o *ήc@sddlmZddlmZddlmZmZddlmZm Z ddl m Z ddl m Z ddlmZmZmZmZmZmZmZmZmZmZmZmZ dd d Zd dZd defd dddZd S))Tuple)oo)GtLt)DummySymbol)Abs)And) AssignmentAddAugmentedAssignment CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal-q=NFcCs|dur t}t}d}ndd}|j}| ||} t|| t||g} |r?t||gd|j|} | d| g| dd} tt ||} t t |t t dg} |durx|pZtd d }t |d}| t || t|dt| t||} t| t| }| |g}|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 NdeltacSs|SN)xrr?/tmp/pip-target-vg8gfxp4/lib/python/sympy/codegen/algorithms.pyAsz newtons_method..z{}=%12.5g {}=%12.5g\nr)typevalueT)integer)rrnamediffr r rformatrrr rrrdeducedappendr rrr )exprwrtatolrdebugitermaxcounterWrappername_d delta_exprwhl_bdyprntreqdeclars v_counterwhlblckrrrnewtons_methods,.   r6cCs*t|tr |jj}|St|tr|j}|Sr) isinstancer variablesymbolr)argrrr _symbol_ofVs  r;newton)rc Ks|dur|f}dd|D}|dur td|j}||r d}t||fd|i||}t|tr6|j}|j dd|D} | rOt dd t t | td d |D} t|t|} tt|| | |d 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 NcSs*i|]}t|tr|jtd|jjqS)z(*%s))r7rr9rr!.0prrr s z+newtons_method_function..d_rcSsh|]}t|qSr)r;r=rrr sz*newtons_method_function..zMissing symbols in params: %sz, css|]}t|tVqdSr)rrr=rrr sz*newtons_method_function..)attrs)rr!hasr6xreplacer7rbody free_symbols difference ValueErrorjoinmapstrtupler rrr) r&r'params func_namerDrkwargs pointer_subsalgo not_in_paramsr2rGrrrnewtons_method_function^s$)  rU)rNFNN)sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesrsympy.logic.boolalgr sympy.codegen.astr r r r rrrrrrrrr6r;rUrrrrs   8 H