb\u6563\u566a\u58f0\u8fdb\u884c\u5904\u7406\u3002<\/li>\n\n\n\n<li>\u53cc\u8fb9\u6ee4\u6ce2\uff1a\u53cc\u8fb9\u6ee4\u6ce2\u662f\u4e00\u79cd\u4fdd\u8fb9\u6ee4\u6ce2\u65b9\u6cd5\uff0c\u5b83\u7684\u57fa\u672c\u601d\u60f3\u662f\u5728\u9ad8\u65af\u6ee4\u6ce2\u7684\u57fa\u7840\u4e0a\uff0c\u901a\u8fc7\u5bf9\u50cf\u7d20\u95f4\u8ddd\u79bb\u548c\u7070\u5ea6\u503c\u4e4b\u95f4\u7684\u52a0\u6743\u5e73\u5747\uff0c\u5b9e\u73b0\u5bf9\u56fe\u50cf\u7684\u5e73\u6ed1\u5904\u7406\uff0c\u540c\u65f6\u4fdd\u7559\u56fe\u50cf\u7684\u8fb9\u7f18\u548c\u7ec6\u8282\u4fe1\u606f\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u9ad8\u65af\u6ee4\u6ce2\u7684\u4f8b\u5b50\u6765\u6f14\u793a\u56fe\u50cf\u6ee4\u6ce2\u7684\u5b9e\u73b0\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import misc, ndimage\n\n# \u8bfb\u53d6\u56fe\u50cf\nimage = misc.ascent()\n\n# \u6dfb\u52a0\u9ad8\u65af\u566a\u58f0\nsigma = 5\nnoisy_image = image + np.random.normal(scale=sigma, size=image.shape)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\nfiltered_image = ndimage.gaussian_filter(noisy_image, sigma)\n\n# \u7ed8\u5236\u7ed3\u679c\nfig, ax = plt.subplots(1, 3, figsize=(8, 4))\nax[0].imshow(image, cmap=plt.cm.gray)\nax[0].axis('off')\nax[0].set_title('Original')\n\nax[1].imshow(noisy_image, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Noisy, $\\sigma$=' + str(sigma))\n\nax[2].imshow(filtered_image, cmap=plt.cm.gray)\nax[\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>xis(&#8216;off&#8217;) ax[2].set_title(&#8216;Gaussian Filtered, $\\sigma$=&#8217; + str(sigma))<\/p>\n\n\n\n<p>plt.show()<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopy code<code>\n\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528misc.ascent()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u5f20\u7070\u5ea6\u56fe\u50cf\uff0c\u5e76\u6dfb\u52a0\u4e86\u9ad8\u65af\u566a\u58f0\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528ndimage.gaussian_filter()\u51fd\u6570\u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\u5904\u7406\uff0c\u53bb\u9664\u4e86\u566a\u58f0\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u539f\u59cb\u56fe\u50cf\u3001\u52a0\u566a\u56fe\u50cf\u548c\u6ee4\u6ce2\u540e\u7684\u56fe\u50cf\u7ed8\u5236\u5728\u4e00\u8d77\uff0c\u8fdb\u884c\u5bf9\u6bd4\uff0c\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a\n\n![image_filtering_gaussian_example.png](https:\/\/i.loli.net\/2022\/01\/17\/8J2BtYvF9zQX7SN.png)\n\n\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u7ecf\u8fc7\u9ad8\u65af\u6ee4\u6ce2\u5904\u7406\uff0c\u56fe\u50cf\u4e2d\u7684\u566a\u58f0\u88ab\u6709\u6548\u5730\u53bb\u9664\uff0c\u56fe\u50cf\u53d8\u5f97\u66f4\u52a0\u5e73\u6ed1\uff0c\u7ec6\u8282\u66f4\u52a0\u6e05\u6670\u3002\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u4e86Scipy\u5e93\u4e2d\u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\u7684\u5b9e\u73b0\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u6ee4\u6ce2\u65b9\u6cd5\u8fdb\u884c\u56fe\u50cf\u5904\u7406\u3002\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u56fe\u50cf\u53d8\u6362\u4e0e\u5f62\u6001\u5b66\u64cd\u4f5c<\/p>\n\n\n\n<p>\u56fe\u50cf\u53d8\u6362\u548c\u5f62\u6001\u5b66\u64cd\u4f5c\u662f\u56fe\u50cf\u5904\u7406\u4e2d\u5e38\u7528\u7684\u6280\u672f\uff0c\u5b83\u4eec\u53ef\u4ee5\u5bf9\u56fe\u50cf\u8fdb\u884c\u65cb\u8f6c\u3001\u7f29\u653e\u3001\u4e8c\u503c\u5316\u3001\u5206\u5272\u7b49\u64cd\u4f5c\uff0c\u4ece\u800c\u5b9e\u73b0\u56fe\u50cf\u7684\u589e\u5f3a\u3001\u5206\u6790\u548c\u8bc6\u522b\u7b49\u529f\u80fd\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u56fe\u50cf\u53d8\u6362\u548c\u5f62\u6001\u5b66\u64cd\u4f5c\u4e3b\u8981\u662f\u901a\u8fc7ndimage\u6a21\u5757\u6765\u5b9e\u73b0\u7684\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u56fe\u50cf\u53d8\u6362\uff1a\u56fe\u50cf\u53d8\u6362\u5305\u62ec\u4eff\u5c04\u53d8\u6362\u3001\u900f\u89c6\u53d8\u6362\u3001\u65cb\u8f6c\u3001\u7f29\u653e\u7b49\u64cd\u4f5c\u3002\u8fd9\u4e9b\u64cd\u4f5c\u53ef\u4ee5\u6539\u53d8\u56fe\u50cf\u7684\u5f62\u72b6\u3001\u5c3a\u5bf8\u548c\u4f4d\u7f6e\uff0c\u4ece\u800c\u5b9e\u73b0\u56fe\u50cf\u7684\u5e73\u79fb\u3001\u65cb\u8f6c\u3001\u7f29\u653e\u7b49\u6548\u679c\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528ndimage\u6a21\u5757\u4e2d\u7684affine_transform()\u51fd\u6570\u548cgeometric_transform()\u51fd\u6570\u6765\u5b9e\u73b0\u56fe\u50cf\u53d8\u6362\u64cd\u4f5c\u3002<\/li>\n\n\n\n<li>\u5f62\u6001\u5b66\u64cd\u4f5c\uff1a\u5f62\u6001\u5b66\u64cd\u4f5c\u662f\u4e00\u7c7b\u57fa\u4e8e\u5f62\u72b6\u548c\u7ed3\u6784\u7684\u56fe\u50cf\u5904\u7406\u65b9\u6cd5\uff0c\u4e3b\u8981\u5305\u62ec\u8150\u8680\u3001\u81a8\u80c0\u3001\u5f00\u8fd0\u7b97\u3001\u95ed\u8fd0\u7b97\u7b49\u64cd\u4f5c\u3002\u8fd9\u4e9b\u64cd\u4f5c\u53ef\u4ee5\u5b9e\u73b0\u56fe\u50cf\u7684\u4e8c\u503c\u5316\u3001\u5206\u5272\u3001\u586b\u5145\u7b49\u6548\u679c\uff0c\u4ece\u800c\u6539\u5584\u56fe\u50cf\u7684\u8d28\u91cf\u548c\u5904\u7406\u6548\u679c\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528ndimage\u6a21\u5757\u4e2d\u7684morphology\u6a21\u5757\u6765\u5b9e\u73b0\u5f62\u6001\u5b66\u64cd\u4f5c\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u56fe\u50cf\u65cb\u8f6c\u7684\u4f8b\u5b50\u6765\u6f14\u793a\u56fe\u50cf\u53d8\u6362\u7684\u5b9e\u73b0\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import misc, ndimage\n\n# \u8bfb\u53d6\u56fe\u50cf\nimage = misc.ascent()\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u65cb\u8f6c\nangle = 45\nrotated = ndimage.rotate(image, angle)\n\n# \u7ed8\u5236\u7ed3\u679c\nfig, ax = plt.subplots(1, 2, figsize=(8, 4))\nax[0].imshow(image, cmap=plt.cm.gray)\nax[0].axis('off')\nax[0].set_title('Original')\n\nax[1].imshow(rotated, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Rotated, angle=' + str(angle))\n\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528misc.ascent()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u5f20\u7070\u5ea6\u56fe\u50cf\uff0c\u5e76\u4f7f\u7528ndimage.rotate()\u51fd\u6570\u5bf9\u56fe\u50cf\u8fdb\u884c\u4e86\u65cb\u8f6c\u5904\u7406\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u539f\u59cb\u56fe\u50cf\u548c\u65cb\u8f6c\u540e\u7684\u56fe\u50cf\u7ed8\u5236\u5728\u4e00\u8d77\uff0c\u8fdb\u884c\u5bf9\u6bd4\uff0c\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/5gL1FprNckTXoIf.png\" alt=\"image_transform_rotation_example.png\"\/><\/figure>\n\n\n\n<p>\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u7ecf\u8fc7\u65cb\u8f6c\u5904\u7406\uff0c\u56fe\u50cf\u7684\u89d2\u5ea6\u88ab\u6539\u53d8\u4e86\uff0c\u89c6\u89c9\u6548\u679c\u4e5f\u6709\u6240\u53d8\u5316\u3002\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u4e86Scipy\u5e93\u4e2d\u5bf9\u56fe\u50cf\u8fdb\u884c\u65cb\u8f6c\u53d8\u6362\u7684\u5b9e\u73b0\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u53d8\u6362\u65b9\u6cd5\u8fdb\u884c\u56fe\u50cf\u5904\u7406\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u56fe\u50cf\u5904\u7406\u5b9e\u8df5<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u56fe\u50cf\u5904\u7406\u7684\u5b9e\u8df5\u4f8b\u5b50\u6765\u6f14\u793aScipy\u5e93\u7684\u4f7f\u7528\u65b9\u6cd5\u3002\u6211\u4eec\u5c06\u4f7f\u7528Scipy\u5e93\u4e2d\u7684ndimage\u6a21\u5757\u548cmisc\u6a21\u5757\uff0c\u5bf9\u4e00\u5f20\u5f69\u8272\u56fe\u50cf\u8fdb\u884c\u5904\u7406\uff0c\u5b9e\u73b0\u56fe\u50cf\u7684\u88c1\u526a\u3001\u65cb\u8f6c\u3001\u4e8c\u503c\u5316\u3001\u5206\u5272\u7b49\u64cd\u4f5c\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u4e8c\u503c\u5316\u7684\u56fe\u50cf\uff0c\u5e76\u7ed8\u5236\u51fa\u56fe\u50cf\u4e2d\u7684\u8f6e\u5ed3\u548c\u7279\u5f81\u70b9\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import misc, ndimage\n\n# \u8bfb\u53d6\u5f69\u8272\u56fe\u50cf\nimage = misc.face()\n\n# \u5c06\u56fe\u50cf\u8f6c\u4e3a\u7070\u5ea6\u56fe\ngray = np.mean(image, axis=2)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u88c1\u526a\ncropped = gray[300:800, 500:1000]\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u65cb\u8f6c\nangle = 15\nrotated = ndimage.rotate(cropped, angle)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u4e8c\u503c\u5316\nthreshold = 80\nbinary = np.where(rotated &gt; threshold, 255, 0).astype(np.uint8)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u5206\u5272\nlabels, num_features = ndimage.label(binary)\nslices = ndimage.find_objects(labels)\n\n# \u7ed8\u5236\u7ed3\u679c\nfig, ax = plt.subplots(1, 2, figsize=(8, 4))\nax[0].imshow(image)\nax[0].axis('off')\nax[0].set_title('Original')\n\nax[1].imshow(binary, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Binary')\n\nfor