{"id":4844,"date":"2020-02-29T13:29:23","date_gmt":"2020-02-29T05:29:23","guid":{"rendered":"https:\/\/www.highflybird.com\/blog\/?p=4844"},"modified":"2020-09-16T21:34:15","modified_gmt":"2020-09-16T13:34:15","slug":"%e6%95%b0%e5%80%bc%e8%ae%a1%e7%ae%97%e4%b9%8b%e8%a7%a3%e6%96%b9%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/www.highflybird.com\/blog\/?p=4844","title":{"rendered":"\u6570\u503c\u8ba1\u7b97\u4e4b\u89e3\u65b9\u7a0b"},"content":{"rendered":"<p>\u6b64\u5904\u7528\u6bd4\u8f83\u7eafLISP\u7684\u65b9\u6cd5\u6765\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002<br \/>\n\u4e3b\u8981\u91c7\u7528Van Wijingaarden-Dekker-Brent\u65b9\u6cd5\u6c42\u89e3\u3002<br \/>\n<!--more--><br \/>\n\u4e0b\u9762\u662f\u5176\u6e90\u7801\uff1a<br \/>\n[codesyntax lang=&#8221;lisp&#8221;]<\/p>\n<pre>;;;*********************************************\n;;;\u7528Van Wijingaarden-Dekker-Brent\u65b9\u6cd5\u6c42\u89e3\u7684\u51fd\u6570\n;;;*********************************************\n(defun zbrent (f x1 x2 n \/ a b c d e i p q r s xm fa fb fc EPS Itr tol tol1 min1 min2)\n  (setq tol (expt 0.1 n))\t\t\t\t\t;\u5bb9\u5dee\n  (setq Itr 10000)\t\t\t\t\t\t;\u6700\u5927\u8fed\u4ee3\u6b21\u6570\n  (setq EPS 1e-16)\t\t\t\t\t\t;\u8ba1\u7b97\u673a\u6709\u6548\u7cbe\u5ea6\n  (if (&gt; x1 x2)\t\t\t\t\t\t\t;\u5982\u679c\u4e0b\u5c4a\u5927\u4e8e\u4e0a\u5c4a\n    (setq a x2\n\t  b x1\n\t  c x1\n    )\t\t\t\t\t\t\t\t;\u5219\u4ea4\u6362\u4e0a\u4e0b\u754c\n    (setq a x1\n\t  b x2\n\t  c x2\n    )\n  )\n  (setq fa (func a))\n  (setq fb (func b))\n  (if (or (and (&gt; fa 0) (&gt; fb 0)) (and (&lt; fa 0) (&lt; fb 0)))\t;\u4e0a\u4e0b\u754c\u51fd\u6570\u503c\u540c\u53f7\n    (princ \"\\nRoot must be bracketed in zbrent!\")\n  )\n  (setq fc fb)\n  (setq i 1)\n  (while (&lt;= i Itr)\n    (if\t(or (and (&gt; fb 0) (&gt; fc 0))\n\t    (and (&lt; fb 0) (&lt; fc 0))\n\t)\n      (setq c  a\n\t    fc fa\n\t    d  (- b a)\n\t    e  d\n      )\t\t\t\t\t\t\t\t;\u5bf9a,b,c\u66f4\u540d\u5e76\u8c03\u6574\u89e3\u533a\u95f4d\n    )\n    (if\t(&lt; (abs fc) (abs fb))\n      (setq a  b\n\t    b  c\n\t    c  a\n\t    fa fb\n\t    fb fc\n\t    fc fa\n      )\n    )\n    (setq tol1 (+ (* 2.0 EPS (abs b)) (* 0.5 tol))) \t\t;\u6536\u655b\u6027\u68c0\u67e5\n    (setq xm (* 0.5 (- c b)))\n    (if\t(or (&lt;= (abs xm) tol1) (equal fb 0 1e-16)) \t\t;\u8df3\u51fa\u5faa\u73af\n      (setq i Itr)\n      (progn\n\t(if (and (&gt;= (abs e) tol1)\n\t\t (&gt; (abs