{"id":256892,"date":"2015-05-09T20:27:02","date_gmt":"2015-05-09T16:27:02","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=256892"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=256892","title":{"rendered":"\u041e\u0431 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438, \u043c\u0435\u0442\u043e\u0434\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u0421\u041b\u0410\u0423 \u043d\u0430 Delphi. \u0427\u0430\u0441\u0442\u044c 1"},"content":{"rendered":"<p>     \t\u041e\u0431 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 (\u0410\u0414) \u043d\u0430 \u0425\u0430\u0431\u0440\u0435 \u0443\u0436\u0435 \u043f\u0438\u0441\u0430\u043b\u043e\u0441\u044c <a href=\"http:\/\/habrahabr.ru\/company\/intel\/blog\/170729\/\">\u0437\u0434\u0435\u0441\u044c<\/a> \u0438 <a href=\"http:\/\/habrahabr.ru\/post\/63055\/\">\u0437\u0434\u0435\u0441\u044c<\/a>. \u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0410\u0414 \u0434\u043b\u044f Delphi (\u043f\u0440\u043e\u0442\u0435\u0441\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043e \u0432 Embarcadero XE2, XE6) \u0432\u043c\u0435\u0441\u0442\u0435 \u0441 \u0443\u0434\u043e\u0431\u043d\u044b\u043c\u0438 \u043a\u043b\u0430\u0441\u0441\u0430\u043c\u0438 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 f(x) = 0 \u0438 \u0441\u0438\u0441\u0442\u0435\u043c F(X) = 0. \u041b\u044e\u0431\u044b\u0435 \u0441\u0441\u044b\u043b\u043a\u0438 \u043d\u0430 \u0433\u043e\u0442\u043e\u0432\u044b\u0435 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0435 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0438 \u043f\u0440\u0438\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0442\u0441\u044f, \u0441\u0430\u043c \u0436\u0435 \u044f \u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0433\u043e \u043d\u0435 \u043d\u0430\u0448\u0435\u043b, \u043d\u0435 \u0441\u0447\u0438\u0442\u0430\u044f \u043e\u0442\u043b\u0438\u0447\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u044f \u0421\u041b\u0410\u0423 \u0441 \u0440\u0430\u0437\u0440\u044f\u0436\u0435\u043d\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 (\u0441\u043c. \u043f\u043e\u0434 \u043a\u0430\u0442\u043e\u043c).<\/p>\n<p>  <a name=\"habracut\"><\/a><br \/>  \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0432 \u0441\u0430\u043c\u043e\u043c \u043d\u0430\u0447\u0430\u043b\u0435 \u043e\u0442\u043c\u0435\u0442\u0438\u043c \u0434\u043b\u044f \u0441\u0435\u0431\u044f, \u0447\u0442\u043e \u0432\u044b\u0431\u043e\u0440 Delphi \u043e\u0431\u0443\u0441\u043b\u043e\u0432\u043b\u0435\u043d legacy-\u043a\u043e\u0434\u043e\u043c, \u0442\u0435\u043c \u043d\u0435 \u043c\u0435\u043d\u0435\u0435 \u043d\u0430 C++ \u0437\u0430\u0434\u0430\u0447\u0443 \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c. \u0412\u043e-\u043f\u0435\u0440\u0432\u044b\u0445, \u0434\u043b\u044f \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u041d\u044c\u044e\u0442\u043e\u043d\u043e\u0432\u0441\u043a\u043e\u0433\u043e (\u0431\u0430\u0437\u043e\u0432\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043c\u0435\u0442\u043e\u0434 \u0411\u0440\u043e\u0439\u0434\u0435\u043d\u0430) \u0442\u0438\u043f\u0430 \u0438\u043c\u0435\u044e\u0442\u0441\u044f <a href=\"https:\/\/www.google.ru\/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=1&amp;cad=rja&amp;uact=8&amp;ved=0CBwQFjAA&amp;url=http%3A%2F%2Fe-maxx.ru%2Fbookz%2Ffiles%2Fnumerical_recipes.pdf&amp;ei=kOOwVLmuCcbvauzEguAB&amp;usg=AFQjCNH1zwq1qHzRBjVMAeUorZsf3HfuHg&amp;sig2=ELEcigWCWp0CNnM4Yk_Z1Q&amp;bvm=bv.83339334,d.d2s\">Numerical Recipes in C++<\/a>. \u0420\u0430\u043d\u0435\u0435 \u00ab\u0420\u0435\u0446\u0435\u043f\u0442\u044b\u00bb \u0431\u044b\u043b\u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0430 \u0447\u0438\u0441\u0442\u043e\u043c C \u0438 \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u043b\u043e\u0441\u044c \u0434\u0435\u043b\u0430\u0442\u044c \u0441\u0432\u043e\u0438 \u043a\u043b\u0430\u0441\u0441\u043e\u0432\u044b\u0435 \u043e\u0431\u0435\u0440\u0442\u043a\u0438. \u0412\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u044f\u0442\u044c \u043e\u0434\u043d\u0443 \u0438\u0437 \u0410\u0414-\u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a \u0438\u0437 \u0441\u043f\u0438\u0441\u043a\u0430 <a href=\"http:\/\/www.autodiff.org\/?module=Tools&amp;language=C%2FC%2B%2B\">Autodiff.org<\/a>. \u041f\u043e \u043c\u043e\u0435\u043c\u0443 \u043e\u043f\u044b\u0442\u0443 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f CPPAD \u0431\u044b\u0441\u0442\u0440\u0435\u0435 FADBAD \u0438 Trilinos::Sacado \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u043d\u0430 30%, \u0441\u0430\u043c\u0430\u044f \u0436\u0435 \u0431\u044b\u0441\u0442\u0440\u0430\u044f, \u0441\u0443\u0434\u044f \u043f\u043e \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044e, \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0430 \u044d\u0442\u043e \u043d\u043e\u0432\u0430\u044f <a href=\"http:\/\/www.met.reading.ac.uk\/clouds\/adept\/\">ADEPT<\/a>. \u0412-\u0442\u0440\u0435\u0442\u044c\u0438\u0445, \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0447\u043d\u043e-\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u044f\u0442\u044c \u043f\u0440\u043e\u0432\u0435\u0440\u0435\u043d\u043d\u044b\u0439 \u0432\u0440\u0435\u043c\u0435\u043d\u0435\u043c <a href=\"http:\/\/www.boost.org\/doc\/libs\/1_57_0\/libs\/numeric\/ublas\/doc\/\">uBlas <\/a>, \u043b\u0438\u0431\u043e \u043d\u043e\u0432\u044b\u0435 \u0438 \u0431\u044b\u0441\u0442\u0440\u044b\u0435 \u043a\u043e\u043d\u043a\u0443\u0440\u0435\u043d\u0442\u044b <a href=\"http:\/\/arma.sourceforge.net\/\">Armadillo <\/a> \u0438 <a href=\"https:\/\/code.google.com\/p\/blaze-lib\/\">blaze-lib<\/a> \u2014 \u044d\u0442\u043e \u0435\u0441\u043b\u0438 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0421\u041b\u0410\u0423 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0438 (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <a href=\"http:\/\/faculty.cse.tamu.edu\/davis\/suitesparse.html\">SuiteSparce<\/a> \u0438\u043b\u0438 <a href=\"http:\/\/www.pardiso-project.org\/\">Pardiso<\/a> \u0434\u043b\u044f \u043f\u0440\u044f\u043c\u044b\u0445 \u0438 <a href=\"http:\/\/www.osl.iu.edu\/research\/itl\/\">ITL<\/a> \u0434\u043b\u044f \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u043c\u0435\u0442\u043e\u0434\u043e\u0432). \u041f\u0440\u0438\u0432\u043b\u0435\u043a\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0430\u043a\u0436\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u0435\u0439 \u0421\u041b\u0410\u0423 <a href=\"http:\/\/eigen.tuxfamily.org\/index.php?title=Main_Page\">Eigen<\/a>, <a href=\"http:\/\/www.simunova.com\/mtl4\">MTL<\/a>, <a href=\"http:\/\/www.mcs.anl.gov\/petsc\/\">PETSc<\/a> (\u0438\u043c\u0435\u044e\u0442\u0441\u044f \u0442\u0430\u043a\u0436\u0435 <a href=\"http:\/\/www.mcs.anl.gov\/petsc\/petsc-current\/docs\/manualpages\/SNES\/\">\u041d\u044c\u044e\u0442\u043e\u043d\u043e\u0432\u0441\u043a\u0438\u0435 \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u0438 \u043d\u0430 C<\/a>). \u0412\u0441\u044f \u0442\u0440\u0438\u0430\u0434\u0430 \u0438\u0437 \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0430 \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d\u0430, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043c\u043d\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e, \u0442\u043e\u043b\u044c\u043a\u043e \u0432 <a href=\"http:\/\/trilinos.org\/packages\/nox-and-loca\/\">Trilinos<\/a>.<\/p>\n<h2>\u041e \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0438 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/h2>\n<p>  \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0438 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e. \u041a \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u043c\u0435\u0442\u043e\u0434\u0430\u043c \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u0440\u0443\u0447\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435, \u0441\u0438\u043c\u0432\u043e\u043b\u044c\u043d\u043e\u0435 (Maple, Wolfram \u0438 \u0442.\u043f.) \u0438 \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435, \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u043d\u043e\u0435 \u0432 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430\u0445 \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u043e\u0433\u043e \u044f\u0437\u044b\u043a\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. <\/p>\n<p>  \u0421\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0439 \u0442\u0440\u0435\u043d\u0434 \u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0410\u0414 \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u043d \u043e\u0434\u043d\u043e\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u043f\u0440\u0438\u0447\u0438\u043d\u043e\u0439 \u2014 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u043e\u0439 \u0442\u0435\u0445\u043d\u0438\u043a\u0438 \u0443\u0441\u0442\u0440\u0430\u043d\u044f\u0435\u0442\u0441\u044f \u0438\u0437\u0431\u044b\u0442\u043e\u0447\u043d\u043e\u0441\u0442\u044c \u043a\u043e\u0434\u0430 \u0438 \u0435\u0433\u043e \u0434\u0443\u0431\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435. \u0414\u0440\u0443\u0433\u043e\u0439 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 (\u0441\u0438\u0441\u0442\u0435\u043c) \u0441\u0435\u0442\u043e\u0447\u043d\u044b\u043c\u0438 \u043c\u0435\u0442\u043e\u0434\u0430\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f F(X) \u0441\u0430\u043c \u043f\u043e \u0441\u0435\u0431\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <a href=\"http:\/\/habrahabr.ru\/post\/93570\/\">\u043d\u0435\u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435\u0439<\/a>. \u0412 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447\u0430\u0445 \u043d\u0435\u0432\u044f\u0437\u043a\u0430 F(X) \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u0441\u0443\u043f\u0435\u0440\u043f\u043e\u0437\u0438\u0446\u0438\u0435\u0439 \u0432\u044b\u0437\u043e\u0432\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441 \u0440\u0430\u0437\u043d\u044b\u0445 \u0441\u043b\u043e\u0435\u0432 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b \u0438 \u0440\u0443\u0447\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0442\u0435\u0440\u044f\u0435\u0442 \u0441\u0432\u043e\u044e \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0441\u0442\u044c. \u0421\u043b\u0435\u0434\u0443\u0435\u0442 \u0442\u0430\u043a\u0436\u0435 \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u043f\u0440\u0438 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 \u043d\u0435\u0441\u0442\u0430\u0446\u0438\u043e\u043d\u0430\u0440\u043d\u044b\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0432 F(X) \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u043c \u0448\u0430\u0433\u0435 \u043f\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438, \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442 \u043c\u0435\u043d\u044f\u0442\u044c\u0441\u044f \u0438 \u0441\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 X. \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0410\u0414 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u043c \u0441\u043a\u043e\u043d\u0446\u0435\u043d\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u043d\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 F(X), \u043e\u0434\u043d\u0430\u043a\u043e \u043d\u0435 \u0441\u043d\u0438\u043c\u0430\u0435\u0442 \u0432\u043e\u043f\u0440\u043e\u0441 \u043e \u0432\u0435\u0440\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 dF(X)\/dX. \u0414\u0435\u043b\u043e \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u043f\u0440\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0438 \u043d\u0435\u0432\u044f\u0437\u043e\u043a \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0437\u0430\u0431\u044b\u0442\u044c \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u044c \u0442\u0438\u043f \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043e\u0447\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0441\u043e \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0433\u043e double \u043d\u0430 \u0442\u0438\u043f \u0410\u0414 (\u0430 \u043c\u043d\u043e\u0433\u0438\u0435 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0438 \u0438\u043c\u0435\u044e\u0442 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0438\u043f\u0430 \u0410\u0414 \u043a double), \u0442\u0435\u043c \u0441\u0430\u043c\u044b\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0431\u0443\u0434\u0443\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u044b \u043d\u0435\u043a\u043e\u0440\u0440\u0435\u043a\u0442\u043d\u043e. \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0432 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u0434\u0430\u0436\u0435 \u043f\u0440\u0438 \u043d\u0430\u043b\u0438\u0447\u0438\u0438 \u043e\u0448\u0438\u0431\u043e\u043a \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0445 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043c\u0435\u0442\u043e\u0434 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043c\u043e\u0436\u0435\u0442 \u0441\u0445\u043e\u0434\u0438\u0442\u044c\u0441\u044f, \u0445\u043e\u0442\u044c \u0438 \u0437\u0430 \u0432\u043e\u0437\u0440\u043e\u0441\u0448\u0435\u0435 \u0447\u0438\u0441\u043b\u043e \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0439. \u042d\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043d\u0435\u0437\u0430\u043c\u0435\u0442\u043d\u043e \u043f\u0440\u0438 \u043e\u0434\u043d\u0438\u0445 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442\u044c \u043a \u0440\u0430\u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430 \u043f\u0440\u0438 \u0434\u0440\u0443\u0433\u0438\u0445.