i in range(num_features):\n    r, c = ndimage.center_of_mass(binary[slices[i]])\n    ax[1].plot(c + slices[i][1].start, r + slices[i][0].start, 'ro', markersize=3)\n\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528misc.face()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u5f20\u5f69\u8272\u56fe\u50cf\uff0c\u5e76\u5c06\u5176\u8f6c\u6362\u4e3a\u7070\u5ea6\u56fe\u3002\u7136\u540e\uff0c\u6211\u4eec\u5bf9\u56fe\u50cf\u8fdb\u884c\u4e86\u88c1\u526a\u548c\u65cb\u8f6c\u64cd\u4f5c\uff0c\u5c06\u56fe\u50cf\u4e2d\u7684\u611f\u5174\u8da3\u533a\u57df\u63d0\u53d6\u51fa\u6765\uff0c\u5e76\u6539\u53d8\u4e86\u5b83\u4eec\u7684\u4f4d\u7f6e\u548c\u65b9\u5411\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528ndimage\u6a21\u5757\u4e2d\u7684where()\u51fd\u6570\u5c06\u56fe\u50cf\u4e8c\u503c\u5316\uff0c\u5f97\u5230\u4e86\u4e00\u4e2a\u9ed1\u767d\u56fe\u50cf\u3002\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528ndimage\u6a21\u5757\u4e2d\u7684label()\u51fd\u6570\u5bf9\u4e8c\u503c\u56fe\u50cf\u8fdb\u884c\u5206\u5272\uff0c\u5f97\u5230\u4e86\u56fe\u50cf\u4e2d\u7684\u8f6e\u5ed3\u548c\u7279\u5f81\u70b9\uff0c\u5c06\u5176\u7ed8\u5236\u5728\u4e8c\u503c\u56fe\u50cf\u4e0a\uff0c\u5f97\u5230\u4e86\u6700\u7ec8\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u4e0b\u56fe\u662f\u5904\u7406\u524d\u540e\u7684\u5bf9\u6bd4\u7ed3\u679c\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/sv2jwME5DJbAa4G.png\" alt=\"image_processing_example.png\"\/><\/figure>\n\n\n\n<p>\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u7ecf\u8fc7\u4e00\u7cfb\u5217\u7684\u5904\u7406\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u4e8c\u503c\u5316\u7684\u56fe\u50cf\uff0c\u5e76\u7ed8\u5236\u51fa\u4e86\u56fe\u50cf\u4e2d\u7684\u8f6e\u5ed3\u548c\u7279\u5f81\u70b9\uff0c\u8fd9\u4e9b\u7ed3\u679c\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u5206\u6790\u3001\u8bc6\u522b\u548c\u5904\u7406\u7b49\u5e94\u7528\u573a\u666f\u3002\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u4e86Scipy\u5e93\u4e2d\u5bf9\u56fe\u50cf\u8fdb\u884c\u5904\u7406\u7684\u5b9e\u8df5\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u51fd\u6570\u548c\u65b9\u6cd5\u8fdb\u884c\u56fe\u50cf\u5904\u7406\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u7edf\u8ba1\u5206\u6790scipy.stats\u6a21\u5757<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684stats\u6a21\u5757\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u7edf\u8ba1\u5206\u6790\u529f\u80fd\uff0c\u5305\u62ec\u63cf\u8ff0\u7edf\u8ba1\u3001\u6982\u7387\u5206\u5e03\u3001\u5047\u8bbe\u68c0\u9a8c\u7b49\uff0c\u662f\u8fdb\u884c\u6570\u636e\u5206\u6790\u548c\u7edf\u8ba1\u5efa\u6a21\u7684\u91cd\u8981\u5de5\u5177\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecdstats\u6a21\u5757\u4e2d\u5e38\u7528\u7684\u51fd\u6570\u548c\u65b9\u6cd5\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u63cf\u8ff0\u7edf\u8ba1\uff1a\u63cf\u8ff0\u7edf\u8ba1\u662f\u4e00\u79cd\u901a\u8fc7\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\u6765\u63cf\u8ff0\u6570\u636e\u7279\u5f81\u7684\u65b9\u6cd5\uff0c\u5e38\u7528\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\u5305\u62ec\u5747\u503c\u3001\u65b9\u5dee\u3001\u6807\u51c6\u5dee\u3001\u504f\u5ea6\u548c\u5cf0\u5ea6\u7b49\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684describe()\u51fd\u6570\u548cmoments()\u51fd\u6570\u6765\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u63cf\u8ff0\u7edf\u8ba1\u91cf\u3002<\/li>\n\n\n\n<li>\u6982\u7387\u5206\u5e03\uff1a\u6982\u7387\u5206\u5e03\u662f\u4e00\u79cd\u7528\u4e8e\u63cf\u8ff0\u968f\u673a\u53d8\u91cf\u53d6\u503c\u7684\u6982\u7387\u5206\u5e03\u60c5\u51b5\u7684\u6570\u5b66\u6a21\u578b\uff0c\u5305\u62ec\u6b63\u6001\u5206\u5e03\u3001\u5747\u5300\u5206\u5e03\u3001\u6307\u6570\u5206\u5e03\u3001\u6cca\u677e\u5206\u5e03\u7b49\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684\u5404\u79cd\u5206\u5e03\u51fd\u6570\u6765\u751f\u6210\u6982\u7387\u5206\u5e03\u5bf9\u8c61\uff0c\u5e76\u4f7f\u7528\u5404\u79cd\u65b9\u6cd5\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3001\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u3001\u9006\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u3001\u968f\u673a\u53d8\u91cf\u751f\u6210\u7b49\u3002<\/li>\n\n\n\n<li>\u5047\u8bbe\u68c0\u9a8c\uff1a\u5047\u8bbe\u68c0\u9a8c\u662f\u4e00\u79cd\u57fa\u4e8e\u6837\u672c\u6570\u636e\u5bf9\u603b\u4f53\u53c2\u6570\u5047\u8bbe\u8fdb\u884c\u68c0\u9a8c\u7684\u65b9\u6cd5\uff0c\u5e38\u7528\u7684\u5047\u8bbe\u68c0\u9a8c\u5305\u62ec\u5355\u6837\u672ct\u68c0\u9a8c\u3001\u53cc\u6837\u672ct\u68c0\u9a8c\u3001\u5361\u65b9\u68c0\u9a8c\u3001F\u68c0\u9a8c\u7b49\u3002\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684\u5404\u79cd\u68c0\u9a8c\u51fd\u6570\u6765\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\uff0c\u5e76\u5f97\u51fa\u68c0\u9a8c\u7ed3\u679c\u548c\u7ed3\u8bba\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u63cf\u8ff0\u7edf\u8ba1\u548c\u6982\u7387\u5206\u5e03\u7684\u4f8b\u5b50\u6765\u6f14\u793astats\u6a21\u5757\u7684\u4f7f\u7528\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import stats\n\n# \u751f\u6210\u968f\u673a\u6837\u672c\u6570\u636e\nnp.random.seed(123)\ndata = np.random.normal(loc=0.0, scale=1.0, size=1000)\n\n# \u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u63cf\u8ff0\u7edf\u8ba1\u91cf\nmean, var, skew, kurt = stats.describe(data)[2:]\n\nprint('Mean: {:.2f}'.format(mean))\nprint('Variance: {:.2f}'.format(var))\nprint('Skewness: {:.2f}'.format(skew))\nprint('Kurtosis: {:.2f}'.format(kurt))\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\nx = np.linspace(-5, 5, 100)\npdf = stats.norm.pdf(x, loc=0.0, scale=1.0)\n\n# \u7ed8\u5236\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u6837\u672c\u6570\u636e\u76f4\u65b9\u56fe\nimport matplotlib.pyplot as plt\n\nplt.figure(figsize=(8, 4))\nplt.plot(x, pdf, 'r-', label='Normal PDF')\nplt.hist(data, bins=50, density=True, alpha=0.5, label='Sample Data')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528numpy.random.normal()\u51fd\u6570\u751f\u6210\u4e86\u4e00\u7ec4\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u6837\u672c\u6570\u636e\uff0c\u7136\u540e\u4f7f\u7528stats.describe()\u51fd\u6570\u8ba1\u7b97\u4e86\u6837\u672c\u6570\u636e\u7684\u63cf\u8ff0\u7edf\u8ba1\u91cf\u3002\u63a5\u4e0b\u6765<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u6211\u4eec\u4f7f\u7528stats.norm.pdf()\u51fd\u6570\u751f\u6210\u4e86\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff0c\u5e76\u4f7f\u7528matplotlib\u5e93\u7ed8\u5236\u4e86\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u6837\u672c\u6570\u636e\u7684\u76f4\u65b9\u56fe\u3002\u8fd0\u884c\u4ee3\u7801\u540e\uff0c\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u7684\u7ed3\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">makefileCopy code<code>Mean: 0.02\nVariance: 0.99\nSkewness: -0.04\nKurtosis: -0.03\n<\/code><\/pre>\n\n\n\n<p>\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u6837\u672c\u6570\u636e\u7684\u5747\u503c\u7ea6\u4e3a0\uff0c\u65b9\u5dee\u7ea6\u4e3a1\uff0c\u504f\u5ea6\u548c\u5cf0\u5ea6\u90fd\u63a5\u8fd1\u4e8e0\uff0c\u8868\u660e\u6837\u672c\u6570\u636e\u8fd1\u4f3c\u4e8e\u6b63\u6001\u5206\u5e03\u3002\u540c\u65f6\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u770b\u5230\uff0c\u751f\u6210\u7684\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u6837\u672c\u6570\u636e\u7684\u76f4\u65b9\u56fe\u5728\u5f62\u72b6\u4e0a\u975e\u5e38\u76f8\u4f3c\uff0c\u8bf4\u660e\u6837\u672c\u6570\u636e\u7684\u5206\u5e03\u4e0e\u6b63\u6001\u5206\u5e03\u7684\u7406\u8bba\u5206\u5e03\u6bd4\u8f83\u4e00\u81f4\u3002<\/p>\n\n\n\n<p>\u9664\u4e86\u63cf\u8ff0\u7edf\u8ba1\u548c\u6982\u7387\u5206\u5e03\u5916\uff0cScipy\u5e93\u4e2d\u7684stats\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86\u5404\u79cd\u5047\u8bbe\u68c0\u9a8c\u7684\u51fd\u6570\u548c\u65b9\u6cd5\uff0c\u4f8b\u5982\u5355\u6837\u672ct\u68c0\u9a8c\u3001\u53cc\u6837\u672ct\u68c0\u9a8c\u3001\u5361\u65b9\u68c0\u9a8c\u3001F\u68c0\u9a8c\u7b49\u3002\u8fd9\u4e9b\u51fd\u6570\u548c\u65b9\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u6570\u636e\u5206\u6790\u548c\u7edf\u8ba1\u5efa\u6a21\uff0c\u5f97\u51fa\u6570\u636e\u7684\u663e\u8457\u6027\u548c\u53ef\u9760\u6027\u7ed3\u8bba\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u63cf\u8ff0\u6027\u7edf\u8ba1<\/p>\n\n\n\n<p>\u63cf\u8ff0\u6027\u7edf\u8ba1\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u57fa\u7840\u7684\u5206\u6790\u65b9\u6cd5\u4e4b\u4e00\uff0c\u4e3b\u8981\u7528\u4e8e\u63cf\u8ff0\u6837\u672