ó ¡¼™\c@`sâddlmZmZmZddlmZmZmZmZm Z m Z m Z m Z ddl mZmZmZmZmZmZmZmZmZmZmZmZdd ed d d„Zd„Zd de ƒd„Zd S( i(tabsolute_importtdivisiontprint_function(tAndtGttLttAbstDummytootTupletSymbol( t AssignmenttAddAugmentedAssignmentt CodeBlockt DeclarationtFunctionDefinitiontPrinttReturntScopetWhiletVariabletPointertrealgê-™—q=cC`sŒ|d kr$tƒ}t}d}nd„}|j}| |j|ƒ} t|| ƒt||ƒg} |r­t||gdj|j|ƒƒ} | d| g| d} nt t |ƒ|ƒ} t t |dt dtƒƒg} |d k rZ|ptdtƒ}t j|dƒ}| jt |ƒƒ| jt|dƒƒt| t||ƒƒ} nt| t| Œƒ}| |g}|t|ŒƒS( sX 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 tdeltacS`s|S(N((tx((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pyt;ts{0}=%12.5g {1}=%12.5g\niittypetvaluetintegerN(tNoneRRtnametdiffR R RtformatRRRRRRtTruetdeducedtappendRRRR (texprtwrttatolRtdebugtitermaxtcountertWrappertname_dt delta_exprtwhl_bdytprnttreqtdeclarst v_countertwhltblck((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pytnewtons_method s,+     $!  cC`s=t|tƒr|jj}nt|tƒr9|j}n|S(N(t isinstanceRtvariabletsymbolR(targ((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pyt _symbol_ofPs  tnewtonc K`sA|d kr|f}nd„|Dƒ}|jdd ƒ}|d krttd|jƒ}|j|ƒrtd }qtnt||d||j|ƒ}t|tƒr°|j }n|j j t d„|Dƒƒƒ} | rıt ddjtt| ƒƒƒ‚ntd„|Dƒƒ} t|t|ƒƒ} tt|| | d|ƒS( s Generates an AST for a function implementing the Newton-Raphson method. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable params : iterable of symbols Symbols appearing in expr that are taken as constants during the iterations (these will be accepted as parameters to the generated function). func_name : str Name of the generated function. attrs : Tuple Attribute instances passed as ``attrs`` to ``FunctionDefinition``. \*\*kwargs : Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`. Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.algorithms import newtons_method_function >>> from sympy.codegen.pyutils import render_as_module >>> from sympy.core.compatibility import exec_ >>> x = symbols('x') >>> expr = cos(x) - x**3 >>> func = newtons_method_function(expr, x) >>> py_mod = render_as_module(func) # source code as string >>> namespace = {} >>> exec_(py_mod, namespace, namespace) >>> res = eval('newton(0.5)', namespace) >>> abs(res - 0.865474033102) < 1e-12 True See Also ======== sympy.codegen.ast.newtons_method cS`s;i|]1}t|tƒrtd|jjƒ|j“qS(s(*%s)(R6RR R8R(t.0tp((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pys „s Rtd_cs`s|]}t|ƒVqdS(N(R:(R<R=((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pys ssMissing symbols in params: %ss, cs`s|]}t|tƒVqdS(N(RR(R<R=((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pys ‘stattrsN(RtpopR RthasR5txreplaceR6Rtbodyt free_symbolst differencetsett ValueErrortjointmaptstrttupleR RRR( R%R&tparamst func_nameR?tkwargst pointer_subsRtalgot not_in_paramsR1RC((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pytnewtons_method_functionXs$*     ! "%N(t __future__RRRtsympyRRRRRRR R tsympy.codegen.astR R R RRRRRRRRRRtFalseR5R:RR(((s7lib/python2.7/site-packages/sympy/codegen/algorithms.pyts :R D