<\/p>\n<p>  \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043a\u0430\u043a\u043e\u0439 \u0431\u044b \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f df\/dx \u043d\u0435 \u0431\u044b\u043b \u0432\u044b\u0431\u0440\u0430\u043d, \u0435\u0433\u043e \u043a\u0440\u0430\u0439\u043d\u0435 \u0436\u0435\u043b\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u0441 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c (f(x + h) \u2014 f(x)) \/ h, \u0438\u043d\u0430\u0447\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u0443\u0434\u0443\u0442 \u043e\u0441\u0442\u0430\u0432\u0430\u0442\u044c\u0441\u044f \u0441\u043e\u043c\u043d\u0435\u043d\u0438\u044f \u0432 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u043a\u043e\u0434\u0430. \u0415\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0443\u0442 \u0441 \u0442\u043e\u0447\u043d\u043e\u0441\u0442\u044c\u044e \u0441 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u043c\u0438 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438, \u0442\u0435\u043c \u043d\u0435 \u043c\u0435\u043d\u0435\u0435 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043f\u0440\u0438\u0435\u043c \u044e\u043d\u0438\u0442-\u0442\u0435\u0441\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u041c\u043e\u0436\u043d\u043e \u0432\u044b\u0433\u0440\u0443\u0437\u0438\u0442\u044c \u0432 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u044b\u0435 \u0444\u0430\u0439\u043b\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 X, F(X) \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 dF(X)\/dX \u0438 \u0432\u044b\u043b\u043e\u0436\u0438\u0442\u044c \u043d\u0430 SVN. \u0417\u0430\u0442\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c dF(X)\/dX \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e \u0438 \u0441\u043e\u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0444\u0430\u0439\u043b \u043f\u043e\u0432\u0435\u0440\u0445 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0433\u043e, \u043f\u043e\u0441\u043b\u0435 \u0447\u0435\u0433\u043e \u0432\u0438\u0437\u0443\u0430\u043b\u044c\u043d\u043e \u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c \u0444\u0430\u0439\u043b\u044b \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u043e\u0439. \u0417\u0434\u0435\u0441\u044c \u0412\u044b \u0432\u0441\u0435\u0433\u0434\u0430 \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u043c\u0435\u043d\u044f\u043b\u0438\u0441\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0438 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043b\u043e\u043a\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0441 \u0431\u043e\u043b\u044c\u0448\u0438\u043c\u0438 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u044f\u043c\u0438 (\u043d\u0435 \u0432 \u0434\u043e\u043b\u044f\u0445) \u2014 \u0432 \u044d\u0442\u043e\u043c \u043c\u0435\u0441\u0442\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043e\u0448\u0438\u0431\u043a\u0430 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f.<\/p>\n<h2>\u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0410\u0414<\/h2>\n<p>  \u0412 Embarcadero Delphi \u0434\u043e \u0432\u0435\u0440\u0441\u0438\u0438 XE5 \u043e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u043f\u0435\u0440\u0435\u0433\u0440\u0443\u0437\u043a\u0438 \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0434\u043b\u044f \u043a\u043b\u0430\u0441\u0441\u043e\u0432, \u043d\u043e \u0435\u0441\u0442\u044c \u0442\u0430\u043a\u0430\u044f \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440 record <a href=\"http:\/\/docwiki.embarcadero.com\/RADStudio\/XE3\/en\/Operator_Overloading_(Delphi)\">(\u0441\u0441\u044b\u043b\u043a\u0430)<\/a>:  <\/p>\n<pre><code class=\"delphi\">TAutoDiff = packed record public     class operator Equal(a, b: TAutoDiff): Boolean;     class operator Negative(v: TAutoDiff): TAutoDiff;     class operator Add(a, b: TAutoDiff): TAutoDiff;     \/\/\u0438 \u0434\u0430\u043b\u0435\u0435 \u043f\u043e \u0441\u043f\u0438\u0441\u043a\u0443 end; <\/code><\/pre>\n<p>  \u041e\u0431\u044b\u0447\u043d\u043e \u0432 \u0410\u0414 \u043d\u0430 C++ \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u043e\u0439 \u0438 \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u043e\u0440\u0435. \u0412 Delphi \u043d\u0435\u043b\u044c\u0437\u044f (<a href=\"http:\/\/www.thedelphigeek.com\/2015\/01\/implementing-record-assignment-operator.html\">\u0435\u0441\u0442\u044c \u043f\u043e\u043f\u044b\u0442\u043a\u0438 \u043e\u0431\u043e\u0439\u0442\u0438<\/a>) \u043f\u0435\u0440\u0435\u0433\u0440\u0443\u0437\u0438\u0442\u044c \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440 \u043f\u0440\u0438\u0441\u0432\u0430\u0438\u0432\u0430\u043d\u0438\u044f \u0434\u043b\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440 \u0438 \u0432 \u0441\u0432\u044f\u0437\u0438 \u0441 \u043f\u043e\u0431\u0438\u0442\u043e\u0432\u044b\u043c \u043a\u043e\u043f\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0434\u0435\u043b\u0430\u0442\u044c \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u0434\u043b\u0438\u043d\u044b. \u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430 TAutoDiff.n_all \u0434\u043e\u043b\u0436\u043d\u0430 \u0438\u0437\u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e \u0437\u0430\u0434\u0430\u0432\u0430\u0442\u044c\u0441\u044f \u0432\u0440\u0443\u0447\u043d\u0443\u044e.