EdddlmZddlmZddlmZmZddlmZm Z ddl m Z ddl m Z ddlmZmZmZmZmZmZmZmZmZmZmZmZ dd Zd Zd d efd ddZd S))Tuple)oo)GtLt)DummySymbol)Abs)And) AssignmentAddAugmentedAssignment CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal-q=NFcD|t}t}d}n d}|j}| ||z } t || t ||g} |r@t ||gd|j|} | d| g| ddz} tt||} tt|ttg} ||ptd }tj|d}| t|| t |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 8lib/python3.11/site-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_methodr:s\ +tyy~~%J%,,.DS%.P.PQG 3c5\#;#B#B38V#T#TUU1:t$wqrr{2 SZZ  C8EB???@@AG-0U4000$Wa00 {9--...-gq99:::#r'7++,, Y( ) )C cU?D 79d# $ $$r ct|tr |jj}nt|tr|j}|Sr) isinstancervariablesymbolr)args r _symbol_ofr@Vs>#{##l! C " "j Jr newton)rc \||f}d|D}|.td|jz}||rd}t||fd|i||}t |t r|j}|j d|D} | r8tdd tt| ztd|D} t|t!|} t#t$|| | | S) 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 Nc|i|]9}t|t|jtd|jjz:S)z(*%s))r<rr>rr%.0ps r z+newtons_method_function..sK???z!W'='=?AHfWqx}%<==???r d_rc,h|]}t|Sr)r@rDs r z*newtons_method_function..s1P1P1PA*Q--1P1P1Pr zMissing symbols in params: %sz, c3@K|]}t|tVdSr)rrrDs r z*newtons_method_function..s,66!HQ%%666666r )attrs)rr%hasr:xreplacer<rbody free_symbols difference ValueErrorjoinmapstrtupler rrr) r*r+params func_namerMrkwargs pointer_subsalgo not_in_paramsr6rPs rnewtons_method_functionr^^sIR??#???L tch'' 88E?? E $ ; ;5 ;F ; ; D D\ R RD$y%001P1P1P1P1PQQM_8499SmE\E\;];]]^^^66v66666G T6#;; ' 'D dIwE J J JJr )rNFNN)sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesr sympy.logic.boolalgr sympy.codegen.astr r r rrrrrrrrrr:r@r^rr rrfs''''''!!!!!!********--------444444###### V