B [}@sddlmZmZmZddlmZmZmZmZm Z m Z m Z m Z m Z mZddlmZmZmZmZmZmZmZmZmZmZmZmZdddZd d Zdd e fd d ZdS))absolute_importdivisionprint_function) AndGtLtAbsDummyooTupleSymbolFunctionPow) AssignmentAddAugmentedAssignment CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal-q=NFcCs|dkrt}t}d}ndd}|j}| ||} t|| t||g} |r~t||gd|j|} | d| g| dd} tt ||} t t |t t dg} |dk r|ptd d }t |d}| t || t|dt| t||} t| t| }| |g}|t|S) aX Generates an AST for Newton-Raphson method (a root-finding algorithm). 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|S)N)xrr7lib/python3.7/site-packages/sympy/codegen/algorithms.py;sz newtons_method..z{0}=%12.5g {1}=%12.5g\nr)typevalueT)Zinteger)r rnameZdiffrrrformatrrrrrr Zdeducedappendrrrr)exprwrtZatolrdebugZitermaxZcounterZWrapperZname_dZ delta_exprZwhl_bdyZprntZreqdeclarsZ v_counterZwhlZblckrrrnewtons_method s,+  r+cCs(t|tr|jj}nt|tr$|j}|S)N) isinstancerZvariablesymbolr)argrrr _symbol_ofPs    r/Znewtonc Ks|dkr|f}dd|D}|dd}|dkrLtd|j}||rLd}t||fd|i||}t|trx|j}|j t dd|D} | rt dd tt| td d|D} t|t|} tt|| | |d S) a Generates an AST for a function implementing the Newton-Raphson method. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable params : iterable of symbols Symbols appearing in expr that are taken as constants during the iterations (these will be accepted as parameters to the generated function). func_name : str Name of the generated function. attrs : Tuple Attribute instances passed as ``attrs`` to ``FunctionDefinition``. \*\*kwargs : Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`. Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.algorithms import newtons_method_function >>> from sympy.codegen.pyutils import render_as_module >>> from sympy.core.compatibility import exec_ >>> x = symbols('x') >>> expr = cos(x) - x**3 >>> func = newtons_method_function(expr, x) >>> py_mod = render_as_module(func) # source code as string >>> namespace = {} >>> exec_(py_mod, namespace, namespace) >>> res = eval('newton(0.5)', namespace) >>> abs(res - 0.865474033102) < 1e-12 True See also ======== - sympy.codegen.ast.newtons_method NcSs*i|]"}t|trtd|jj|jqS)z(*%s))r,rr r-r$).0prrr sz+newtons_method_function..rZd_css|]}t|VqdS)N)r/)r0r1rrr sz*newtons_method_function..zMissing symbols in params: %sz, css|]}t|tVqdS)N)rr)r0r1rrrr3s)attrs)popr r$Zhasr+Zxreplacer,rbodyZ free_symbols differenceset ValueErrorjoinmapstrtuplerrrr) r'r(ZparamsZ func_namer4kwargsZ pointer_subsrZalgoZ not_in_paramsr*r6rrrnewtons_method_functionXs$)   r?)rNFNN)Z __future__rrrZsympyrrrrr r r r r rZsympy.codegen.astrrrrrrrrrrrrr+r/r?rrrrs 08 D