<\/p>\n<h3>\u041f\u0440\u0438\u043c\u0435\u0440 1<\/h3>\n<p>  <\/p>\n<pre><code class=\"delphi\">procedure TestAutoDiff_1; var   i: integer;   x, dy: double;   x_ad, y_ad: TAutoDiff; begin   x := 4;    \/\/\u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0437\u0430\u043d\u0443\u043b\u0435\u043d\u0438\u0435 \u0432\u0441\u0435\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043f\u0440\u0438 \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438   x_ad.Init;    \/\/\u0441\u0434\u0435\u043b\u0430\u0435\u043c x_ad \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u043e\u0439   x_ad := x;    assert(x_ad.val = x);   for i := 0 to TAutoDiff.n_all - 1 do     assert(x_ad.dx[i] = 0);    \/\/\u0441\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u0441 \u0440\u0443\u0447\u043d\u044b\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c   x_ad.dx[0] := 1;   y_ad := sqr(x_ad) + 1 \/ x_ad;    dy := 2 * x - 1 \/ sqr(x);\/\/\u0432\u043c\u0435\u0441\u0442\u043e x \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c x_ad   assert(y_ad.dx[0] = dy); end; <\/code><\/pre>\n<p>  \u041d\u0430 \u0434\u0430\u043d\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0435 \u043f\u0435\u0440\u0435\u0433\u0440\u0443\u0436\u0435\u043d\u044b \u043f\u043e\u0447\u0442\u0438 \u0432\u0441\u0435 \u0431\u0438\u043d\u0430\u0440\u043d\u044b\u0435 \u0438 \u0443\u043d\u0430\u0440\u043d\u044b\u0435 \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u044b, \u0437\u0430 \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435\u043c \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0431\u0443\u043b\u0435\u0432\u044b\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441\u0434\u0432\u0438\u0433\u0430. \u041d\u0435\u0434\u043e\u0441\u0442\u0430\u044e\u0449\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043b\u0435\u0433\u043a\u043e \u0434\u043e\u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u044c\u043d\u043e.<\/p>\n<h2>\u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0410\u0414 \u0434\u043b\u044f \u0440\u0430\u0437\u0440\u044f\u0436\u0435\u043d\u043d\u044b\u0445 \u043c\u0430\u0442\u0440\u0438\u0446<\/h2>\n<p>  \u0421 \u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 n_all \u044d\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0435, \u0432\u0435\u0434\u044c \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u0441\u0442\u0443\u043f\u0430\u0442\u044c \u0438\u0437\u0432\u043d\u0435. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0434\u043b\u044f \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u043e\u0441\u043b\u0430\u0431\u0438\u0442\u044c. \u0414\u0435\u043b\u043e \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c \u043e \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0445 \u043c\u0435\u0442\u043e\u0434\u0430\u0445 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0438 \u0441\u043f\u043b\u043e\u0448\u043d\u044b\u0445 \u0441\u0440\u0435\u0434, \u0442\u043e \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u044e\u0449\u0438\u0435 \u0432 \u043d\u0438\u0445 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0438\u043c\u0435\u044e\u0442 \u0440\u0430\u0437\u0440\u0435\u0436\u0435\u043d\u043d\u0443\u044e \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0443 \u2014 \u043a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u044d\u0442\u043e \u00ab\u0441\u0445\u0435\u043c\u0430 \u043a\u0440\u0435\u0441\u0442\u00bb \u0434\u043b\u044f \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u041b\u0430\u043f\u043b\u0430\u0441\u0430, \u043a\u043e\u0433\u0434\u0430 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0434\u043b\u044f \u0443\u0437\u043b\u0430 \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 (i, j) (\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u043c\u0441\u044f 2D) \u0437\u0430\u0434\u0435\u0439\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u044b \u0442\u043e\u043b\u044c\u043a\u043e 5 \u0443\u0437\u043b\u043e\u0432: (i, j), (i-1, j), (i+1, j), (i, j-1), (i, j+1). \u041e\u0431\u043e\u0431\u0449\u0430\u044f \u0438\u0434\u0435\u044e \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0437\u0430\u043b\u043e\u0436\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0434\u043b\u044f \u0434\u0430\u043d\u043d\u043e\u0439 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438:  <\/p>\n<pre><code class=\"delphi\">const n_juncs = 5;\/\/\u0437\u0430\u0434\u0430\u0435\u043c \u0447\u0438\u0441\u043b\u043e \u0441\u043e\u0441\u0435\u0434\u043d\u0438\u0445 \u0443\u0437\u043b\u043e\u0432 const n_junc_vars = 1;\/\/\u0437\u0430\u0434\u0430\u0435\u043c \u0447\u0438\u0441\u043b\u043e \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u0432 \u0443\u0437\u043b\u0435 const n_all = n_juncs * n_junc_vars; <\/code><\/pre>\n<p>  \u041f\u0443\u0441\u0442\u044c \u043e\u0431\u0449\u0435\u0435 \u0447\u0438\u0441\u043b\u043e \u0443\u0437\u043b\u043e\u0432 \u0432 \u0440\u0435\u0448\u0430\u0435\u043c\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435 N. \u0422\u043e\u0433\u0434\u0430 \u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 N_all = N * n_junc_vars \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432, \u0438\u0437 \u043d\u0438\u0445 \u043d\u0435\u043d\u0443\u043b\u0435\u0432\u044b\u0445 \u0442\u043e\u043b\u044c\u043a\u043e n_all. \u0415\u0441\u043b\u0438 \u0437\u0430\u0432\u0435\u0441\u0442\u0438 \u0442\u0435\u043f\u0435\u0440\u044c \u0432\u043d\u0443\u0442\u0440\u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u044b TAutoDiff \u0446\u0435\u043b\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 n_juncs, \u043a\u0430\u0436\u0434\u044b\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u0438\u043d\u0434\u0435\u043a\u0441 \u0443\u0437\u043b\u0430 \u043e\u0442 0 \u0434\u043e N-1, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044e dx \u0441 \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u043c \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u043c \u0438\u0437 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u0430 [0, n_all-1] \u043c\u043e\u0436\u043d\u043e \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 dx_global \u0441 \u0443\u0436\u0435 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u043c \u0438\u043d\u0434\u0435\u043a\u0441\u043e\u043c \u0438\u0437 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u0430 [0, N_all-1]. \u041f\u0440\u0438\u043c\u0435\u0440 2 \u0438\u043b\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442 \u0434\u0435\u0442\u0430\u043b\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0442\u0430\u043a\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0440\u0444\u0435\u0439\u0441\u0430, \u043f\u043b\u044e\u0441\u044b \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0431\u0443\u0434\u0443\u0442 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043b\u043d\u043e \u0432\u0438\u0434\u043d\u044b \u043f\u0440\u0438 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043c\u0435\u0442\u043e\u0434\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043d\u0438\u0436\u0435.