MZdddlmZddlmZddlmZmZddlmZm Z ddl m Z ddl m Z ddlmZmZmZmZmZmZmZmZmZmZmZmZ dd Zd Zdd efdd d Zy))Tuple)oo)GtLt)DummySymbol)Abs)And) AssignmentAddAugmentedAssignment CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerrealNc|t}t}d}nd}|j}| |j|z } t || t ||g} |r5t ||gdj|j|} | d| g| ddz} tt||} tt|ttg} |q|xs td }tj|d}| jt|| jt |dt!| t#||} t%| t'| }| |gz}|t'|S) ay Generates 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 expr Absolute 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``. 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, dx) >>> algo.has(Assignment(dx, -expr/expr.diff(x))) True References ========== .. [1] https://en.wikipedia.org/wiki/Newton%27s_method Ndeltac|SN)xs :/usr/lib/python3/dist-packages/sympy/codegen/algorithms.pyz newtons_method..AsAz{}=%12.5g {}=%12.5g\nr)typevalueT)integer)rrnamediffr r rformatrr rrrrdeducedappendr rrr )exprwrtatolrdebugitermaxcounterWrappername_d delta_exprwhl_bdyprntreqdeclars v_counterwhlblcks rnewtons_methodr9sE\ }tyy~%J%,.DS%.PQG c5\#;#B#B388V#TU1:t$wqr{2 SZ C8EB?@AG0U40$$Wa0 {9-.-gq9:#r'7+, Y( )C cU?D 9d# $$rct|tr|jj}|St|tr |j}|Sr) isinstancervariablesymbolr)args r _symbol_ofr?Vs<#{#ll!! J C "jj Jrnewton)rc ||f}|Dcic]?}t|tr-|jtd|jjzA}}|+td|jz}|j |rd}t ||fd|i|j|} t| tr | j} |jj|Dchc] }t|c}} | r+tddjtt | zt#d|D} t%| t'|} t)t*|| | |Scc}wcc}w) a Generates 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_rzMissing symbols in params: %sz, c3<K|]}t|tywr)rr).0ps r z*newtons_method_function..s6!HQ%6s)attrs)r;rr=rr$hasr9xreplacerbody free_symbols differencer? ValueErrorjoinmapstrtupler rrr) r)r*params func_namerGrkwargsrE pointer_subsalgo not_in_paramsr5rJs rnewtons_method_functionrX^s4R~#?z!W'=HHfWqxx}}%<==?L? }tchh' 88E?E $ ;5 ;F ; D D\ RD$yy%%001PA*Q-1PQM8499SmE\;]]^^6v66G T6#; 'D dIwE JJ?2Qs AEE)g-q=NFNN)sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesr sympy.logic.boolalgr sympy.codegen.astr r r rrrrrrrrrr9r?rXrrrr`s]'!*-4# V