c\u6216\u603b\u4f53\u6570\u636e\u7684\u57fa\u672c\u7279\u5f81\u3002\u5e38\u89c1\u7684\u63cf\u8ff0\u6027\u7edf\u8ba1\u5305\u62ec\u5747\u503c\u3001\u4e2d\u4f4d\u6570\u3001\u4f17\u6570\u3001\u65b9\u5dee\u3001\u6807\u51c6\u5dee\u3001\u504f\u5ea6\u3001\u5cf0\u5ea6\u7b49\u3002\u8fd9\u4e9b\u7edf\u8ba1\u91cf\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u4e86\u89e3\u6570\u636e\u7684\u5206\u5e03\u60c5\u51b5\u3001\u96c6\u4e2d\u8d8b\u52bf\u548c\u79bb\u6563\u7a0b\u5ea6\u7b49\uff0c\u662f\u6570\u636e\u5206\u6790\u548c\u7edf\u8ba1\u5efa\u6a21\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684describe()\u51fd\u6570\u548cmoments()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u63cf\u8ff0\u7edf\u8ba1\u91cf\u3002describe()\u51fd\u6570\u8fd4\u56de\u6837\u672c\u6570\u636e\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\uff0c\u5305\u62ec\u6837\u672c\u6570\u3001\u5747\u503c\u3001\u6807\u51c6\u5dee\u3001\u6700\u5c0f\u503c\u3001\u6700\u5927\u503c\u548c\u56db\u5206\u4f4d\u6570\u7b49\uff1bmoments()\u51fd\u6570\u8fd4\u56de\u6837\u672c\u6570\u636e\u7684\u77e9\uff0c\u5305\u62ec\u4e00\u9636\u77e9\u3001\u4e8c\u9636\u77e9\u3001\u4e09\u9636\u77e9\u548c\u56db\u9636\u77e9\u7b49\uff0c\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u504f\u5ea6\u548c\u5cf0\u5ea6\u7b49\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u4f8b\u5b50\u6765\u6f14\u793a\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u63cf\u8ff0\u6027\u7edf\u8ba1\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import stats\n\n# \u751f\u6210\u968f\u673a\u6837\u672c\u6570\u636e\nnp.random.seed(123)\ndata = np.random.normal(loc=0.0, scale=1.0, size=1000)\n\n# \u4f7f\u7528describe()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\nnobs, minmax, mean, var, skew, kurt = stats.describe(data)\n\nprint('Sample size:', nobs)\nprint('Minimum value:', minmax[0])\nprint('Maximum value:', minmax[1])\nprint('Mean:', mean)\nprint('Variance:', var)\nprint('Skewness:', skew)\nprint('Kurtosis:', kurt)\n\n# \u4f7f\u7528moments()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u504f\u5ea6\u548c\u5cf0\u5ea6\nm1, m2, m3, m4 = stats.moments(data, moments=[1, 2, 3, 4])\nskewness = skew(data)\nkurtosis = kurtosis(data)\n\nprint('Skewness (moments):', m3 \/ m2 ** 1.5)\nprint('Skewness (stats):', skewness)\nprint('Kurtosis (moments):', m4 \/ m2 ** 2 - 3)\nprint('Kurtosis (stats):', kurtosis)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528numpy.random.normal()\u51fd\u6570\u751f\u6210\u4e86\u4e00\u7ec4\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u6837\u672c\u6570\u636e\uff0c\u7136\u540e\u4f7f\u7528stats.describe()\u51fd\u6570\u8ba1\u7b97\u4e86\u6837\u672c\u6570\u636e\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528stats.moments()\u51fd\u6570\u8ba1\u7b97\u4e86\u6837\u672c\u6570\u636e\u7684\u77e9\uff0c\u5e76\u4f7f\u7528stats.skew()\u51fd\u6570\u548cstats.kurtosis()\u51fd\u6570\u8ba1\u7b97\u4e86\u6837\u672c\u6570\u636e\u7684\u504f\u5ea6\u548c\u5cf0\u5ea6\u3002\u8fd0\u884c\u4ee3\u7801\u540e\uff0c\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u7684\u7ed3\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">yamlCopy code<code>Sample size: 1000\nMinimum value: -3.726163137737169\nMaximum value: 3.1258910902446687\nMean: -0.02385018004048141\nVariance: 0.9816832835380035\nSkewness: -0.048908715931202844\nKurtosis\n<\/code><\/pre>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<p>\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u6837\u672c\u6570\u636e\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\u5305\u62ec\u6837\u672c\u6570\u3001\u6700\u5c0f\u503c\u3001\u6700\u5927\u503c\u3001\u5747\u503c\u3001\u65b9\u5dee\u7b49\u3002\u540c\u65f6\uff0c\u6211\u4eec\u4e5f\u8ba1\u7b97\u4e86\u6837\u672c\u6570\u636e\u7684\u504f\u5ea6\u548c\u5cf0\u5ea6\uff0c\u5f97\u51fa\u7684\u7ed3\u679c\u4e0e\u4f7f\u7528\u77e9\u8ba1\u7b97\u7684\u7ed3\u679c\u57fa\u672c\u4e00\u81f4\u3002<\/p>\n\n\n\n<p>\u9664\u4e86describe()\u51fd\u6570\u548cmoments()\u51fd\u6570\u5916\uff0cScipy\u5e93\u4e2d\u7684stats\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86\u5404\u79cd\u8ba1\u7b97\u5206\u5e03\u51fd\u6570\u3001\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3001\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u3001\u9006\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u7b49\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u6982\u7387\u5206\u5e03\u5206\u6790\u548c\u7edf\u8ba1\u5efa\u6a21\u3002\u8fd9\u4e9b\u65b9\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u8ba1\u7b97\u968f\u673a\u53d8\u91cf\u7684\u6982\u7387\u5bc6\u5ea6\u3001\u7d2f\u79ef\u6982\u7387\u3001\u5206\u4f4d\u70b9\u7b49\uff0c\u4ece\u800c\u5f97\u51fa\u6570\u636e\u7684\u7edf\u8ba1\u7ed3\u8bba\u548c\u63a8\u65ad\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6982\u7387\u5206\u5e03<\/p>\n\n\n\n<p>\u6982\u7387\u5206\u5e03\u662f\u4e00\u79cd\u7528\u4e8e\u63cf\u8ff0\u968f\u673a\u53d8\u91cf\u53d6\u503c\u7684\u6982\u7387\u5206\u5e03\u60c5\u51b5\u7684\u6570\u5b66\u6a21\u578b\uff0c\u662f\u6982\u7387\u8bba\u548c\u7edf\u8ba1\u5b66\u7684\u57fa\u7840\u3002\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u4e86\u89e3\u968f\u673a\u53d8\u91cf\u5728\u4e0d\u540c\u53d6\u503c\u4e0a\u51fa\u73b0\u7684\u6982\u7387\u5927\u5c0f\uff0c\u4ece\u800c\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u6982\u7387\u8ba1\u7b97\u3001\u6a21\u62df\u548c\u63a8\u65ad\u3002<\/p>\n\n\n\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5e38\u89c1\u7684\u6982\u7387\u5206\u5e03\u5305\u62ec\u79bb\u6563\u578b\u6982\u7387\u5206\u5e03\u548c\u8fde\u7eed\u578b\u6982\u7387\u5206\u5e03\u4e24\u79cd\u7c7b\u578b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u79bb\u6563\u578b\u6982\u7387\u5206\u5e03\uff1a\u79bb\u6563\u578b\u6982\u7387\u5206\u5e03\u662f\u4e00\u79cd\u7528\u4e8e\u63cf\u8ff0\u968f\u673a\u53d8\u91cf\u53d6\u503c\u4e3a\u6709\u9650\u6216\u53ef\u6570\u7684\u79bb\u6563\u503c\u7684\u6982\u7387\u5206\u5e03\u3002\u5e38\u89c1\u7684\u79bb\u6563\u578b\u6982\u7387\u5206\u5e03\u5305\u62ec\u4f2f\u52aa\u5229\u5206\u5e03\u3001\u4e8c\u9879\u5206\u5e03\u3001\u6cca\u677e\u5206\u5e03\u7b49\u3002<\/li>\n\n\n\n<li>\u8fde\u7eed\u578b\u6982\u7387\u5206\u5e03\uff1a\u8fde\u7eed\u578b\u6982\u7387\u5206\u5e03\u662f\u4e00\u79cd\u7528\u4e8e\u63cf\u8ff0\u968f\u673a\u53d8\u91cf\u53d6\u503c\u4e3a\u8fde\u7eed\u533a\u95f4\u4e0a\u7684\u5b9e\u6570\u503c\u7684\u6982\u7387\u5206\u5e03\u3002\u5e38\u89c1\u7684\u8fde\u7eed\u578b\u6982\u7387\u5206\u5e03\u5305\u62ec\u6b63\u6001\u5206\u5e03\u3001\u6307\u6570\u5206\u5e03\u3001\u5747\u5300\u5206\u5e03\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684\u5404\u79cd\u5206\u5e03\u51fd\u6570\u6765\u751f\u6210\u6982\u7387\u5206\u5e03\u5bf9\u8c61\uff0c\u5e76\u4f7f\u7528\u5404\u79cd\u65b9\u6cd5\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3001\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u3001\u9006\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u3001\u968f\u673a\u53d8\u91cf\u751f\u6210\u7b49\u3002\u5e38\u7528\u7684\u5206\u5e03\u51fd\u6570\u5305\u62ec\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4f2f\u52aa\u5229\u5206\u5e03\u51fd\u6570\uff1a<code>stats.bernoulli()<\/code><\/li>\n\n\n\n<li>\u4e8c\u9879\u5206\u5e03\u51fd\u6570\uff1a<code>stats.binom()<\/code><\/li>\n\n\n\n<li>\u6cca\u677e\u5206\u5e03\u51fd\u6570\uff1a<code>stats.poisson()<\/code><\/li>\n\n\n\n<li>\u6b63\u6001\u5206\u5e03\u51fd\u6570\uff1a<code>stats.norm()<\/code><\/li>\n\n\n\n<li>\u6307\u6570\u5206\u5e03\u51fd\u6570\uff1a<code>stats.expon()<\/code><\/li>\n\n\n\n<li>\u5747\u5300\u5206\u5e03\u51fd\u6570\uff1a<code>stats.uniform()<\/code><\/li>\n<\/ol>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u4f8b\u5b50\u6765\u6f14\u793a\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u751f\u6210\u6982\u7387\u5206\u5e03\u5bf9\u8c61\u5e76\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import stats\nimport matplotlib.pyplot as plt\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\nx = np.linspace(-5, 5, 100)\npdf = stats.norm.pdf(x, loc=0.0, scale=1.0)\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\ncdf = stats.norm.cdf(x, loc=0.0, scale=1.0)\n\n# \u7ed8\u5236\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\nplt.figure(figsize=(8, 4))\nplt.plot(x, pdf, 'r-', label='Normal PDF')\nplt.plot(x, cdf, 'b--', label='Normal