<\/p>\n<h3>\u041f\u0440\u0438\u043c\u0435\u0440 2<\/h3>\n<p>  <\/p>\n<pre><code class=\"delphi\">procedure TestAutoDiff_2; const N = 100;\/\/\u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u0440\u0430\u0441\u0447\u0435\u0442\u043d\u043e\u0439 \u0441\u0435\u0442\u043a\u0438 N x N const i = 50; const j = 50;  \/\/\u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0438\u043d\u0434\u0435\u043a\u0441\u0430 \u0443\u0437\u043b\u0430 (i, j) \/\/\u0432 \u043f\u043e\u0441\u0442\u0440\u043e\u0447\u043d\u043e\u0435 \u0445\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u0435 (\u043d\u0443\u043c\u0435\u0440\u0430\u0446\u0438\u044f \u0441 0) function Splice2d(i, j: integer): integer; begin   result := ((i - 1) * N + j - 1); end;  var   k: integer;   n_junc_vars: integer;   x: TAutoDiff;   juncs_offset: TAutoDiffJuncVector;\/\/\u0432\u0435\u043a\u0442\u043e\u0440 begin   \/\/n_juncs \u044f\u0447\u0435\u0435\u043a \u0441 \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u044f\u043c\u0438   juncs_offset[0] := Splice2d(i - 1, j);   juncs_offset[1] := Splice2d(i, j - 1);   juncs_offset[2] := Splice2d(i, j);   juncs_offset[3] := Splice2d(i, j + 1);   juncs_offset[4] := Splice2d(i + 1, j);    n_junc_vars := TAutoDiff.n_junc_vars;    \/\/\u0437\u0430\u0434\u0430\u0435\u043c, \u0447\u0442\u043e \u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u0435 dx:   \/\/\u043f\u0435\u0440\u0432\u044b\u0435 n_junc_vars \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u0443\u0437\u043b\u0443 juncs_offset[0]   \/\/\u0432\u0442\u043e\u0440\u044b\u0435 n_junc_vars \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u0443\u0437\u043b\u0443 juncs_offset[1]   \/\/\u0442\u0440\u0435\u0442\u044c\u0438 n_junc_vars \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u0443\u0437\u043b\u0443 juncs_offset[2]   \/\/\u0447\u0435\u0442\u0432\u0435\u0440\u0442\u044b\u0435 n_junc_vars \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u0443\u0437\u043b\u0443 juncs_offset[3]   \/\/\u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 n_junc_vars \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a \u0443\u0437\u043b\u0443 juncs_offset[4]   x.Init(juncs_offset);    \/\/\u0435\u0441\u043b\u0438 \u0432 dx_global \u043f\u0435\u0440\u0435\u0434\u0430\u0442\u044c \u0438\u043d\u0434\u0435\u043a\u0441 \u0432\u043d\u0435 \u0437\u0430\u0434\u0430\u043d\u043d\u044b\u0445 juncs_offset,   \/\/\u0442\u043e \u0435\u0441\u043b\u0438 \u043e\u043d \u0441\u0442\u043e\u0438\u0442 \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 \u0437\u043d\u0430\u043a\u0430 \u0440\u0430\u0432\u043d\u043e, \u0442\u043e \u0432\u0435\u0440\u043d\u0435\u0442 0,   \/\/\u0438\u043d\u0430\u0447\u0435 - \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442 \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435   for k := 0 to n_junc_vars - 1 do begin     x.dx_global[Splice2d(i - 1, j) * n_junc_vars + k] := 1;     assert(x.dx[0 * n_junc_vars + k] = 1);      x.dx_global[Splice2d(i, j - 1) * n_junc_vars + k] := 1;     assert(x.dx[1 * n_junc_vars + k] = 1);      x.dx_global[Splice2d(i, j) * n_junc_vars + k] := 1;     assert(x.dx[2 * n_junc_vars + k] = 1);      x.dx_global[Splice2d(i, j + 1) * n_junc_vars + k] := 1;     assert(x.dx[3 * n_junc_vars + k] = 1);      x.dx_global[Splice2d(i + 1, j) * n_junc_vars + k] := 1;     assert(x.dx[4 * n_junc_vars + k] = 1);   end; end; <\/code><\/pre>\n<p>  \u0412 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0447\u0430\u0441\u0442\u0438 \u043f\u043b\u0430\u043d\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u0438\u0435 \u043a\u043b\u0430\u0441\u0441\u0430 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u041d\u044c\u044e\u0442\u043e\u043d\u043e\u0432\u0441\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0432\u043e\u043f\u0440\u043e\u0441\u0430 \u0432\u044b\u0431\u043e\u0440\u0430 \u0440\u0430\u0437\u0440\u044f\u0436\u0435\u043d\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u044f \u0421\u041b\u0410\u0423.<br \/>  \u041f\u043e\u043a\u0430 \u0436\u0435 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u044e \u0447\u0438\u0442\u0430\u0442\u0435\u043b\u044f\u043c:  <\/p>\n<ul>\n<li>\u043f\u043e\u043f\u0440\u043e\u0431\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0410\u0414 \u043d\u0430 C++11 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0441\u0435\u043c\u0430\u043d\u0442\u0438\u043a\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u0449\u0435\u043d\u0438\u0439: 1) \u044d\u0442\u043e \u0434\u043e\u043b\u0436\u043d\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u043e\u0447\u0435\u043d\u044c \u0431\u044b\u0441\u0442\u0440\u043e; 2) \u043c\u043e\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u043e\u0431\u043e\u0439\u0442\u0438\u0441\u044c \u043f\u0435\u0440\u0435\u0433\u0440\u0443\u0437\u043a\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u043e\u0432 \u0431\u0435\u0437 expression templates; 3) \u044d\u0442\u043e \u0431\u0443\u0434\u0435\u0442 \u0432\u043f\u0435\u0440\u0432\u044b\u0435.<\/li>\n<li>\u0438\u0434\u0435\u044e \u0434\u043b\u044f \u043a\u0443\u0440\u0441\u043e\u0432\u043e\u0439 \u043f\u043e \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0410\u0414 \u043d\u0430 Roslyn CTP: \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u0441\u0440\u0430\u0437\u0443 \u0441 \u0441\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0434\u0435\u0440\u0435\u0432\u043e\u043c, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0432\u0441\u044e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044e \u043e\u0431 \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u0445 \u0432 F(X). <\/li>\n<\/ul>\n<div class=\"spoiler\"><b class=\"spoiler_title\">\u0424\u0430\u0439\u043b \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0438 AutoDiff.pas<\/b><\/p>\n<div class=\"spoiler_text\">\n<pre><code class=\"delphi\">unit AutoDiff;  interface  const SMALL = 1e-12; const n_juncs = 5;  type   TAutoDiffJuncVector = array[0..n_juncs - 1] of integer;    TAutoDiff = packed record     const n_junc_vars = 10;     const n_all = n_juncs * n_junc_vars;   private     juncs_offset: TAutoDiffJuncVector;      \/\/&lt;0 \u0435\u0441\u043b\u0438 \u0432\u043d\u0435 