{"id":78,"date":"2017-05-05T12:38:33","date_gmt":"2017-05-05T09:38:33","guid":{"rendered":"http:\/\/siteblog.tuc.gr\/nispanoudakis\/?p=78"},"modified":"2018-04-17T16:37:07","modified_gmt":"2018-04-17T13:37:07","slug":"%cf%85%cf%80%ce%bf%ce%bb%ce%bf%ce%b3%ce%b9%cf%83%ce%bc%cf%8c%cf%82-%ce%b1%ce%ba%cf%81%cf%8c%cf%84%ce%b1%cf%84%cf%89%ce%bd-%cf%83%cf%85%ce%bd%ce%ac%cf%81%cf%84%ce%b7%cf%83%ce%b7%cf%82-%ce%b4%cf%8d","status":"publish","type":"post","link":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/2017\/05\/05\/%cf%85%cf%80%ce%bf%ce%bb%ce%bf%ce%b3%ce%b9%cf%83%ce%bc%cf%8c%cf%82-%ce%b1%ce%ba%cf%81%cf%8c%cf%84%ce%b1%cf%84%cf%89%ce%bd-%cf%83%cf%85%ce%bd%ce%ac%cf%81%cf%84%ce%b7%cf%83%ce%b7%cf%82-%ce%b4%cf%8d\/","title":{"rendered":"\u03a5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \u03b4\u03cd\u03bf \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd"},"content":{"rendered":"

\u038c\u03c4\u03b1\u03bd \u03b8\u03ad\u03bb\u03c9 \u03bd\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03c9 \u03c4\u03b1 \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \u03b4\u03cd\u03bf \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03ba\u03ac\u03bd\u03c9 \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03c5\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2. \u03a0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9, \u03bc\u03b9\u03b1 \u03ad\u03c4\u03bf\u03b9\u03bc\u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03bf Matlab<\/a> \u03ba\u03b1\u03b9 \u03c4\u03bf Octave<\/a> \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03c4\u03c9\u03bd \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd 3D \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c4\u03b1 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9. \u039f \u03ba\u03ce\u03b4\u03b9\u03ba\u03b1\u03c2 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03bf\u03c5\u03bb\u03ad\u03c8\u03b5\u03b9 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03b9\u03ba\u03cc \u03c0\u03b1\u03ba\u03ad\u03c4\u03bf (symbolic package), \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b9\u03c2 \u03c4\u03c5\u03c0\u03b9\u03ba\u03ad\u03c2 \u03b5\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03c4\u03c9\u03bd matlab (symbolic math toolbox<\/a>) \u03ba\u03b1\u03b9 octave (octsympy<\/a>).<\/p>\n

\u0395\u03ac\u03bd \u03b8\u03ad\u03bb\u03b5\u03c4\u03b5 \u03bd\u03b1 \u03bc\u03ac\u03b8\u03b5\u03c4\u03b5 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03c0\u03af\u03c3\u03c9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2 \u03c3\u03b1\u03c2 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ad\u03bc\u03c0\u03c9 \u03c3\u03c4\u03b9\u03c2 \u03c3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2<\/a> \u03c4\u03bf\u03c5 \u039a\u03b1\u03b8. \u0393\u03b5\u03ce\u03c1\u03b3\u03b9\u03bf\u03c5 \u0391\u03bd\u03b4\u03c1\u03bf\u03c5\u03bb\u03ac\u03ba\u03b7.<\/p>\n

\u039b\u03bf\u03b9\u03c0\u03cc\u03bd \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03ba\u03b1\u03b9 \u03bb\u03ad\u03bc\u03b5, \u03bf \u03ba\u03ce\u03b4\u03b9\u03ba\u03b1\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf:<\/p>\n