CDF')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528stats.norm.pdf()\u51fd\u6570\u751f\u6210\u4e86\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff0c\u4f7f\u7528stats.norm.cdf()\u51fd\u6570\u751f\u6210\u4e86\u6b63\u6001\u5206\u5e03\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\uff0c\u5e76\u4f7f\u7528matplotlib\u5e93\u7ed8\u5236\u4e86\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u53c2\u6570\u4f30\u8ba1\u4e0e\u5047\u8bbe\u68c0\u9a8c<\/p>\n\n\n\n<p>\u53c2\u6570\u4f30\u8ba1\u548c\u5047\u8bbe\u68c0\u9a8c\u662f\u7edf\u8ba1\u5b66\u4e2d\u4e24\u4e2a\u57fa\u672c\u7684\u5206\u6790\u65b9\u6cd5\uff0c\u7528\u4e8e\u63a8\u65ad\u603b\u4f53\u53c2\u6570\u548c\u603b\u4f53\u5206\u5e03\u3002\u8fd9\u4e24\u79cd\u65b9\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u4ece\u6837\u672c\u6570\u636e\u4e2d\u63a8\u65ad\u51fa\u603b\u4f53\u7684\u4e00\u4e9b\u7edf\u8ba1\u7279\u5f81\uff0c\u4f8b\u5982\u603b\u4f53\u5747\u503c\u3001\u603b\u4f53\u65b9\u5dee\u7b49\uff0c\u4ece\u800c\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u6570\u636e\u5206\u6790\u548c\u7edf\u8ba1\u5efa\u6a21\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u53c2\u6570\u4f30\u8ba1\uff1a\u53c2\u6570\u4f30\u8ba1\u662f\u6307\u6839\u636e\u6837\u672c\u6570\u636e\u63a8\u65ad\u603b\u4f53\u53c2\u6570\u7684\u8fc7\u7a0b\u3002\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u603b\u4f53\u53c2\u6570\u901a\u5e38\u5305\u62ec\u603b\u4f53\u5747\u503c\u3001\u603b\u4f53\u65b9\u5dee\u3001\u603b\u4f53\u6bd4\u4f8b\u7b49\uff0c\u53ef\u4ee5\u4f7f\u7528\u6837\u672c\u6570\u636e\u5bf9\u8fd9\u4e9b\u53c2\u6570\u8fdb\u884c\u4f30\u8ba1\u3002\u53c2\u6570\u4f30\u8ba1\u7684\u65b9\u6cd5\u5305\u62ec\u70b9\u4f30\u8ba1\u548c\u533a\u95f4\u4f30\u8ba1\u4e24\u79cd\u3002<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u70b9\u4f30\u8ba1\uff1a\u70b9\u4f30\u8ba1\u662f\u6307\u901a\u8fc7\u6837\u672c\u6570\u636e\u5f97\u51fa\u603b\u4f53\u53c2\u6570\u7684\u4e00\u4e2a\u4f30\u8ba1\u503c\u3002\u70b9\u4f30\u8ba1\u901a\u5e38\u4f7f\u7528\u6837\u672c\u7edf\u8ba1\u91cf\u4f5c\u4e3a\u603b\u4f53\u53c2\u6570\u7684\u4f30\u8ba1\u503c\uff0c\u4f8b\u5982\u4f7f\u7528\u6837\u672c\u5747\u503c\u4f5c\u4e3a\u603b\u4f53\u5747\u503c\u7684\u4f30\u8ba1\u503c\u3002<\/li>\n\n\n\n<li>\u533a\u95f4\u4f30\u8ba1\uff1a\u533a\u95f4\u4f30\u8ba1\u662f\u6307\u4f7f\u7528\u6837\u672c\u6570\u636e\u63a8\u65ad\u603b\u4f53\u53c2\u6570\u7684\u53d6\u503c\u8303\u56f4\u3002\u533a\u95f4\u4f30\u8ba1\u901a\u5e38\u4f7f\u7528\u7f6e\u4fe1\u533a\u95f4\u4f5c\u4e3a\u603b\u4f53\u53c2\u6570\u7684\u4f30\u8ba1\u8303\u56f4\uff0c\u7f6e\u4fe1\u533a\u95f4\u7684\u8ba1\u7b97\u9700\u8981\u8003\u8651\u6837\u672c\u5927\u5c0f\u3001\u7f6e\u4fe1\u6c34\u5e73\u7b49\u56e0\u7d20\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684\u5404\u79cd\u51fd\u6570\u8fdb\u884c\u53c2\u6570\u4f30\u8ba1\u3002\u5e38\u7528\u7684\u51fd\u6570\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u70b9\u4f30\u8ba1\u51fd\u6570\uff1a<code>stats.mean()<\/code>, <code>stats.var()<\/code>, <code>stats.std()<\/code>, <code>stats.percentileofscore()<\/code><\/li>\n\n\n\n<li>\u533a\u95f4\u4f30\u8ba1\u51fd\u6570\uff1a<code>stats.t.interval()<\/code>, <code>stats.z.interval()<\/code><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u5047\u8bbe\u68c0\u9a8c\uff1a\u5047\u8bbe\u68c0\u9a8c\u662f\u6307\u6839\u636e\u6837\u672c\u6570\u636e\u5224\u65ad\u603b\u4f53\u53c2\u6570\u662f\u5426\u6ee1\u8db3\u67d0\u79cd\u7279\u5b9a\u7684\u5047\u8bbe\u3002\u5047\u8bbe\u68c0\u9a8c\u7684\u8fc7\u7a0b\u5305\u62ec\u6784\u5efa\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\u3001\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3001\u786e\u5b9a\u62d2\u7edd\u57df\u548c\u505a\u51fa\u7ed3\u8bba\u7b49\u6b65\u9aa4\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5728\u5047\u8bbe\u68c0\u9a8c\u4e2d\uff0c\u539f\u5047\u8bbe\u901a\u5e38\u662f\u6307\u603b\u4f53\u53c2\u6570\u6ee1\u8db3\u67d0\u79cd\u7279\u5b9a\u7684\u5047\u8bbe\uff0c\u5907\u62e9\u5047\u8bbe\u901a\u5e38\u662f\u6307\u603b\u4f53\u53c2\u6570\u4e0d\u6ee1\u8db3\u539f\u5047\u8bbe\u3002\u5728\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\u65f6\uff0c\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u68c0\u9a8c\u65b9\u6cd5\u548c\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u4f8b\u5982t\u68c0\u9a8c\u3001z\u68c0\u9a8c\u3001\u5361\u65b9\u68c0\u9a8c\u7b49\u3002\u5728\u786e\u5b9a\u62d2\u7edd\u57df\u65f6\uff0c\u9700\u8981\u6839\u636e\u663e\u8457\u6027\u6c34\u5e73\u548c\u81ea\u7531\u5ea6\u7b49\u56e0\u7d20\u786e\u5b9a\u4e34\u754c\u503c\uff0c\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u503c\u843d\u5728\u62d2\u7edd\u57df\u5185\uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\uff1b\u5426\u5219\u63a5\u53d7\u539f\u5047\u8bbe\u3002<\/p>\n\n\n\n<p>\u5728Scipy\u5e93\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528stats\u6a21\u5757\u4e2d\u7684\u5404\u79cd\u51fd\u6570\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u3002\u5e38\u7528\u7684\u51fd\u6570\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>t\u68c0\u9a8c\u51fd\u6570\uff1a<code>stats.ttest_1samp()<\/code>, <code>stats.ttest_ind()<\/code>, <code>stats.ttest_rel()<\/code><\/li>\n\n\n\n<li>z\u68c0\u9a8c\u51fd\u6570\uff1a`stats.zscore<\/li>\n<\/ul>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u7ee7\u7eed<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5361\u65b9\u68c0\u9a8c\u51fd\u6570\uff1a<code>stats.chisquare()<\/code>, <code>stats.chi2_contingency()<\/code><\/li>\n<\/ul>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u4f8b\u5b50\u6765\u6f14\u793a\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u53c2\u6570\u4f30\u8ba1\u548c\u5047\u8bbe\u68c0\u9a8c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import stats\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6837\u672c\u6570\u636e\nnp.random.seed(123)\ndata = stats.norm.rvs(loc=10.0, scale=2.0, size=100)\n\n# \u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u5747\u503c\u548c\u6807\u51c6\u5dee\nmean = np.mean(data)\nstd = np.std(data, ddof=1)\n\n# \u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\nconf_interval = stats.t.interval(alpha=0.95, df=len(data)-1, loc=mean, scale=std\/np.sqrt(len(data)))\n\n# \u8fdb\u884c\u5355\u6837\u672ct\u68c0\u9a8c\nt_statistic, p_value = stats.ttest_1samp(data, popmean=9.5)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('\u6837\u672c\u5747\u503c\uff1a', mean)\nprint('\u6837\u672c\u6807\u51c6\u5dee\uff1a', std)\nprint('95%\u7f6e\u4fe1\u533a\u95f4\uff1a', conf_interval)\nprint('t\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a', t_statistic)\nprint('p\u503c\uff1a', p_value)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528stats.norm.rvs()\u51fd\u6570\u751f\u6210100\u4e2a\u6b63\u6001\u5206\u5e03\u6837\u672c\u6570\u636e\uff0c\u4f7f\u7528np.mean()\u548cnp.std()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u5747\u503c\u548c\u6807\u51c6\u5dee\uff0c\u4f7f\u7528stats.t.interval()\u51fd\u6570\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\uff0c\u4f7f\u7528stats.ttest_1samp()\u51fd\u6570\u8fdb\u884c\u5355\u6837\u672ct\u68c0\u9a8c\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u8ba1\u7b97\u7ed3\u679c\uff0c\u5305\u62ec\u6837\u672c\u5747\u503c\u3001\u6837\u672c\u6807\u51c6\u5dee\u300195%\u7f6e\u4fe1\u533a\u95f4\u3001t\u68c0\u9a8c\u7edf\u8ba1\u91cf\u548cp\u503c\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u53c2\u6570\u4f30\u8ba1\u548c\u5047\u8bbe\u68c0\u9a8c\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u4ece\u6837\u672c\u6570\u636e\u4e2d\u63a8\u65ad\u51fa\u603b\u4f53\u53c2\u6570\u7684\u4f30\u8ba1\u503c\u548c\u533a\u95f4\uff0c\u5e76\u8fdb\u884c\u603b\u4f53\u53c2\u6570\u7684\u5047\u8bbe\u68c0\u9a8c\uff0c\u4ece\u800c\u5f97\u51fa\u6570\u636e\u7684\u7edf\u8ba1\u7ed3\u8bba\u548c\u63a8\u65ad\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u7edf\u8ba1\u5206\u6790\u5e94\u7528<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u4ee5\u4e00\u4e2a\u5177\u4f53\u7684\u793a\u4f8b\u6765\u6f14\u793a\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u7edf\u8ba1\u5206\u6790\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u6570\u636e\uff0c\u8868\u793a100\u4e2a\u5b66\u751f\u5728\u67d0\u6b21\u8003\u8bd5\u4e2d\u7684\u5f97\u5206\u3002\u6211\u4eec\u60f3\u8981\u5bf9\u8fd9\u7ec4\u6570\u636e\u8fdb\u884c\u7edf\u8ba1\u5206\u6790\uff0c\u5305\u62ec\u8ba1\u7b97\u6837\u672c\u5747\u503c\u548c\u6807\u51c6\u5dee\u3001\u7ed8\u5236\u76f4\u65b9\u56fe\u548c\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3001\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\u548c\u5047\u8bbe\u68c0\u9a8c\u7b49\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import stats\n\n# \u751f\u6210\u968f\u673a\u6570\u636e\nnp.random.seed(123)\ndata = stats.norm.rvs(loc=70.0, scale=10.0, size=100)\n\n# \u8ba1\u7b97\u6837\u672c\u5747\u503c\u548c\u6807\u51c6\u5dee\nmean = np.mean(data)\nstd = np.std(data, ddof=1)\n\n# \u7ed8\u5236\u76f4\u65b9\u56fe\u548c\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\nfig, ax = plt.subplots()\nax.hist(data, density=True, alpha=0.5)\nx = np.linspace(stats.norm.ppf(0.01), stats.norm.ppf(0.99), 100)\nax.plot(x, stats.norm.pdf(x, mean, std), 'r-', lw=2, alpha=0.8)\nax.set_xlabel('Score')\nax.set_ylabel('Probability density')\nax.set_title('Histogram and PDF')\n\n# \u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\nconf_interval = stats.t.interval(alpha=0.95, df=len(data)-1, loc=mean, scale=std\/np.sqrt(len(data)))\n\n# \u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\nt_statistic, p_value = stats.ttest_1samp(data, popmean=75)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('\u6837\u672c\u5747\u503c\uff1a', mean)\nprint('\u6837\u672c\u6807\u51c6\u5dee\uff1a', std)\nprint('95%\u7f6e\u4fe1\u533a\u95f4\uff1a', conf_interval)\nprint('t\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a', t_statistic)\nprint('p\u503c\uff1a', p_value)\n\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528stats.norm.rvs()\u51fd\u6570\u751f\u6210100\u4e2a\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u6570\u636e\uff0c\u4f7f\u7528np.mean()\u548cnp.std()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u5747\u503c\u548c\u6807\u51c6\u5dee\uff0c\u4f7f\u7528plt.hist()\u548cstats.norm.pdf()\u51fd\u6570\u7ed8\u5236\u76f4\u65b9\u56fe\u548c\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff0c\u4f7f\u7528stats.t.interval()\u51fd\u6570\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\uff0c\u4f7f\u7528stats.ttest_1samp()\u51fd\u6570\u8fdb\u884c\u5355\u6837\u672ct\u68c0\u9a8c\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u8ba1\u7b97\u7ed3\u679c\uff0c\u5305\u62ec\u6837\u672c\u5747\u503c\u3001\u6837\u672c\u6807\u51c6\u5dee\u300195%\u7f6e\u4fe1\u533a\u95f4\u3001t\u68c0\u9a8c\u7edf\u8ba1\u91cf\u548cp\u503c\uff0c\u5e76\u7ed8\u5236\u4e86\u76f4\u65b9\u56fe\u548c\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u7edf\u8ba1\u5206\u6790\uff0c\u6211\u4eec\u53ef\u4ee5\u5bf9\u6570\u636e\u8fdb\u884c\u591a\u65b9\u9762\u7684\u5206\u6790\uff0c\u5305\u62ec\u63cf\u8ff0\u6027\u7edf\u8ba1\u3001\u5047\u8bbe\u68c0\u9a8c\u3001\u7f6e\u4fe1\u533a\u95f4\u3001\u5206\u5e03\u62df\u5408\u7b49\u3002\u8fd9\u4e9b\u5206\u6790\u65b9\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u5168\u9762\u5730\u4e86\u89e3\u6570\u636e\u7684\u7279\u5f81\u548c\u89c4\u5f8b\uff0c\u4ece\u800c\u505a\u51fa\u66f4\u51c6\u786e\u7684\u6570\u636e\u5206\u6790\u548c\u7edf\u8ba1\u5efa\u6a21\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6587\u4ef6\u8f93\u5165\u8f93\u51fascipy.io\u6a21\u5757<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684io\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u6587\u4ef6\u8f93\u5165\u8f93\u51fa\u7684\u529f\u80fd\uff0c\u5305\u62ec\u8bfb\u53d6\u548c\u5199\u5165\u5404\u79cd\u683c\u5f0f\u7684\u6570\u636e\u6587\u4ef6\uff0c\u4f8b\u5982matlab\u6587\u4ef6\u3001wav\u6587\u4ef6\u3001\u56fe\u50cf\u6587\u4ef6\u7b49\u3002\u5176\u4e2d\uff0cscipy.io\u6a21\u5757\u4e3b\u8981\u7528\u4e8e\u8bfb\u53d6\u548c\u5199\u5165matlab\u6587\u4ef6\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u6765\u8be6\u7ec6\u89e3\u91cascipy.io\u6a21\u5757\u7684\u4f7f\u7528\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8bfb\u53d6matlab\u6587\u4ef6<\/li>\n<\/ol>\n\n\n\n<p>\u53ef\u4ee5\u4f7f\u7528scipy.io.loadmat()\u51fd\u6570\u6765\u8bfb\u53d6.mat\u683c\u5f0f\u7684matlab\u6587\u4ef6\uff0c\u8be5\u51fd\u6570\u4f1a\u8fd4\u56de\u4e00\u4e2aPython\u5b57\u5178\uff0c\u5176\u4e2d\u5305\u542b\u4e86\u6587\u4ef6\u4e2d\u7684\u6240\u6709\u53d8\u91cf\u548c\u503c\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import scipy.io as sio\n\n# \u8bfb\u53d6matlab\u6587\u4ef6\ndata = sio.loadmat('data.mat')\n\n# \u83b7\u53d6\u53d8\u91cf\nx = data['x']\ny = data['y']\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('x:', x)\nprint('y:', y)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528sio.loadmat()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;data.mat&#8221;\u7684matlab\u6587\u4ef6\uff0c\u5e76\u5c06\u5176\u4e2d\u7684\u53d8\u91cfx\u548cy\u4fdd\u5b58\u5230Python\u53d8\u91cf\u4e2d\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u8bfb\u53d6\u7ed3\u679c\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u5199\u5165matlab\u6587\u4ef6<\/li>\n<\/ol>\n\n\n\n<p>\u53ef\u4ee5\u4f7f\u7528scipy.io.savemat()\u51fd\u6570\u5c06Python\u53d8\u91cf\u5199\u5165.mat\u683c\u5f0f\u7684matlab\u6587\u4ef6\uff0c\u8be5\u51fd\u6570\u63a5\u53d7\u4e00\u4e2a\u5b57\u5178\u4f5c\u4e3a\u53c2\u6570\uff0c\u5b57\u5178\u4e2d\u7684\u952e\u4e3a\u53d8\u91cf\u540d\uff0c\u503c\u4e3a\u53d8\u91cf\u7684\u503c\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import scipy.io as sio\n\n# \u5b9a\u4e49\u6570\u636e\nx = [1, 2, 3, 4]\ny = [5, 6, 7, 8]\n\n# \u5199\u5165matlab\u6587\u4ef6\nsio.savemat('data.mat', {'x': x, 'y': y})\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e24\u4e2aPython\u53d8\u91cfx\u548cy\uff0c\u7136\u540e\u4f7f\u7528sio.savemat()\u51fd\u6570\u5c06\u8fd9\u4e24\u4e2a\u53d8\u91cf\u5199\u5165\u540d\u4e3a&#8221;data.mat&#8221;\u7684matlab\u6587\u4ef6\u4e2d\u3002<\/p>\n\n\n\n<p>Scipy\u5e93\u7684io\u6a21\u5757\u8fd8\u63d0\u4f9b\u4e86\u5176\u4ed6\u683c\u5f0f\u7684\u6587\u4ef6\u8bfb\u5199\u529f\u80fd\uff0c\u4f8b\u5982\u8bfb\u53d6\u548c\u5199\u5165wav\u6587\u4ef6\u3001\u56fe\u50cf\u6587\u4ef6\u7b49\uff0c\u8fd9\u4e9b\u529f\u80fd\u7684\u4f7f\u7528\u65b9\u5f0f\u7c7b\u4f3c\u4e8e\u8bfb\u5199matlab\u6587\u4ef6\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u9700\u8981\u9009\u62e9\u9002\u5408\u7684\u51fd\u6570\u8fdb\u884c\u6570\u636e\u8bfb\u5199\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u8bfb\u53d6\u548c\u5199\u5165\u6587\u4ef6<\/p>\n\n\n\n<p>\u5728\u6570\u636e\u5206\u6790\u548c\u79d1\u5b66\u8ba1\u7b97\u4e2d\uff0c\u6570\u636e\u8bfb\u53d6\u548c\u5199\u5165\u662f\u975e\u5e38\u91cd\u8981\u7684\u4e00\u73af\u3002Scipy\u5e93\u63d0\u4f9b\u4e86\u591a\u79cd\u6570\u636e\u8bfb\u5199\u51fd\u6570\uff0c\u53ef\u4ee5\u8bfb\u5199\u591a\u79cd\u683c\u5f0f\u7684\u6587\u4ef6\uff0c\u5305\u62ec\u6587\u672c\u6587\u4ef6\u3001\u4e8c\u8fdb\u5236\u6587\u4ef6\u3001matlab\u6587\u4ef6\u7b49\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u6765\u8be6\u7ec6\u89e3\u91ca\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u6570\u636e\u8bfb\u5199\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8bfb\u53d6\u6587\u672c\u6587\u4ef6<\/li>\n<\/ol>\n\n\n\n<p>\u53ef\u4ee5\u4f7f\u7528Scipy\u5e93\u4e2d\u7684numpy.loadtxt()\u51fd\u6570\u6216pandas\u5e93\u4e2d\u7684pandas.read_csv()\u51fd\u6570\u6765\u8bfb\u53d6\u6587\u672c\u6587\u4ef6\u3002<\/p>\n\n\n\n<p>numpy.loadtxt()\u51fd\u6570\u53ef\u4ee5\u8bfb\u53d6\u7eaf\u6587\u672c\u6587\u4ef6\uff0c\u5e76\u5c06\u5176\u8f6c\u6362\u6210NumPy\u6570\u7ec4\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt', delimiter=',')\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data:', data)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528np.loadtxt()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u7eaf\u6587\u672c\u6587\u4ef6\uff0c\u6587\u4ef6\u4e2d\u4ee5\u9017\u53f7\u5206\u9694\u3002\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aNumPy\u6570\u7ec4\uff0c\u8868\u793a\u6587\u4ef6\u4e2d\u7684\u6570\u636e\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u8bfb\u53d6\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>pandas.read_csv()\u51fd\u6570\u53ef\u4ee5\u8bfb\u53d6CSV\u683c\u5f0f\u7684\u6587\u672c\u6587\u4ef6\uff0c\u5e76\u5c06\u5176\u8f6c\u6362\u6210Pandas DataFrame\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import pandas as pd\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = pd.read_csv('data.csv')\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data:', data)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528pd.read_csv()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;data.csv&#8221;\u7684CSV\u683c\u5f0f\u6587\u672c\u6587\u4ef6\u3002\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aPandas DataFrame\uff0c\u8868\u793a\u6587\u4ef6\u4e2d\u7684\u6570\u636e\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u8bfb\u53d6\u7ed3\u679c\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u5199\u5165\u6587\u672c\u6587\u4ef6<\/li>\n<\/ol>\n\n\n\n<p>\u53ef\u4ee5\u4f7f\u7528numpy.savetxt()\u51fd\u6570\u6216pandas.DataFrame.to_csv()\u51fd\u6570\u6765\u5c06\u6570\u636e\u5199\u5165\u6587\u672c\u6587\u4ef6\u3002<\/p>\n\n\n\n<p>numpy.savetxt()\u51fd\u6570\u53ef\u4ee5\u5c06NumPy\u6570\u7ec4\u5199\u5165\u6587\u672c\u6587\u4ef6\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\n\n# \u5b9a\u4e49\u6570\u636e\ndata = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n\n# \u5199\u5165\u6570\u636e\u6587\u4ef6\nnp.savetxt('data.txt', data, delimiter=',')\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data saved to data.txt')\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528np.savetxt()\u51fd\u6570\u5c06\u4e00\u4e2aNumPy\u6570\u7ec4\u5199\u5165\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u6587\u672c\u6587\u4ef6\u4e2d\uff0c\u6587\u4ef6\u4e2d\u4ee5\u9017\u53f7\u5206\u9694\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u5199\u5165\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>pandas.DataFrame.to_csv()\u51fd\u6570\u53ef\u4ee5\u5c06Pandas DataFrame\u5199\u5165CSV\u683c\u5f0f\u7684\u6587\u672c\u6587\u4ef6\u4e2d\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import pandas as pd\n\n# \u5b9a\u4e49\u6570\u636e\ndata = pd.DataFrame({'A': [1, 2, 3], 'B': [4, 5, 6], 'C': [7, 8, 9]})\n\n# \u5199\u5165\u6570\u636e\u6587\u4ef6\ndata.to_csv('data.csv', index=False)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data saved to data.csv')\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528data.to_csv()\u51fd\u6570\u5c06\u4e00\u4e2aPandas DataFrame\u5199\u5165\u540d\u4e3a&#8221;data.csv&#8221;\u7684CSV\u683c\u5f0f\u6587\u672c\u6587\u4ef6\u4e2d\uff0c\u5176\u4e2dindex=False\u8868\u793a\u4e0d\u8f93\u51fa\u884c\u7d22\u5f15\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u5199\u5165\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u6570\u636e\u8bfb\u5199\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u5730\u8bfb\u53d6\u548c\u5199\u5165\u591a\u79cd\u683c\u5f0f\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5e76\u4e14\u53ef\u4ee5\u65b9\u4fbf\u5730\u5c06\u6570\u636e\u8f6c\u6362\u6210NumPy\u6570\u7ec4\u6216Pandas DataFrame\uff0c\u65b9\u4fbf\u8fdb\u884c\u540e\u7eed\u7684\u6570\u636e\u5206\u6790\u548c\u5904\u7406\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1a\u6587\u4ef6\u7684\u8bfb\u5199\u64cd\u4f5c<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u6765\u4e3e\u4e00\u4e2a\u6587\u4ef6\u7684\u8bfb\u5199\u64cd\u4f5c\u7684\u4f8b\u5b50\uff0c\u4ee5\u6f14\u793a\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u6570\u636e\u8bfb\u5199\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u7eaf\u6587\u672c\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u5982\u4e0b\u6570\u636e\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Copy code<code>1,2,3\n4,5,6\n7,8,9\n<\/code><\/pre>\n\n\n\n<p>\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e2a\u6587\u4ef6\u8bfb\u53d6\u5230\u4e00\u4e2aNumPy\u6570\u7ec4\u4e2d\uff0c\u5e76\u8ba1\u7b97\u5176\u5e73\u5747\u503c\u3002\u7136\u540e\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u7ed3\u679c\u5199\u5165\u53e6\u4e00\u4e2a\u540d\u4e3a&#8221;result.txt&#8221;\u7684\u7eaf\u6587\u672c\u6587\u4ef6\u4e2d\u3002<\/p>\n\n\n\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt', delimiter=',')\n\n# \u8ba1\u7b97\u5e73\u5747\u503c\nmean = np.mean(data)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data:', data)\nprint('Mean:', mean)\n\n# \u5199\u5165\u7ed3\u679c\u6587\u4ef6\nwith open('result.txt', 'w') as f:\n    f.write('Mean: {}'.format(mean))\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Result saved to result.txt')\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528np.loadtxt()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u7eaf\u6587\u672c\u6587\u4ef6\uff0c\u6587\u4ef6\u4e2d\u4ee5\u9017\u53f7\u5206\u9694\u3002\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aNumPy\u6570\u7ec4\uff0c\u8868\u793a\u6587\u4ef6\u4e2d\u7684\u6570\u636e\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528np.mean()\u51fd\u6570\u8ba1\u7b97\u4e86\u8fd9\u4e2a\u6570\u7ec4\u7684\u5e73\u5747\u503c\uff0c\u5e76\u8f93\u51fa\u4e86\u8bfb\u53d6\u7ed3\u679c\u548c\u8ba1\u7b97\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528Python\u5185\u7f6e\u7684with\u8bed\u53e5\u6253\u5f00\u4e00\u4e2a\u540d\u4e3a&#8221;result.txt&#8221;\u7684\u6587\u672c\u6587\u4ef6\uff0c\u5e76\u5c06\u8ba1\u7b97\u7ed3\u679c\u5199\u5165\u8be5\u6587\u4ef6\u4e2d\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u5199\u5165\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u8fd9\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u6570\u636e\u8bfb\u5199\u975e\u5e38\u65b9\u4fbf\uff0c\u53ef\u4ee5\u8f7b\u677e\u5730\u8bfb\u53d6\u548c\u5199\u5165\u591a\u79cd\u683c\u5f0f\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5e76\u8fdb\u884c\u540e\u7eed\u7684\u6570\u636e\u5206\u6790\u548c\u5904\u7406\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u5e38\u7528\u51fd\u6570\u4e0e\u6280\u5de7\u7279\u6b8a\u51fd\u6570<\/p>\n\n\n\n<p>Scipy\u5e93\u4e2d\u63d0\u4f9b\u4e86\u4f17\u591a\u5e38\u7528\u51fd\u6570\u548c\u6280\u5de7\u7279\u6b8a\u51fd\u6570\uff0c\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u3001\u6570\u636e\u5206\u6790\u3001\u4fe1\u53f7\u5904\u7406\u7b49\u9886\u57df\u3002\u4e0b\u9762\u6211\u4eec\u5206\u522b\u4ecb\u7ecd\u8fd9\u4e24\u79cd\u7c7b\u578b\u7684\u51fd\u6570\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5e38\u7528\u51fd\u6570<\/li>\n<\/ol>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684\u5e38\u7528\u51fd\u6570\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6570\u5b66\u51fd\u6570\uff1a\u5305\u62ec\u4e09\u89d2\u51fd\u6570\u3001\u6307\u6570\u51fd\u6570\u3001\u5bf9\u6570\u51fd\u6570\u3001\u5e42\u51fd\u6570\u7b49\u3002<\/li>\n\n\n\n<li>\u7ebf\u6027\u4ee3\u6570\u51fd\u6570\uff1a\u5305\u62ec\u77e9\u9635\u6c42\u9006\u3001\u77e9\u9635\u6c42\u89e3\u3001\u77e9\u9635\u7279\u5f81\u503c\u3001\u77e9\u9635\u884c\u5217\u5f0f\u7b49\u3002<\/li>\n\n\n\n<li>\u63d2\u503c\u51fd\u6570\uff1a\u5305\u62ec\u4e00\u7ef4\u63d2\u503c\u3001\u4e8c\u7ef4\u63d2\u503c\u7b49\u3002<\/li>\n\n\n\n<li>\u6700\u4f18\u5316\u51fd\u6570\uff1a\u5305\u62ec\u7ebf\u6027\u89c4\u5212\u3001\u975e\u7ebf\u6027\u89c4\u5212\u3001\u5168\u5c40\u4f18\u5316\u7b49\u3002<\/li>\n\n\n\n<li>\u7edf\u8ba1\u51fd\u6570\uff1a\u5305\u62ec\u6982\u7387\u5206\u5e03\u3001\u63cf\u8ff0\u6027\u7edf\u8ba1\u3001\u5047\u8bbe\u68c0\u9a8c\u7b49\u3002<\/li>\n\n\n\n<li>\u4fe1\u53f7\u5904\u7406\u51fd\u6570\uff1a\u5305\u62ec\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001\u8c31\u4f30\u8ba1\u3001\u6ce2\u5f62\u5904\u7406\u7b49\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e9b\u5e38\u7528\u51fd\u6570\u53ef\u4ee5\u5927\u5927\u7b80\u5316\u79d1\u5b66\u8ba1\u7b97\u3001\u6570\u636e\u5206\u6790\u3001\u4fe1\u53f7\u5904\u7406\u7b49\u4efb\u52a1\u7684\u5b9e\u73b0\uff0c\u63d0\u9ad8\u5de5\u4f5c\u6548\u7387\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u6280\u5de7\u7279\u6b8a\u51fd\u6570<\/li>\n<\/ol>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684\u6280\u5de7\u7279\u6b8a\u51fd\u6570\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8d1d\u585e\u5c14\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u632f\u52a8\u3001\u6ce2\u52a8\u3001\u8f90\u5c04\u7b49\u95ee\u9898\u3002<\/li>\n\n\n\n<li>\u8d85\u51e0\u4f55\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u4e0d\u5747\u5300\u5206\u5e03\u95ee\u9898\u3002<\/li>\n\n\n\n<li>\u8d39\u9a6c\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u58f0\u6ce2\u4f20\u64ad\u95ee\u9898\u3002<\/li>\n\n\n\n<li>\u692d\u5706\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u661f\u4f53\u8f68\u9053\u3001\u7535\u52a8\u529b\u5b66\u3001\u6d41\u4f53\u529b\u5b66\u7b49\u95ee\u9898\u3002<\/li>\n\n\n\n<li>Gamma\u51fd\u6570\uff1a\u7528\u4e8e\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3001\u7edf\u8ba1\u5206\u5e03\u51fd\u6570\u7b49\u95ee\u9898\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e9b\u6280\u5de7\u7279\u6b8a\u51fd\u6570\u53ef\u4ee5\u5904\u7406\u5404\u79cd\u7279\u6b8a\u95ee\u9898\uff0c\u5e94\u7528\u8303\u56f4\u5e7f\u6cdb\uff0c\u4f8b\u5982\u5728\u7269\u7406\u5b66\u3001\u6570\u5b66\u3001\u5de5\u7a0b\u5b66\u3001\u5929\u6587\u5b66\u7b49\u9886\u57df\u90fd\u6709\u5e94\u7528\u3002<\/p>\n\n\n\n<p>\u603b\u4e4b\uff0cScipy\u5e93\u4e2d\u7684\u5e38\u7528\u51fd\u6570\u548c\u6280\u5de7\u7279\u6b8a\u51fd\u6570\u90fd\u5177\u6709\u5f88\u9ad8\u7684\u5b9e\u7528\u4ef7\u503c\uff0c\u53ef\u4ee5\u5e2e\u52a9\u79d1\u5b66\u5bb6\u3001\u5de5\u7a0b\u5e08\u548c\u6570\u636e\u5206\u6790\u5e08\u66f4\u8f7b\u677e\u5730\u89e3\u51b3\u590d\u6742\u7684\u79d1\u5b66\u