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u0430     function IsIgnoreJuncOffset: boolean;     function IndexOf_dx(glob_indx: integer): integer;     function Get_dx_global(glob_indx: integer): double;     procedure Set_dx_global(glob_indx: integer; val: double);      procedure PrepareBinaryOp(a, b: TAutoDiff);     procedure PrepareUnaryOp(v: TAutoDiff);   public     val: double;     dx: array[0..n_all - 1] of double;      procedure Init; overload;     procedure Init(juncs_offset: TAutoDiffJuncVector); overload;      procedure Independent(ir: integer); overload;     procedure Independent(juncs_offset: TAutoDiffJuncVector; ir: integer; orient_from_beg: boolean = true); overload;      property dx_global[glob_indx: integer]: double read Get_dx_global write Set_dx_global;      procedure SetVal(v: TAutoDiff);     procedure NoJac(flg: boolean);      class operator Implicit(v: double): TAutoDiff; overload;     class operator Implicit(v: TAutoDiff): double; overload;      class operator Equal(a, b: TAutoDiff): Boolean;     class operator Equal(a: double; b: TAutoDiff): Boolean; overload;     class operator Equal(a: TAutoDiff; b: double): Boolean; overload;      class operator NotEqual(a, b: TAutoDiff): Boolean;     class operator NotEqual(a: double; b: TAutoDiff): Boolean; overload;     class operator NotEqual(a: TAutoDiff; b: double): Boolean; overload;      class operator LessThan(a, b: TAutoDiff): Boolean;     class operator LessThan(a: double; b: TAutoDiff): Boolean; overload;     class operator LessThan(a: TAutoDiff; b: double): Boolean; overload;      class operator LessThanOrEqual(a, b: TAutoDiff): Boolean;     class operator LessThanOrEqual(a: double; b: TAutoDiff): Boolean; overload;     class operator LessThanOrEqual(a: TAutoDiff; b: double): Boolean; overload;      class operator GreaterThan(a, b: TAutoDiff): Boolean;     class operator GreaterThan(a: double; b: TAutoDiff): Boolean; overload;     class operator GreaterThan(a: TAutoDiff; b: double): Boolean; overload;      class operator GreaterThanOrEqual(a, b: TAutoDiff): Boolean;     class operator GreaterThanOrEqual(a: double; b: TAutoDiff): Boolean; overload;     class operator GreaterThanOrEqual(a: TAutoDiff; b: double): Boolean; overload;      class operator Negative(v: TAutoDiff): TAutoDiff;     class operator Positive(v: TAutoDiff): TAutoDiff;      class operator Add(a, b: TAutoDiff): TAutoDiff;     class operator Add(a: double; b: TAutoDiff): TAutoDiff; overload;     class operator Add(a: TAutoDiff; b: double): TAutoDiff; overload;      class operator Subtract(a, b: TAutoDiff): TAutoDiff;     class operator Subtract(a: double; b: TAutoDiff): TAutoDiff; overload;     class operator Subtract(a: TAutoDiff; b: double): TAutoDiff; overload;      class operator Multiply(a, b: TAutoDiff): TAutoDiff;     class operator Multiply(a: double; b: TAutoDiff): TAutoDiff; overload;     class operator Multiply(a: TAutoDiff; b: double): TAutoDiff; overload;      class operator Divide(a, b: TAutoDiff): TAutoDiff;     class operator Divide(a: double; b: TAutoDiff): TAutoDiff; overload;     class operator Divide(a: TAutoDiff; b: double): TAutoDiff; overload;   end;    function sqr(v: TAutoDiff): TAutoDiff; overload;   function sqrt(v: TAutoDiff): TAutoDiff; overload;   function exp(v: TAutoDiff): TAutoDiff; overload;   function ln(v: TAutoDiff): TAutoDiff; overload;   \/\/v(x) ^ n(x)   function power(a: TAutoDiff; n: double): TAutoDiff; overload;   function power(a: double; n: TAutoDiff): TAutoDiff; overload;   function power(a: TAutoDiff; n: TAutoDiff): TAutoDiff; overload;   function abs(v: TAutoDiff): TAutoDiff; overload;   function min(a, b: TAutoDiff): TAutoDiff;   function max(a, b: TAutoDiff): TAutoDiff;  \/\/ function IfThen(flg: Boolean; const on_true: TAutoDiff; const on_false: TAutoDiff): TAutoDiff;   function clamp(val, min, max: TAutoDiff): TAutoDiff;   \/\/todo: log_a    function abs(v: double): double; overload;   function sqrt(v: double): double; overload;   function sqr(v: double): double; overload;   function exp(v: double): double; overload;   function ln(v: double): double; overload;    procedure swap(var x, y: TAutoDiff); overload;   procedure swap(var x, y: double); overload;  implementation  uses Math, SysUtils;  \/\/==============================================================================  procedure TAutoDiff.PrepareBinaryOp(a, b: TAutoDiff); var   i: integer; begin   if a.juncs_offset[0] &gt;= 0 then begin     if (b.juncs_offset[0] &gt;= 0) then begin       for i := 0 to n_juncs - 1 do begin         if a.juncs_offset[i] &lt;&gt; b.juncs_offset[i] then           raise Exception.Create('PrepareBinaryOp: must be a.juncs_offset[i] = b.juncs_offset[i]');       end;     end;      juncs_offset := a.juncs_offset;   end else begin     juncs_offset := b.juncs_offset;   end; end;  procedure TAutoDiff.PrepareUnaryOp(v: TAutoDiff); var   i: integer; begin   juncs_offset := v.juncs_offset;\/\/\u043a\u043e\u043f\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0441\u0442\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043c\u0430\u0441\u0441\u0438\u0432\u0430 (\u043d\u0435 \u043f\u043e \u0441\u0441\u044b\u043b\u043a\u0435) end;  \/\/==============================================================================  procedure TAutoDiff.Init; var   i: integer; begin   for i := 0 to n_juncs - 1 do begin     juncs_offset[i] := 0;   end;    Init(juncs_offset); end;  procedure TAutoDiff.Init(juncs_offset: TAutoDiffJuncVector); var   i: integer; begin   for i := 0 to n_all - 1 do begin     dx[i] := 0;   end;    for i := 0 to n_juncs - 1 do begin     self.juncs_offset[i] := juncs_offset[i];   end; end;  procedure TAutoDiff.Independent(ir: integer); begin   Independent(juncs_offset, ir); end;  procedure TAutoDiff.Independent(juncs_offset: TAutoDiffJuncVector; ir: integer; orient_from_beg: boolean); var   i, loc_i, junc_i: integer; begin   Init(juncs_offset);    loc_i := IndexOf_dx(ir);   if loc_i &gt;= 0 then begin     dx[loc_i] := 1;   end else     assert(false); end;  function TAutoDiff.IsIgnoreJuncOffset: boolean; var   i, beg: integer; begin   result := true;   for i := 1 to n_juncs - 1 do begin     if juncs_offset[i] &lt;&gt; juncs_offset[0] then begin       result := false;       break;     end;   end; end;  function TAutoDiff.IndexOf_dx(glob_indx: integer): integer; var   i, offset: integer; begin   if IsIgnoreJuncOffset then begin     offset := glob_indx - juncs_offset[0] * n_junc_vars;     