\h SSKJr SSKJr SSKJrJr SSKJrJ r SSK J r SSK J r Jr SSKJr SSKJrJrJrJrJrJrJrJrJrJrJrJrJr SS KJ r SS S S S S S S S S.Sjjr!Sr"S S\"54S S.Sjjr#g ))Tuple)oo)GtLt)DummySymbol)Abs)MinMax)And) AssignmentAddAugmentedAssignmentbreak_ CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal)isnanNgؗҼr!saRq \)rtoldebugitermaxcounterdelta_fncse handle_nanboundsc Uc[5n[n Sn OSn URn U"X5nU (aTSSKJn U "UR 5/5ununUVVs/sHunn[ UU5PM nnnU[ UU5/- nO [ X>5/nU b'U[[U5[U [55/- nU[X5/- nU b)U[ U[[XS5U S55/- nU(a-[X/SRURU 55nUU/- n[![#U5X$[#U5--5n[%['U[([*S95/nUbsU=(d [SS 9n[&R,"US5nUR/[%U55 UR/[US55 [1U[3Xv55n[U[U65nUnU(a5UR/[U/S RUR555 UU/- nU "[U65$s snnf) aGenerates an AST for Newton-Raphson method (a root-finding algorithm). Explanation =========== Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's method of root-finding. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable. atol : number or expression Absolute tolerance (stopping criterion) rtol : number or expression Relative tolerance (stopping criterion) delta : Symbol Will be a ``Dummy`` if ``None``. debug : bool Whether to print convergence information during iterations itermax : number or expr Maximum number of iterations. counter : Symbol Will be a ``Dummy`` if ``None``. delta_fn: Callable[[Expr, Symbol], Expr] computes the step, default is newtons method. For e.g. Halley's method use delta_fn=lambda e, x: -2*e*e.diff(x)/(2*e.diff(x)**2 - e*e.diff(x, 2)) cse: bool Perform common sub-expression elimination on delta expression handle_nan: Token How to handle occurrence of not-a-number (NaN). bounds: Optional[tuple[Expr, Expr]] Perform optimization within bounds Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.ast import Assignment >>> from sympy.codegen.algorithms import newtons_method >>> x, dx, atol = symbols('x dx atol') >>> expr = cos(x) - x**3 >>> algo = newtons_method(expr, x, atol=atol, delta=dx) >>> algo.has(Assignment(dx, -expr/expr.diff(x))) True References ========== .. [1] https://en.wikipedia.org/wiki/Newton%27s_method deltacU$r)rs r r! newtons_method..PsAr"r)r(z{}=%12.5g {}=%12.5g\n)typevalueT)integerz {}=%12.5g\n)rrnamesympy.simplify.cse_mainr(factorr rrrrrr r rformatrr rrrrdeducedappendr r)exprwrtatolr,r#r$r%r&r'r(r)r*Wrappername_d delta_exprcsesreddumsub_ewhl_bdyprntreqdeclars v_counterwhlblcks r newtons_methodrKsv }$$J /J--/01 fs<@ADjc5:c5)DAJuc*++e01E%, *f(EFGG &s233G JsCC(;VAY$GHII c\#;#B#B388V#TUD6 SZSX - .C8EB?@AG0U40$$Wa0 {9-.-gq9:#r'+, Y( )C D  E3%!6!6sxx!@ABSEMD 9d# $$3BsIc[U[5(aURRnU$[U[5(a URnU$r) isinstancervariablesymbolr)args r _symbol_ofrQssB#{##ll!! J C " "jj Jr"newton)r,c UcU4nUVs0sHGn[U[5(dMUR[SURR-5_MI nnUc0[SUR-5nUR U5(aSn[ X4SU0UD6RU5n [U [5(a U Rn URRUVs1sHn[U5iM sn5n U (a+[SSR[[ U 55-5e[#SU55n [%U ['U55n [)[*X;XS9$s snfs snf) aYGenerates an AST for a function implementing the Newton-Raphson method. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable params : iterable of symbols Symbols appearing in expr that are taken as constants during the iterations (these will be accepted as parameters to the generated function). func_name : str Name of the generated function. attrs : Tuple Attribute instances passed as ``attrs`` to ``FunctionDefinition``. \*\*kwargs : Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`. Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.algorithms import newtons_method_function >>> from sympy.codegen.pyutils import render_as_module >>> x = symbols('x') >>> expr = cos(x) - x**3 >>> func = newtons_method_function(expr, x) >>> py_mod = render_as_module(func) # source code as string >>> namespace = {} >>> exec(py_mod, namespace, namespace) >>> res = eval('newton(0.5)', namespace) >>> abs(res - 0.865474033102) < 1e-12 True See Also ======== sympy.codegen.algorithms.newtons_method Nz(*%s)d_r,zMissing symbols in params: %sz, c3B# UHn[U[5v M g7fr)rr).0ps r *newtons_method_function..s6v!HQ%%vs)attrs)rMrrOrr4hasrKxreplacerbody free_symbols differencerQ ValueErrorjoinmapstrtuplerrrr) r:r;params func_namerZr,kwargsrW pointer_subsalgo not_in_paramsrGr]s r newtons_method_functionrk{s<R~#?#z!W'=>AHHfWqxx}}%<==#? }tchh' 88E??E $ ;5 ;F ; D D\ RD$yy%%001PA*Q-1PQM8499SmE\;]]^^6v66G T6#; 'D dI JJ?2QsE)1E)%E.)g-q=N)$sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesr (sympy.functions.elementary.miscellaneousr r sympy.logic.boolalgr sympy.codegen.astr rrrrrrrrrrrrsympy.codegen.cfunctionsrrKrQrkr.r"r rusv'!*-4=#+U`%e58Q`%F/3heg9K`d9Kr"