$$ <\/p>\n \u5176\u4e2d$p \\in {\\Bbb {R}}, p \\geq 1$<\/p>\n $L_1$\u8303\u6570\uff1a$ \\mid \\mid x\\mid\\mid1 = \\sum<\/em>{i} x_i $ Frobenius\u8303\u6570\u662f\u7528\u6765\u8861\u91cf\u77e9\u9635\u7684\u5927\u5c0f\uff0c\u5176\u5b9a\u4e49\uff1a<\/p>\n $$ \u5c31\u662f\u77e9\u9635\u7684\u6bcf\u4e2a\u5143\u7d20\u53d6\u5e73\u65b9\u518d\u6c42\u548c\uff0c\u6700\u7ec8\u5f00\u5e73\u65b9\u3002\u7c7b\u4f3c\u4e8e$L_2$\u8303\u6570\u3002<\/p>\n x\u8868\u793a\u8981\u5ea6\u91cf\u7684\u5411\u91cf\uff0cord\u8868\u793a\u8303\u6570\u7684\u79cd\u7c7b<\/p>\n \u8303\u6570\u7406\u8bba\u7684\u4e00\u4e2a\u5c0f\u63a8\u8bba\u544a\u8bc9\u6211\u4eec\uff1a$l_1 \\geq l2 \\geq l<\/em>\\infty$<\/p>\n Lp\u8303\u6570 $$ \\mid\\mid x\\mid\\midp = (\\sum{i}|x_i|^p)^{\\frac { […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[527],"tags":[531],"class_list":["post-2102","post","type-post","status-publish","format-standard","hentry","category-ai","tag-531"],"_links":{"self":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2102"}],"version-history":[{"count":0,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2102\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\\mid\\mid x\\mid\\midp = (\\sum<\/em>{i}|x_i|^p)^{\\frac {1} {p}}
\n$$<\/p>\n
\n$L_2$\u8303\u6570\uff1a$ \\mid \\mid x\\mid\\mid2 = \\sqrt{\\sum<\/em>{i} xi^2} $
\n$L<\/em>\\infty$\u8303\u6570\uff1a$ \\mid \\mid x\\mid\\mid_\\infty = max \\mid x_i\\mid $<\/p>\nFrobenius\u8303\u6570<\/h2>\n
\n||x||F = \\sqrt{\\sum<\/em>{i,j}A_{i,j}^2}
\n$$<\/p>\nPython\u5b9e\u73b0<\/h2>\n
norm(x, ord=None, axis=None, keepdims=False)<\/code><\/pre>\n\n\n
\n \n\u53c2\u6570<\/th>\n \u8bf4\u660e<\/th>\n \u8ba1\u7b97\u65b9\u6cd5<\/th>\n<\/tr>\n<\/thead>\n \n \u9ed8\u8ba4<\/td>\n \u4e8c\u8303\u6570\uff1a$l_2$<\/td>\n $\\sqrt{x_1^2 + x_2^2 + \\cdots + x_n^2}$<\/td>\n<\/tr>\n \n ord=2<\/td>\n \u4e8c\u8303\u6570\uff1a$l_2$<\/td>\n \u540c\u4e0a<\/td>\n<\/tr>\n \n ord=1<\/td>\n \u4e00\u8303\u6570\uff1a$l_1$<\/td>\n $\\mid x_1\\mid + \\mid x_2\\mid + \\cdots + \\mid x_n\\mid$<\/td>\n<\/tr>\n \n ord=np.inf<\/td>\n \u65e0\u7a77\u8303\u6570\uff1a$l_\\infty$<\/td>\n $max(\\mid x_i\\mid)$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Numpy<\/h3>\n
import numpy as np\n\n# \u5411\u91cf\nx = np.arange(9) - 4\n# \u77e9\u9635\nA = x.reshape((3, 3))\nprint(A)\n# L1\u8303\u6570\nprint(np.linalg.norm(x, 1))\n# L2\u8303\u6570\nprint(np.linalg.norm(x, 2))\n# L\u6b63\u65e0\u7a77\u8303\u6570\nprint(np.linalg.norm(x, np.inf))\n# L\u8d1f\u65e0\u7a77\u8303\u6570\nprint(np.linalg.norm(x, -np.inf))\n# Frobenius\u8303\u6570\nprint(np.linalg.norm(A))<\/code><\/pre>\nNumpy<\/h3>\n
import numpy as np\nfrom scipy import linalg\n\n# \u5411\u91cf\nx = np.arange(9) - 4\n# \u77e9\u9635\nA = x.reshape((3, 3))\nprint(A)\n# L1\u8303\u6570\nprint(linalg.norm(x,1))\n# L2\u8303\u6570\nprint(linalg.norm(x,2))\n# L\u6b63\u65e0\u7a77\u8303\u6570\nprint(linalg.norm(x,np.inf))\n# L\u8d1f\u65e0\u7a77\u8303\u6570\nprint(linalg.norm(x,-np.inf))\n# Frobenius\u8303\u6570\nprint(linalg.norm(A))<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"