if (0 &lt;= offset) and (offset &lt; n_junc_vars) then       result := offset     else       result := -1;   end else begin     for i := 0 to n_juncs - 1 do begin       offset := glob_indx - juncs_offset[i] * n_junc_vars;       if (0 &lt;= offset) and (offset &lt; n_junc_vars) then begin         assert(n_junc_vars &lt;= n_junc_vars);          if (offset &lt; n_junc_vars) then begin           result := i * n_junc_vars + offset;           exit;         end;       end;     end;     result := -1;   end; end;  function TAutoDiff.Get_dx_global(glob_indx: integer): double; var   loc_i: integer; begin   loc_i := IndexOf_dx(glob_indx);   if loc_i &gt;= 0 then     result := dx[loc_i]   else     result := 0; end;  procedure TAutoDiff.Set_dx_global(glob_indx: integer; val: double); var   loc_i: integer; begin   loc_i := IndexOf_dx(glob_indx);   if loc_i &gt;= 0 then     dx[loc_i] := val   else     assert(false); end;  procedure TAutoDiff.SetVal(v: TAutoDiff); begin   val := v.val; end;  class operator TAutoDiff.Implicit(v: double): TAutoDiff; begin   result.val := v;   result.NoJac(true); end;  procedure TAutoDiff.NoJac(flg: boolean); const NO_JAC_MARK = -1; var   i: integer; begin   Init;    if flg then begin     for i := 0 to n_juncs - 1 do begin       juncs_offset[i] := NO_JAC_MARK;     end;   end; end;  class operator TAutoDiff.Implicit(v: TAutoDiff): double; begin   result := v.val; end;  class operator TAutoDiff.Equal(a, b: TAutoDiff): Boolean; begin   result := (a.val = b.val); end;  class operator TAutoDiff.Equal(a: double; b: TAutoDiff): Boolean; begin   result := (a = b.val); end;  class operator TAutoDiff.Equal(a: TAutoDiff; b: double): Boolean; begin   result := (a.val = b); end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.NotEqual(a, b: TAutoDiff): Boolean; begin   result := (a.val &lt;&gt; b.val); end;  class operator TAutoDiff.NotEqual(a: double; b: TAutoDiff): Boolean; begin   result := (a &lt;&gt; b.val); end;  class operator TAutoDiff.NotEqual(a: TAutoDiff; b: double): Boolean; begin   result := (a.val &lt;&gt; b); end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.LessThan(a, b: TAutoDiff): Boolean; begin   result := (a.val &lt; b.val); end;  class operator TAutoDiff.LessThan(a: double; b: TAutoDiff): Boolean; begin   result := (a &lt; b.val); end;  class operator TAutoDiff.LessThan(a: TAutoDiff; b: double): Boolean; begin   result := (a.val &lt; b); end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.LessThanOrEqual(a, b: TAutoDiff): Boolean; begin   result := (a.val &lt;= b.val); end;  class operator TAutoDiff.LessThanOrEqual(a: double; b: TAutoDiff): Boolean; begin   result := (a &lt;= b.val); end;  class operator TAutoDiff.LessThanOrEqual(a: TAutoDiff; b: double): Boolean; begin   result := (a.val &lt;= b); end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.GreaterThan(a, b: TAutoDiff): Boolean; begin   result := (a.val &gt; b.val); end;  class operator TAutoDiff.GreaterThan(a: double; b: TAutoDiff): Boolean; begin   result := (a &gt; b.val); end;  class operator TAutoDiff.GreaterThan(a: TAutoDiff; b: double): Boolean; begin   result := (a.val &gt; b); end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.GreaterThanOrEqual(a, b: TAutoDiff): Boolean; begin   result := (a.val &gt;= b.val); end;  class operator TAutoDiff.GreaterThanOrEqual(a: double; b: TAutoDiff): Boolean; begin   result := (a &gt;= b.val); end;  class operator TAutoDiff.GreaterThanOrEqual(a: TAutoDiff; b: double): Boolean; begin   result := (a.val &gt;= b); end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.Negative(v: TAutoDiff): TAutoDiff; begin   result := - 1 * v; end;  class operator TAutoDiff.Positive(v: TAutoDiff): TAutoDiff; begin   result := v; end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.Add(a, b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a.val + b.val;   result.PrepareBinaryOp(a, b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i] + b.dx[i];   end; end;  class operator TAutoDiff.Add(a: double; b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a + b.val;   result.PrepareUnaryOp(b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := b.dx[i];   end; end;  class operator TAutoDiff.Add(a: TAutoDiff; b: double): TAutoDiff; var   i: integer; begin   result.val := a.val + b;   result.PrepareUnaryOp(a);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i];   end; end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.Subtract(a, b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a.val - b.val;   result.PrepareBinaryOp(a, b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i] - b.dx[i];   end; end;  class operator TAutoDiff.Subtract(a: double; b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a - b.val;   result.PrepareUnaryOp(b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := - b.dx[i];   end; end;  class operator TAutoDiff.Subtract(a: TAutoDiff; b: double): TAutoDiff; var   i: integer; begin   result.val := a.val - b;   result.PrepareUnaryOp(a);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i];   end; end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.Multiply(a, b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a.val * b.val;   result.PrepareBinaryOp(a, b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i] * b.val + a.val * b.dx[i];   end; end;  class operator TAutoDiff.Multiply(a: double; b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a * b.val;   result.PrepareUnaryOp(b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a * b.dx[i];   end; end;  class operator TAutoDiff.Multiply(a: TAutoDiff; b: double): TAutoDiff; var   i: integer; begin   result.val := a.val * b;   result.PrepareUnaryOp(a);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i] * b;   end; end;  \/\/------------------------------------------------------------------------------  class operator TAutoDiff.Divide(a, b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a.val \/ b.val;   result.PrepareBinaryOp(a, b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := (a.dx[i] * b.val - a.val * b.dx[i]) \/ System.sqr(b.val);   end; end;  class operator TAutoDiff.Divide(a: double; b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := a \/ b.val;   result.PrepareUnaryOp(b);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := - a * b.dx[i] \/ System.sqr(b.val);   end; end;   class operator TAutoDiff.Divide(a: TAutoDiff; b: double): TAutoDiff; var   i: integer; begin   