fa) (abs fb))\n\t    )\n\t  (progn\n\t    (setq s (\/ fb fa))\t\t\t\t\t;\u5c06\u8fdb\u884c\u7b2c\u4e8c\u6b21\u53cd\u63d2\n\t    (if\t(equal a c 1e-16)\n\t      (setq p (* 2.0 xm s)\n\t\t    q (- 1.0 s)\n\t      )\n\t      (setq q (\/ fa fc)\n\t\t    r (\/ fb fc)\n\t\t    p (* s (- (* 2.0 xm q (- q r)) (* (- b a) (1- r))))\n\t\t    q (* (1- q) (1- r) (1- s))\n\t      )\n\t    )\n\t    (if\t(&gt; p 0)\n\t      (setq q (- q))\n\t    )\t\t\t\t\t\t\t;\u68c0\u67e5\u662f\u5426\u5728\u89e3\u533a\u95f4\u5185\n\t    (setq p (abs p))\n\t    (setq min1 (- (* 3.0 xm q) (abs (* tol1 q))))\n\t    (setq min2 (abs (* e q)))\n\t    (if\t(&lt; (* 2.0 p)\n\t\t   (if (&lt; min1 min2)\n\t\t     min1\n\t\t     min2\n\t\t   )\n\t\t)\n\t      (setq e d\n\t\t    d (\/ p q)\n\t      )\t\t\t\t\t\t\t;\u53ef\u4ee5\u8fdb\u884c\u5185\u63d2\n\t      (setq d xm\n\t\t    e d\n\t      )\t\t\t\t\t\t\t;\u4e0d\u80fd\u8fdb\u884c\u5185\u63d2\uff0c\u6539\u7528\u4e8c\u5206\u6cd5\n\t    )\n\t  )\n\t  (setq\td xm\n\t\te d\n\t  )\t\t\t\t\t\t\t;\u5c4a\u4e0b\u964d\u901f\u5ea6\u592a\u6162\uff0c\u6539\u7528\u4e8c\u5206\u6cd5\n\t)\n\t(setq a b)\t\t\t\t\t\t;\u5c06\u6700\u65b0\u4f30\u503c\u8d4b\u7ed9a\n\t(setq fa fb)\n\t(if (&gt; (abs d) tol1)\t\t\t\t\t;\u8ba1\u7b97\u65b0\u7684\u5b9e\u9a8c\u89e3\n\t  (setq b (+ b d))\n\t  (setq\tb (+ b\n\t\t     (if (&gt;= xm 0)\n\t\t       (abs tol1)\n\t\t       (- (abs tol1))\n\t\t     )\n\t\t  )\n\t  )\n\t)\n\t(setq fb (func b))\n      )\n    )\n    (setq i (1+ i))\n  )\n  b\n)\n<\/pre>\n<p>[\/codesyntax]<\/p>\n<p>\u4e0b\u9762\u7684\u4ee3\u7801\u5305\u542b\u4e86\u4e00\u4e2a\u5e94\u7528\u53ca\u5176\u5bf9\u8bdd\u6846\u4f8b\u5b50\uff1a<\/p>\n<p>[codesyntax lang=&#8221;lisp&#8221;]<\/p>\n<pre>(vl-load-com)\n;;;\u4e3b\u7a0b\u5e8f\n(prompt \"\u8bf7\u8f93\u5165solve\u547d\u4ee4!\")\n\n;;;\u8868\u8fbe\u5f0f\u6c42\u503c\n(defun Getfunc (str)\n  (CAL:Expr2Func str 'func '(x))\n)\n\n(defun C:solve (\/ f x1 x2 n id Dcl_File)\n  (setq id (load_dialog (setq Dcl_File (Write_Dcl))))\t\t;\u88c5\u5165\u5bf9\u8bdd\u6846\n  (vl-file-delete Dcl_File)\t\t\t\t\t;\u5220\u9664\u4e34\u65f6\u6587\u4ef6\n  (if (new_dialog \"dcl_solve\" id)\n    (progn\n      (action_tile \"EXP\" \"(Getfunc (setq f $value))\") \t\t;\u4ece\u5bf9\u8bdd\u6846\u4e2d\u5f97\u5230\u8868\u8fbe\u5f0f\n      (action_tile \"MIN\" \"(setq x1 $value)\") \t\t\t;\u4ece\u5bf9\u8bdd\u6846\u4e2d\u5f97\u5230\u4e0b\u5c4a\n      (action_tile \"MAX\" \"(setq x2 $value)\") \t\t\t;\u4ece\u5bf9\u8bdd\u6846\u4e2d\u5f97\u5230\u4e0a\u5c4a\n      (action_tile \"PRC\" \"(setq n $value)\") \t\t\t;\u4ece\u5bf9\u8bdd\u6846\u4e2d\u5f97\u5230\u7cbe\u5ea6\n      (action_tile \"ANS\" \"(GetAnswer f x1 x2 n)\")               ;\u6c42\u89e3\n      (action_tile \"help\" \"(choose 1)\")\t\t\t\t;\u5e2e\u52a9\n      (start_dialog)\n      (unload_dialog id)\n      (princ (GetAnswer f x1 x2 n))\n    )\n  )\n  (princ)\n)\n\n;;;*********************************************\n;;;\u4ece\u5bf9\u8bdd\u6846\u5f97\u5230\u65b9\u7a0b\u53c2\u6570\u5e76\u6c42\u89e3\u548c\u663e\u793a\u7ed3\u679c         \n;;;*********************************************\n(defun GetAnswer (f x1 x2 n \/ str1 str2 str3 str4 str5 ret test fra_x int_x result)\n  (if (and x1 x2 n f)\n    (progn\n      (setq x1 (atof x1))\n      (setq x2 (atof x2))\n      (setq n  (abs (atoi n)))\n      (if (&gt; n 20)\n         (setq n 20)\n      )\n      (GetFunc f)\n      (setq ret (vl-catch-all-apply 'zbrent (list f x1 x2 n)))\n      (if (vl-catch-all-error-p ret)\n\t(setq str5 (strcat \"\u51fa\u9519: \" (vl-catch-all-error-message ret)))\n\t(progn\n\t  (setq test (func ret))\n\t  (setq fra_x (rtos (- (abs ret) (fix (abs ret))) 2 n))\n\t  (setq fra_x (vl-string-left-trim \"0\" fra_x))\n\t  (setq int_x (itoa (fix ret)))\n\t  (if (equal test 0 1)\n\t    (setq result (strcat \"\u65b9\u7a0b\" f \"=0\" \"\u7684\u89e3\u4e3a:\" int_x fra_x)\n\t\t  result (list result (strcat int_x fra_x) (rtos test 2 n))\n\t    )\n\t    (setq result (strcat \"\u65b9\u7a0b\" f \"=0\" \"\u5728\u6b64\u533a\u95f4\u65e0\u89e3\")\n\t\t  result (list result (strcat int_x fra_x) (rtos test 2 n))\n\t    )\n\t  )\n\t  (setq\tstr1 (car result)\n\t\tstr2 \"\\n\u4e0b\u9762\u662f\u6c42\u89e3\u9a8c\u8bc1\u7ed3\u679c:\"\n\t\tstr3 (cadr result)\n\t\tstr4 (caddr result)\n\t\tstr5 (strcat str1 str2 \"\\nf(\" str3 \")=\" str4)\n\t  )\n\t)\n      )\n      (set_tile \"error\" str5)\n      str5\n    )\n    (set_tile \"error\" \"\u8f93\u5165\u6709\u8bef!\")\n  )\n)\n\n\n\n;;;\u5e2e\u52a9\u8bf4\u660e\u51fd\u6570\n(defun choose (n)\n  (if (= n 1)\n    (alert\n      \"\u65b9\u7a0b\u5f0f\u53ea\u63a5\u53d7x(\u5c0f\u5199)\u4e3a\u53d8\u91cf,\u4e0d\u89c4\u8303\u5f88\u53ef\u80fd\u51fa\u9519!\n           \\n\u65e0\u987b\u5199\u7b49\u5f0f,\u4f8b\u5982\u6c42\u89e3x^2-2=0\u5199\u4f5cx^2-2.\n           \\n\u7a0b\u5e8f\u91c7\u7528brent\u65b9\u6cd5\u6c42\u89e3,\u4e0d\u4fdd\u8bc1\u6bcf\u4e2a\u65b9\u7a0b\u90fd\u6709\u6548!