o 8Va@sddlmZmZmZmZmZmZmZmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZmZ  dddZdd Zdd efdd d d ZdS))AndGtLtAbsDummyooTupleSymbol) 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:/usr/lib/python3/dist-packages/sympy/codegen/algorithms.py<sz newtons_method..z{}=%12.5g {}=%12.5g\nr)typevalueT)Zinteger)rrnameZdiffr r rformatrrr rrrZdeducedappendrrrr )exprwrtZatolrdebugZitermaxZcounterZWrapperZname_dZ delta_exprZwhl_bdyZprntZreqdeclarsZ v_counterZwhlZblckrrrnewtons_method s,.   r'cCs*t|tr |jj}|St|tr|j}|Sr) isinstancer variablesymbolr)argrrr _symbol_ofQs  r,Znewton)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))r(rr*r r .0prrr s z+newtons_method_function..Zd_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)r r Zhasr'Zxreplacer(rbodyZ free_symbols difference ValueErrorjoinmapstrtupler rrr) r#r$paramsZ func_namer3rkwargsZ pointer_subsZalgoZ not_in_paramsr&r4rrrnewtons_method_functionYs$)  r=)rNFNN)Zsympyrrrrrrrr Zsympy.codegen.astr r r r rrrrrrrrr'r,r=rrrrs(8 H