result.val := a.val \/ b;   result.PrepareUnaryOp(a);    for i := 0 to result.n_all - 1 do begin     result.dx[i] := a.dx[i] \/ b;   end; end;  \/\/==============================================================================  function sqr(v: TAutoDiff): TAutoDiff; var   i: integer;   d: double; begin   result.val := System.sqr(v.val);   result.PrepareUnaryOp(v);    d := 2 * v.val;   for i := 0 to v.n_all - 1 do begin     result.dx[i] := d * v.dx[i];   end; end;  function sqrt(v: TAutoDiff): TAutoDiff; var   i: integer;   d: double; begin   result.val := System.sqrt(v.val);   result.PrepareUnaryOp(v);    if abs(result.val) &lt; SMALL then     d := 0   else     d := 0.5 \/ result.val;    for i := 0 to v.n_all - 1 do begin     result.dx[i] := d * v.dx[i];   end; end;  function exp(v: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := System.exp(v.val);   result.PrepareUnaryOp(v);    for i := 0 to v.n_all - 1 do begin     result.dx[i] := result.val * v.dx[i];   end; end;  function ln(v: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := System.ln(v.val);   result.PrepareUnaryOp(v);    for i := 0 to v.n_all - 1 do begin     result.dx[i] := v.dx[i] \/ v.val;   end; end;  function power(a: TAutoDiff; n: double): TAutoDiff; var   i: integer;   d: double; begin   result.val := Math.power(a.val, n);   result.PrepareUnaryOp(a);    d := n * Math.power(a.val, n - 1);   for i := 0 to result.n_all - 1 do begin     result.dx[i] := d * a.dx[i];   end; end;  function power(a: double; n: TAutoDiff): TAutoDiff; var   i: integer;   d: double; begin   result.val := Math.power(a, n.val);   result.PrepareUnaryOp(n);    d := ln(n) * result.val;   for i := 0 to n.n_all - 1 do begin     result.dx[i] := d * n.dx[i];   end; end;  function power(a: TAutoDiff; n: TAutoDiff): TAutoDiff; var   i: integer;   d: double; begin   result.val := Math.power(a.val, n.val);   result.PrepareUnaryOp(n);    d := Math.power(a.val, n.val - 1);   for i := 0 to n.n_all - 1 do begin     result.dx[i] := d * (n.val * a.dx[i] + a.val * ln(a.val) * n.dx[i]);   end; end;  function abs(v: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := System.abs(v.val);   result.PrepareUnaryOp(v);    for i := 0 to v.n_all - 1 do begin     result.dx[i] := Math.sign(v.val) * v.dx[i];   end; end;  function min(a, b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := Math.min(a.val, b.val);   result.PrepareBinaryOp(a, b);    if a.val &lt; b.val then begin     for i := 0 to result.n_all - 1 do begin       result.dx[i] := a.dx[i];     end;   end else begin     for i := 0 to result.n_all - 1 do begin       result.dx[i] := b.dx[i];     end;   end; end;  function max(a, b: TAutoDiff): TAutoDiff; var   i: integer; begin   result.val := Math.max(a.val, b.val);   result.PrepareBinaryOp(a, b);    if a.val &gt; b.val then begin     for i := 0 to result.n_all - 1 do begin       result.dx[i] := a.dx[i];     end;   end else begin     for i := 0 to result.n_all - 1 do begin       result.dx[i] := b.dx[i];     end;   end; end;  function IfThen(flg: Boolean; const on_true: TAutoDiff; const on_false: TAutoDiff): TAutoDiff; begin   if flg then     result := on_true   else     result := on_false; end;  function clamp(val, min, max: TAutoDiff): TAutoDiff; begin   Result := IfThen(val &lt; min, min, IfThen(max &lt; val, max, val)); end;  procedure Swap(var x, y: TAutoDiff); var tmp: TAutoDiff; begin   tmp := x;   x := y;   y := tmp; end;  procedure Swap(var x, y: double); var tmp: double; begin   tmp := x;   x := y;   y := tmp; end; \/\/============================================================================== function abs(v: double): double; begin   result := System.Abs(v); end; function sqrt(v: double): double; begin   result := System.sqrt(v); end; function sqr(v: double): double; begin   result := System.sqr(v); end; function exp(v: double): double; begin   result := system.Exp(v); end; function ln(v: double): double; begin   result := system.Ln(v); end; end. <\/code><\/pre>\n<p>  <\/div>\n<\/div>\n<div class=\"clear\"><\/div>\n<p> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"http:\/\/habrahabr.ru\/post\/247379\/\"> http:\/\/habrahabr.ru\/post\/247379\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>     \t\u041e\u0431 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 (\u0410\u0414) \u043d\u0430 \u0425\u0430\u0431\u0440\u0435 \u0443\u0436\u0435 \u043f\u0438\u0441\u0430\u043b\u043e\u0441\u044c <a href=\"http:\/\/habrahabr.ru\/company\/intel\/blog\/170729\/\">\u0437\u0434\u0435\u0441\u044c<\/a> \u0438 <a href=\"http:\/\/habrahabr.ru\/post\/63055\/\">\u0437\u0434\u0435\u0441\u044c<\/a>. \u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0410\u0414 \u0434\u043b\u044f Delphi (\u043f\u0440\u043e\u0442\u0435\u0441\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043e \u0432 Embarcadero XE2, XE6) \u0432\u043c\u0435\u0441\u0442\u0435 \u0441 \u0443\u0434\u043e\u0431\u043d\u044b\u043c\u0438 \u043a\u043b\u0430\u0441\u0441\u0430\u043c\u0438 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 f(x) = 0 \u0438 \u0441\u0438\u0441\u0442\u0435\u043c F(X) = 0. \u041b\u044e\u0431\u044b\u0435 \u0441\u0441\u044b\u043b\u043a\u0438 \u043d\u0430 \u0433\u043e\u0442\u043e\u0432\u044b\u0435 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0435 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0438 \u043f\u0440\u0438\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0442\u0441\u044f, \u0441\u0430\u043c \u0436\u0435 \u044f \u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0433\u043e \u043d\u0435 \u043d\u0430\u0448\u0435\u043b, \u043d\u0435 \u0441\u0447\u0438\u0442\u0430\u044f \u043e\u0442\u043b\u0438\u0447\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u044f \u0421\u041b\u0410\u0423 \u0441 \u0440\u0430\u0437\u0440\u044f\u0436\u0435\u043d\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 (\u0441\u043c. \u043f\u043e\u0434 \u043a\u0430\u0442\u043e\u043c).<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-256892","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/256892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=256892"}],"version-history":[{"count":0,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/256892\/revisions"}],"wp:attachment":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=256892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=256892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=256892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}