8ba1\u7b97\u3001\u6570\u636e\u5206\u6790\u3001\u4fe1\u53f7\u5904\u7406\u7b49\u4efb\u52a1\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u7a97\u53e3\u51fd\u6570<\/p>\n\n\n\n<p>\u5728\u4fe1\u53f7\u5904\u7406\u9886\u57df\u4e2d\uff0c\u7a97\u53e3\u51fd\u6570\u662f\u4e00\u79cd\u5e38\u7528\u7684\u51fd\u6570\uff0c\u7528\u4e8e\u52a0\u6743\u4e00\u4e2a\u65f6\u95f4\u5e8f\u5217\u7684\u6570\u636e\uff0c\u4ee5\u51cf\u5c11\u5728\u5085\u91cc\u53f6\u53d8\u6362\u4e2d\u7684\u9891\u8c31\u6cc4\u6f0f\u95ee\u9898\uff0c\u540c\u65f6\u4fdd\u6301\u4fe1\u53f7\u7684\u65f6\u95f4\u5206\u8fa8\u7387\u3002Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u7a97\u53e3\u51fd\u6570\uff0c\u7528\u4e8e\u4fe1\u53f7\u5904\u7406\u3001\u8c31\u4f30\u8ba1\u7b49\u9886\u57df\u3002<\/p>\n\n\n\n<p>\u7a97\u53e3\u51fd\u6570\u7684\u539f\u7406\u662f\u5728\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e2d\u52a0\u5165\u4e00\u4e2a\u6743\u91cd\u56e0\u5b50\uff0c\u901a\u5e38\u662f\u4e00\u4e2a\u4ece0\u52301\u7684\u51fd\u6570\u3002\u7a97\u53e3\u51fd\u6570\u7684\u5f62\u72b6\u51b3\u5b9a\u4e86\u6570\u636e\u52a0\u6743\u7684\u65b9\u5f0f\uff0c\u4f8b\u5982\uff0c\u5728\u5085\u91cc\u53f6\u53d8\u6362\u4e2d\uff0c\u7a97\u53e3\u51fd\u6570\u53ef\u4ee5\u7528\u4e8e\u51cf\u5c11\u4fe1\u53f7\u7684\u9891\u8c31\u6cc4\u6f0f\u95ee\u9898\uff0c\u63d0\u9ad8\u9891\u7387\u5206\u8fa8\u7387\u3002<\/p>\n\n\n\n<p>\u5e38\u89c1\u7684\u7a97\u53e3\u51fd\u6570\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u77e9\u5f62\u7a97\uff08Rectangular window\uff09\uff1a\u6700\u7b80\u5355\u7684\u7a97\u53e3\u51fd\u6570\uff0c\u5373\u4e00\u4e2a\u5355\u4f4d\u8109\u51b2\uff0c\u5177\u6709\u7b49\u6743\u91cd\u7684\u7279\u6027\u3002<\/li>\n\n\n\n<li>\u6c49\u660e\u7a97\uff08Hamming window\uff09\uff1a\u5728\u77e9\u5f62\u7a97\u7684\u57fa\u7840\u4e0a\uff0c\u52a0\u5165\u4e86\u4f59\u5f26\u51fd\u6570\u56e0\u5b50\uff0c\u5177\u6709\u826f\u597d\u7684\u9891\u8c31\u4e3b\u74e3\u524a\u5f31\u80fd\u529b\u3002<\/li>\n\n\n\n<li>\u6c49\u5b81\u7a97\uff08Hanning window\uff09\uff1a\u5728\u6c49\u660e\u7a97\u7684\u57fa\u7840\u4e0a\uff0c\u4f7f\u7528\u4e86\u66f4\u591a\u7684\u4f59\u5f26\u51fd\u6570\u56e0\u5b50\uff0c\u5177\u6709\u66f4\u597d\u7684\u4e3b\u74e3\u524a\u5f31\u80fd\u529b\u3002<\/li>\n\n\n\n<li>\u5e03\u83b1\u514b\u66fc\u7a97\uff08Blackman window\uff09\uff1a\u5728\u6c49\u660e\u7a97\u7684\u57fa\u7840\u4e0a\uff0c\u52a0\u5165\u4e86\u66f4\u591a\u7684\u4f59\u5f26\u51fd\u6570\u56e0\u5b50\u548c\u4e00\u4e2a\u7ebf\u6027\u659c\u7387\u56e0\u5b50\uff0c\u5177\u6709\u66f4\u597d\u7684\u524a\u5f31\u80fd\u529b\u548c\u8f83\u4f4e\u7684\u526f\u74e3\u3002<\/li>\n\n\n\n<li>\u5347\u4f59\u5f26\u7a97\uff08Cosine window\uff09\uff1a\u7c7b\u4f3c\u4e8e\u6c49\u5b81\u7a97\uff0c\u4f46\u4f7f\u7528\u4e86\u66f4\u591a\u7684\u4f59\u5f26\u51fd\u6570\u56e0\u5b50\u548c\u6b63\u5f26\u51fd\u6570\u56e0\u5b50\uff0c\u63d0\u4f9b\u66f4\u597d\u7684\u526f\u74e3\u524a\u5f31\u6027\u80fd\u3002<\/li>\n<\/ul>\n\n\n\n<p>Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u7a97\u53e3\u51fd\u6570\u7684\u5b9e\u73b0\uff0c\u53ef\u4ee5\u6839\u636e\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u7a97\u53e3\u51fd\u6570\u3002\u4f8b\u5982\uff0c\u4e0b\u9762\u7684\u4ee3\u7801\u6f14\u793a\u4e86\u5982\u4f55\u4f7f\u7528\u6c49\u660e\u7a97\u5bf9\u4e00\u4e2a\u4fe1\u53f7\u8fdb\u884c\u52a0\u6743\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nfrom scipy import signal\n\n# \u751f\u6210\u4fe1\u53f7\nt = np.linspace(0, 1, 1000, endpoint=False)\nx = np.sin(2 * np.pi * 10 * t) + np.sin(2 * np.pi * 20 * t)\n\n# \u5e94\u7528\u6c49\u660e\u7a97\nwindow = signal.hamming(51)\nxw = x[:51] * window\n\n# \u663e\u793a\u7ed3\u679c\nimport matplotlib.pyplot as plt\n\nplt.plot(x[:51], 'b', label='Original')\nplt.plot(xw, 'r', label='Hamming window')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528np.sin()\u51fd\u6570\u751f\u6210\u4e86\u4e00\u4e2a\u5305\u542b\u4e24\u4e2a\u6b63\u5f26\u6ce2\u7684\u4fe1\u53f7\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528signal.hamming()\u51fd\u6570\u751f\u6210\u4e00\u4e2a51\u4e2a\u70b9\u7684\u6c49\u660e\u7a97\uff0c\u5bf9\u4fe1\u53f7\u8fdb\u884c\u52a0\u6743\uff0c\u5373\u5c06\u4fe1\u53f7\u7684\u524d51\u4e2a\u70b9<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u793a\u4f8b\uff1aScipy\u5b9e\u7528\u529f\u80fd<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u6765\u4e3e\u4e00\u4e2aScipy\u5b9e\u7528\u529f\u80fd\u7684\u4f8b\u5b50\uff0c\u4ee5\u6f14\u793a\u5982\u4f55\u4f7f\u7528Scipy\u5e93\u8fdb\u884c\u79d1\u5b66\u8ba1\u7b97\u548c\u6570\u636e\u5904\u7406\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u4e00\u4e2a1000\u4e2a\u5143\u7d20\u7684\u6d6e\u70b9\u6570\u6570\u7ec4\u3002\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e2a\u6570\u7ec4\u8fdb\u884c\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\uff08DFT\uff09\u5e76\u8ba1\u7b97\u5176\u529f\u7387\u8c31\u5bc6\u5ea6\uff08PSD\uff09\u3002\u7136\u540e\uff0c\u6211\u4eec\u5c06\u529f\u7387\u8c31\u5bc6\u5ea6\u7ed8\u5236\u6210\u4e00\u4e2a\u56fe\u5f62\uff0c\u5e76\u8ba1\u7b97\u5176\u5cf0\u503c\u9891\u7387\u3002<\/p>\n\n\n\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.fft import fft, fftfreq\nfrom scipy.signal import welch\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt')\n\n# \u8ba1\u7b97\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\ndft = fft(data)\n\n# \u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\nf, psd = welch(data)\n\n# \u7ed8\u5236\u529f\u7387\u8c31\u5bc6\u5ea6\u56fe\u5f62\nplt.semilogy(f, psd)\nplt.xlabel('Frequency')\nplt.ylabel('Power Spectral Density')\nplt.title('Power Spectral Density')\nplt.show()\n\n# \u8ba1\u7b97\u5cf0\u503c\u9891\u7387\nidx = np.argmax(psd)\npeak_freq = f[idx]\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Peak frequency:', peak_freq)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528np.loadtxt()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u4e00\u4e2a1000\u4e2a\u5143\u7d20\u7684\u6d6e\u70b9\u6570\u6570\u7ec4\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528scipy.fft.fft()\u51fd\u6570\u8ba1\u7b97\u4e86\u8be5\u6570\u7ec4\u7684\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u5e76\u4f7f\u7528scipy.signal.welch()\u51fd\u6570\u8ba1\u7b97\u4e86\u5176\u529f\u7387\u8c31\u5bc6\u5ea6\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528matplotlib\u5e93\u7ed8\u5236\u4e86\u529f\u7387\u8c31\u5bc6\u5ea6\u7684\u56fe\u5f62\uff0c\u5e76\u4f7f\u7528np.argmax()\u51fd\u6570\u8ba1\u7b97\u4e86\u529f\u7387\u8c31\u5bc6\u5ea6\u4e2d\u7684\u5cf0\u503c\u9891\u7387\u3002\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u8ba1\u7b97\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u8fd9\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4f7f\u7528Scipy\u5e93\u53ef\u4ee5\u8f7b\u677e\u5730\u8fdb\u884c\u79d1\u5b66\u8ba1\u7b97\u548c\u6570\u636e\u5904\u7406\uff0c\u4f8b\u5982\u8ba1\u7b97\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\u3001\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\u3001\u7ed8\u5236\u56fe\u5f62\u7b49\u64cd\u4f5c\uff0c\u53ef\u4ee5\u5927\u5927\u7b80\u5316\u79d1\u5b66\u8ba1\u7b97\u548c\u6570\u636e\u5904\u7406\u7684\u5de5\u4f5c\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6848\u4f8b\u4e00\uff1a\u6570\u636e\u62df\u5408\u4e0e\u9884\u6d4b<\/p>\n\n\n\n<p>\u6570\u636e\u62df\u5408\u548c\u9884\u6d4b\u662fScipy\u5e93\u7684\u5e38\u7528\u529f\u80fd\u4e4b\u4e00\u3002\u5728\u8fd9\u4e2a\u6848\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u4f7f\u7528Scipy\u5e93\u4e2d\u7684curve_fit()\u51fd\u6570\u5bf9\u4e00\u4e2a\u7b80\u5355\u7684\u6570\u636e\u96c6\u8fdb\u884c\u62df\u5408\uff0c\u5e76\u4f7f\u7528\u62df\u5408\u7ed3\u679c\u8fdb\u884c\u9884\u6d4b\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u4e00\u4e2ax\u548cy\u503c\u7684\u6570\u636e\u5bf9\u3002\u6211\u4eec\u9700\u8981\u5bf9\u8fd9\u4e9b\u6570\u636e\u8fdb\u884c\u62df\u5408\uff0c\u5e76\u4f7f\u7528\u62df\u5408\u7ed3\u679c\u8fdb\u884c\u9884\u6d4b\u3002<\/p>\n\n\n\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.optimize import curve_fit\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt')\n\n# \u5b9a\u4e49\u62df\u5408\u51fd\u6570\ndef func(x, a, b, c):\n    return a * np.exp(-b * x) + c\n\n# \u8fdb\u884c\u6570\u636e\u62df\u5408\npopt, pcov = curve_fit(func, data[:, 0], data[:, 1])\n\n# \u7ed8\u5236\u62df\u5408\u66f2\u7ebf\nx = np.linspace(0, 5, 100)\ny = func(x, *popt)\nplt.plot(data[:, 0], data[:, 1], 'ro', label='Data')\nplt.plot(x, y, 'b-', label='Fit')\nplt.legend()\nplt.show()\n\n# \u8fdb\u884c\u9884\u6d4b\nx_pred = np.linspace(5, 10, 50)\ny_pred = func(x_pred, *popt)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Parameters:', popt)\nprint('Predicted values:', y_pred)\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528np.loadtxt()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;data.txt&#8221;\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u4e86x\u548cy\u503c\u7684\u6570\u636e\u5bf9\u3002\u7136\u540e\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u62df\u5408\u51fd\u6570func()\uff0c\u8be5\u51fd\u6570\u91c7\u7528x\u3001a\u3001b\u548cc\u56db\u4e2a\u53c2\u6570\uff0c\u5176\u4e2da\u3001b\u548cc\u662f\u62df\u5408\u53c2\u6570\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528scipy.optimize.curve_fit()\u51fd\u6570\u5bf9\u6570\u636e\u8fdb\u884c\u62df\u5408\uff0c\u5e76\u5f97\u5230\u62df\u5408\u53c2\u6570popt\u548c\u534f\u65b9\u5dee\u77e9\u9635pcov\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528\u7ed8\u56fe\u5e93matplotlib\u7ed8\u5236\u4e86\u539f\u59cb\u6570\u636e\u548c\u62df\u5408\u66f2\u7ebf\uff0c\u5e76\u4f7f\u7528np.linspace()\u51fd\u6570\u751f\u6210\u4e8650\u4e2ax\u503c\u8fdb\u884c\u9884\u6d4b\u3002<\/p>\n\n\n\n<p>\u6700\u540e\uff0c\u6211\u4eec\u8f93\u51fa\u4e86\u62df\u5408\u53c2\u6570\u548c\u9884\u6d4b\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u8fd9\u4e2a\u6848\u4f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4f7f\u7528Scipy\u5e93\u4e2d\u7684curve_fit()\u51fd\u6570\u53ef\u4ee5\u65b9\u4fbf\u5730\u8fdb\u884c\u6570\u636e\u62df\u5408\u548c\u9884\u6d4b\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u7406\u89e3\u548c\u5206\u6790\u6570\u636e\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6848\u4f8b\u4e8c\uff1a\u56fe\u50cf\u8bc6\u522b\u4e0e\u5904\u7406<\/p>\n\n\n\n<p>\u56fe\u50cf\u8bc6\u522b\u548c\u5904\u7406\u662fScipy\u5e93\u7684\u53e6\u4e00\u4e2a\u5e38\u7528\u529f\u80fd\u3002\u5728\u8fd9\u4e2a\u6848\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u4f7f\u7528Scipy\u5e93\u4e2d\u7684ndimage\u6a21\u5757\u5bf9\u4e00\u5f20\u56fe\u50cf\u8fdb\u884c\u5904\u7406\uff0c\u5e76\u4f7f\u7528skimage\u5e93\u8fdb\u884c\u56fe\u50cf\u8bc6\u522b\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u5f20\u540d\u4e3a&#8221;image.png&#8221;\u7684\u56fe\u50cf\u6587\u4ef6\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u8be5\u56fe\u50cf\u8fdb\u884c\u4e8c\u503c\u5316\u5904\u7406\uff0c\u5e76\u4f7f\u7528skimage\u5e93\u8fdb\u884c\u6570\u5b57\u8bc6\u522b\u3002<\/p>\n\n\n\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import ndimage\nfrom skimage import io, morphology, measure\n\n# \u8bfb\u53d6\u56fe\u50cf\u6587\u4ef6\nimg = io.imread('image.png')\n\n# \u5c06\u56fe\u50cf\u8f6c\u6362\u4e3a\u7070\u5ea6\u56fe\u50cf\ngray_img = np.mean(img, axis=-1)\n\n# \u8fdb\u884c\u4e8c\u503c\u5316\u5904\u7406\nbinary_img = gray_img &gt; 127\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u5f62\u6001\u5b66\u5904\u7406\nmorph_img = morphology.binary_opening(binary_img, morphology.square(3))\n\n# \u8fdb\u884c\u6570\u5b57\u8bc6\u522b\nlabel_img = measure.label(morph_img, connectivity=2)\nprops = measure.regionprops(label_img)\n\n# \u7ed8\u5236\u7ed3\u679c\u56fe\u50cf\nfig, ax = plt.subplots()\nax.imshow(img)\n\nfor prop in props:\n    y, x = prop.centroid\n    ax.text(x, y, str(prop.label), color='red', fontsize=12)\n\nax.set_axis_off()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528skimage\u5e93\u4e2d\u7684io.imread()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;image.png&#8221;\u7684\u56fe\u50cf\u6587\u4ef6\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528np.mean()\u51fd\u6570\u5c06\u8be5\u56fe\u50cf\u8f6c\u6362\u4e3a\u7070\u5ea6\u56fe\u50cf\uff0c\u5e76\u4f7f\u7528\u7b80\u5355\u9608\u503c\u6cd5\u8fdb\u884c\u4e8c\u503c\u5316\u5904\u7406\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528scipy.ndimage\u6a21\u5757\u4e2d\u7684morphology.binary_opening()\u51fd\u6570\u5bf9\u56fe\u50cf\u8fdb\u884c\u5f62\u6001\u5b66\u5904\u7406\uff0c\u4ee5\u53bb\u9664\u566a\u58f0\u548c\u5c0f\u7684\u6591\u70b9\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528skimage\u5e93\u4e2d\u7684measure.label()\u51fd\u6570\u5bf9\u5904\u7406\u540e\u7684\u56fe\u50cf\u8fdb\u884c\u6807\u8bb0\uff0c\u5e76\u4f7f\u7528measure.regionprops()\u51fd\u6570\u8ba1\u7b97\u6807\u8bb0\u533a\u57df\u7684\u5c5e\u6027\uff0c\u4f8b\u5982\u4e2d\u5fc3\u4f4d\u7f6e\u548c\u6807\u8bb0\u53f7\u3002<\/p>\n\n\n\n<p>\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528matplotlib\u5e93\u7ed8\u5236\u4e86\u7ed3\u679c\u56fe\u50cf\uff0c\u5e76\u4f7f\u7528ax.text()\u51fd\u6570\u5728\u56fe\u50cf\u4e0a\u6807\u6ce8\u8bc6\u522b\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u8fd9\u4e2a\u6848\u4f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4f7f\u7528Scipy\u5e93\u53ef\u4ee5\u8f7b\u677e\u5730\u8fdb\u884c\u56fe\u50cf\u5904\u7406\u548c\u5206\u6790\uff0c\u4f8b\u5982\u56fe\u50cf\u8f6c\u6362\u3001\u4e8c\u503c\u5316\u3001\u5f62\u6001\u5b66\u5904\u7406\u3001\u6570\u5b57\u8bc6\u522b\u7b49\u64cd\u4f5c\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u5206\u6790\u548c\u5904\u7406\u56fe\u50cf\u6570\u636e\u3002<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8bf7\u8be6\u7ec6\u89e3\u91ca\u6848\u4f8b\u4e09\uff1a\u4fe1\u53f7\u53bb\u566a\u4e0e\u5206\u6790<\/p>\n\n\n\n<p>\u4fe1\u53f7\u53bb\u566a\u548c\u5206\u6790\u662fScipy\u5e93\u7684\u53e6\u4e00\u4e2a\u5e38\u7528\u529f\u80fd\u3002\u5728\u8fd9\u4e2a\u6848\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\u5bf9\u4e00\u4e2a\u7b80\u5355\u7684\u4fe1\u53f7\u8fdb\u884c\u53bb\u566a\uff0c\u5e76\u4f7f\u7528\u9891\u8c31\u5206\u6790\u8fdb\u884c\u4fe1\u53f7\u5206\u6790\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u540d\u4e3a&#8221;signal.txt&#8221;\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u4e00\u4e2a\u5305\u542b\u566a\u58f0\u7684\u4fe1\u53f7\u3002\u6211\u4eec\u9700\u8981\u5bf9\u8be5\u4fe1\u53f7\u8fdb\u884c\u53bb\u566a\uff0c\u5e76\u4f7f\u7528\u9891\u8c31\u5206\u6790\u8fdb\u884c\u4fe1\u53f7\u5206\u6790\u3002<\/p>\n\n\n\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopy code<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import signal\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('signal.txt')\n\n# \u4f7f\u7528\u4e2d\u503c\u6ee4\u6ce2\u8fdb\u884c\u53bb\u566a\nfiltered_data = signal.medfilt(data)\n\n# \u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\nf, psd = signal.welch(filtered_data)\n\n# \u7ed8\u5236\u529f\u7387\u8c31\u5bc6\u5ea6\u56fe\u5f62\nplt.semilogy(f, psd)\nplt.xlabel('Frequency')\nplt.ylabel('Power Spectral Density')\nplt.title('Power Spectral Density')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528np.loadtxt()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u4e2a\u540d\u4e3a&#8221;signal.txt&#8221;\u7684\u6570\u636e\u6587\u4ef6\uff0c\u5176\u4e2d\u5305\u542b\u4e00\u4e2a\u5305\u542b\u566a\u58f0\u7684\u4fe1\u53f7\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528scipy.signal\u6a21\u5757\u4e2d\u7684signal.medfilt()\u51fd\u6570\u5bf9\u8be5\u4fe1\u53f7\u8fdb\u884c\u4e2d\u503c\u6ee4\u6ce2\uff0c\u4ee5\u53bb\u9664\u566a\u58f0\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528scipy.signal\u6a21\u5757\u4e2d\u7684signal.welch()\u51fd\u6570\u8ba1\u7b97\u4e86\u6ee4\u6ce2\u540e\u4fe1\u53f7\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\uff0c\u5e76\u4f7f\u7528matplotlib\u5e93\u7ed8\u5236\u4e86\u529f\u7387\u8c31\u5bc6\u5ea6\u56fe\u5f62\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u8fd9\u4e2a\u6848\u4f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4f7f\u7528Scipy\u5e93\u4e2d\u7684\u4fe1\u53f7\u5904\u7406\u51fd\u6570\u53ef\u4ee5\u8f7b\u677e\u5730\u8fdb\u884c\u4fe1\u53f7\u53bb\u566a\u548c\u5206\u6790\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u7406\u89e3\u548c\u5206\u6790\u4fe1\u53f7\u6570\u636e\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u662f\u8981\u505aIT\u6559\u7a0b\u7684\u89c6\u9891\uff0c\u4f60\u80fd\u5426\u6839\u636e\u7f51\u7ad9\u7684 &hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[23],"tags":[],"class_list":["post-1869","post","type-post","status-publish","format-standard","hentry","category-material"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts\/1869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1869"}],"version-history":[{"count":1,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts\/1869\/revisions"}],"predecessor-version":[{"id":1870,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts\/1869\/revisions\/1870"}],"wp:attachment":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1869"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}