function akrotata(syn,pedia_timwn)\r\n%Ypologizei akrotata synartisis syn me 2 metablhtes x, y. \r\n%H sinartisi f dinetai ws alfarithmitiko kai proairetika mporeite na dwsete ta pedia timwn gia ta x, y me th morfi [x_min,x_max, y_min, y_max] (metabliti pedia_timwn). \r\n%An den balete timh sta pedia_timwn tote sto grafima 0a deite tin syn otan ta x,y anikoyn sto [-pi,pi].\r\nsyms x y f;\r\nf=sym(syn);\r\nfx=diff(f,x,1);\r\nfy=diff(f,y,1);\r\n[a,b]=solve(fx==0,fy==0);\r\nif nargin < 2\r\n    pedia_timwn = [-pi,pi,-pi,pi];\r\nend\r\nezsurf(f,pedia_timwn);\r\nif size(a) > 0\r\n    fxx=diff(f,x,2);\r\n    fyy=diff(f,y,2);\r\n    fxy=diff(diff(f,x),y);\r\n    for i=1:size(a)\r\n        vfxx=double(subs(subs(fxx,x,a(i)), y, b(i)));\r\n        vfyy=double(subs(subs(fyy,x,a(i)), y, b(i)));\r\n        vfxy=double(subs(subs(fxy,x,a(i)), y, b(i)));\r\n        vfxy2=vfxy^2;\r\n        vfxx_times_vfyy = vfxx*vfyy;\r\n        if vfxx < 0 && vfyy < 0 && vfxx_times_vfyy > vfxy2\r\n            sprintf('\\nYparxei topiko megisto sto shmeio (%f, %f, %f)',double(a(i)), double(b(i)), double(subs(subs(f,x,a(i)), y, b(i))))\r\n        elseif vfxx > 0 && vfyy > 0 && vfxx_times_vfyy > vfxy2\r\n            sprintf('\\nYparxei topiko elaxisto sto shmeio (%f, %f, %f)',double(a(i)), double(b(i)), double(subs(subs(f,x,a(i)), y, b(i))))\r\n        elseif vfxx_times_vfyy < vfxy2\r\n            sprintf('\\nSagmatiko  shmeio (%f, %f, %f)',double(a(i)), double(b(i)), double(subs(subs(f,x,a(i)), y, b(i))))\r\n        end\r\n    end\r\nelse\r\n    disp('Den yparxoun akrotata')\r\nend<\/pre>\n
\u03a0\u03bb\u03b7\u03ba\u03c4\u03c1\u03bf\u03bb\u03bf\u03b3\u03ae\u03c3\u03c4\u03b5 \u03ae \u03b5\u03c0\u03b9\u03ba\u03bf\u03bb\u03bb\u03ae\u03c3\u03c4\u03b5 \u03c4\u03bf\u03bd \u03ba\u03ce\u03b4\u03b9\u03ba\u03b1 \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c1\u03c7\u03b5\u03af\u03bf akrotata.m , \u03b5\u03c0\u03b9\u03bb\u03ad\u03be\u03c4\u03b5 \u03c4\u03bf\u03bd \u03c6\u03ac\u03ba\u03b5\u03bb\u03bf \u03c3\u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03c4\u03bf \u03ad\u03c7\u03b5\u03c4\u03b5 \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03c3\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c4\u03bf \u03b4\u03bf\u03ba\u03b9\u03bc\u03ac\u03c3\u03b5\u03c4\u03b5 \u03b5\u03ba\u03c4\u03b5\u03bb\u03ad\u03c3\u03c4\u03b5 \u03c3\u03c4\u03bf \u03c0\u03b1\u03c1\u03ac\u03b8\u03c5\u03c1\u03bf \u03b5\u03bd\u03c4\u03bf\u03bb\u03ce\u03bd \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03b5\u03bd\u03c4\u03bf\u03bb\u03ae:<\/p>\n
>> akrotata('(x^2+4*y^2)*exp(1-x^2-y^2)',[-2,2,-2,2])<\/pre>\n
\u0397 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03c3\u03c7\u03ae\u03bc\u03b1:<\/p>\n
\"figure_akrotata\"<\/a><\/p>\n
\u0395\u03bd\u03ce \u03b7 \u03ad\u03be\u03bf\u03b4\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b5\u03b9\u03ba\u03cc\u03bd\u03b1:<\/p>\n
\"screenshot_octave_akrotata\"<\/a><\/p>\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
\u038c\u03c4\u03b1\u03bd \u03b8\u03ad\u03bb\u03c9 \u03bd\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03c9 \u03c4\u03b1 \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \u03b4\u03cd\u03bf \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03ba\u03ac\u03bd\u03c9 \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03c5\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2. \u03a0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9, \u03bc\u03b9\u03b1 \u03ad\u03c4\u03bf\u03b9\u03bc\u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03bf Matlab \u03ba\u03b1\u03b9 \u03c4\u03bf Octave \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03c4\u03c9\u03bd \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd 3D \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c4\u03b1 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9. \u039f \u03ba\u03ce\u03b4\u03b9\u03ba\u03b1\u03c2 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03bf\u03c5\u03bb\u03ad\u03c8\u03b5\u03b9 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03b9\u03ba\u03cc \u03c0\u03b1\u03ba\u03ad\u03c4\u03bf (symbolic package), \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b9\u03c2 \u03c4\u03c5\u03c0\u03b9\u03ba\u03ad\u03c2 … \u03a3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03b1\u03bd\u03ac\u03b3\u03bd\u03c9\u03c3\u03b7\u03c2 \u03a5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \u03b4\u03cd\u03bf \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":77,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19,15,16,21,17,20],"tags":[],"class_list":["post-78","post","type-post","status-publish","format-standard","hentry","category-3d-","category-matlab","category-octave","category-symbolic","category-17","category-20"],"_links":{"self":[{"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/posts\/78","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/users\/77"}],"replies":[{"embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/comments?post=78"}],"version-history":[{"count":10,"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/posts\/78\/revisions"}],"predecessor-version":[{"id":157,"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/posts\/78\/revisions\/157"}],"wp:attachment":[{"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/media?parent=78"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/categories?post=78"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/nispanoudakis\/wp-json\/wp\/v2\/tags?post=78"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}