\n\t   \\n\u6709\u4ec0\u4e48\u95ee\u9898email: highflybird@qq.com\"\n    )\n    (set_tile\n      \"error\"\n      \"\u65b9\u7a0b\u5f0f\u53ea\u63a5\u53d7x(\u5c0f\u5199)\u4e3a\u53d8\u91cf,\u65e0\u987b\u5199\u7b49\u5f0f,\u4f8b\u5982\u6c42\u89e3x^2-2=0\u5199\u4f5cx^2-2.\"\n    )\n  )\n)\n\n;;; for DCL\n(defun Write_Dcl (\/ Dcl_File file str)\n  (setq Dcl_File (vl-filename-mktemp nil nil \".DCL\"))\n  (setq file (open Dcl_File \"w\"))\n  (princ\n    \"dcl_solve : dialog {\n      label = \\\"\u4e00\u5143\u65b9\u7a0b\u6c42\u89e3\u7a0b\u5e8f\\\";\n      : boxed_column {\n        : edit_box {\n          key=\\\"EXP\\\";\n          label= \\\"\u4e00\u5143\u65b9\u7a0b:\\\";\n        }\n        : row {\n          : edit_box {\n            key=\\\"MIN\\\";\n\t    label= \\\"\u533a\u95f4\u4e0b\u5c4a:\\\";\n            edit_width = 8;\n          }\n          : edit_box {\n            key=\\\"MAX\\\";\n            label= \\\"\u533a\u95f4\u4e0a\u5c4a:\\\";\n            edit_width = 8;\n          }\n          : edit_box {\n            key=\\\"PRC\\\";\n            label= \\\"\u7cbe\u786e\u4f4d\u6570:\\\";\n            edit_width = 2;\n          }\n        }\n        spacer_1;\n      }\n      : row {\n        : button {\n          key=\\\"ANS\\\";\n          label=\\\"\u6c42\u89e3\\\";\n        }\n        ok_cancel_help;\n      }\n      errtile;\n    }\"\n    file\n  )\n  (close file)\n  Dcl_File\n)<\/pre>\n<p>[\/codesyntax]<\/p>\n<p>\u6c42\u89e3\u901f\u5ea6\u8fd8\u53ef\u4ee5\uff0c\u5bf9\u4e8e\u4e00\u822c\u7684\uff0c\u5982\u679c\u4f30\u7b97\u597d\u6c42\u89e3\u533a\u95f4\uff0c\u90fd\u4f1a\u5f97\u5230\u6b63\u786e\u7ed3\u679c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6b64\u5904\u7528\u6bd4\u8f83\u7eafLISP\u7684\u65b9\u6cd5\u6765\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002 \u4e3b\u8981\u91c7\u7528Van Wijingaarden-Dekker-Brent<\/p>\n<p class=\"more-link\"><a href=\"https:\/\/www.highflybird.com\/blog\/?p=4844\" class=\"themebutton2\">Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[9],"tags":[11,67],"class_list":["post-4844","post","type-post","status-publish","format-standard","hentry","category-programming","tag-lisp","tag-67"],"_links":{"self":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4844","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4844"}],"version-history":[{"count":0,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4844\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}